experimental flow dynamics in automotive exhaust systems with

KATHOLIEKE UNIVERSITEIT LEUVENFACULTEIT INGENIEURSWETENSCHAPPENDEPARTEMENT WERKTUIGKUNDEAFDELING TOEGEPASTE MECHANICAEN ENERGIECONVERSIECelestijnenlaan 300A, B-3001 Leuven, België

EXPERIMENTAL FLOW DYNAMICS

IN AUTOMOTIVE EXHAUST SYSTEMS

WITH CLOSE-COUPLED CATALYST

Jury:Prof. dr. ir. A. Haegemans, voorzitterProf. dr. ir. E. Van den Bulck, promotorProf. dr. ir. M. BaelmansProf. dr. ir. P. SasProf. dr. ir. R. Sierens (Universiteit Gent, B)Prof. dr. ir. R. Baert (Technische Universiteit Eindhoven, NL)Prof. dr. S. Benjamin (Coventry University, UK)

Proefschrift voorgedragen tothet behalen van het doctoraatin de ingenieurswetenschappen

door

Tim PERSOONS

U.D.C. 621.43 Augustus 2006

c© Katholieke Universiteit Leuven - Faculteit IngenieurswetenschappenArenbergkasteel, B-3001 Leuven, België

Alle rechten voorbehouden. Niets uit deze uitgave mag worden verveelvoudigd en/of openbaar gemaaktworden door middel van druk, fotokopie, microfilm, elektronische of op welke andere wijze ook zondervoorafgaandelijke schriftelijke toestemming van de uitgever.

All rights reserved. No part of this publication may be reproduced in any form by print, photoprint,microfilm, or any other means without written permission from the publisher.

Wettelijke Depot: D/2006/7515/47ISBN 90-5682-713-8

iii

VoorwoordDe inwendige verbrandingsmotor “. . . the greatest evil ever visited upon Man-kind.” volgens J.R. R.Tolkien, maar wát een onderzoeksobject! Met veel en-thousiasme begon ik in 1999 als onderzoeker bij Prof. Eric Van den Bulck tewerken op de regeling van motoren. Twee jaar later kreeg ik de kans om het fas-cinerende domein van de stromingsmechanica te combineren met mijn interessevoor motoren.

Als promotor verdient Eric een serieuze pluim, en niet alleen voor zijn on-geëvenaarde fysische achtergrondkennis. Hij slaagt erin keer op keer de juistebalans te vinden tussen onderzoeksvrijheid en de zó noodzakelijke sturendeacties. Altijd is er tijd voor een babbel, een illustratieve uitleg of een intrige-rende vraag. Eric geeft de ultieme invulling aan het concept promotor, en hoetoepasselijk is dat voor een thesis rond katalysatoren?

Werken bij TME is altijd een aangename ervaring geweest. De verschillendecollega’s, secretaresses en techniekers vormen een hechte groep. Bedankt alle-maal, voor de humor, de waardevolle en -loze discussies, en voor de steun opde momenten dat het minder plezant was. Tegen het einde van dit boek aan,komt vooral de levenswijsheid aangereikt door een illustere technieker terugboven “. . . ’t leste komt alles onder ’t dak”.

Een dikke merci aan mijn vrienden buiten het werk – burgies en andere,aan mijn vriendin Nathalie, mijn broer en zussen, ouders en grootouders omer altijd te zijn met raad en daad, en de occasionele dosis realiteitszin buitende academische wereld. In het bijzonder, bedankt mama en papa, om mijaltijd mijn eigen keuzes te laten maken, hoe absurd ook: “zoudt ge niet beterindustrieel doen, daar is toch meer vraag naar”, en vijf jaar later: “doctoreren?dat verdient toch niet”. Maar serieus: merci!

Nathalie, mijn allerliefste, gij maakt alles meer dan dubbel de moeite waard.Uw dankwoord moest het langst worden, maar woorden schieten te kort.

Tim Heverlee, augustus 2006

iv

AbstractIncreasingly stringent vehicle emissions legislation leads to the integration ofthe close-coupled catalyst into the automotive exhaust manifold. Obtaining auniform catalyst velocity distribution is not straightforward, yet remains crucialfor optimal catalyst operation, in terms of maximizing pollutant conversionefficiency, minimizing pressure loss and avoiding local catalyst degradation.

This thesis has developed an experimental methodology to obtain time-resolved bidirectional velocity distributions with high spatial and temporal res-olution, suitable for validation of computational fluid dynamics.

The charged motored engine flow rig is developed, which generates pulsat-ing flow in the exhaust system, similar to fired engine operation yet at ambienttemperature. The setup is analyzed in terms of the exhaust stroke flow simi-larity with fired engine conditions.

A novel oscillating hot-wire anemometer is developed to measure local in-stantaneous bidirectional velocity, and has been successfully applied to measureflow reversal in a close-coupled catalyst manifold.

The validity of the addition principle has been statistically established, interms of the dimensionless scavenging number S. A critical value Scrit marksthe validity limit of the addition principle, and may be interpreted as thecollector efficiency in terms of catalyst flow uniformity.

The highly transient flow dynamics in the close-coupled catalyst manifoldare studied experimentally, based on time-resolved full catalyst cross-sectionvelocity distributions, revealing extensive periodic flow reversal and strong res-onance fluctuations.

A one-dimensional gas dynamic model of the exhaust system has been val-idated and used to predict the flow dynamics outside the scope of the experi-mental setup. Numerically determined frequency response functions facilitatethe understanding of the observed gas dynamic resonance phenomena.

v

Korte samenvattingSteeds strengere emissiewetgeving voor voertuigen maakt de voorkatalysatortot een geïntegreerd deel van de uitlaatcollector van verbrandingsmotoren.Stromingsuniformiteit in de katalysator is moeilijk te bekomen, maar cruciaalvoor een optimale katalysatorwerking met het oog op maximaal omzettings-rendement, minimale drukval en het vermijden van lokale degradatie.

Deze thesis ontwikkelde een experimentele methodologie voor het bekomenvan tijdsafhankelijke bidirectionele snelheidsverdelingen met hoge resolutie inruimte en tijd, geschikt voor de validatie van computational fluid dynamics.

De ontwikkelde stromingsopstelling met opgeladen aangedreven motor ge-nereert in het uitlaatsysteem een pulserende stroming, gelijkaardig aan eenwerkende motor, maar bij omgevingstemperatuur. De stroming is geanalyseerdwat betreft gelijkvormigheid met werkende motorcondities.

Een oscillerende hittedraad anemometer is ontwikkeld om lokale ogenblik-kelijke bidirectionele snelheid te meten. Deze is gekalibreerd en toegepast omterugstroming te meten in een uitlaatcollector met voorkatalysator.

De geldigheid van het additieprincipe is statistisch ondersteund in relatietot het dimensieloze scavenging getal S. Een kritische waarde Scrit bepaalt degeldigheidsgrens van het additieprincipe, en kan geïnterpreteerd worden als eencollectorefficiëntie met betrekking tot stromingsuniformiteit in de katalysator.

De stromingsdynamica in de uitlaatcollector is experimenteel onderzocht,aan de hand van tijdsafhankelijke snelheidsverdelingen in de volledige katalysa-tordoorsnede. De katalysator is onderhevig aan sterke periodieke terugstromingen snelheidsfluctuaties, ten gevolge van gasdynamische resonanties.

Een gasdynamisch ééndimensionaal model van het uitlaatsysteem is gevali-deerd, en voorspelt de stroming buiten het werkingsgebied van de experimen-tele opstelling. De experimenteel waargenomen gasdynamische resonanties zijnverklaard door numeriek bepaalde transfer functies.

List of symbols

Symbols

A Cross-sectional area [m2]b Cylinder bore [m]Cd Discharge coefficient [-], for flow through exhaust valvesc Speed of sound [m/s]cp, cv Specific heat capacity of air at constant pressure and volume [J/(kg K)]d Diameter [m]e,E Index and number of ensembles [-]f Frequency [Hz]h Height [m]i, I Index and number of measurement points [-]j, J Index and number of crankshaft positions [-]k Spring stiffness [N/m]L Length [m]M Mass flow rate [kg/s]m Mass [kg]Ma Mach number [-]N Engine crankshaft speed [rpm]ne, nr Number of exhaust valves and runners [-]P P-value of hypothesis test [-]p Pressure [Pa]Q Volumetric flow rate [m3/s]Re Reynolds number [-], usually based on runner diameter and mean run-

ner velocityRf OHW oscillation frequency, Rf = 120fo/N [-]r Specific gas constant of air [J/(kg K)]rS , rM Shape and magnitude similarity measure [-], Eqs. (4.12) and (4.28)S Scavenging number [-], Eq. (4.42)s Piston stroke [m]T Temperature [K]

vii

viii List of symbols

Tp, Ts Flow pulsation and diffuser residence time scale [s], Eqs. (4.46)and (4.43)

t Time [s]U Velocity [m/s], along length axis of catalystV Volume [m3]x, y Measurement plane coordinates [m]xo OHW oscillation amplitude [m]z Lengthwise coordinate [m]

Subscripts

a Ambient conditionsbb Blow-by leakage through piston-cylinder clearancec Combustioncyl Cylinderd Diffusere Exhaust, or exhaust valve (opening)H Helmholtz resonancei Intake, or intake valve (closing)m Mean, i.e. spatial area averageo Oscillating hot-wire (OHW)p Hot-wire prober Exhaust runnerref Referencerel Relatives Standard conditions, i.e. 101325 Pa and 273.15 K

Greek symbols

α OHW probe velocity tolerance factor [-]∆, δ Absolute and relative 95% uncertainty or deviation∆θ Exhaust valve opening duration [rad-crankshaft]η Flow uniformity or conversion efficiency [-]γ Ratio of specific heats of air, γ = cp/cv [-]µ, ν Dynamic [Pa·s] and kinematic viscosity of air [m2/s]ρ Density [kg/m3]% Volumetric compression ratio [-]θ Angular position [rad or ]ω Angular velocity [rad/s]

Contents

Voorwoord iii

Abstract iv

Korte samenvatting v

List of symbols vii

Contents ix

1 Introduction: Exhaust systems 11.1 Legal background . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Aspects of manifold design . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Catalyst . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Deactivation . . . . . . . . . . . . . . . . . . . . . . . . 4Conversion efficiency . . . . . . . . . . . . . . . . . . . . 6Pressure loss . . . . . . . . . . . . . . . . . . . . . . . . 8Design compromise . . . . . . . . . . . . . . . . . . . . . 8

1.2.2 Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Pressure loss . . . . . . . . . . . . . . . . . . . . . . . . 10Flow dynamics . . . . . . . . . . . . . . . . . . . . . . . 13Thermal load . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3 Motivation for this thesis . . . . . . . . . . . . . . . . . . . . . 171.4 Overview of manifold flow research . . . . . . . . . . . . . . . . 19

1.4.1 Flow distribution . . . . . . . . . . . . . . . . . . . . . . 19Isothermal flow rigs . . . . . . . . . . . . . . . . . . . . 20Isochoric flow rigs . . . . . . . . . . . . . . . . . . . . . 22

1.4.2 Flow dynamics . . . . . . . . . . . . . . . . . . . . . . . 23Isochoric flow rigs: Fired . . . . . . . . . . . . . . . . . 24Isochoric flow rigs: Motored . . . . . . . . . . . . . . . . 26

1.4.3 Contributions of this thesis . . . . . . . . . . . . . . . . 271.5 Goals and scope . . . . . . . . . . . . . . . . . . . . . . . . . . 291.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

ix

x Contents

2 Experimental approach 332.1 Exhaust manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 332.2 Pulsating flow rigs . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.2.1 Isothermal flow rig . . . . . . . . . . . . . . . . . . . . . 362.2.2 Isochoric flow rig: Charged motored engine (CME) . . . 40

2.3 Exhaust stroke flow similarity . . . . . . . . . . . . . . . . . . . 442.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 442.3.2 Thermodynamic analysis . . . . . . . . . . . . . . . . . 462.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.4 Flow rate measurement . . . . . . . . . . . . . . . . . . . . . . 542.4.1 ISO orifice . . . . . . . . . . . . . . . . . . . . . . . . . . 542.4.2 Laminar flow element (LFE) . . . . . . . . . . . . . . . 562.4.3 Cylinder pressure . . . . . . . . . . . . . . . . . . . . . . 59

2.5 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.5.1 Ensemble averaging . . . . . . . . . . . . . . . . . . . . 62

Ensemble-averaged quantities . . . . . . . . . . . . . . . 62Uncertainty analysis . . . . . . . . . . . . . . . . . . . . 64

2.5.2 Cycle-resolved analysis . . . . . . . . . . . . . . . . . . . 642.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3 Oscillating hot-wire anemometer (OHW) 713.1 Introduction: Measuring bidirectional velocity . . . . . . . . . . 723.2 Hot-wire anemometer . . . . . . . . . . . . . . . . . . . . . . . 763.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.4 Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.5 Hot-wire probes . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.6 Calibration approach . . . . . . . . . . . . . . . . . . . . . . . . 85

3.6.1 Calibration wind tunnel . . . . . . . . . . . . . . . . . . 853.6.2 Laser Doppler anemometer . . . . . . . . . . . . . . . . 893.6.3 Calibration procedure . . . . . . . . . . . . . . . . . . . 89

3.7 Calibration results . . . . . . . . . . . . . . . . . . . . . . . . . 903.7.1 Calibration charts . . . . . . . . . . . . . . . . . . . . . 903.7.2 Phase-locked results . . . . . . . . . . . . . . . . . . . . 933.7.3 Non-dimensional scaling analysis . . . . . . . . . . . . . 943.7.4 Discussion of the calibration results . . . . . . . . . . . 97

3.8 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4 Addition principle 1034.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.2 Validation approach . . . . . . . . . . . . . . . . . . . . . . . . 1064.3 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.3.1 Flow uniformity measures . . . . . . . . . . . . . . . . . 107Weltens’ flow uniformity index . . . . . . . . . . . . . . 107Mean-to-maximum velocity ratio . . . . . . . . . . . . . 109

4.3.2 Distribution similarity . . . . . . . . . . . . . . . . . . . 110

Contents xi

Shape similarity measure . . . . . . . . . . . . . . . . . 110Spatial autocorrelation . . . . . . . . . . . . . . . . . . . 113Magnitude similarity measure . . . . . . . . . . . . . . . 115

4.3.3 Flow characteristic . . . . . . . . . . . . . . . . . . . . . 1224.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 125

4.4.1 Isothermal flow rig . . . . . . . . . . . . . . . . . . . . . 126Manifold A . . . . . . . . . . . . . . . . . . . . . . . . . 127Manifold B . . . . . . . . . . . . . . . . . . . . . . . . . 132

4.4.2 Isochoric flow rig . . . . . . . . . . . . . . . . . . . . . . 138Manifold B . . . . . . . . . . . . . . . . . . . . . . . . . 138

4.4.3 Summary of the results . . . . . . . . . . . . . . . . . . 1404.5 Interpretation of the results . . . . . . . . . . . . . . . . . . . . 1444.6 Discussion: A physical interpretation . . . . . . . . . . . . . . . 149

4.6.1 Scalar mixing analogy . . . . . . . . . . . . . . . . . . . 1494.6.2 Hypothesis: Collector efficiency . . . . . . . . . . . . . . 150

4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5 Flow dynamics 1555.1 Time-resolved flow distributions . . . . . . . . . . . . . . . . . . 156

5.1.1 Isothermal flow rig . . . . . . . . . . . . . . . . . . . . . 156Manifold A . . . . . . . . . . . . . . . . . . . . . . . . . 156Manifold B . . . . . . . . . . . . . . . . . . . . . . . . . 165

5.1.2 Isochoric flow rig . . . . . . . . . . . . . . . . . . . . . . 170Mean velocity . . . . . . . . . . . . . . . . . . . . . . . . 170Velocity distributions . . . . . . . . . . . . . . . . . . . 175

5.2 Flow reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1825.2.1 OHW validation . . . . . . . . . . . . . . . . . . . . . . 1825.2.2 Experimental results . . . . . . . . . . . . . . . . . . . . 1855.2.3 Numerical analysis . . . . . . . . . . . . . . . . . . . . . 187

Model description . . . . . . . . . . . . . . . . . . . . . 187Results without cold end: Free discharge . . . . . . . . . 193Results with cold end . . . . . . . . . . . . . . . . . . . 198Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 202

5.2.4 Discussion: Physical relevance of catalyst flow reversal . 2025.3 Helmholtz resonance . . . . . . . . . . . . . . . . . . . . . . . . 204

5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2045.3.2 Analytical model . . . . . . . . . . . . . . . . . . . . . . 2055.3.3 Experimental results . . . . . . . . . . . . . . . . . . . . 2085.3.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . 213

Isothermal flow rig . . . . . . . . . . . . . . . . . . . . . 213Isochoric flow rig: Without cold end . . . . . . . . . . . 214Isochoric flow rig: With cold end . . . . . . . . . . . . . 218

5.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 2205.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

xii Contents

6 Design considerations 2256.1 Addition principle . . . . . . . . . . . . . . . . . . . . . . . . . 2256.2 Flow dynamics: Helmholtz resonance . . . . . . . . . . . . . . . 2266.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

7 Conclusion 2317.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2317.2 Suggestions for future research . . . . . . . . . . . . . . . . . . 235

A Catalyst substrate flow 241A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241A.2 Momentum transfer . . . . . . . . . . . . . . . . . . . . . . . . 242

A.2.1 Fully developed laminar flow . . . . . . . . . . . . . . . 243A.2.2 Developing laminar flow . . . . . . . . . . . . . . . . . . 243A.2.3 Entrance and exit losses . . . . . . . . . . . . . . . . . . 245A.2.4 Flow acceleration . . . . . . . . . . . . . . . . . . . . . . 246A.2.5 Oblique entrance . . . . . . . . . . . . . . . . . . . . . . 247A.2.6 Overall . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

A.3 Mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249A.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . 249A.3.2 Homogeneous reaction kinetics . . . . . . . . . . . . . . 250A.3.3 Heterogeneous reaction kinetics . . . . . . . . . . . . . . 251

B Exhaust stroke flow similarity 253

C Velocity measurement techniques 259C.1 Thermal anemometry . . . . . . . . . . . . . . . . . . . . . . . 259C.2 Optical anemometry . . . . . . . . . . . . . . . . . . . . . . . . 260

D Modeling one-dimensional gas dynamics 267D.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . 267

D.1.1 Decoupling the Euler equations . . . . . . . . . . . . . . 268D.1.2 Discretization schemes . . . . . . . . . . . . . . . . . . . 270

First order upwind schemes . . . . . . . . . . . . . . . . 270Second order TVD schemes . . . . . . . . . . . . . . . . 271

D.1.3 Zero-dimensional volumes . . . . . . . . . . . . . . . . . 272D.1.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . 273

D.2 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . 273D.2.1 Sod’s shock tube . . . . . . . . . . . . . . . . . . . . . . 273

Description . . . . . . . . . . . . . . . . . . . . . . . . . 273Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 275

D.2.2 Frequency response of a pipe . . . . . . . . . . . . . . . 275Description . . . . . . . . . . . . . . . . . . . . . . . . . 275Analytical . . . . . . . . . . . . . . . . . . . . . . . . . . 277Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 277

D.2.3 Frequency response of a muffler . . . . . . . . . . . . . . 278Description . . . . . . . . . . . . . . . . . . . . . . . . . 278

Contents xiii

Analytical . . . . . . . . . . . . . . . . . . . . . . . . . . 279Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 279

D.3 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280D.3.1 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . 280D.3.2 Temporal resolution . . . . . . . . . . . . . . . . . . . . 280

D.4 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281D.4.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . 281D.4.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 282D.4.3 Multisine signals . . . . . . . . . . . . . . . . . . . . . . 282

Nederlandse samenvatting 2871 Inleiding: Uitlaatsystemen . . . . . . . . . . . . . . . . . . . . . 287

1.1 Achtergrond . . . . . . . . . . . . . . . . . . . . . . . . . 2871.2 Ontwerpaspecten . . . . . . . . . . . . . . . . . . . . . . 2881.3 Literatuuroverzicht . . . . . . . . . . . . . . . . . . . . . 2891.4 Doelstellingen van de thesis . . . . . . . . . . . . . . . . 290

2 Experimentele aanpak . . . . . . . . . . . . . . . . . . . . . . . 2912.1 Experimentele opstellingen . . . . . . . . . . . . . . . . 2912.2 Stromingsgelijkvormigheid . . . . . . . . . . . . . . . . . 2922.3 Datareductie . . . . . . . . . . . . . . . . . . . . . . . . 292

3 Oscillerende hittedraad anemometer (OHW) . . . . . . . . . . . 2933.1 Inleiding . . . . . . . . . . . . . . . . . . . . . . . . . . . 2933.2 Methodologie . . . . . . . . . . . . . . . . . . . . . . . . 2933.3 Kalibratie . . . . . . . . . . . . . . . . . . . . . . . . . . 2943.4 Toepassing en validatie . . . . . . . . . . . . . . . . . . 295

4 Additieprincipe . . . . . . . . . . . . . . . . . . . . . . . . . . . 2954.1 Datareductie . . . . . . . . . . . . . . . . . . . . . . . . 2954.2 Resultaten . . . . . . . . . . . . . . . . . . . . . . . . . 2954.3 Fysische interpretatie . . . . . . . . . . . . . . . . . . . 297

5 Stromingsdynamica . . . . . . . . . . . . . . . . . . . . . . . . . 2975.1 Experimentele resultaten . . . . . . . . . . . . . . . . . 2975.2 Numerieke analyse . . . . . . . . . . . . . . . . . . . . . 298

6 Ontwerpoverwegingen . . . . . . . . . . . . . . . . . . . . . . . 3007 Conclusie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

Bibliography 303

Curriculum vitae 313

List of publications 314

Index 316

Chapter 1

Introduction: Exhaustsystems

1.1 Legal background

The European Parliament and Council ratified Directive 98/69/EC [1] on 13October 1998, relating to measures against air pollution by motor vehicle emis-sions. Amending the original 1970 Directive 70/220/EEC, Directive 98/69/ECenforces Euro III and Euro IV emission standards on newly registered vehicles,as of 2000 and 2005 respectively. The Euro V standard will take effect as of2008, but has yet to be ratified in a Directive. Table 1.1 shows the evolution ofthe maximum emission levels for carbon monoxide (CO), hydrocarbons (CxHy),nitrous oxides (NOx) and particulate matter (PM). The emissions are measuredduring a standardized vehicle homologation procedure performed on a chassisdynamometer.

Table 1.1 – Tailpipe emission limits for passenger cars below 2500 kg, according tosuccessive EU standards

Standard Limit values [g/km]CO CxHy+NOx PM

Petrol Diesel Petrol Diesel Petrol Diesel1992, Euro I 2.72 2.72 0.97 0.97 - - - 0.141996, Euro II 2.20 1.00 0.50 0.7/0.91 - - - 0.08/0.11

CO CxHy NOx PMPetrol Diesel Petrol Diesel Petrol Diesel Petrol Diesel

2000, Euro III 2.30 0.64 0.20 - 0.15 0.50 - 0.052005, Euro IV 1.00 0.50 0.10 - 0.08 0.25 - 0.0252008, Euro V 1.00 0.50 0.075 - 0.06 0.20 0.005 0.005

1

2 Chapter 1 Introduction: Exhaust systems

The increasingly stricter emissions legislation has been the main promotorof technological advances in internal combustion engines over the last years,and will continue to be so in the face of new regulations. Technological ad-vances may be noted in different engine aspects. Firstly, limiting the gener-ation of pollutant emissions is mostly related to (i) engine construction (e.g.valve timing, combustion chamber layout) and (ii) engine management (e.g.feedback-controlled fuel injection using lambda-sensors, exhaust gas recircula-tion). Secondly, and most importantly for this thesis, (iii) the exhaust systemensures the appropriate aftertreatment of pollutants.

In order to meet emission standards, any present exhaust system containsat least one catalytic converter. Although this thesis deals with catalysts typi-cally found in passenger cars and light-duty vehicles, the work is applicable tomotorcycles and heavy-duty vehicles as well. In stoichiometric petrol engines,a three-way catalyst simultaneously oxidizes CO and CxHy to CO2 and water,and reduces NOx to nitrogen. Diesel engines are fitted with an oxidation cat-alyst, although NOx constitutes a major fraction of diesel pollutant emissions.

The catalytic material decreases the activation energy of the reactions andcauses adequate reaction rates at typical exhaust system temperatures (400 to800 C). The catalyst material temperature must exceed the light-off tempera-ture (250 to 400 C) to attain significant reaction rates.

From Euro III onwards, the regulations incorporate the emissions producedduring engine cold start, while the catalyst is still inactive. Rapid catalystwarm-up is ensured by placing the catalyst in the hot end of the exhaust sys-tem close to the engine, making it an integral part of the exhaust manifold.This so-called close-coupled catalyst (CCC) reduces cold start emissions con-siderably when compared to a traditional underfloor catalyst, mounted in thedownstream tailpipe section or cold end. Figure 1.1 defines the nomenclatureon a schematic diagram of a typical modern four-cylinder gasoline engine.

Tighter limits for NOx and PM in Euro IV and V (Table 1.1) are encour-aging further developments such as regenerative particulate filters for dieselengines, and NOx-traps for diesel and lean-burn petrol engines. Both particu-late filters and NOx-traps contain catalytic material to promote soot oxidationand NOx reduction respectively.

The present research into the flow in CCC manifolds focuses on three-wayor oxidation catalysts. However, its relevance extends towards NOx traps, PM(soot) filters or any filtering device or heat exchanger subjected to a complexpulsating and diverging flow.

Section 1.6 presents the goals and scope of this thesis, with respect toincreasing the knowledge on transient internal flows in manifolds with close-coupled catalysts.

1For indirect and direct injection diesel engines, respectively

1.2 Aspects of manifold design 3

underbody catalyst

driving direction

muffler tailpipe

diffuser

exit cone

close-coupled catalyst

runners(headers)

manifold(collector)

hot end cold end

downpipe

Figure 1.1 – Exhaust system nomenclature

1.2 Aspects of manifold design

This section discusses important aspects in the design of an exhaust manifoldwith close-coupled catalyst. In terms of achieving an optimal operation anda maximum lifetime of the catalyst, Sect. 1.2.1 demonstrates that the cata-lyst velocity distribution is paramount. The major purpose of the manifold isto ensure the appropriate distribution of exhaust gases towards the catalyst.Section 1.2.2 discusses design aspects specific to the manifold’s task of flowdistribution.

Nomenclature In this thesis, the term manifold denotes the combi-nation of runners and diffuser, excluding the close-coupled catalyst, asdepicted in Fig. 1.1. As such, the design aspects are discussed separatelyin Sects. 1.2.1 (catalyst) and 1.2.2 (manifold).

Nevertheless, the catalyst is an integrated part of the overall hot endstructure, comprising the manifold, catalyst, exit cone and downpipe. Assuch, in some cases a ‘pars pro toto’ interpretation is used that denotesthe hot end structure as a whole.

1.2.1 Catalyst

An automotive catalytic converter contains noble metal particles, typicallyplatinum (Pt), palladium (Pd) and rhodium (Rh), that act as catalyst forthe designated reactions. The active metals are distributed as fine particlesin the washcoat, containing mainly porous aluminum oxide (Al2O3) to enlargethe surface area. The washcoat is typically applied to a ceramic cordierite(2MgO · 2Al2O3 · 5SiO2) substrate [56], although folded metal foil substrates


Figure 1.2 – Catalyst substrates: (left) metal and (right) ceramic

are also in use. Figure 1.2 shows an example (unwashcoated) substrate of eachtype.

The substrate consists of parallel channels with a typical hydraulic diameterd of 1 mm and wall thickness t of 100 µm. Table 1.2 presents an overview oftypical ceramic substrate cell dimensions. The geometric surface area av isdefined as av = 4 d/ (d+ t+ tw)2 [cm2/cm3], where tw/2 is the washcoat layerthickness, as shown in Fig. 1.3.

During this thesis, only ceramic substrates are used since these featuretighter dimensional tolerances on the cell distribution. The velocity distributionin a metal catalyst contains strong gradients due to local differences in the celldistribution. These are of no particular interest to the design of the manifoldin terms of flow distribution.

The quantity av represents the amount of surface area available for reactionsper given catalyst volume. The dimensionless porosity ε is defined as therelative open frontal area, or symbolically ε = d2/ (d+ t+ tw)2. The trendis towards a smaller wall thickness and higher cell density.

Deactivation

Deactivation or degradation of a catalyst reduces the reaction rate. Althoughdeactivation is inevitable, a good manifold design minimizes its overall magni-tude and avoids excessive local degradation.

Bartholomew [11] and Forzatti and Lietti [38] review catalyst deactiva-tion in general due to chemical, thermal, physical and mechanical processes.

2The substrate cell type is defined as wall thickness/cell density, where the wall thicknessis expressed in mil (1 mil = 1/1000 inch) and the cell density is expressed in cpsi or cells/inch2.


x

L zy

td+t+t

monolithwashcoat

½ tw

w

Figure 1.3 – Ceramic substrate catalyst nomenclature

Table 1.2 – Ceramic catalyst substrate dimensions

Type2 Geometric parametersd av t ε

mm cm−1 µm -6.5/400 1.10 27.4 165 0.764.3/400 1.16 28.8 109 0.844.3/600 0.93 34.5 109 0.803.5/600 0.95 35.3 89 0.842.5/900 0.78 43.7 64 0.86

Neyestanaki et al. [80] review deactivation in automotive catalysts.Chemical deactivation is caused by strong chemisorption of certain poisons

on catalytic surfaces, decreasing their reactivity. For automotive catalysts,contaminants in the engine lubricating oil and fuel (e.g. P, Pb, Zn, S) consti-tute catalyst poisons. Chemical deactivation is proportional to the amount ofprocessed exhaust gas. Areas in the catalyst cross-section with a high time-averaged velocity are more subject to chemical deactivation. A uniform velocitydistribution ensures uniform chemical deactivation, and thereby maximum cat-alyst lifetime.

Thermal deactivation results from several different processes [11, 38]. Themain process decreases the active surface area through sintering, which involvescrystallite growth in the catalyst phase and blockage of active elements due tocollapsing substrate pores. The sintering rate is usually fitted by a correlationof the form:

d

dt

(S

S0

)= −ks

(S

S0− Seq

S0

)n

(1.1)


∆T

T

rz

z

Figure 1.4 – Diffuser and catalyst: Basic flow pattern and streamwise temperatureevolution

where S, S0 and Seq are respectively the time-dependent, initial and equilibriumsurface area [m2], ks is the sintering rate constant [s−1] and n is the sinteringorder [-] (typically n = 2). The rate constant ks increases exponentially withthe temperature, and becomes significant above 500 C [11]. In petrol engines,the close-coupled catalyst may reach temperatures in excess of 1000 C. Conse-quently, any change in temperature significantly affects the degree of thermaldeactivation.

The catalyst substrate temperature depends in a complicated way on thevelocity, temperature and reactant concentration distribution at the catalystinlet. The catalyst reactions are exothermic. The gas temperature increases byan order of magnitude of 100 C as it passes through the catalyst. A qualitativeevolution of the mass-flow averaged temperature is shown in Fig. 1.4. Thetemperature rise ∆T increases for (i) increasing inlet reactant concentration(e.g. misfire causes a large quantity of hydrocarbons that oxidize in the catalyst)and (ii) increasing catalyst residence time, which corresponds to decreasingvelocity. Heat conduction through the catalyst substrate in axial and radialdirection also affects the temperature distribution.

Furthermore, this thesis has shown that periodic flow reversal occurs. Fig-ure 1.4 depicts a typical flow pattern in an axisymmetric diffuser and catalyst,including backflow near the outer edges of the catalyst. In case of strong flowreversal, hot processed gas may be recycled through the catalyst, leading toa further increase in catalyst temperature. The influence of flow reversal oncatalytic conversion, the catalyst temperature distribution or thermal deacti-vation is unknown. Yet considering the exponential temperature dependenceof thermal deactivation in Eq. (1.1), this effect should not be discarded.

Conversion efficiency

The conversion efficiency ηC [-] is defined as the relative decrease in the overallpollutant species concentration at the catalyst outlet, compared to the inlet


0 0.2 0.4 0.6 0.8 10

1

2

4

6

8

10

ηC

= 0.99

ηC

= 0.92

ηC

= 0.77

ηC

= 0.56

ηC

= 0.29

Radius r/R (-)

Vel

ocity

U/U

m (

-)

Figure 1.5 – Influence of the flow distribution on the conversion efficiency ηC , basedon a homogeneous catalyst model

concentration. Appendix A.3 discusses the different approaches for modelingthe mass transfer with catalytic reactions. The actual catalytic reaction kineticsmay be very crudely approximated by a set of homogeneous reactions for eachspecies.

Using this crude approximation, an analytical expression may be derivedfor the conversion efficiency ηC (see Eq. (A.24) as a function of the velocitydistribution U (x, y):

ηC,i =

∮A

(1− exp

(− Ki L

U (x, y)

))ρU (x, y) dA(

1− exp(−Ki L

Um

))m

where the index i refers to the considered species, Ki is a reaction rate con-stant [1/(m3s)] and L is the catalyst length [m].

Merely as an example, Fig. 1.5 shows several velocity distributions U (r)for an axisymmetric catalyst. r/R represents the dimensionless radius of thesubstrate, where r/R = 0 is the catalyst centerline and r/R = 1 is the outeredge, as depicted in Fig. 1.4. For each velocity distribution, the correspondingvalue of the conversion efficiency ηC is obtained using Eq. (A.24), where thereaction rate constant K is estimated arbitrarily.

In spite of the oversimplified model, Fig. 1.5 indicates the sensitivity ofthe conversion efficiency to flow non-uniformity. The main external boundarycondition influencing the amount of converted gas is the residence time of thegas in the catalyst τU ∝ L/U [s], where L is the catalyst length [m] and U isthe channel mean gas velocity [m/s]. Instead of τU , the amount of conversionis determined by the ratio of τU to the limiting time scale for the chemicalkinetics (see App. A.3). A high ratio of residence time to kinetics time scale


ensures an adequate conversion level. Consequently, conversion is lower in highvelocity regions.

The kinetics time scale is considered to be the transverse diffusion time scale,defined as τD,t = d2/Dm [s], where Dm is the molecular diffusivity [m2/s] ofthe species. In that case, the conversion efficiency ηC is related to τU/τD,t ∝(L/d2)εA/Q , where Q is the volumetric flow rate [m3/s].

Pressure loss

The catalyst is one of the main contributors to the overall exhaust systempressure drop or backpressure. Increased backpressure decreases the engineefficiency in two ways: (i) the pumping losses increase with the exhaust systembackpressure, and (ii) the residual exhaust gas that remains in the cylindersafter the exhaust stroke increases with backpressure. The importance of thesecond indirect effect is often neglected, yet an increase in the residual gas massdecreases proportionally the amount of fresh mixture that can be inducted dur-ing the following intake stroke, thereby influencing the amount of heat releasedduring combustion and the indicated efficiency. As such, backpressure directlyand indirectly influences engine efficiency and specific fuel consumption.

Flow in the substrate channels is incompressible (Ma < 0.3) and laminar(Re < 2300). Appendix A.2 describes the different aspects adding to the pres-sure drop. Neglecting the effects of inlet and exit loss and the development ofthe laminar boundary layer, the pressure drop ∆p is proportional to the chan-nel velocity U/ε, where U is by convention the axial velocity immediately up-stream of the substrate. Assuming a fixed volumetric flow rate Q = U A [m3/s],∆p ∼ 4f (L/d ) ρU2/2 ∝

(L/d2)Q/(εA) .

The three-dimensional velocity distribution in the diffuser is influenced in acomplicated way by the presence of the catalyst substrate. Seemingly unimpor-tant effects such as the pressure drop due to oblique flow entry greatly affectthe flow distribution [15, 43]. Still, this effect is usually neglected in CFDsimulations of flow in CCC manifolds.

For a given catalyst geometry, the minimum pressure drop is obtained for auniform, axial inlet velocity profile. In the case of a non-uniform velocity distri-bution, the high velocity regions create a local high pressure drop. The pressuredrop distribution throughout the remainder of the catalyst cross-section is bal-anced by other forces, such as radial (outward) flow or swirling (tangential)flow.

Design compromise

The cost of a catalyst is mainly due to the precious metals incorporated inthe washcoat. As such, the total washcoat volume Vcoat should be minimized.Assuming an invariable washcoat thickness, Vcoat is proportional to the totalcatalytic surface area, or symbolically Vcoat ∝ av AL ∝ εAL/d.

The flow uniformity ηU influences both the pressure drop and conversionefficiency. Section 4.3.1 presents several ways of quantifying the flow uniformity.For now, it is sufficient to keep in mind that ηU varies between zero and unity,


Table 1.3 – Catalyst design criteria

Criterion ParametersA L d ε

(i) cost% % % 1 %(ii) ∆p % 1 % 11 1(iii) ηC 1 1 1 %% 1(iv) ηU 1 1 %% 1Optimum 1 ∼ % 11

where ηU = 1 corresponds to a perfectly uniform velocity distribution and whenηU ' 0, the entire flow passes through a single channel.

The relationship between the flow uniformity and geometric parameters isdifficult to estimate. However, a high flow uniformity is increasingly difficultto achieve for a larger catalyst cross-sectional area A. On the other hand,the flow becomes increasingly more uniform as the pressure drop coefficientK [-] increases. K is defined as the ratio of pressure drop to dynamic pressure,or K ∼ 4f (L/d ) ∝

(L/d2)εA/Q . Combining both assumptions, the flow

uniformity varies as ηU ∼(L/d2)ε/Q .

The influence of the catalyst geometric parameters A, L, d and ε can besummarized as follows:

(i) Precious metal cost ∝ Vcoat ∝ εAL/d

(ii) Pressure drop ∆p ∼(L/d2

)Q/ (εA)

(iii) Conversion efficiency ηC ∼ τU ∝(L/d2

)εA/Q

(iv) Flow uniformity ηU ∼(L/d2

)ε/Q

Table 1.3 indicates the relationship between the desired change in the fourabove stated criteria and the determining geometrical parameters. For instance,∆p decreases (%) mainly by increasing d (11) and to a lesser extent by increasingA (1) and ε (1), and decreasing L (%).

Although Table 1.3 is based on crude assumptions, it presents a remarkablyaccurate summary of the design compromises involved in automotive catalystdesign.

Based on Table 1.3, the porosity ε should be maximized, which correspondsto minimizing the substrate wall thickness. This is beneficial for all criteria,except the precious metal costs. The channel diameter d should be minimalto maximize conversion and flow uniformity, although this causes a penalty inpressure drop.

Table 1.2 shows some typical substrate cell structures that are used in au-tomotive catalysts. The listing is roughly chronological from top to bottom.The trend is indeed towards thin-walled substrates (t 6 2 mil) with a highercell density (> 900 cpsi), which are additionally characterized by a lower ther-mal mass, thus providing faster warm-up. This is demonstrated by Wiehl and


Vogt [112], describing the recent advances and evolution in ceramic catalystsubstrates.

Table 1.3 indicates that the catalyst cross-sectional area A should be max-imized to the minimize pressure drop and maximize the conversion efficiency.However, the diffuser’s performance for obtaining a good flow uniformity shouldbe taken into account here. Inadequate manifold design leads to a non-uniformvelocity distribution, which is detrimental for the pressure drop and conversionefficiency. Furthermore, it causes local deactivation which reduces the catalystlifetime.

1.2.2 Manifold

As previously indicated, the manifold’s main task is to distribute the exhaustgases towards the close-coupled catalyst. The short distance available betweenengine and catalyst entails particular issues for the manifold’s pressure loss,flow dynamics and thermal load.

Pressure loss

The pressure drop over the manifold itself (i.e. excluding the catalyst) is ofthe same order of magnitude as the catalyst pressure drop. The short distancebetween the engine and CCC requires exhaust runners with a small length-to-diameter ratio, featuring multiple out-of-plane bends with small curvatureradius-to-diameter ratio (see Figs. 1.7, 1.9, 2.1). The runners converge intoa diffuser that aims to distribute the flow across the catalyst cross-section.Flow in the exhaust manifold is highly pulsating and three-dimensional, fea-turing strong secondary flows and vortices created by the short curved runners.Fiedler [36] and Miller [74] provide an explanation for the creation of secondaryswirling flows in interacting bend combinations that are typical for exhaust sys-tems with close-coupled catalyst.

Furthermore, runners that enter the diffuser at an oblique angle cause strongmixing in the diffuser. With reference to Fig. 1.6, an oblique entry anglecorresponds e.g. to values of α or β close to 90 . This is beneficial for a goodflow uniformity, at the cost of an increase in pressure drop. Figure 1.7 showstwo examples of exhaust manifolds with different entry angles. The variant inFig. 1.7 (left) exhibits a lower pressure drop yet also a worse flow uniformitycompared to the variant in Fig. 1.7 (right), where the runners enter the diffuserat a more oblique angle.

Wendland and Matthes [109] and Wendland et al. [110] provide a correlationbetween the non-dimensional catalyst pressure drop (denoted ‘smoothing index’n in [109, 110]) versus a measure of the flow non-uniformityM . This correlationis given in Fig. 1.8, and is based on experimental data for different types ofunderfloor catalysts, obtained on a stationary water flow bench and in firedengine conditions. M is defined as Umax/Um − 1, where Umax and Um are themaximum and mean catalyst velocity, respectively. The smoothing index n isdefined as the ratio of the catalyst pressure drop to the dynamic pressure in the


β

α

Figure 1.6 – Connection of a runner into the diffuser

Figure 1.7 – Influence of runner layout on the pressure drop (Source: [2])

inlet pipe upstream of the diffuser, or symbolically n = ∆p/(ρU2

m/2)

(Ai/A )2,where Ai and A are the cross-sectional area of the inlet pipe and the catalyst,respectively. Figure 1.8 shows a good logarithmic agreement between M andn, for different geometrical variants and flow conditions.

The numerical example below provides an order-of-magnitude estimationfor the contribution to the total exhaust system pressure drop by individualcomponents. The relationship between the catalyst pressure drop and the flowuniformity is quite complex, and is not included in the numerical example.

Numerical example The pressure drop of the exhaust system for atypical modern mid-range passenger car engine originates mainly from(i) the runners and diffuser, (ii) the catalyst, (iii) the muffler and (iv) theexhaust pipe itself (see Fig. 1.1). The calculation below is for a 2000 cm3

4-cylinder gasoline engine. The diameters of the runners, catalyst andexhaust pipe are estimated at 35, 122 and 50 mm, respectively.

• Runners and diffuser — The runner pressure drop is estimated


Figure 1.8 – Maldistribution versus smoothing index (Source: [109, 110])

based on two closely spaced 90 bends, forming a 90 out-of-planeangle. This is the typical form of an exhaust runner in a compactclose-coupled catalyst exhaust system:

∆p = KrunnerρU2

r

2

∆p = nKbCfCReCb−bρU2

r

2(1.2)

where Krunner represents the runner pressure drop coefficient [-], nis the number of bends (= 2) and ρU2

r /2 represents the dynamicpressure [Pa] based on the mean runner velocity. Kb is the pressuredrop coefficient of a single 60 bend with infinite inlet and outletpipes. According to Miller [74] (Fig. 9.2), Kb ' 0.11 for a radius-of-curvature = 2D. Cf is a correction for a rough instead of asmooth pipe. Cf = frough/fsmooth , where f is the friction factor3,obtained from e.g. the implicit Colebrook-White [30] correlation forfully developed turbulent flow in a rough pipe:

1√f

= −4.06 log10

„k/D

3.71+

1.255

Re√

f

«(1.3)

where k is the wall roughness (e.g. 0.025 mm for a smooth steelpipe). CRe is a correction for low Reynolds number, given byFig. 9.3 [74] (CRe ' 1.65 for Re = 50 000). Cb−b is the bendinteraction coefficient, given by Fig. 10.3 [74] for a 90 out-of-planecombination (Cb−b ' 0.725). In total, the runner pressure dropcoefficient Krunner ' 0.79.The diffuser pressure drop is estimated based on a sudden expansionwith a diameter ratio of 0.5, which corresponds to Kdiffuser ' 0.5.

3The Fanning friction factor is used throughout this thesis, defined according to ∆p =4f (L/D ) ρU2/2 . The Fanning friction factor is 1/4 of the Darcy friction factor.


• Catalyst — The pressure drop in the catalyst is estimated assumingfully developed laminar flow. As shown in App. A.2, the actualpressure drop is higher, due to contraction and expansion loss, andthe development of the boundary layer. For square channels, thefriction factor is found analytically to be f ' 14.227/Re . Thepressure drop coefficient Kcatalyst = 4f (l/d ), where l and d arethe catalyst length and hydraulic diameter of the catalyst channels.Due to the laminar flow regime, Kcatalyst is inversely proportionalto the flow rate.

• Muffler — Due to the multitude of muffler designs, the pressuredrop in the muffler is roughly estimated based on the assumptionthat the muffler consists of two consecutive expansions with infinitediameter ratio. In this case, the dynamic pressure is completely losttwice, which corresponds to a pressure drop coefficient Kmuffler = 2.

• Exhaust pipe — The exhaust pipe is assumed to be 5 m long, 50 mmin diameter, and made of stainless steel with wall roughness k =0.025 mm. The friction factor is determined from Eq. (1.3).

The table below shows the contribution to the total pressure drop of eachcomponent, for different engine speeds:

Engine speed N 2000 4000 6000 rpm∆prunner+diffuser 23 92 207 mbar∆pcatalyst 32 64 96 mbar∆pmuffler 12 46 104 mbar∆pexhaust pipe 15 51 107 mbar∆ptotal 81 253 514 mbar

The contribution to the total pressure drop of each component is of com-parable magnitude. An acceptable value for the maximum total pressuredrop is 500 to 800 mbar. Traditionally, the cold end (muffler, exhaustpipe) contributes 50 to 60%, and the hot end contributes 40 to 50%.Recently, the compactness of the hot end has lead to a relative increasein hot end pressure drop.

Flow dynamics

An excellent overview of acoustical properties of exhaust systems as a whole ispresented in the doctoral work of Boonen [21]. Further background informationon the design of exhaust silencers and resonators is given in e.g. Davis et al.[33].

However, this thesis is mainly concerned with the lower frequency flow dy-namics of the exhaust manifold. As shown in Chap. 4, these dynamics influencethe time-averaged flow distribution and the flow uniformity. Consequently, theyhave an effect on the system backpressure, conversion efficiency and catalystageing.

As shown in Chap. 5, the low frequency dynamics in close-coupled cata-lyst manifolds are governed by a Helmholtz-type resonance phenomenon. In


acoustics and exhaust silencer literature, Helmholtz resonators are typically en-countered as silencer elements, mounted perpendicular to the main flow duct.The term Helmholtz resonance used in this thesis differs from that meaning, asdiscussed in Sect. 5.3.

The insert below provides some background information on pressure wavetuning, and its significance with respect to modern compact exhaust systemsand this thesis.

Background: Pressure wave tuning The initial phase of the ex-haust stroke is known as blowdown, during which the combustion prod-ucts in the cylinder expand from the residual cylinder pressure to theexhaust system pressure. The hot pulse of fast moving exhaust gas cre-ates a positive (compression) pressure wave traveling down the runnerat the speed of sound c =

√γrT ' 640 m/s (for T = 800 C). The

blowdown ends roughly 1 to 5 milliseconds later, when the cylinder pres-sure and exhaust pressure have equalized. At this point, the momentumstored in the fast moving blowdown pulse starts a negative (expansionor rarefaction) pressure wave down the runner.

It is beneficial for the cylinder scavenging if this negative pressure wouldpersist near the exhaust port during the remainder of the exhaust stroke,also called the displacement phase. However, the negative pressure grad-ually disappears as the piston moves upwards and expels the remainingcombustion products.

At some point, the initial compression wave reaches a cross-section en-largement. The enlargement can be a junction with another runner, adiffuser (e.g. followed by a catalyst), or the open atmosphere (e.g. in caseof a high powered racing engine). As the compression wave encountersthe enlargement, it starts a reflected expansion wave backwards up therunner. If the expansion wave reaches the exhaust port before the ex-haust valve closes, the low pressure helps the cylinder scavenging, similarto the first expansion wave created after the blowdown.

In a typical four-stroke engine, the intake valve opens before top deadcenter (' −10 ca), whereas the exhaust valve closes after top dead center(' +10 ca). If the rarefaction wave reaches the exhaust port during thevalve overlap period, the negative exhaust pressure helps the inductionof fresh mixture from the intake runner.

The exhaust waves only feature this beneficial effect if the length of theexhaust runners L is such that the time for the wave to travel twicethe runner length 2L/c (i.e. one compression wave traveling down andone expansion wave traveling up) corresponds to the time between thebeginning of the exhaust stroke and the valve overlap. Therefore, onespecific exhaust system creates a positive scavenging effect for only anarrow engine speed range.

Increasing the engine performance at speeds above 5000 rpm requiresrunners of at least 500 mm long. Preferably, each cylinder should havean individual runner of equal length without junctions, and all runnersshould converge in a collector with a large cross-section.


Such configuration is denoted an ‘N-in-1’ exhaust, where N is the numberof converging runners. Due to the piping size and complexity, this typeof exhaust is rarely used for any purpose other than racing.

For a four-cylinder engine, a 4-in-2-in-1 is a simpler exhaust configura-tion, consisting of four runners that converge pairwise in two Y-junctions,followed by a third Y-junction that connects to the cold end. This con-figuration offers a reduced peak performance increase when comparedto a 4-in-1 exhaust, yet the optimum engine speed range is broader. Acompression wave that reaches the Y-junction reflects back through bothconnected runners, resulting in a weaker expansion wave. The typical en-gine firing order is 1–3–4–2. Two pairs are formed by ‘opposite’ cylindersthat are 180 ca out of phase, i.e. cylinders 1 and 4 are paired, and 2 and3 are paired. Pairing opposite cylinders means that the compression wavegenerated by the second cylinder’s blowdown does not interfere with thefirst cylinder’s displacement phase.

To distinguish between a standard exhaust and a high-performance wavetuned exhaust, a different terminology is often used in the literature: Fora standard exhaust, the term runner is used in conjunction with manifold,describing short curved pipes issuing in an arbitrarily shaped manifoldvolume with no regard for pressure wave tuning. The manifold’s shape isdetermined only by the easiest way of connecting the exhaust ports to thedownpipe. Such a standard manifold is traditionally made of low-cost,heavy cast iron. By contrast, the term header denotes a long runner madeof smooth steel pipe and gradual bends, which issues into a collector,rather than a manifold. A collector forms a cross-section enlargementthat produces good rarefaction waves. Flow from the incoming headersexits the collector straight-through, minimizing losses due to flow turning.In this thesis, no distinction is made between runners or headers, andmanifold or collector. The manifold denotes the combination of runnersand diffuser, as depicted in Fig. 1.1.

Long runners are required to benefit from the pressure wave tuning effect.This is generally incompatible with rapid catalyst warm-up. Indeed,tighter emissions regulations lead to compact manifolds with integratedclose-coupled catalyst. The time scales associated with the pressure wavetravel in the short curved runners are too small to be of any benefit forcylinder scavenging.

However, engines for high performance passenger cars attempt to com-bine a N-in-2-in-1 or N-in-1 exhaust with a close-coupled catalyst. Diezet al. [34] describes the evolution in the exhaust system of two succes-sive generations of top-end petrol engines. The new generation consistsof a V10-engine with a 5-in-1 manifold (shown in Fig. 1.9) with inte-grated close-coupled catalyst on both cylinder banks. The old genera-tion consists of a V8-engine with 4-in-2-in-1 manifold and two underfloorcatalysts.

Missy et al. [75] discuss a numerical study of the chemical kinetics andlight-off behavior in a 4-in-2-in-1 exhaust system. Two close-coupledcatalysts are used following each of the first Y-junctions pairing cylinders1, 4 and 2, 3.


Figure 1.9 – Example of equal length runners (diffuser not shown) for a V10-engine(Source: [34])

The above cases [34, 75] are rather exceptional. The typical exhaustsystem for a modern engine is more concerned with rapid catalyst warm-up than with gaining performance in the high engine speed range. State-of-the-art exhaust systems such as developed by Bosal are made of steelpiping instead of cast iron. This results in a weight reduction and a lowerthermal mass, which accelerates warm-up.

Heywood [47] provides general background information on the gas exchangeprocess during intake and exhaust stroke. Stone [96] provides an introductionto gas dynamics related to manifold design. Benson et al. [50, 19] discuss waveaction simulation models and their application to pressure wave tuning, as wellas wave-tuned intake and exhaust manifolds.

Thermal load

The flow inside the runners and diffuser causes a certain distribution of wallshear stress and heat transfer coefficient. Areas of excessive temperature or hotspots form on the walls where the (internal) convective heat transfer coefficientis high. A hot spot which coincides with a vulnerable structural part (e.g.welds, a protective catalyst mat or lining material) causes differential thermalexpansion and thermal stresses. These stresses add to the existing cyclic ther-mal stresses induced by successive heating and cooling cycles. The stressesweaken the component and may result in premature failure.

This situation is aggravated by the ever increasing mean temperature ofthe hot end. Indeed, most new exhaust system components (e.g. close-coupledcatalyst, particulate filter, . . . ) require a minimal enthalpy loss in the man-ifold. Fast warm-up requirements lead to a light-weight manifold, assembledfrom thin sheet metal. Furthermore, radiation shields and thermal insulationprotect other components in the engine compartment against external heattransfer from the exhaust system. This increases the temperatures of the ex-haust system materials, and raises the importance of accurate prediction ofinternal flow and heat transfer in the exhaust manifold.

1.3 Motivation for this thesis 17

1.3 Motivation for this thesis

Exhaust manifold design requires state-of-the-art knowledge of fluid dynam-ics and heat transfer for this complex flow. Numerical flow simulation usingcommercially available computational fluid dynamics (CFD) software does notnecessarily yield reliable results, since the flow is characterized by non-isotropicturbulence and three-dimensional boundary layers inside the runners and dif-fuser. These conditions are not ideally suited for RANS simulations (i.e. solvingthe Reynolds-averaged Navier-Stokes equations) with conventional turbulencemodels.

Interestingly, industrial design procedures rely almost entirely on numericalstudies using CFD. The majority of the calculations involve stationary flow,due to the high computational cost associated with transient CFD calculationsfor such a complex three-dimensional turbulent flow. These stationary flowpredictions are used to estimate the backpressure, the catalyst flow uniformity,and other flow-related criteria. Furthermore, the stationary flow results areused as boundary condition in finite element modeling to predict the surfacetemperatures and the thermal stresses.

The catalyst velocity distributions in Fig. 1.10 demonstrate the level ofuncertainty associated with CFD predictions of flow in close-coupled catalystmanifolds. Fig. 1.10a, b and c are CFD results of stationary flow throughrunner 1 of manifold A, used in this thesis (see Sect. 2.1). Cases 1.10a, b and cdiffer only in terms of the inlet boundary conditions to the runner. Case 1.10aand b feature a uniform axial velocity distribution, whereas case 1.10c features apeaked axial velocity distribution into the runner. Swirl is applied to the runnerinlet in cases 1.10b and c, whereas case 1.10a does not feature swirl. One mayappreciate a considerable effect on the catalyst velocity distribution. Case 1.10cmay be seen to correspond best to the experimental result in Fig. 1.10d. Yetsuch experimental data are not available in the industrial design environment,making it impossible to assess the accuracy of the numerical flow predictionsupon which the design is based.

Taking into account the given difficulties regarding accurate numerical sim-ulations, the principal motivation of this thesis is to develop high-quality ex-perimental methods for determining the transient velocity distribution in thecatalyst. These data are useful for validation and optimization of the numericalapproach.

Given the strong pulsating nature of the exhaust flow, the question ariseswhether using stationary predictions is at all justifiable. This specific issueforms an important motivation for the experimental approach to this research.This thesis [88, 86] introduces the addition principle for flow in close-coupledcatalyst manifolds. The addition principle (see Chap. 4) states the following:

Addition principle The time-averaged catalyst velocity distri-bution in pulsating flow can be predicted by a linear combinationof velocity distributions that results from stationary flow througheach of the exhaust runners, for equal volumetric flow rate.


(a) (b)

(c) 0

0.5

1

1.5

2

2.5

3

-30 -15 0 15 30

-30

-15

0

15

30

Stationary velocity U (-)

x (mm)

y (m

m)

0.25

0.25

0.5

0.5

0.5

0.5

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0.75

0.75

0.75

0.75

1

1

1

1

1.5

1.5

1.5

2

2

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2.5

2.5

3

Runner 1, Qref

= 109.3 m3/h

Um

= 8.018 m/s, ηm

= 0.342, ηw

= 0.689

(d)

Figure 1.10 – Example of discrepancies between (a, b, c) numerical and (d) ex-perimental results for the stationary flow distribution in a close-coupled catalyst(Source: [2])

If the principle is proved valid, it implies that transient CFD is not requiredfor designing a manifold with close-coupled catalyst with respect to the catalystflow distribution and that steady state CFD simulations suffice.

For the industrial design of these systems within an automotive Tier 1supplier, the validity of the addition principle carries huge implications, sincethe calculation time for transient CFD is at least an order of magnitude highercompared to stationary CFD. This significant gain in calculation time is directlyreflected in terms of a reduced development time, which is crucial for obtainingnew contracts from original equipment manufacturers (OEMs).

Section 1.4 reviews the available literature, specifically focusing on the in-fluence of stationary and pulsating flow on the time-averaged catalyst flow uni-formity. Based on the above motivations and the available literature, Sect. 1.6defines the goals and scope of this thesis.

1.4 Overview of manifold flow research 19

1.4 Overview of manifold flow research

There are several sources available in literature discussing experimental andnumerical studies of flow in close-coupled catalysts.

Earlier studies (1970 till 2000) (e.g. Howitt and Sekella [51], Lemme andGivens [64], Kim et al. [60]) examine the pressure drop and velocity distribu-tion in exhaust systems with catalysts under stationary flow conditions. Theassumption of stationary flow is justifiable for flow through an underbody (un-derfloor) catalyst, typically located 1 to 2 m downstream from the engine.

Wendland et al. [110] discuss an experimental study of underbody catalystswith different diffuser and exit cone geometries on a stationary flow rig. Theauthors compare theoretical and empirical expressions for the catalyst pressuredrop to their measurements. The authors refer to Wendland and Matthes [109]for a correlation between a flow non-uniformity measure (based on the ratio ofmaximum to mean velocity) and the pressure drop coefficient (defined as theratio of the pressure drop to the dynamic pressure upstream of the diffuser).This correlation, shown in Fig. 1.8, is obtained from experiments on severaldifferent underbody catalysts, with one or two monoliths, with a circular oroval cross-section, with a centered inlet pipe yet offset or centered outlet pipe.

With the introduction of close-coupled catalysts, the attention has movedto studying the these systems in pulsating flow conditions (1995 till present).As such, the literature review in this section focuses on pulsating flow studies.

In this field of research, velocity measurements are generally performedusing hot-wire anemometry (HWA), laser Doppler anemometry (LDA). Othervelocity measurement techniques prove less successful. For example, the pitot-static probe suffers from an insufficient sensitivity in the low velocity range anda limited bandwidth. Lambert et al. [61] even propose using a fast responsetrace gas detection system to determine the velocity magnitude and directionin catalyst systems.

The following sections review the relevant literature. A distinction is madebetween results concerning the time-averaged flow distribution (Sect. 1.4.1) andthe time-varying flow dynamics (Sect. 1.4.2). Finally, Sect. 1.4.3 reviews theoriginal contributions of this thesis to the existing literature.

1.4.1 Flow distribution

Several authors (Benjamin et al. [13], Voeltz et al. [104], Breuer et al. [23],Nagel and Diringer [79]) discuss velocity measurements and CFD calculationson close-coupled catalyst manifolds in stationary flow conditions. Most of thesestudies are aimed at maximizing the catalyst flow uniformity, while minimizingthe pressure drop, often through parametric studies of diffuser and runnergeometry or mechanical flow dispersers.

However, the most interesting studies (see below) are performed in pulsatingflow, either on (i) an isothermal pulsating flow rig, (ii) an isochoric or engineflow rig. The isochoric or engine flow rig may be motored (i.e. driven at constantspeed, without internal combustion) or fired (i.e. braked at constant speed, with


internal combustion).

Isothermal flow rigs

The easiest way of reproducing the pulsating flow in an exhaust system in alaboratory setup is by means of incorporating a pulsator device (e.g. rotatingvalve, rotating disk or other fast-response flow control device) into a stationaryflow rig. The flow generated in this way differs significantly from the exhaustflow in a fired engine (see Sect. 2.3). However this type of setup is frequentlyused because of its simplicity, and its independently adjustable pulsation fre-quency and flow rate. Furthermore, stationary flow rigs are commonly used byexhaust system manufacturers to measure the steady state pressure drop. Theisothermal flow rig used during this thesis is described in Sect. 2.2.1.

Benjamin et al. [17] discuss experimental results on an axisymmetric man-ifold with catalyst, mounted on an isothermal flow bench with rotating diskpulsator. The authors perform a parametric study of the influence of the dif-fuser shape on the catalyst flow distribution. The paper provides time-resolvedvelocity data at the inlet and exit of the catalyst brick, for a broad range ofpulsation frequency and flow rate. Although no comparison is made betweenpulsating and stationary flow in terms of the addition principle, the authorsdefine a non-dimensional number as the ratio of pulsation period to diffuserresidence time, based on the runner velocity. A similar number is used to char-acterize the flow conditions in this thesis. A good correlation exists between anon-uniformity measure and the non-dimensional number.

Liu et al. [69] use the experimental set up of Benjamin et al. [17], with moreoverlapping inlet velocity pulse shapes. Liu et al. [69] do not refer to any non-dimensional correlation, however the authors report a lower uniformity due tooverlapping inlet flow pulses when compared to the results of Benjamin et al.[17] featuring non-overlapping pulses. As the pulsation frequency increases,non-uniformity decreases, i.e. the flow uniformity increases (see Fig. 1.11). Thisis in agreement with the findings of this thesis. From Fig. 1.11 also follows thatoverlapping inlet flow pulses (

) result in a lower uniformity when compared

to non-overlapping pulses ( ). In this thesis, a slightly higher uniformity is

observed in the absence of overlap between exhaust valve openings.Benjamin et al. [16] performed a number of steady and pulsating flow exper-

iments on several types of novel contoured catalyst brick designs, all referencedto a standard type catalyst brick similar to the one used in this research. Theresults for the standard type brick shown in Fig. 1.12 indicate that the flowuniformity (Note: the plot shows non-uniformity) increases from steady flowover low pulsation frequencies to high pulsation frequencies, and that flow uni-formity decreases for increasing flow rate, both in steady and pulsating flowconditions. This is confirmed by the results of this thesis.

For the CFD predictions, Benjamin et al. [16, 15] model the catalyst flowresistance using a pressure loss correction for oblique flow entrance into themonolith. This effect is not included in the porous volume model included in

4See explanation of valve overlap on page 35.


Figure 1.11 – Comparison of non-uniformity index, with (

) and with-

out ( ) inter-cylinder4 exhaust valve

overlap (Source: [69])

Figure 1.12 – Non-uniformity indexas a function of flow rate and pulsationfrequency (Source: [16])

Figure 22 Experimental velocity profiles for the Standard substrate compared to CFD predictions with and without entrance effect. Figure 1.13 – Experimental versus simulated catalyst velocity distribution, with-

out ( ) and with (

) oblique flow entrance correction (Source: [16, 15])

commercially available CFD packages. The porous volume model is used torepresent a distributed catalyst monolith flow resistance, without having tomodel the small individual monolith channels. By incorporating a correctionfor oblique flow entrance in the numerical model, Benjamin et al. [16, 15] obtainthe results shown in Fig. 1.13, revealing a much better correspondence betweenthe simulated and experimental velocity distribution. The oblique entranceloss is further discussed in App. A.2. Haimad [43] provides more details onthe practical implementation of the oblique entrance correction in the CFDsoftware.

Using the same oblique entrance correction approach [16, 15], Benjaminet al. [18] provides a comparison between experimental and numerical velocitydistributions, obtained on an isothermal flow rig, using a production model CCexhaust manifold. Figure 1.14 shows that incorporating the oblique entrancecorrection significantly improves the correspondence between numerical andexperimental results, although the correspondence is still imperfect.

Kim and Cho [58] used an isothermal flow rig with rotating disk to generate


b (scale as a)

c (scale as a)

Fig. 5 Velocity contours with pulsating flow. 25Hz: (a) port 1 HWA measurements, v,, Re 72000: (b) port 1 CFD case7, without entrance effects, v,, Re 69800; ( c ) port I CFD case 8, with entranceeffects,~, , Re 69 800: (d) view angle

Figure 1.14 – (a) Experimental versus (b, c) simulated catalyst velocity distribution,(b) without and (c) with oblique flow entrance correction (Source: [18])

pulsating flow in the CC exhaust manifold also used by Park et al. [81] and Kimet al. [59]. The authors conclude that the time-averaged velocity distributionis more uniform in pulsating conditions compared to stationary flow.

Bressler et al. [22] performed time-averaged velocity measurements of pul-sating flow in a four-runner manifold with a close-coupled catalyst. Measure-ments have been performed on an isothermal flow bench with rotating disk togenerate the pulsating flow. The authors used trace gas injection to determinethe load on the catalyst from each cylinder. Bressler et al. [22] provide qual-itative confirmation of the addition principle’s validity. Results are presentedaccording to the non-dimensional ratio of exhausted gas volume per cylinderand per cycle to the diffuser volume. This ratio is actually identical to the scav-enging number S used in this thesis and a similar number used by Benjaminet al. [17]. Although no correlation is presented, their results indicate that theflow uniformity is unaffected by engine speed as long as the non-dimensionalratio remains constant.

Isochoric flow rigs

A more realistic flow is generated in the exhaust system by using the internalcombustion engine for which the exhaust is designed. To contrast an isothermalflow rig, the term isochoric (i.e. isovolumetric or constant volume) is chosen,since the gas is exhausted by a reciprocating volumetric machine. Of course,the volume changes during the working cycle, yet the term isochoric refers tothe displacement of an equal volume per working cycle from the intake to theexhaust side.

The engine can be driven (or motored) without combustion by an electricmotor, resulting in cold flow in the exhaust. The most realistic flow is of course


generated by running the engine with combustion (or fired), yet this situationseverely complicates the velocity measurements. The motored engine approachallows measurement of the catalyst velocity distribution with a good spatialand temporal resolution.

Background The exhaust stroke of an internal combustion engine, ei-ther motored or fired, consists of two phases: the blowdown and displace-ment phase.

The blowdown phase starts when the exhaust valve(s) open. Typically,the exhaust valve opens around 40 ca before bottom dead center5. Theblowdown phase ends when the residual cylinder pressure has expandedto equal the exhaust manifold pressure. The blowdown phase is rela-tively short (see the discussion on flow similarity in Sect. 2.3.2), and ischaracterized by a high peak flow rate and high transients. The end ofthe blowdown corresponds roughly to bottom dead center, depending onengine speed and residual cylinder pressure.

During the subsequent displacement phase, the piston moves upward andexpels the remaining gas from the cylinder. This causes a low peak flowrate and low transients.

The two-stage exhaust stroke in an isochoric flow rig is quite different fromthe single-stage exhaust pulse generated by an isothermal flow rig. Section. 2.3discusses the exhaust stroke flow similarity of an isothermal and a motoredengine flow rig, compared to true fired engine conditions.

Arias-Garcia et al. [7] performed time-averaged measurements using HWAof both steady and pulsating flow in a CCC manifold. Both an isothermal ax-isymmetric flow bench with rotating disk pulse generator (Benjamin et al. [17])and a motored engine with atmospheric inlet are used for generating the pulsat-ing flow. Results from the isothermal flow bench do not correlate well with themotored engine results, probably due to interaction effects caused by exhaustvalve overlap, which is absent in the flow bench set up. The time-averagedvelocity distribution in pulsating flow is more uniform than for steady flow.Computational fluid dynamic (CFD) calculations underestimate the velocitymagnitude by 50 %, thus overestimating the flow uniformity.

1.4.2 Flow dynamics

This section reviews the existing literature in terms of time-varying flow effects,in particular the occurrence of (i) gas dynamic resonances and (ii) periodic flowreversal through the catalyst.

The relatively low frequency (below 500 Hz) gas dynamic resonances arepredominantly encountered in manifolds mounted on an isochoric flow rig. Thefluctuations aggravate flow separation and recirculation in the diffuser, sinceperiodic flow reversal through the catalyst is reported only on isochoric flowrigs. Both Hwang et al. [53] and Kim and Cho [58] present phase-locked LDA

5Crankshaft angle position is expressed in ‘ca’.


Figure 1.15 – Experimental ( ) ver-

sus simulated ( ) time-resolved mean

catalyst velocity (Source: [59])

Figure 1.16 – Experimental (left)versus simulated (right) velocity distri-bution in the diffuser, during exhauststroke of cylinder 1 (Source: [81])

results obtained on an isothermal flow rig. Although LDA is capable of mea-suring bidirectional velocity, no flow reversal is observed.

Isochoric flow rigs: Fired

Park et al. [81] and Kim et al. [59] used phase-locked LDA to measure thetime-resolved local velocity in a CCC manifold on a fired engine. The authorsmeasured in several points along a straight line, upstream of the catalyst brick.The study of Park et al. [81] revealed the existence of a distinct high-frequencyvelocity fluctuation during the displacement phase. This phenomenon is causedby Helmholtz resonances, which is not explained by the authors and whichhas been observed and analyzed in this thesis (see Sect. 5.3). The authorsconclude that measurement data and results of transient CFD predictions arein good agreement, although this comparison appears questionable. Figure 1.15from [59] shows a reasonable comparison between the computed and measuredmean catalyst velocity. However, Fig. 1.16 from [81] shows a poor comparisonbetween computational and measurement data in terms of the local velocity inthe diffuser.

Adam et al. [4] use a one-dimensional gas dynamic model to provide bound-ary conditions for a transient three-dimensional CFD simulation of the flow ina CCC manifold. The simulation results give clear evidence of Helmholtz res-onances in fired engine conditions.

Liu et al. [70] combine a one- and three-dimensional model in the same wayas Adam et al. [4]. The authors present simulations for a fired and motoredengine with atmospheric intake conditions in Fig. 1.17. For fired engine con-ditions, the simulated exhaust runner velocity (

) indicates the presence of

Helmholtz resonances. The motored engine simulations ( ) do not exhibit

similar fluctuations, possibly because the intake system is atmospheric insteadof charged. Based on Fig. 1.17, the flow rate appears somewhat lower for themotored engine case, compared to the fired engine case. As such, the ‘exci-tation level’ to trigger the gas dynamic resonances may be quite different for


Figure 1.17 – Simulated runner velocity for fired ( ) versus motored (

) engine

(Source: [70])

both cases.Flow reversal was predicted numerically in motored and fired engine con-

ditions. However, measurements using LDA in fired conditions do not showflow reversal. Perhaps this is due to the limited spatial availability of measure-ments: the LDA results are only obtained in a few points along a straight line,downstream of the catalyst.

Regardless of differences in exhaust system geometries, the findings of thepresent research are in agreement with those of Adam et al. [4], Liu et al.[70] and Park et al. [81]. Section 5.3 discusses and explains the Helmholtzresonances observed in the current study and in the literature.

Tsinoglou and Koltsakis [99] present a numerical study of catalyst hydrocar-bon conversion efficiency in pulsating flow. The authors non-dimensionalize thepulsation frequency with the catalyst residence time. This so-called pulsationindex is used to plot the conversion efficiency for different pulse shapes. For ahigh pulsation index, the conversion efficiency reaches unity and becomes inde-pendent of the pulsation index. For a low pulsation index, conversion efficiencyis well predicted by a quasi-steady model. The pulsation index is inverselyproportional to the scavenging number used in this thesis.

Lambert et al. [61] use a fast-response flame ionization detector which iscapable of measuring hydrocarbon trace gas concentrations at up to 1 kHz. Thelocal velocity is determined based on the time-of-flight of a propane trace gas‘tuft’. The bandwidth of the overall measurement system (including a propaneinjector, based on an inkjet printer valve) is roughly 160 Hz. One propanepulse is injected every 16 crankshaft revolutions, at a preset delay with respectto a crankshaft index pulse. This is too low to capture the fast dynamics in aclose-coupled system.

Nevertheless, the authors present time-resolved phase-locked velocity dataobtained in the center of an underbody catalyst, mounted on a fired enginerun at constant speeds between 1500 and 2000 rpm, and engine load6 varying

6Throughout this thesis, the term engine load denotes the ratio of the engine torque T tothe maximum engine torque Tmax (NOT the ratio of the engine power Tω, relative to themaximum engine power (Tω)max). The adjectives zero, part and full load correspond very


Figure 1.18 – Experimental ( ) and simulated (

) catalyst velocity for fired

engine (Source: [70])

between zero and part load. Remarkably, the authors show the occurrence ofvelocity reversal in these conditions, in spite of the position of the underbodycatalyst, far from the engine.

Isochoric flow rigs: Motored

Numerical and experimental results found in the literature [70, 81, 59] on afired engine indicate flow reversal in the catalyst following each blowdown. Liuet al. [70] present fired engine simulations (

) in Fig. 1.18 that clearly exhibit

flow reversal. Surprisingly, measurements using LDA ( ) do not show flow

reversal. Perhaps this is due to the small number of LDA measurement pointswhere measurements could be performed.

Flow reversal has also been observed in the current research using a motoredengine flow rig (see Sect. 2.2.2). The occurrence of flow reversal throughoutthe engine operating range may be surprising, considering the pressure dropassociated with the close-coupled catalyst (see the numerical example compar-ing the pressure drop of different exhaust system components in Sect. 1.2.2).The current research uses an exhaust manifold with free discharge into atmo-sphere, i.e. without exit cone and cold end. The shape of the exit cone andthe backpressure of the cold end (including muffler and possibly an underfloorcatalyst) might influence the catalyst velocity distribution. However, the ab-sence of the exit cone and tailpipe is not solely responsible for the occurrence offlow reversal. Liu et al. [70], Park et al. [81] and Kim et al. [59] present resultsshowing flow reversal in a close-coupled catalyst in fired conditions, includingthe entire exhaust system downstream of the CCC manifold. Flow reversalconsistently occurs after each blowdown. In the absence of blowdown such ason an isothermal flow rig, flow reversal is not likely to occur. This is confirmedby Hwang et al. [53] using LDA in a CCC manifold on an isothermal flow rig.

roughly to T/Tmax < 0.25, 0.25 6 T/Tmax < 0.25 and 0.75 6 T/Tmax 6 1 respectively.Because of the (near) linear relation between the intake manifold pressure pi and the enginetorque, the engine load can also be considered the ratio of actual to maximum intake pressurepi/pi,max .


1.4.3 Contributions of this thesis

The available literature on experimental and numerical studies of flow in ex-haust systems is presented above. Due to the inherent variability in the designsof these systems, the relevance of a number of studies [60, 104, 23, 79, 8] remainsrestricted to particular geometries. This contrasts with research of in-cylinderflows, where the shape of the combustion chamber is more or less identicalthroughout different engines.

In spite of the geometric variability and the three-dimensional, pulsatingflow, the influence of geometry and flow conditions on the catalyst flow unifor-mity [22, 17, 88, 99, 86], the validity of the addition principle (Eq. (4.1)) [88, 86],catalytic conversion efficiency [99] and the pressure drop [109, 110] can be ex-pressed in terms of appropriately chosen non-dimensional numbers, such as thescavenging number (Eq. (1.4)) [88, 86] or similar numbers [22, 17, 99].

The main contribution of Persoons et al. [88] is the experimental validationof the addition principle for two types of close-coupled catalyst manifolds: onewith and one without exhaust valve overlap. The study uses an isothermalpulsating flow rig. Pulsating flow is generated using two different pulsators: arotating valve and a motored cylinder head. The set up is described in detailin Sect. 2.2.1.

Two non-dimensional similarity measures are used to quantify the correla-tion between pulsating and stationary velocity distributions. The selection ofthese measures and their statistical characteristics are discussed in Sect. 4.3.2.Both scalars are correlated to the non-dimensional scavenging number S (seeSect. 4.3.3). S equals the ratio of apparent flow pulsation period to diffuserresidence time:

S =apparent flow pulsation period

diffuser residence time=Tp

Ts(1.4)

The scavenging number S is large for low engine speed, high flow rate or smalldiffuser volume. In that case, exhausted flow pulses from each cylinder inter-act only slightly, and there is a good correspondence between pulsating andstationary distributions. When S is sufficiently large, the addition principleis expected to be valid. S is small for high engine speed, low flow rate orlarge diffuser volume. In that case, exhausted flow pulses interact to a higherdegree, likely resulting in a bad correlation between pulsating and stationarydistributions.

The findings in Persoons et al. [88] concerning the addition principle areconfirmed to some extent by Benjamin et al. [17] and Bressler et al. [22]. Theseauthors use a similar non-dimensional number to characterize the flow condi-tions, as the ratio of flow pulsation time scale to diffuser residence time scale.

Persoons et al. [86] provide further confirmation of these findings [88], usinga charged motored engine (CME) flow rig. In spite of the different flow gen-erated by both rigs, the data [88, 86] correlate remarkably well. An improveddefinition of the apparent flow pulsation period is introduced, which takes intoaccount the higher frequency content in the isochoric rig’s exhaust flow. From


the correlation of the velocity distribution similarity measures versus the scav-enging number S follows a critical scavenging number Scrit. Scrit may beconsidered a dimensionless measure of the manifold efficiency with respect tocatalyst flow uniformization.

Chapter 4 discusses the experimental validation of the addition principle.The relationship between this research and the findings of Benjamin et al. [17]and Bressler et al. [22] are summarized in Sect. 4.5.

Isothermal flow rig experiments by Persoons et al. [88] revealed fluctua-tions in the mean (or area-averaged) catalyst velocity, with a frequency thatis independent of engine speed and flow rate. Surprisingly, the strength ofthe fluctuations depends on the type of pulsator used. Fluctuations are onlyobserved when using a cylinder head with poppet valves, not when using arotating valve. As explained in Chap. 5, Sect. 5.3, the cylinder head type ofpulsator generates a much stronger excitation for the flow inside the manifold.The excitation is higher in amplitude and frequency content, compared to arotating valve.

Similar yet much stronger fluctuations are observed on a motored engineflow rig [84]. These fluctuations are explained as Helmholtz resonances inSect. 5.3. In fact, a number of authors using isochoric flow rigs [81, 59, 4, 70, 14]show similar resonances, although explanations as to their origin vary.

In summary, the main contribution of the publications that followed fromthis thesis [88, 87, 86, 83, 84, 85] are:

• Experimental approach — The establishment of an experimental approachthat enables high spatial and temporal resolution velocity measurementsin the catalyst cross-section, in pulsating flow similar to fired engine con-ditions [88, 87, 86, 84, 85].

• Addition principle — The experimental validation of the addition princi-ple (Eq. (4.1)), based on the correlation between the scavenging numberS (Eq. (1.4)) and two non-dimensional measures that characterize thesimilarity between velocity distributions obtained in pulsating and sta-tionary flow. The validation is supported by statistical hypothesis testingfor these similarity measures [88, 86].

• Resonances — The strong mean velocity fluctuations that are observedin isochoric flow rigs and numerical simulations of exhaust flow in firedand motored engines [81, 59, 4, 70, 14] have been explained as Helmholtzresonances. This assumption is confirmed by means of the frequencyresponse function of a one-dimensional gas dynamic model of the exhaustmanifold [84, 85].

• Flow reversal — The occurrence of instantaneous local flow reversal isreported in close-coupled catalyst exhaust systems, subject to fired engineconditions [70, 81, 59]. Given the inherent inability of HWA to discernthe velocity direction, all sources in the literature use an LDA systemwith frequency shifting to obtain bidirectional velocity measurements.

1.6 Goals and scope 29

Problems with optical access and seeding particle concentration result ina limited spatial and temporal resolution.

Through the introduction of a novel way of measuring bidirectional ve-locity using oscillating hot-wire anemometry (see Chap. 3) [83], time-resolved local flow reversal has been detected and quantified in an iso-choric flow rig [84, 85].

1.5 Goals and scope of this thesis

The goal of this thesis is the experimental study of pulsating flow in moderncompact close-coupled catalyst exhaust manifolds for internal combustion en-gines. Instead of using a fired engine involving a number of practical problemsdue to the hot corrosive exhaust gas environment, the study uses cold pulsatingflow rigs. This should enable the use of velocity measurement techniques thatyield a high spatial and temporal resolution. The accuracy and resolution of theobtained measurement data should enable detailed validation of computationalfluid dynamic calculations.

The thesis focuses on the most relevant flow-related aspect to the designof the exhaust manifold: the catalyst velocity distribution. As discussed inSect. 1.2, obtaining a uniform catalyst velocity distribution is crucial for an op-timal manifold design, in terms of minimal local catalyst degradation, minimalpressure drop and maximal conversion efficiency.

In particular, the thesis investigates the influence of (i) transient flow bound-ary conditions (similar to fired engine conditions) and (ii) geometrical aspects(e.g. pre-catalyst diffuser volume, number and length of exhaust runners, ex-haust valve timing) on the time-resolved catalyst velocity distribution.

Wherever the experimental data have difficulty in explaining the governingphysics, a one-dimensional gas dynamic model of the exhaust system shall beused to further the understanding of the flow dynamics.

Not within the scope of this thesis are:

• Computational fluid dynamics — Part of the measurement results havebeen used for the validation of a CFD approach, during a funded coop-eration with an industrial partner [2]. The CFD calculations are per-formed by the industrial partner. This thesis focuses on the experimentalmethodology only.

• Catalytic chemistry kinetics — The catalytic reaction chemistry withinthe converter under fired engine conditions. Nevertheless, the conversionefficiency is estimated using a simplified homogeneous and heterogeneousmodel of the reaction kinetics, as described in App. A.3.

• Other aspects — Some additional aspects in the design of exhaust man-ifolds, such as heat transfer, acoustics and vibration are not within thescope of this thesis.


1.6 Outline of this thesis

Chapter 2 presents the experimental approach, which encompasses (i) theexperimental flow rigs and (ii) the instrumentation and data reduction.

Section 2.2 describes the two flow rigs used during this thesis, each capa-ble of generating a well-controlled pulsating flow in an exhaust manifoldwith close-coupled catalyst.

Section 2.3 discusses the exhaust stroke flow similarity between the pul-sating flow rigs (using cold flow) and the true conditions in a manifoldmounted on a fired engine. The thermodynamic analysis used in Sect. 2.3is elaborated in App. B.

Section 2.4 discusses three different flow rate measurement techniquesused in this thesis. An accurate flow rate measurement is crucial toserve as reference for the velocity distribution measurements. Section 2.4explains how to overcome the particular issues involved in flow rate mea-surements in pulsating flow.

Since the thesis deals primarily with measuring periodic phenomena,Sect. 2.5 presents the basic concepts of data reduction for conditionalsampling and phase-locked averaging. The more advanced cycle-resolvedanalysis is briefly introduced and demonstrated in practice in Sect. 2.5.2.

Chapter 3 presents the measurement technique used to determine the time-resolved velocity distribution in the close-coupled catalyst. The selectionof hot-wire anemometry as the most suitable technique is clarified inApp. C.

Section 3.1 indicates the problems in obtaining accurate bidirectionalvelocity measurements. In fact, hot-wire anemometry is intrinsically in-sensitive to the velocity direction.

The remainder of Chap. 3 presents a novel oscillating hot-wire anemome-ter (OHW) to overcome this problem. The methodology is presented inSect. 3.3. Section 3.4 describes the mechanical oscillator designed for thispurpose.

Section 3.6 discusses the calibration procedure, which allows to use theOHW on the pulsating flow rig to quantify the time-resolved bidirec-tional velocity. The OHW is calibrated in a custom-built wind tunnel(Sect. 3.6.1). Laser Doppler anemometry has been used as a referencevelocity measurement, phase-locked with the oscillating probe’s motion(Sect. 3.6.2).

Section 3.7 presents and interprets the calibration results. Section 3.7.3formulates general selection and operation criteria for the OHW, basedon a non-dimensional scaling analysis.

Chapter 4 presents the experimental validation of the addition principle(Eq. (4.1)). Section 4.3 discusses the elaborate data reduction used in

1.6 Outline 31

this chapter to assess the similarity between a pair of velocity distribu-tions.Section 4.4 presents the experimental results for both pulsating flow rigsand both exhaust manifolds. The combined results are interpreted inSect. 4.5. The similarity measures introduced in Sect. 4.3 establish aremarkable correlation with a single non-dimensional flow characteristic,the scavenging number S (Eq. (4.42)). The correlations in Fig. 4.29 resultin a critical value for the scavenging number Scrit, which determines thevalidity range of the addition principle.Section 4.6 provides an physical interpretation to the findings of Sect. 4.5.This complex flow behaves like a zero-dimensional scalar mixing process.Using this analogy, Sect. 4.6.2 introduces the hypothetical concept of acollector efficiency ηD, which equals the critical value of the scavengingnumber Scrit. As indicated in Chap. 7, this hypothesis warrants furtherresearch.

Chapter 5 discusses the time-varying flow phenomena in exhaust systemswith close-coupled catalyst, whereas Chap. 4 is more concerned with time-averaged results.Section 5.1 presents selected results of time-resolved velocity distribu-tions for different pulsating flow rigs, exhaust manifolds and operatingconditions.Section 5.2 discusses the occurrence of periodic flow reversal in the close-coupled catalyst. Section 5.2.1 validates the oscillating hot-wire anemo-meter (see Chap. 3) in conditions where considerable flow reversal isknown to occur in the catalyst. The validation is performed with re-spect to integral flow rate measurements. The OHW is used to measurebidirectional velocity in the isochoric pulsating flow rig.The experimental data in Sect. 5.2.2 are obtained using the OHW ap-proach, revealing the time-resolved velocity distribution throughout theentire catalyst cross-section, including areas of negative velocity.Section 5.2.3 describes the use of a one-dimensional gas dynamic modelof the exhaust system to simulate the occurrence of flow reversal in termsof the mean velocity. Appendix D discusses the gas dynamic model indetail.Through numerical simulation, Sect. 5.2.3 establishes the influence oncatalyst flow reversal of the presence of the exit cone and cold end.Section 5.3 discusses the resonance fluctuations observed in the time-resolved mean catalyst and runner velocity. The same phenomenon isobserved by other authors, yet has never been satisfactorily explained.Section 5.3.2 provides an analytical explanation of the Helmholtz reso-nance.Section 5.3.4 uses the same one-dimensional gas dynamic model (seeApp. D) to explain the resonance phenomenon numerically. Gas dynamic


frequency response functions of the exhaust manifold are determined, re-vealing the nature of the resonating system responsible for these strongvelocity fluctuations in the catalyst.

Chapter 6 formulates some brief comments that interlink the findings ofChaps. 4 and 5, and explains how the addition principle’s validity isinfluenced by the flow dynamics.

Chapter 7 formulates the general conclusions of this thesis, and suggests somefuture research opportunities.

Appendix A provides an overview of the mechanisms of wall friction andother sources of pressure loss, as well as catalytic reaction kinetics inautomotive catalysts.

Appendix B contains the thermodynamic analytical derivation for assessingthe exhaust stroke flow similarity between the pulsating flow rigs usingin this thesis and actual fired engine conditions. These derivations areused in Sect. 2.3.

Appendix C reviews the advantages and disadvantages of some competingtechniques for measuring time-resolved gas velocity (i.e. thermal and op-tical anemometry).

Appendix D describes the numerical one-dimensional gas dynamic modelthat has been implemented to help understand the flow dynamics (seeSects. 5.2.3 and 5.3.4). A brief explanation is given on decoupling anddiscretizing the Euler equations. The gas dynamics code is validatedusing some benchmark problems. Finally, some comments are given onidentification methods by means of multisine signals.

Chapter 2

Experimental approach

“The men of experiment are like the ant; they only collect and use: thereasoners resemble spiders, who make cobwebs out of their own substance.But the bee takes a middle course; it gathers its material from the flowersof the garden and of the field, but transforms and digests it by a power ofits own.”

Francis Bacon (English philosopher, 1561, †1626)

This chapter presents the experimental approach, comprising two parts: (i) theexperimental setup and (ii) the instrumentation and data reduction.

Sections 2.1 and 2.2 describes the exhaust manifolds and the two pulsat-ing flow rigs used during this thesis. To facilitate the velocity measurements,the pulsating flow rigs operate using air at ambient temperature, whereas theexhaust manifold in a fired engine is subjected to hot, corrosive exhaust gas.Section 2.3 discusses the exhaust stroke flow similarity between the pulsatingflow rigs and the fired engine conditions.

Section 2.4 discusses the flow rate measurement techniques, which serve asa reference for the velocity distribution measurements. Section 2.5 presentsthe basic concepts of data reduction for conditional sampling and phase-lockedaveraging. Section 2.5.2 briefly discusses the effects of cyclic variation, whichis a typical phenomenon occurring in volumetric reciprocating machinery.

2.1 Exhaust manifoldsTwo exhaust manifolds with close-coupled catalyst have been used during theresearch, denoted manifolds A and B. The specifications are given in Table 2.1.Each manifold is designed for an indirect injection petrol internal combustion

33

34 Chapter 2 Experimental approach

engine. Both engines are typical recent generation Otto engines, featuringdouble overhead camshafts, four valves per cylinder, and a cross-flow pent-rooftype combustion chamber. The engine block and cylinder head are made of castaluminium. The bore-to-stroke ratio is approximately 1 : 1. The compressionratio is 10 : 1. The intake is atmospheric and throttle valve controlled. The fuelis injected in a multi-point sequential manner, and is electronically controlled.The specific brake torque is between 90 and 95 Nm/l at 4000 rpm. The specificbrake power is between 45 and 49 kW/l at around 6000 rpm. Both enginescomply with Euro III emissions standards.

Table 2.1 – Exhaust manifold specifications

Manifold A Manifold BEngine 3175 cm3 V-6 1199 cm3 I-4Valve timing7 −12 | 242 | −246 | 10 −13 | 220 | −220 | 13Firing order8 1–4–2–6–3–5 1–3–4–2Runners 31.5 mm, L = 150, 90,

120 mm 28.0 mm, L = 160, 80,160, 80 mm

Diffuser volume Vd = 141.4 cm3 Vd = 390.2 cm3

Catalyst ceramic 3/600 monolith, square channelscircular 63 mm,L = 52 mm

oval 151×101 mm,L = 137 mm

Figure 2.1 shows manifolds A and B, indicating the runner numbering thatstarts from the engine’s distribution side. The exhaust gas oxygen sensor up-stream of each catalyst has been replaced by a flush-mounted plug that accom-modates a static pressure tap and a temperature probe.

The choice of manifolds A and B is not arbitrary: Manifold A is fitted to thehead of one cylinder bank of a V-6 engine. In fact, two very similar manifoldsare used on either side of the engine. Cylinders are numbered starting atthe distribution side from 1 to 3 and 4 to 6, for the first and second bankrespectively. The firing order is 1–4–2–6–3–5. As such, the phase differencebetween the valve timing of three cylinders in one bank is 720 ca/3 = 240 ca.This phase difference is comparable to the total exhaust valve opening period(Table 2.1). Therefore, the exhaust strokes of individual cylinders occur nearlysequentially. The exhausted flow pulses issue into the exhaust manifold withoutoverlap between the cylinders.

By contrast, manifold B belongs to an inline four-cylinder engine, with aphase difference between the valve timings of 720 ca/4 = 180 ca. This leadsto an overlap of roughly 60 ca between the exhaust strokes. The exhaust flowpulses in manifold B interact to a higher degree when compared to manifold

8The valve timing is given as four crankshaft positions (ca), relative to top dead centerprior to the intake stroke. IO | IC | EO | EC correspond respectively to intake valve openingand closing (IO, IC) and exhaust valve opening and closing (EO, EC).

8The V-6 engine features two exhaust manifolds. Manifold A corresponds to the under-lined cylinders 1, 2 and 3.

2.1 Exhaust manifolds 35

y x

1

2

3

(a)

x

y

1

2

3

4

(b)

Figure 2.1 – Exhaust manifolds (a) A and (b) B

A. This is important with respect to the findings in Chap. 4 concerning thevalidity of the addition principle.

Note that this valve overlap should not be confused with the general conceptof valve overlap in four-stroke internal combustion engines. The general intra-cylinder valve overlap denotes the difference between exhaust valve closing andintake valve opening of an individual cylinder. The above discussed overlapbetween the exhaust strokes of different cylinders shall be denoted the inter -cylinder valve overlap to avoid confusion.

No exit cone or tailpipe is connected to either manifold, thus allowing accessto measure the velocity distribution in the catalyst. Since only cold pulsatingflow is used in this research, this poses no problems, other than a high noiselevel. The velocity distribution could be slightly influenced by the absence ofthe exit cone and the backpressure of the tailpipe. However, as indicated inSect. 1.4.2, the occurrence of flow reversal in particular is not influenced by thepresence or absence of the exit cone.

The gas exits the catalyst monolith as tiny laminar jets. Each jet experi-ences a sudden expansion, according to the open frontal area ratio. At a normaldistance to the outlet face z = 0 mm, the velocity distribution contains veryhigh transverse gradients due to the blockage by the channel walls. Furtherdownstream as z increases, the neighboring jets are mixing, which averages outthe transverse gradients. This mixing process occurs at a transverse lengthscale comparable to the channel diameter d ' 1 mm.

Measurements show that this small-scale mixing process is complete for


θ /2, ω/2

Rootscompressor

throttlevalve

∆pp i, ti

ISO standardized flow rate orifice

pcat

U

surge vessel

duct

sect

ion

with

m

ount

ing

plat

eFigure 2.2 – Isothermal flow rig, with cylinder head mounted

z > 20 mm. All measurements are performed in a measurement plane atz = 25 mm. Instead of the exit cone, a cylindrical exit sleeve is mounteddownstream of the catalyst, with the same perimeter. Since the exit sleeveis 40 mm long, the velocity is measured well within the sleeve, thus avoidingentrainment of surrounding air.

The transverse length scale of the interesting features of the velocity distri-bution is of the order of 10 to 100 mm (i.e. the order of magnitude of the runneror catalyst containment hydraulic diameter). The large-scale transverse veloc-ity gradients are largely unchanged at z = 25 mm, since their characteristiclength scale is one to two orders of magnitude greater than d.

Thus, the measurement position z = 25 mm is a compromise between(i) avoiding the laminar jet mixing region and (ii) retaining the large-scale ve-locity distribution. Other researchers choose a similar measurement position.For instance, Arias-Garcia et al. [7] suggest z = 30 mm, based on doctoralthesis research by Clarkson [28]. Lemme and Givens [64] show that the jets aresufficiently mixed at z = 25.4 mm.

2.2 Pulsating flow rigs

2.2.1 Isothermal flow rig

The isothermal dynamic flow bench consists of a surge vessel with removableduct section and mounting plate. Figure 2.2 shows a schematic diagram ofthe set up. The isothermal flow rig mimics flow from infinitely large combus-

2.2 Pulsating flow rigs 37

1

2

3

Figure 2.3 – Rotating valve ( 1© stator, 2© rotor, 3© rotor bearing block and motorcoupling)

tion chambers. The exhaust stroke flow similarity with respect to true engineconditions is discussed in Sect. 2.3.

A Roots compressor delivers a maximum air flow rate of 350 Nm3/h at300 mbar overpressure. The compressor is driven by a variable speed drive.The compressor feeds the surge vessel via a long pipe section with a standard-ized flow rate measurement orifice. A throttling valve is inserted between thecompressor and the long pipe section.

The flow rate is determined using an orifice, according to ISO Standard5167-1991(E) [54]. The standard restricts the use of the orifice to steady orslowly varying flows. The surge vessel’s volume provides adequate damping ofthe pulsations caused by the pulsating flow generator, based on ISO TechnicalReport 3313-1998(E) [55]. This is discussed more in detail in Sect. 2.4.1. Theadditional uncertainty on the orifice flow rate reading in pulsating flow causedby using the time-averaged value of the differential pressure is below 0.5% forall measurement conditions. However, the orifice reading is only used duringstationary operation to check the flow rate calculated from the catalyst velocitydistribution. The agreement is well within the error bounds of the orificemeasurement (' 5 %).

For manifold A, both a rotating valve and the original cylinder head havebeen used to generate the pulsating flow on the isothermal flow rig.

The rotating valve has been chosen since it constitutes a very simple wayof generating pulsating flow. Other authors have used e.g. a rotating disk [22,7, 17, 58] to obtain the same result. Furthermore, in the open position, therotating valve does not obstruct the flow in any way, whereas the poppet valvesof a cylinder head always disturb the flow. This lack of obstruction is partic-ularly advantageous for comparison of results to numerical simulations, sincethe rotating valve requires fairly simple inlet boundary conditions.

For manifold B, only the corresponding cylinder head is used as pulsator.


1

3

2

Figure 2.4 – Isothermal flow rig, with rotating valve and manifold A mounted ( 1©surge vessel, 2© duct section with trace gas injectors, 3© rotating valve)

The same surge vessel is used, with a modified duct section and pulsator mount-ing plate.

Figure 2.3 shows the components that make up the rotating valve. It con-sists of a solid cylinder rotor with rectangular holes, that rotates with a tighttolerance in a stator. O-ring seals are inserted between neighboring exhaustport sections of the rotating valve, thereby eliminating cross-flow within thevalve body (not shown in Fig. 2.3). The geometry of the holes correspondsto the original cylinder head’s exhaust port cross-sectional area, and to theexhaust valve timing.

Figure 2.4 shows the isothermal flow rig, with the rotating valve and man-ifold A mounted. In the base of the duct section ( 2© in Fig. 2.4), one solenoidactuated injector is incorporated for each duct, i.e. for each cylinder. Theseinjectors have been used to inject small amounts of trace gases (e.g. CH4, NO,CO). Each injector is controlled to inject sequentially, during the exhaust pe-riod of its cylinder. The objective of the trace gas injection is to determine thepartial load on the catalyst from each cylinder. These measurements are notdirectly relevant within the scope of this thesis.

The rotating valve is driven by an electric motor, which is controlled by avariable speed drive. The motor is located behind the valve in Fig. 2.4. Therequired motor power is low, since only the valve’s internal friction must beovercome. The valve shaft position is monitored by an angular encoder, whichis not shown in Fig. 2.4. It is mounted on the protruding end of the valve shaft.

The encoder9 is of the sinusoidal incremental type, featuring an angularaccuracy better than 0.1 . The index pulse of this encoder is used to trig-ger the hot-wire anemometer, thus phase-locking the measurement to the flowpulsation.

9Heidenhain ERN180, 3600 lines per revolution, sinusoidal incremental interface


Figure 2.5 – Isothermal flow rig,with cylinder head and manifold Amounted

Figure 2.6 – Isothermal flow rig, withcylinder head and manifold B mounted

A more powerful speed-controlled electric motor drives the cylinder head’sexhaust camshaft using a timing belt. Figure 2.5 shows the isothermal flowrig set up with manifold A and its cylinder head mounted. The encoder ismounted on a shaft extending from the camshaft’s timing belt pulley. In thecase of manifold A, the intake camshaft remains stationary, in such a positionthat all intake valves are closed. This is possible because of the lack of inter-cylinder valve overlap (above). To eliminate any leakage due to marginallyopened intake valves, the intake ports are sealed as well. As Fig. 2.5 shows,the surge vessel is inclined so that the flow exits the catalyst horizontally, withthe sole purpose of facilitating the velocity distribution measurements.

For manifold B, the intake and exhaust camshafts are driven by a timingchain mechanism, including a chain guide and oil-pressurized chain tensioner.As Fig. 2.6 shows, the chain mechanism is contained within the original timingchain cover and a backing plate. The timing chain drives both camshafts. Onthe isothermal flow rig, the crankshaft sprocket is not driven by the crankshaft(since there is no crankshaft). Instead, a customized chain drive shaft is usedthat fits the original sprocket. The shaft is supported by two roller bearings,and sealed using the original crankshaft oil seal in the timing chain cover. Atiming belt is used to connect the electric motor and the chain drive shaft.The rotary encoder is mounted on the chain drive shaft. The intake ports aresealed externally in the same way as for manifold A. The motion of the intakevalves could slightly influence the flow inside the flow rig ducts, but this is ofno interest to the present research.

When the cylinder head is used to generate pulsating flow, forced lubrication


θ , ω

screw compressor

buffer vessel

pressure regulator

∆p p i, ti p cyl

laminar flow meter

pcat

tcat

U

Figure 2.7 – Isochoric flow rig

is required for the moving parts (e.g. camshaft bearings, followers, tappets,poppet valves). Also, several components require a sufficiently high oil pressurefor proper operation (e.g. hydraulic valve clearance adjusters, timing chaintensioner). Therefore, an externally driven pump (shown in the bottom leftof Fig. 2.5) supplies the cylinder head with engine lubricating oil through theappropriate feed channels, at a pressure of approximately 5 bar. The oil returnsfrom the cylinder head through the force of gravity, along the original oil drainchannels. The returning oil flows to a reservoir (shown underneath the surgevessel in Figs. 2.5 and 2.6), from which it is pumped back up through a filterin a continuous loop.

2.2.2 Isochoric flow rig: Charged motored engine (CME)

The isochoric or charged motored engine (CME) flow rig consists of a four-cylinder internal combustion engine, mounted on a dynamic engine test standwith an electric DC motor. The engine corresponds to manifold B. Its specifi-cations are given in Table 2.1.

Figure 2.7 schematically depicts the CME flow rig. The compressed air isproduced using a screw compressor, which delivers a maximum flow rate of250 Nm3/h (' 300 kg/h) at 8 atm(10). A pressure regulator ( 2© in Fig. 2.9)maintains a constant pressure in the engine intake system, varying between

10Throughout the thesis, the standard unit of pressure is atm, defined as 1 atm =101325 Pa. Unless stated otherwise, all pressures are given in absolute values. Pressuresrelative to atmospheric pressure (= 1 atm) are indicated in atm-r.


Doctoral defence Tim Persoons – 11 May 2006 (dry run) 1/20

com

bust

ion

Experimental approachPulsating flow rigs (2)

IntroductionGoal and scopeOverviewExperimental approach

Flow rigsSimilarity

Oscillating hot-wireApproachCalibrationValidation

Addition principleApproachResultsSummaryDiscussion

Experimental dynamicsResultsFlow reversalHelmholtz

Numerical dynamicsModelResultsHelmholtz

Conclusion

pcyl

Vcyl

pint > 1pres

pexh ≅ 1

CME flow rig

engineload

pcyl

Vcyl

pint < 1

pres

pexh ≅ 1

Fired engine

engineload

TDC BDC TDC BDC

EVO EVO

Figure 2.8 – Comparison of the indicator diagram for (a) a fired engine and (b) theisochoric flow rig

1.00 atm to 2.25 atm in the current study. The exhaust stroke flow similarity(Sect. 2.3) shows that this roughly corresponds to the range of zero to fullengine load in true fired engine conditions. The screw compressor’s maximumflow rate limits the engine speed in the performed measurements to 3000 rpm.

Figure 2.8 shows the difference between a fired gasoline engine and theisochoric flow rig in terms of their schematic indicator diagram, showing theevolution of cylinder pressure pcyl versus cylinder volume Vcyl. TDC, BDC andEVO respectively denote top dead center, bottom dead center and exhaust valveopening. In spite of the differences, the residual cylinder state (immediatelyprior to the exhaust valve opening) forms the initial conditions for the exhauststroke. Therefore, only the residual state is of importance to obtaining a similarexhaust stroke in the isochoric flow rig.

Figure 2.8a shows that the intake pressure pint for the fired engine is belowatmospheric pressure, due to the throttled intake manifold. After compression,combustion and expansion, the residual cylinder pressure pres is indicated. Theexhaust stroke itself is indicated as a bold line.

The indicator diagram for the isochoric flow rig (Fig. 2.8b) features substan-tial differences. The intake pressure pint is greater than atmospheric pressure,resulting in a much higher pressure following the compression stroke comparedto the fired engine. Since there is no combustion phase, there is no pressurerise near top dead center. Theoretically, the pressure would decrease alongthe same line during the expansion stroke. However in reality, the pressure islower during the expansion stroke, as a result of losses. Gas mass is lost fromthe cylinder due to blow-by leakage, and internal energy is lost due to heatexchange with the walls. Most importantly, the exhaust stroke resembles quitewell to the fired engine case, given the appropriate setting of the intake systempressure pint.

In a fired engine (Fig. 2.8a), the engine load is varied by adjusting thethrottle, which changes the intake manifold density and thereby the amount ofheat released during combustion. As a result, also the residual pressure varies.


In the isochoric flow rig (Fig. 2.8b), the residual cylinder state is variedby changing the setting of the intake manifold pressure pint, by means of thepressure regulator ( 2© in Fig. 2.9).

The engine is motored at a constant speed by means of the test stand DCmotor ( 1© in Fig. 2.9). The aforementioned encoder9 records the crankshaftposition ( 4© in Fig. 2.9). To enable charging the engine with compressed air,the original intake system has been replaced by a reinforced intake system withidentical manifold volume and runner dimensions. The engine is run withoutcombustion and fuel injection, to obtain cold clean pulsating flow in the ex-haust system. The original exhaust valve timing as mentioned in Table 2.1 isunchanged. However, the intake camshaft is retarded by 30 ca to avoid unphys-ical blow-through from the high-pressure intake to the low-pressure exhaustsystem during intake/exhaust valve overlap. The valve timing used during theexperiments is therefore 17 | 250 | −220 | 13.

Applying an intra-cylinder or intake/exhaust valve overlap period is com-mon to all four-stroke internal combustion engines. The valve overlap maxi-mizes the indicated efficiency. In an engine with a pressure wave tuned exhaustsystem, a rarefaction (expansion) wave arrives at the exhaust port during valveoverlap. This negative pressure (i) helps to scavenge the combustion chamberof exhaust gas, and (ii) helps to start the induction of fresh mixture from theintake runner. At a low engine speed or in case of excessive valve overlap, back-flow can occur from exhaust to intake system. Blow-through of fresh mixturefrom intake to exhaust rarely occurs for naturally aspirated engines.

For turbo- or supercharged (fired) engines, usually a shorter valve overlap(or none at all) is used to prevent blow-through of fresh mixture from intaketo exhaust system. The amount of blow-through is determined by the ratio ofintake to exhaust system pressure.

For the CME flow rig, the exhaust pressure is nearly atmospheric, whilethe intake system pressure reaches a maximum of 2.5 atm. Using the original(naturally aspirated) engine’s valve timing would result in a large blow-throughflow rate, which is not present in fired engine conditions. This would cause anadditional peak flow rate near the end of the exhaust stroke. As such, thevalve overlap is removed by retarding the intake camshaft. The effect of theretarding is indicated in the schematic indicator diagram in Fig. 2.8b.

Figure 2.9 shows how the engine is installed on the test stand. The engineis mounted without vibration dampers onto the rigid test stand frame. Thevelocity measurement probe is mounted on an automated positioning system( 5© in Fig. 2.9) which is fixed securely onto the lab floor, adjacent to the teststand. Much care is taken to avoid any relative motion between the engineexhaust system and the velocity probe.

The intake system flow rate is measured using a laminar flow element meteror LFE ( 3© in Fig. 2.9). The LFE has been calibrated against the ISO stan-dardized orifice used on the isothermal flow rig. Section 2.4.2 discussed thedetails of this system. Partly because of the altered intake timing, the intakeflow rate is highly pulsatile with periods of extensive backflow.

Although the LFE is an appropriate choice of flow rate measurement for


2

1

3

4 5

2

3

5

Figure 2.9 – Isochoric (CME) flow rig, with manifold B mounted ( 1© test stand DCdyno, 2© intake pressure regulator, 3© LFE, 4© encoder, 5© velocity probe positioningsystem)


such flows (see Baker [9]), the intake system flow rate is further verified usinga piezo-electric cylinder pressure sensor. The pressure rise during the compres-sion stroke is used to determine the inducted mass per cylinder per cycle, thusyielding the mass flow rate. Section 2.4.3 elaborates on the cylinder pressure-based flow rate measurement. The intake flow rate reading is accurate to within5 to 10%, and serves as a reference measurement for the flow rate obtained byarea-averaging the catalyst velocity distribution.

The cold pulsating flow generated by the CME flow rig in the exhaustsystem is quite different from the isothermal flow rig. By controlling the intakesystem pressure, the residual cylinder pressure at exhaust valve opening (EO)can be adjusted. This results in a two-stage exhaust stroke with blowdown anddisplacement phases, which is typical of fired engine conditions. The CME flowrig therefore produces cold pulsating flow, which greatly facilitates the velocitymeasurements yet still is very similar to fired engine exhaust conditions.

2.3 Exhaust stroke flow similarity

Ultimately, the research presented in this thesis must apply to flow in exhaustmanifolds in actual fired engine conditions. As discussed in the previous sec-tions, there are some substantial differences with fired engine conditions. Bothisothermal and isochoric flow rigs differ mainly in terms of the temperature ofthe flow.

This section aims to quantitatively assess the similarity of the flow gener-ated by the isothermal and isochoric pulsating flow rigs, with respect to firedengine conditions. Furthermore, this section explains the proper setting of theoperating parameter pi for the isochoric flow rig to resemble a given engineload in fired conditions.

2.3.1 Introduction

The exhaust stroke flow similarity between fired engine conditions and theisothermal and isochoric flow rig are investigated numerically and analytically.

Numerical simulations are performed using a filling-and-emptying internalcombustion engine model written in MATLAB11. The engine model is basedon Watson and Janota [107] and Heywood [47]. The engine is modeled as zero-dimensional volumes (e.g. intake and exhaust manifold, cylinders) combinedwith quasi one-dimensional pipes for the intake runners (see remark below).Within each volume, the equations of conservation of mass and energy aresolved, combined with the ideal gas equation. The model uses the appropriatedescriptions for compressible restricted flow over intake and exhaust valves.The combustion process is modeled using a Wiebe law for single-zone heat re-lease. Heat loss to the combustion chamber walls is incorporated, based on thegenerally accepted correlations by Woschni [113]. Blow-by leakage is taken into

11MATLABTM and SimulinkTM are products of The MathWorks, Inc., 3 Apple Hill Drive,Natick (MA) 01760-2098, USA (http://www.mathworks.com)

http://www.mathworks.com

2.3 Exhaust stroke flow similarity 45

account based on experiments on the CME flow rig (see Fig. 5.21). The modelis solved by means of fixed step fourth order Runge-Kutta time integration.For reasons of numerical stability, the time step is set to different (yet fixed)values during the intake and exhaust stroke and during the compression andexpansion stroke.

Background The term quasi one-dimensional may be interpreted asfollows. The runners are not discretized along their length, as is the casefor a true one-dimensional gas dynamic model, as described in App. D.Instead, a single momentum equation is solved that represents the mo-mentum of the entire gas mass contained within the runner as a single(incompressible) plug flow. This equation is used to estimate the stagna-tion pressure upstream of the intake valves. The gas dynamics are verycrudely simplified in this way. This means a considerable reduction in thecalculation time with respect to a fully one-dimensional model, yet stillestimates the intake ram effect to some extent. A one-dimensional gasdynamic model (implemented in Simulink11) has been used in this thesisfor the investigation of the resonance fluctuations observed in the time-resolved flow rate through the close-coupled catalyst exhaust manifold(see Sect. 5.3).

For an engine speed of 1800 rpm and an exhaust flow rate of 100 m3/h(corresponding to part load conditions), Fig. 2.10 shows the time-resolved non-dimensional velocity in runner 1 of manifold B. The solid (

) and dashed line

( ) represent simulations performed for the CME and isothermal flow rig,

respectively. The markers ( ) indicate the runner velocity measured on the

CME flow rig. The non-dimensional exhaust valve lift is plotted in grey.Figure 2.10 demonstrates that the calculated runner velocity using the

filling-and-emptying model ( ) compares reasonably to the measured veloc-

ity ( ) during the blowdown phase. However, the measured runner velocity

fluctuates substantially during the displacement phase, whereas the simulationdoes not. This is due to the oversimplified numerical model, which models noneof the gas dynamics of the exhaust system. The resonance fluctuations are dis-cussed in detail in Sect. 5.3. In Sect. 5.3.4, a more advanced one-dimensionalgas dynamic model is used which does capture these fluctuations.

Figure 2.10 shows no curve for a fired engine. The runner velocity for a firedengine is qualitatively the same as for the CME flow rig, except that the ratioof the peak velocity values during blowdown and displacement is somewhatdifferent. This is explained in the following section.

The measured runner velocity is only indicative. A hot-film sensor is fixedflush with the runner wall, at the entrance to the runner. As such, the mea-surement indicates rather the wall shear stress than the mean runner velocity.Measuring the actual velocity distribution using a hot-wire probe proved verydifficult in that location, since the wire tends to break due to the highly pul-sating flow, that reaches peak velocities up to Ma = 1. Furthermore, thetemperature in the exhaust system drops as the intake pressure is increased.This is caused by the reduction in internal energy during the compression andexpansion stroke, due to heat loss and blow-by leakage. As the temperature in


Exh

aust

val

ve li

ft (

-)

CME (measured)CME (simulated)ISOT (simulated)

450 540 630 7200

1

2

3

4

5

6

7

8

Crankshaft angle ω t (°)

Run

ner

velo

city

U(r

) (-)

Figure 2.10 – Exhaust runner velocity for isothermal and isochoric flow rig

the exhaust system drops below the dew point temperature, water condensesfrom the air. These condensate droplets form tiny ice particles as the temper-ature drops below 0 C at high intake pressure. The fast moving ice particlesmight also contribute to sensor wire breakage. The problem is only encounteredwhile attempting to measure the velocity in the runner entrance. Downstreamof the catalyst, no such problem arises.

The isothermal flow rig produces a single-stage exhaust pulse, resulting innr quasi-sinusoidal pulses per engine cycle, where nr is the number of runnersissuing into the catalyst. The CME flow rig produces a pulsating flow thatstrongly resembles fired engine conditions. The two-stage exhaust pulses aremore distorted, resulting in an exhaust flow rate with higher frequency con-tent. The difference between measured and simulated velocity in Fig. 2.10 isdue to Helmholtz resonances that are most pronounced during the displace-ment phase. The filling-and-emptying engine model does not incorporate asufficiently accurate exhaust system model to capture this effect.

2.3.2 Thermodynamic analysis

The analysis in this section is based on a purely analytical derivation of the sim-plified thermodynamic evolution of the gas in an reciprocating engine, betweenthe intake stroke and the exhaust stroke. The derivation aims to provide ananalytical expression for the flow rate during the blowdown and displacementphase, as a function of the engine load (i.e. intake system pressure) and thepresence of an internal combustion phase.

Some assumptions are required to be able to extract an analytical expres-sion. The resulting expression needs not be 100 % accurate, since the purposeof the derivation is foremost to assess the exhaust stroke flow similarity betweenthe CME flow rig and a fired engine.


The derivation is performed in three consecutive stages:

(1) Evolution between the end of the intake stroke until the residual state,i.e. immediately before the opening of the exhaust valves.

(2) The blowdown phase, lasting until the residual cylinder pressure hasequalized to the exhaust system pressure.

(3) The displacement phase, where the piston motion determines the flowrate through the exhaust system.

The complete derivation is elaborated in App. B. Here, a brief overview isgiven. Air is taken as working fluid, with thermodynamic properties evaluatedat a fixed mean temperature. During stage (1), the in-cylinder heat loss andblow-by leakage are neglected. The relation between intake and residual statefollows from the conservation of mass and energy (Eq. (B.1)):

ρe

ρi=Vi

Ve;

pe

pi=(Vi

Ve

)γ(

1 +∆Tc

Ti

(V0

Vi

)γ−1)

where ρ is the density [kg/m3], p is the pressure [Pa], V is the cylinder vol-ume [m3], T is the temperature [K] and the subscripts i, e, 0 respectively denoteintake valve closing, exhaust valve opening and top dead center. The adiabatictemperature rise due to combustion equals ∆Tc = φSf/ (cvLf ), where φ isthe product of the equivalence ratio and the combustion efficiency [-], Sf isthe lower heating value of the fuel [J/kg], cv is the specific heat capacity atconstant volume [J/(kg K)] and Lf is the theoretical air-to-fuel ratio [kg/kg].

Stage (2) or the blowdown phase is regarded as the expansion of the resid-ual cylinder pressure at constant cylinder volume. The mass flow rate over theexhaust valves is determined assuming compressible restricted flow, with theappropriate discharge coefficient (see Fig. B.1). The valve lift curve is approx-imated by a cosine function, which in turn is further approximated at smalllift values by a parabolic function. This yields a non-linear partial differentialequation that gives the evolution of the mass of gas m remaining in the cylinder(Eq. (B.8)):

d

dt

(m

me

)= −Cd

neπ3dehe

∆θ2ω2t2

√rTe

Ve

(m

me

) γ+12

f

(pa

pe

(m

me

)−γ)

This equation cannot be solved due to the non-linear function f , whichoriginates from the equation for compressible flow through the exhaust valvethroat. As such, f is approximated by a function such that Eq. (B.8) can besolved (see Eq. (B.10)). From the solution of this partial differential equa-tion follows an Eq. (2.1), describing the maximum mass flow rate during theblowdown phase m1 [kg/s].

Stage (3) or the displacement phase is regarded as volumetric expulsion ofgas at constant pressure. From the conservation of mass and the assumption


of constant density follows Eq. (2.2), describing the maximum mass flow rateduring the displacement phase m2 [kg/s].

In Eqs. (2.1) and (2.2), term i represents the influence of the intake systempressure. It varies roughly between 0.25 and 1 for a fired engine and between 1and 2.5 for the CME. Term ii represents the influence of the temperature riseduring the combustion process. For the CME flow rig, there is no combustion,reducing term ii to 1. For fired engine conditions, term ii equals roughly 3.5.

m1 = ρiViω

(2Cd

neπ3dehe

∆θ2

√rTi

ωVi

) 13(Vi

Ve

) γ−76

·

(1 +

∆Tc

Ti

(V0

Vi

)γ−1)

︸︷︷︸ii

γ−86γ

·(pi

pa

)︸︷︷︸

i

− 43γ

·

(pi

pa

)︸︷︷︸

i

1γ(Vi

Ve

)(1 +

∆Tc

Ti

(V0

Vi

)γ−1)

︸︷︷︸ii

1γ

− 1

(2.1)

m2 = ρi

(πb2

4s

)ω

2

(pi

pa

)︸︷︷︸

i

− 1γ

(1 +

∆Tc

Ti

(V0

Vi

)γ−1)

︸︷︷︸ii

1γ

(2.2)

As the engine load increases, the intake system pressure (or equivalentlyterm i) increases. In that case, Eqs. (2.1) and (2.2) show that the peak massflow rate increases during blowdown (∂m1/∂pi > 0) and decreases during dis-placement (∂m2/∂pi < 0). For the CME flow rig, in the absence of combustion,the intake system pressure should result in peak flow rates comparable to firedengine conditions. An appropriate change in term i should compensate for thechange in term ii. Figure 2.11 shows the evolution of m1 and m2 according toEqs. (2.1) and (2.2) versus the intake pressure, for fired and CME conditions.

m1 and m2 are non-dimensionalized using a reference exhaust flow ratemref [kg/s], assuming a volumetric efficiency of unity:

mref = ρi

(πb2

4s

)ω

4π720180

(2.3)

The symbols are defined in App. B. mref corresponds to a hypothetical exhauststroke lasting 180 ca (hence the factor 720/180 in Eq. (2.3)), where the totalgas mass is exhausted at a constant mass flow rate mref .

Figures 2.11 through 2.16 each compare the exhaust stroke of the firedengine (left) to the CME flow rig (right). Each plot features the intake manifoldpressure pi/pa in abscissa, which corresponds to a range of engine load fromlow to high, from left to right. The solid lines (

) result from the analytical


derivation, whereas the markers ( ,

,

) result from simulations using the

filling-and-emptying engine model.For the CME flow rig at low intake pressure pi, m1 is negative because of

the early opening of the exhaust valve. The cylinder volume at intake valveclosing Vi is smaller than the volume at exhaust valve opening Ve. This is dueto the retarding by 30 ca of the intake camshaft, which is not present for thefired engine with original intake valve timing.

Retarding the intake camshaft avoids unphysical blow-through during(intra-cylinder) valve overlap between intake and exhaust valves. Retainingthe original valve overlap would result in an excessively high peak flow ratecrossing the combustion chamber from the high pressure intake system to thenearly atmospheric pressure in the exhaust system. This does not occur in thefired engine and would disturb the flow during the final stage of the exhauststroke on the CME flow rig. Thus, the intake camshaft timing is retarded.

The high ratio of blowdown to displacement peak flow rate m1/m2 can onlybe achieved on the CME flow rig by increasing the intake pressure pi/pa toroughly 5. In that case however, without altering the compression ratio, themaximum cylinder pressure is too high. Furthermore, because of in-cylinderheat loss, blow-by leakage and the fact that Vi/Ve < 1, the exhaust flow tem-perature drops below 0 C roughly when pi/pa > 2.5. In that case, water vaporcondenses from the air and freezes inside the exhaust manifold. As explainedearlier, this inhibits the use of hot-wire probes for measuring the flow insidethe runner. Furthermore, the ice deposits gradually block the small catalystchannels. Possibilities for extending the operating range include using an airheater in the intake system or changing the intake camshaft entirely. However,none of these options are pursued in this research. As such, the intake systempressure is limited to roughly pi/pa = 2.5.

With respect to flow similarity, not only the mass flow rate-based non-dimensional groups m1/mref , m2/mref and m1/m2 should be taken into ac-count. The Reynolds and Mach number based on mean runner velocity anddiameter are expressed as:

Re =Urdr

µ/ρ(2.4)

Ma =Ur√γrT

(2.5)

where Ur is the runner mean velocity = m/(ρπd2

r/4)

[m/s], dr is the runnerhydraulic diameter [m] and µ is the dynamic viscosity (Pa·s). Assuming theexhaust manifold pressure equals atmospheric pressure, the density ρ can bewritten as:

12The solid lines ( ) result from the analytical derivation; the markers (

,

,

) result

from the filling-and-emptying engine model


0.4 0.5 0.6 0.7 0.8 0.9 1

-1

0

1

2

3

4

5

6

Fired, 1800 rpm

Mas

s fl

ow r

ate

(-)

Intake pressure pi/p

a (-)

M1/M

ref (-) (blowdown)

M2/M

ref (-) (displacement)

M1/M

2 (-)

(a)

1 1.5 2 2.5

-1

0

1

2

3

4

5

6

CME, 1800 rpm

Mas

s fl

ow r

ate

(-)


a (-)

M1/M

ref (-) (blowdown)

M2/M

ref (-) (displacement)

M1/M

2 (-)

(b)

Figure 2.11 – Mass flow rate12 versus engine load pi/pa, for (a) fired engine and(b) CME flow rig

0.4 0.5 0.6 0.7 0.8 0.9 1

-50

0

50

100

150

200

250

Fired, 1800 rpm

Rey

nold

s nu

mbe

r R

e (1

03 )


a (-)

Re1 (103) (blowdown)

Re2 (103) (displacement)

(a)

1 1.5 2 2.5

-50

0

50

100

150

200

250

CME, 1800 rpm

Rey

nold

s nu

mbe

r R

e (1

03 )


a (-)

Re1 (103) (blowdown)

Re2 (103) (displacement)

(b)

Figure 2.12 – Reynolds number12 versus engine load pi/pa, for (a) fired engine and(b) CME flow rig


0.4 0.5 0.6 0.7 0.8 0.9 1

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Fired, 1800 rpm

Peak

Mac

h nu

mbe

r M

a (-

)


a (-)

Ma1 (-) (blowdown)

Ma2 (-) (displacement)

(a)

1 1.5 2 2.5

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

CME, 1800 rpm

Peak

Mac

h nu

mbe

r M

a (-

)Intake pressure p

i/p

a (-)

Ma1 (-) (blowdown)

Ma2 (-) (displacement)

(b)

Figure 2.13 – Mach number12 versus engine load pi/pa, for (a) fired engine and (b)CME flow rig

0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3Fired, 1800 rpm

Scav

engi

ng n

umbe

r S

(-)


a (-)

S (-)

(a)

1 1.5 2 2.50

0.5

1

1.5

2

2.5

3CME, 1800 rpm

Scav

engi

ng n

umbe

r S

(-)


a (-)

S (-)

(b)

Figure 2.14 – Scavenging number12 versus engine load pi/pa, for (a) fired engineand (b) CME flow rig


0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Fired, 1800 rpm

Res

idua

l sta

te


a (-)

pres

/pa (-)

ρres

/ρa (-)

(a)

1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5CME, 1800 rpm

Res

idua

l sta

teIntake pressure p

i/p

a (-)

pres

/pa (-)

ρres

/ρa (-)

(b)

Figure 2.15 – Residual state12 (i.e. prior to exhaust valve opening) versus engineload pi/pa, for (a) fired engine and (b) CME flow rig

0.4 0.5 0.6 0.7 0.8 0.9 10

15

30

45

60Fired, 1800 rpm

540 °ca

Blo

wdo

wn

time

scal

e (°

ca)


a (-)

θ1 - θ

EO (°ca)

(a)

1 1.5 2 2.50

15

30

45

60CME, 1800 rpm

540 °ca

Blo

wdo

wn

time

scal

e (°

ca)


a (-)

θ1 - θ

EO (°ca)

(b)

Figure 2.16 – Blowdown time scale12 versus engine load pi/pa, for (a) fired engineand (b) CME flow rig


ρ = ρi

(pi

pa

)− 1γ

(1 +

∆Tc

Ti

(V0

Vi

)γ−1)− 1

γ

(2.6)

The Reynolds number differs significantly between fired and CME condi-tions, more so than the Mach number. The definition of Re and Ma is givenby Eq. (2.4). The main temperature dependence is in the density (ρ ∼ 1/T )and the dynamic viscosity (µ ∼ T , in first approximation). The ratio of specificheats γ is a much weaker function of T . As such, the following approximateexpressions hold for Re and Ma:

Re ∼ Urdr

T 2(2.7)

Ma ∼ Ur

T 0.5(2.8)

Since the absolute temperature varies roughly by a factor 2 between the CMEflow rig (' 20 C) and fired engine conditions (' 800 C), Re is expected todiffer by a factor 4 and Ma by a factor 1.4 between CME and fired conditions.

However, the velocity Ur should be considered also: the ratio of blowdownto displacement flow rate is greater in a fired engine compared to the CMEflow rig. Figure 2.12 indicates that ReCME/Refired ' 2.5 during blowdownand ReCME/Refired ' 10 during the displacement phase. Figure 2.13 showsthat the Mach number is comparable in CME and fired conditions. Thesefindings agree with the above considerations for the temperature dependence.

Figure 2.16 shows the time scale θ1 − θEO, corresponding to the crankangle difference between exhaust valve opening (EO) and the occurrence ofthe maximum mass flow rate during the blowdown phase. With reference toApp. B, θ1 − θEO equals (360/2π )ωt1, where N is the engine speed, and ωt1is defined according to Eqs. (B.13) and (B.17).

2.3.3 ConclusionFigures 2.11, 2.12, 2.13 and 2.14 summarize the analytical exhaust stroke flowsimilarity. As appears from the figures, the flow conditions in the CME flowrig are not identical to those in a fired engine. For instance, the maximumattainable ratio of peak mass flow rates during blowdown and displacementm1/m2 is only 2.5 for the CME flow rig, compared to 6 for fired conditions. Thepractical limitations are discussed in Sect. 2.3.1. The quantitative assessmentof the similarity level for an isochoric flow rig is valuable in itself, since otherresearchers [7, 70] use motored engine flow rigs as well, albeit without chargingof the intake system.

It is a priori evident that a fully similar flow situation can never be ac-complished, since a 1 : 1 scale set up is used with similar fluid (air, instead ofexhaust gas), yet at a much lower temperature (between 0 and 40 C, insteadof roughly 800 C). To guarantee flow similarity, at least the relevant dimen-sionless numbers Ma and Re should be similar in the experiment and reality.


Considering the above approximations for Re and Ma in Eq. (2.7), keepingMa constant requires reducing the characteristic velocity Ur in the experimentto roughly Ur/1.4 . Taking into account that the geometry is not scaled (i.e. dr

is constant), this causes an increase in Re by a factor 2.8 in the experiment.Therefore, Ma and Re cannot both be kept constant in this type of set up.In fact, due to the inevitable difference between blowdown and displacementphase, neither can be kept constant.

Nevertheless, with regard to the flow dynamics in the manifold and espe-cially for studying the resonance phenomenon, it is important that the fre-quency spectrum of the ‘excitation’ generated by the flow rig on the gas inthe manifold is similar to fired engine conditions. Since the CME features atwo-stage exhaust stroke, this similarity condition is fulfilled.

The strong mean velocity fluctuations and the occurrence of local flow re-versal in the catalyst has been observed in a number of other experimentaland numerical studies, on motored or fired engines. The resonance fluctuationsare observed in runner and catalyst velocity [4, 70, 81]. Different geometriesare investigated in these papers, yet the frequency range seems to correspondto the assumption of a Helmholtz resonance, as suggested in this thesis (seeSect. 5.3).

Flow reversal in runners and catalyst is measured using LDA or predictedusing transient CFD simulations by other authors [4, 70, 81, 59], both in mo-tored and fired engine conditions. This shows that the exhaust stroke flowsimilarity between CME and fired conditions is good enough, although notidentical.

2.4 Flow rate measurementThis section discusses three flow rate measurement techniques used in this the-sis. The flow rate serves as a reference to the measured velocity distributions.The measured mean velocity (i.e. the area integral of the velocity distribution)should correspond to within the error margin of the flow rate measurement(typically between 5 and 10%). Some particular issues are addressed concern-ing flow rate measurement in pulsating flow conditions.

Section 2.4.1 describes the orifice measurement used for the isothermal flowrig. For reasons described below, two alternative methods are used for theisochoric flow rig. Section 2.4.2 describes a laminar flow meter and Sect. 2.4.3describes a cylinder pressure-based method.

2.4.1 ISO orificeOn the isothermal flow rig (see Sect. 2.2.1), the flow rate is measured usingan orifice, according to ISO Standard 5167-1991(E) [54]. The orifice diameteris Do = 60.445 mm, and the inner pipe diameter is D = 103.285 mm (4 inchnominal pipe size). At a pressure of 101325 Pa and a temperature of 293.15 K,the flow rate measurement range is between 0.0206 kg/s (= 57.4 Nm3/h) and0.421 kg/s (= 1173 Nm3/h).

2.4 Flow rate measurement 55

Based on the diameter ratio β = Do/D = 0.585, the lengths of the straightpipe sections upstream and downstream of the orifice are 21D and 10D, re-spectively. These lengths comply for an installation where the upstream pipesection is connected to a single bend only. According to the standard, the mea-surement uncertainty in case of an ideal installation varies between 4.2 % and0.1%. An additional uncertainty of 0.5% is added to these values due to thelimited length of the straight pipe sections.

The standard restricts the use of the orifice to steady or slowly varyingflows. ISO Technical Report 3313-1998(E) [55] describes the error introducedby flow pulsations on the orifice flow rate reading. The dimensionless Hodgsonnumber Ho defines a threshold criterion for the relative flow rate fluctuationsat the measurement device with respect to those generated by the pulsator.Ho [-] is defined as:

Ho =Vsurge f ∆pm

Qm p(2.9)

where Vsurge is the surge vessel volume [m3], f is the pulsation frequency [Hz],∆pm is the time-averaged pressure difference across the orifice [Pa], Qm is thetime-averaged volumetric flow rate [m3/s], p is the surge vessel pressure [Pa].

For sinusoidal flow rate fluctuations, the flow rate at the pulsator can bewritten as Q = Qm(1 + Q sinωt). In that case, the following expression relatesthe Hodgson number to φ, the maximum expected additional uncertainty [-]on the mean flow rate measurement:

Ho

γ>

0.04 Q√φ

(2.10)

where γ is the ratio of specific heats [-] and Q is the relative flow rate fluc-tuation [-] at the pulsator. For sinusoidal pulsating flow, Eq. (2.10) gives theminimum value for Ho, that relates to the minimum volume of the surge vessel.If Eq. (2.10) is fulfilled, the relative error on the mean flow measurement is lessthan 100φ%.

Figure 2.17 represents the worst case encountered in the isothermal flowrig experiments. The circular (

) and triangular (

) markers represent the

dimensionless flow rate at the pulsator and orifice respectively. The relativefluctuating flow rate at the pulsator Q = 0.368. The volume of the surge vesselVsurge = 450 dm3. The Hodgson number Ho = 0.399. Based on Eq. (2.10),the maximum uncertainty introduced by the pulsations φ equals 0.1 %.

Therefore, the surge vessel provides adequate damping of the pulsationscaused by the pulsating flow generator. The additional uncertainty is below0.2% for all measurement conditions. Nevertheless, the orifice reading is onlyused during steady operation to check the flow rate calculated from the velocitydistribution.

The combined uncertainty on the orifice flow rate measurement is approxi-mately 5 %. This includes (i) the uncertainty prescribed by the standard for anideal installation and steady flow (' 4.2 %), and (ii) the additional uncertaintyfor non-ideal installation (' 0.5 %) and (iii) pulsating flow (' 0.2 %).


0 180 360 540 7200

0.5

1

1.5

Crankshaft position ω t (ο)

Flow

rat

e Q

/Qm

(-)

ISO/TR 3313 (E)

PulsatorOrifice

Figure 2.17 – Orifice flow rate measurement in pulsating flow

2.4.2 Laminar flow element (LFE)

Several practical problems inhibit the use of an orifice for measuring the intakesystem flow rate on the CME flow rig (see Sect. 2.2.2). Mainly, the CME flowrig features much stronger flow pulsations in the intake system when comparedto the isothermal flow rig. The pulsations are aggravated by retarding theintake camshaft. Furthermore, the available space around the set up is limited,which makes the installation of long straight pipes upstream and downstreamof the orifice as prescribed by ISO Standard 5167-1991(E) [54] difficult.

Based on ISO Technical Report 3313-1998(E) [55], a surge vessel would berequired to damp the pulsations at the location of the orifice. The requiredsurge vessel volume would be larger than the 450 dm3 for the isothermal flowrig, and it should withstand a pressure of least 3 bar. Considering these diffi-culties, a custom built laminar flow element (LFE) meter (Fig. 2.18) is used tomeasure the flow rate in the intake system of the CME flow rig.

The principle of measurement of the LFE is based on pressure drop dueto laminar flow through small parallel channels. For fully developed laminarflow, the pressure drop is proportional to the volumetric flow rate. The mainadvantage is the response time: if the flow inside the channels is incompressible(Ma < 0.3), the pressure drop responds quasi instantaneously to flow ratevariations. As such, the overall measurement system response time is solelydetermined by the pressure transducer response time. This set up features aresponse time of ' 1 ms.

The pressure drop due to friction is irreversibly lost. Therefore, the cross-section of the element is usually greater than the pipe cross-section, therebyreducing the velocity and pressure drop through the LFE.

This particular LFE consists of an unwashcoated ceramic catalyst mono-lith ( 100 mm, 100 mm long, 900 cpsi, 2.5 mil) that is contained within thecylindrical part 3 in Fig. 2.18. The monolith is kept in position by the shoul-


1 2a 3 2b 4

Figure 2.18 – Laminar flow element (LFE) meter

Figure 2.19 – Laminar flow element (LFE) meter, photograph of version with fourmonoliths in series

ders of parts 2a and 2b. Parts 2a and 2b contain static pressure taps and athermocouple. The flow enters through a shallow-angle diffuser (part 1) andexits through a sharp-angle contraction (part 4). The contraction cone angle issharper when compared to the diffuser to reduce the overall length of the LFE.Figure 2.18 shows the diffuser and contraction that connect to 2 inch nominalpipe diameter. An additional similar diffuser and contraction are available toconnect the LFE to 1 inch nominal pipe diameter, which is used on the CMEflow rig intake system.

On the CME flow rig, the LFE ( 3© in Fig. 2.9) is located downstream of thepressure regulator ( 2© in Fig. 2.9). As such, the magnitude of the unrecoverablepressure drop is of no real importance, since the pressure regulator guaranteesa constant pressure in the intake manifold (downstream of the LFE). A piezo-resistive pressure transducer13 is mounted in the intake manifold, downstreamof the LFE. It measures the static pressure in the intake manifold pi.

13Kristal 4295A, input range 0 to 3 bar, output range 0 to 10 V, combined non-linearity,hysteresis and repeatability 6 0.35 % of the full scale reading, response time 0.2 ms.


The LFE operates at an elevated line pressure, equal to the intake manifoldpressure pi, which varies between 1.0 atm and 2.5 atm during the experimentson the CME flow rig. For the system using a single catalyst element, a pressuredrop of 400 Pa corresponds to a flow rate of 120 m3/h.

The measurement of the differential pressure between the static pressuretaps in parts 2a and 2b (see Fig. 2.9) forms the basis of the LFE flow rate mea-surement. This differential pressure measurement has proven very troublesome.Based on experience during the CME experiments, obtaining an accurate mea-surement of the differential pressure in the order of 1 kPa at an elevated linepressure up to 2.5 atm is not straightforward. As many as three differentialpressure transducers were used. Each had a different working principle, yeteach exhibits a certain degree of drift due to line pressure variations or ambi-ent temperature. This problem proved very hard to overcome even with theassistance of the sensor manufacturer.

The following differential pressure sensors were used during the measure-ments on the CME flow rig:

• HBM DP114 — Inductive displacement sensor connected externally towheatstone bridge measurement amplifier HBM KWS 506. Very highacceleration sensitivity, very high sensitivity to line pressure and ambienttemperature.

• Druck LPM 838115 — Eddy current low displacement diaphragm. Sig-nificant sensitivity to line pressure.

• Druck PMP 417016 — Micro-machined single crystal silicon sensor.

Only the Druck PMP 4170 sensor features an acceptably low line pressuresensitivity. The pressure sensor has been selected based on the relative insensi-tivity to line pressure of its solid state silicon sensor. This sensor was howeveronly available during the final part of the measurement campaign.

Its input pressure range (-7 to 7 kPa) is higher compared to the othersensors, since for a given line pressure sensitivity, the flow rate measurementaccuracy can be improved by increasing the LFE pressure drop. As such, threemore catalyst elements have been added in series with the first element. Forthe meter using four elements, the pressure drop is approximately four timeshigher compared to the single element meter. Figure 2.19 shows a photographof the version with four catalyst elements.

14HBM (Hottinger Baldwin Messtechnik) DP1, input range −1 to 1 kPa, output range 0to 10 V, maximum line pressure 100 bar, combined non-linearity, hysteresis and repeatabilitynot specified, response time ' 1 ms.

15Druck LPM 8381, input range −1 to 1 kPa, output range 0 to 5 V, maximum linepressure 100 bar, combined non-linearity, hysteresis and repeatability 6 0.25 % of the fullscale reading (= 2.5 Pa), response time ' 1 ms.

16Druck PMP 4170, input range -7 to 7 kPa, output range 0 to 2 V, maximum line pressure70 bar, combined non-linearity, hysteresis and repeatability 6 0.08 % of the full scale reading(= 5.6 Pa), response time ' 1 ms.


0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Reference flow rate (m3/h)

LFE

dif

fere

ntia

l pre

ssur

e (k

Pa)

LFE calibration chart

FitMeasurements

Figure 2.20 – Laminar flow element calibration chart

The LFE has been calibrated at atmospheric pressure using the ISO stan-dardized orifice, described in Sect. 2.4.1. Figure 2.20 presents the LFE calibra-tion chart. The circular markers (

) represent the calibration points, and the

solid line ( ) is the fitted calibration curve, based on the predicted relation-

ship between volumetric flow rate and pressure drop in laminar flow channelsdiscussed in App. A.2. This relationship takes into account the contribution tothe total pressure drop from (i) the fully developed laminar flow region, (ii) themomentum lost in the entrance length due to the development of the laminarboundary layer, and (iii) the entrance (i.e. contraction) and exit (i.e. expansionlosses.

The predicted relationship between differential pressure and flow rate isleast square-fitted to the reference flow rate using a single fit parameter, thehydraulic diameter of the catalyst channels. The fitted value of dfit = 0.796 mmcompares well to the geometrical value d = 0.783 mm, obtained from thesubstrate density (i.e. 900 cpsi) and wall thickness (i.e. 2.5 mil).

The estimated uncertainty on the LFE flow rate reading is between 5 and10%.

2.4.3 Cylinder pressure

The CME flow rig features a second flow rate measurement that serves tovalidate the LFE measurement described in Sect. 2.4.2. This second flow ratemeasurement is based on the cylinder pressure rise during the compressionstroke. The second measurement proved necessary after the initial differentialpressure sensor used on the LFE exhibited severe drift as a function of theintake system pressure pi and the ambient temperature.

The motion of the piston is determined by a crank-slider mechanism. Thecombustion chamber volume V is given by the following expression:


V (ωt) =πb2

4

[s

%− 1+s

2(1− cosωt) +

cr

(1−

√1−

( s

2 crsinωt

)2)]

(2.11)

where b, s and cr are the cylinder bore [m], stroke length [m] and connectingrod length [m] respectively, and % is the volumetric compression ratio [-]. %is given by % = Vmax/Vmin , where Vmin is denoted the dead volume [m3] andVmax − Vmin (= πb2s/4 ) is the swept or displaced volume per cylinder [m3].The crankshaft position ωt [ca] is determined by an angular encoder.

Based on the reading of a pressure sensor mounted in the combustion cham-ber, the mass charge m [kg] per cylinder can be determined from the measuredpressure rise during the compression stroke. This calculation is fairly straight-forward, yet assumes adiabatic compression (i.e. no heat transfer to the walls)and the absence of blow-by leakage.

During the compression stroke, these conditions are roughly valid. Themajor contribution to both blow-by leakage and heat loss is (at least in a firedengine) expected during the expansion stroke, when cylinder gas pressure andtemperature are maximal.

Blow-by leakage inevitably occurs due to non-ideal sealing of the combustionpressure by the piston rings. As such, a certain amount of gas escapes from thehigh pressure combustion chamber to the low pressure crankcase (or oil sump).The pressure in the crankcase corresponds to atmospheric or intake pressure,depending on the particular installation of the crankcase ventilation.

The ideal gas law states:

p V = mr T (2.12)

where p and T are cylinder gas pressure [Pa] and temperature [K], m is themass of the inducted gas [kg] and r is the specific gas constant [J/(kgK)], givenby r = R/M , where R is the universal gas constant (= 8.314 J/molK) and Mis the molecular mass of the gas [mol/kg] (e.g. for air, M = 0.02896 mol/kg,therefore r = 287 J/(kg K)).

During the compression, the expression below gives the relationship for anadiabatic change of states:

p (ωt)pi

=(V (ωt)Vi

)γ

(2.13)

where indices i denote the initial state, which corresponds to the end of theintake stroke, and γ is the ratio of specific heats (= cp/cv ). pi and Ti areassumed equal to the time-averaged intake system pressure and temperature.Thus, the induction ram-effect and heat transfer during the intake stroke areignored.

In Eq. (2.13), p (ωt) is measured and V (ωt) is determined from the crank-shaft position and Eq. (2.11), which means that Eq. (2.13) is overdetermined.

2.5 Data reduction 61

As such, the adiabatic assumption is relaxed to a polytropic relationship, andthe exponent γ is replaced by a polytropic coefficient n:

p (ωt)pi

=(V (ωt)Vi

)n

(2.14)

where the value of n is determined during the compression stroke, by averagingthe values of n obtained from the measured p (ωt) and calculated V (ωt):

n = −log(p (ωt)pi

)/log(V (ωt)Vi

)(2.15)

Typically, the polytropic exponent n varies between 1.20 and 1.35, and isonly slightly smaller than the ratio of specific heats κ at the mean tempera-ture during the compression stroke. Using the obtained averaged value of thepolytropic exponent n, the cylinder gas temperature T (ωt) is determined bycombining Eqs. (2.12) and (2.14):

T (ωt)Ti

=(p (ωt)pi

)n−1n

(2.16)

Based on the measured pressure p (ωt), the volume V (ωt) known fromEq. (2.11), and the temperature T (ωt) estimated from Eq. (2.16), the masscylinder charge m is determined using Eq. (2.12) as follows:

m =p (ωt) V (ωt)r T (ωt)

(2.17)

During each compression stroke, the average value of m is retained and usedto determine the mass flow rate m [kg/s] as:

m = ncm

120/N(2.18)

where nc is the number of cylinders.Based on the standard deviation of the cylinder pressure-based flow rate

measurement in consecutive engine cycles, the estimated uncertainty on theaveraged value of the mass flow rate m is below 0.5 %, for a confidence level of95%.

Of course, this uncertainty estimate neglects the introduction of system-atic errors e.g. by neglecting the heat transfer and blow-by leakage during thecompression stroke. Taking these approximation into account, the overall un-certainty is of the same order of magnitude as the LFE flow rate measurement,i.e. 10%.

2.5 Data reductionIdentifying periodic flow patterns requires phase-locked (or conditional) sam-pling. Two data records are phase-locked when their time bases are referenced


to a common starting point, usually defined by a once-per-period trigger signal.Real-life periodic flows consist of a cycle-resolved and an unresolved componentresulting from (quasi) random phenomena such as turbulence, measurementsystem noise, vortex shedding or unsteady flow separation. A data recordspanning a single period is also called an ensemble. Several consecutive datarecords are ensemble-averaged to reduce the contribution of the unresolvedcomponent, thus revealing the cycle-resolved flow.

Phase-locked sampling is widely used in all sorts of periodic flow studies,typically e.g. in turbo machinery and reciprocating machines. Most of thepapers cited in the literature survey in Sect. 1.4 use phase-locked LDA orHWA measurements.

A reference work on HWA measurement techniques by Bruun [25] containsan extensive literature survey on conditional sampling and phase-locked aver-aging applied to HWA and LDA. The survey is subdivided into rotating wakephenomena (e.g. turbo machinery internal flow) and internal combustion en-gine flow, both in-cylinder and intake system flow. However, engine exhaustflow is not included, since only recent evolutions in the exhaust hot end havelead to an interest in velocity field measurements in the exhaust system.

2.5.1 Ensemble averagingThroughout this thesis, mostly two-dimensional velocity distributions are dis-cussed in periodic flow, downstream of a close-coupled catalyst. As such, ve-locity usually refers to the axial (i.e. along the catalyst axis) component U ofthe velocity vector

−→U .

In the following, an abbreviated subscript notation Ui,j,e = U (xi, yi, ωtj , e)is used, where i is the measurement point index, j is the crankshaft positionindex (i.e. time or sample index) and e is the ensemble or engine cycle index.

Ensemble-averaged quantities

The instantaneous local velocity Ui,j,e consists of an ensemble-averaged com-ponent 〈Ui,j〉 = 〈U (xi, yi, ωtj)〉 that represents the main periodic flow anda fluctuating component uF

i,j,e = uF (xi, yi, ωtj , e) caused by unresolved ran-dom phenomena, including turbulence and any other unresolved effects such ascycle-by-cycle variations:

Ui,j,e = 〈Ui,j〉+ uFi,j,e (2.19)

where the angle brackets 〈···〉 denote ensemble-averaging, defined as:

〈Ui,j〉 =1E

E∑e=1

Ui,j,e (2.20)

where E is the number of ensembles.The ensemble-averaged fluctuation intensity uF

i,j′ is a measure of the mag-

nitude of the fluctuating component uFi,j,e, and is defined as:


uFi,j

′=

√√√√ 1E

E∑e=1

(uF

i,j,e

)2=

√√√√ 1E

E∑e=1

(Ui,j,e − 〈Ui,j〉)2 (2.21)

In an ensemble-averaged analysis, this uFi,j′ is taken as a measure of the

turbulence intensity. However, in the presence of cycle-by-cycle variation, thismeasure overestimates actual turbulence, and a better approach is using acycle-resolved analysis, as described below in Sect. 2.5.2.

The time-averaged velocity Ui = U (xi, yi) is defined as:

Ui,j =1J

J∑j=1

〈Ui,j〉 =14π

∫ 4π

θ=0

Ui (θ) dθ (2.22)

where θ = ωt, J is the number of crankshaft positions per engine cycle (i.e.two crankshaft revolutions = 720 ca = 4π rad). For a time-continuous mea-surement technique such as HWA, J is determined by the sampling frequencyand the engine speed. For instance, a temporal resolution of 2 ca (J = 360)at an engine speed of 2000 rpm requires a sampling frequency of J ·N/120 =6000 Hz.

Throughout the thesis, the overbar (···) denoting time-averaging and anglebrackets 〈···〉 denoting ensemble-averaging are often omitted for the sake ofclarity, when the nature of the quantity can be derived from the context.

The mean (or spatial averaged) velocity Um,j = Um (ωtj) is defined as:

Um,j =1A

I∑i=1

Ui,j (xi, yi, ωtj)Ai (xi, yi)

=1A

∫A

U (ωtj) dA (2.23)

where I is the number of grid points, Ai is the cross-sectional area of mea-surement grid cell i [m2] and A is the total cross-sectional area [m2], given byA =

∑Ii=1Ai.

The time-averaged mean velocity Um is defined as:

Um =1J

J∑j=1

Um,j =Q

A(2.24)

where Q is the volumetric flow rate through the catalyst [m3/s]. In all velocitydistributions figures, the non-dimensional velocity U [-] is plotted, defined asU = U/Um . The tilde (˜) is usually omitted from the figures.


Uncertainty analysis

This section briefly discusses the statistical inference for ensemble-averagedquantities.

The absolute uncertainty on Ui,j = U (xi, yi, ωtj) can be obtained from:

∆Ui,j = δUi,j · Ui,j =stde∈[1,E](Ui,j,e)√

E(2.25)

where ∆ denotes the absolute error and δ denotes the relative error on a vari-able. The operator ‘std’ denotes the unbiased estimator for the standard devi-ation, defined as:

stde∈[1,E](Ui,j,e) =

√√√√ 1E − 1

E∑e=1

(Ui,j,e − Ui,j)2 (2.26)

The factor√E in the denominator of Eq. (2.25) originates from the

ensemble-averaging process. As explained in Bendat and Piersol [12], the stan-dard deviation on the average of independent samples (here: Ui,j) equals thestandard deviation on the samples (here: stde=1...E(Ui,j,e)), divided by thesquare root of the number of samples

√E.

It is generally assumed (see Bendat and Piersol [12]) that for ensemble-averaging, samples from consecutive ensembles may be considered indepen-dent. This is not the case for stationary time phenomena, where the temporalautocorrelation should be examined to verify the independence of the samples.

2.5.2 Cycle-resolved analysis

A cycle-resolved analysis (CRA) attempts to split up the velocity fluctuationuF

i,j,e in a cyclic or cycle-by-cycle variation UCi,j,e and the turbulent variation

uTi,j,e:

Ui,j,e = 〈Ui,j〉+ UCi,j,e + uT

i,j,e (2.27)

The measure of the turbulence intensity is now based on uTi,j,e. This measure

is called the ensemble-averaged turbulence intensity, which is defined as:

uTi,j

′=

√√√√ 1E

E∑e=1

(uT

i,j,e

)2=

√√√√ 1E

E∑e=1

(Ui,j,e − 〈Ui,j〉 − UC

i,j,e

)2 (2.28)

The key step in CRA is to determine UCi,j,e. In other words, a criterion

should be found to separate the cyclic fluctuations from the ‘turbulence’. Cyclic


variations are likely low frequency in nature, whereas high-frequency fluctua-tions are presumed to constitute turbulence.

Cycle-resolved analysis is particularly applied to the in-cylinder flow of areciprocating machine. The main source of cyclic variation in a reciprocatingmachine stems from minor variations in the flow pattern during the intakestroke. The in-cylinder flow pattern is slightly different in subsequent cycles,which is denoted cyclic variation. In fired conditions, combustion variables suchas turbulent flame speed are very sensitive to the turbulence intensity. Thepresence of combustion tends to increase the level of cyclic variation. Cyclicvariation refers not only to local variables such as velocity, temperature andgas composition but also to integral quantities such as cylinder pressure, andthe amount of charge.

Cyclic variations increase the rms of the measured quantity. Turbulencequantities that are determined using ensemble-averaging (i.e. without CRA)such as e.g. Eq. (2.21) overestimate the actual value.

Heywood [46] and Catania and Mittica [26] provide valuable reviews ofseveral CRA techniques, for measuring turbulence quantities in the combustionchamber of internal combustion engines.

Many authors have suggested different methods of performing the sep-aration between cyclic variation and turbulence. Lancaster [62] uses non-stationary time averaging (NTA). Rask [89] uses cubic spline fitting (CSF).Liou and Santavicca [68] use an inverse fast Fourier transform technique (IFT).Tiederman et al. [98] use a low-pass filter technique, where the cut-off filter fre-quency is determined similar to the technique by Liou and Santavicca [68].Many more techniques exist, however each technique basically performs a lowpass filtering on the velocity to determine the cyclic variation contribution. Thecut-off filter frequency may be defined explicitly (e.g. in IFT [68]) or implicitly(e.g. in NTA [62] and CSF [89]).

This thesis uses IFT [68], because of the appeal of its physical interpreta-tion. The instantaneous velocity signal Ui,j,e is transformed into the frequencydomain using a fast Fourier transform (Ft). The high frequency content isremoved above a certain cut-off filter frequency f0. The inverse fast Fouriertransform (F−1

f ) results in the cycle-resolved mean velocity:

UCi,j,e = F−1

f (G (f0) · Ft (Ui,j,e − 〈Ui,j〉))

uTi,j,e = Ui,j,e − 〈Ui,j〉 − UC

i,j,e (2.29)

where the filter function G (f0) = 1 − H (f0). H (f0) is the Heaviside stepfunction, so that the filter function G = 1 for f < f0 and G = 0 for f > f0.

The current research follows Liou and Santavicca [68] in selecting the cut-offfrequency f0 based upon the maximum frequency contained in the spectrum ofthe ensemble-averaged mean velocity, or symbolically:

f0 = f

∣∣∣∣∣ maxf∈[0,∞)

Ft (〈Um (ωt)〉) (2.30)


0 180 360 540 7200

0.05

0.1

0.15

0.2

Time-resolved mean turbulence intensity


TI m

, FI m

(-)

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

TIm

(θ), CRAFI

m(θ), PLA

(a)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

-60 -30 0 30 60

-60

-30

0

30

60

Time-averaged turbulence intensity TI (-)

x (mm)

y (m

m)

0.015

0.01

5

0.02

0.02

0.02

0.02

0.02

5

0.02

50.

025

0.025

0.025

0.025

0.025

0.03

0.03

0.03

0.03

0.03

0.03 0

.03

0.03

5

0.035

0.04

0.04

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

= 1.563 m/s, ηm

= 0.594, ηw

= 0.944

(b)

Figure 2.21 – Time-resolved mean turbulence intensity TIm (ωt) [-] (a) and time-averaged turbulence intensity distribution TI [-], using cycle-resolved analysis accord-ing to Liou and Santavicca [68]

In a practical application (see following section), the maximum function inEq. (2.30) is weakened by incorporating a small tolerance factor φ. The valueof f0 corresponds to the maximum frequency where the FFT magnitude isgreater than φ times the maximum magnitude. Figure 2.22 illustrates thevalue of f0 for the example experiment discussed in the following section.

Application

This section presents an example of the time-resolved fluctuation intensity andthe turbulence intensity, determined using cycle-resolved analysis.

Figure 2.21 shows (a) the time-resolved mean turbulence intensityTIm (ωt) [-] and (b) the time-averaged turbulence intensity distribution TI [-].These are obtained on the CME flow rig, using a stationary hot-wire probe.

Figure 2.21a shows the time-resolved mean turbulence intensity TIm ( )

and the fluctuation intensity FIm ( ). Figure 2.21b shows the time-averaged

distribution of turbulence intensity TI. TI and FI are the non-dimensionalequivalents of the dimensional quantities uT

i,j′ and uF

i,j′, defined by Eqs. (2.28)

and (2.21) in Sect. 2.5. TI equals uTi,j′/Ui,j and FI equals uF

i,j′/Ui,j . The

mean quantity TIm is determined as TIm =∑I

i=1 uTi,j′Ai/(UmA) .

The turbulence intensity TI is obtained using cycle-resolved analysis, ac-cording to the inverse fast Fourier transform technique by Liou and San-tavicca [68]. The other approaches discussed in the previous section yieldsimilar results. The separation of cyclic variations and turbulent variationsis essentially based on a low-pass filtering. The cyclic variation spectrum isassumed to consist of mainly ‘low’ frequencies, whereas the turbulent spectrumconsists of ‘high’ frequencies. The approach by Liou and Santavicca [68] to


0 200 400 600 8000

0.05

0.1

0.15

0.2

0.25

0.3

Mean velocity FFT

Frequency f (Hz)

FFT

of

U(ω

t) (

-)

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Tp -1 f

0

Figure 2.22 – FFT of the ensemble-averaged mean velocity Um (ωt) [-] for the caseof Fig. 2.21

discern cyclic and turbulent variations is chosen because of its physical inter-pretation in terms of the frequency spectrum of the ensemble-averaged meanvelocity. The cut-off frequency varies between 200 and 500 Hz from one exper-iment to the other.

For this particular experiment, the cut-off frequency f0 (Eq. (2.30)) is440 Hz. Figure 2.22 presents the FFT spectrum of the ensemble-averagedmean velocity. Since the engine speed is 1200 rpm and the number of runnersnr = 4, the apparent pulsation frequency T−1

p = 40 Hz.The velocity measurement position is 25 mm downstream of the catalyst.

The flow inside the catalyst channels is laminar, since Re Recrit ' 2300. Assuch, any turbulence at the measurement location is the result of the mixing ofthe laminar jets issuing from the catalyst channels. Each jet expands accordingto the monolith porosity ε ' 0.85. Due to the transverse velocity gradients,a complex mixing region exists immediately downstream of the catalyst. It isfound experimentally that after 20 to 25 mm, the jets are sufficiently mixed sothat only the large-scale gradients remain.

In light of the local flow conditions, the turbulence intensity TIm evolutioncorresponding to the solid line (

) in Fig. 2.21a seems a better representa-

tion of the real turbulence intensity, compared to the dashed line ( ) (FIm).

The mean turbulence intensity is around 2.5%, whereas the mean fluctuationintensity is greater than 10 %.

The difference between the dashed ( ) and solid line (

) is a measure

for the magnitude of the cyclic variations. As shown in Fig. 2.21a, the non-dimensional magnitude of the cyclic fluctuations are approximately 7.5 %, rel-ative to the time-averaged mean velocity Um. Such high values are not uncom-mon for reciprocating engines, although somewhat unexpected since the CMEflow rig operates without combustion. In a fired engine, non-linear phenomenaduring the combustion phase increase the cyclic variability (see Heywood [46],


Sect. 9.4).There is no reference turbulence measurement to verify the values obtained

from the cycle resolved analysis. By ‘tweaking’ the cut-off frequency detectionalgorithm, e.g. by changing the tolerance in Eq. (2.30), the difference betweencyclic and turbulent fluctuations may be changed slightly. However, the resultsare found to be quite insensitive to small parameter changes.

The flow conditions in Fig. 2.21 correspond to those in Fig. 5.15b. The peakturbulence intensity occurs following each blowdown phase. Due to the highvelocity and pressure transients following the blowdown, it is not surprisingto find that the turbulence intensity is maximal following these events. Thepost-blowdown transients also induce large-scale flow reversal, as discussed inSect. 5.2.

As this example demonstrates, cycle-resolved analysis (CRA) is essential forextracting second order velocity moments or turbulence quantities in periodicflows with considerable cyclic variation.

Cyclic variation does not directly affect the ensemble-averaged velocity (i.e.first-order velocity moments). As such, it is of no significant importance to thevalidation of the addition principle in Chap. 4, or even to the time-resolvedvelocity distributions and the occurrence of flow reversal discussed in Chap. 5.

2.6 Conclusion

Section 2.2 describes two experimental flow rigs. Both rigs generate pulsatingflow in the exhaust system at ambient temperature, thus enabling the use ofany velocity measurement technique.

The isothermal flow rig (Sect. 2.2.1) is commonly used by a number ofauthors [88, 58, 18, 69, 17, 16, 15, 43, 22], because of its simplicity to use.However, the exhaust stroke flow similarity between the isothermal flow rigand a fired engine is quite poor. The isochoric or charged motored engine(CME) flow rig (Sect. 2.2.2) is developed to mimic the exhaust system flowin fired engine conditions as best as possible, while still operating at ambienttemperature. The CME flow rig features blowdown and displacement phase,typical of the exhaust stroke in a fired engine.

Section 2.3 discusses the exhaust stroke flow similarity between CME andfired engine conditions, based on the thermodynamic analysis described in de-tail in App. B. The CME approach and the thermodynamic derivation of thesimilarity analysis constitute original contributions of this work. Parts of Sec-tion 2.3 have been published in an international journal with review:

[84] T. Persoons, A. Hoefnagels, and E. Van den Bulck. Experi-mental study of flow dynamics in close-coupled catalyst manifolds.Int. J. Engine Res. (in press).

Section 2.4 describes several reference flow rate measurements, which areused to continuously verify the measured velocity distributions in the exhaust

2.6 Conclusion 69

system. Problems involving the accurate measurement of strong pulsating flowrates are adequately addressed.

Section 2.5 describes the data reduction techniques typical for phase-lockedmeasurements of periodic phenomena. Considering the cyclic variability en-countered in reciprocating machinery, several techniques for cycle-resolved anal-ysis (CRA) are discussed. The CRA approach is required for obtaining unbiasedmeasurements of turbulence quantities.

Chapter 3

Oscillating hot-wireanemometer (OHW)

“Measure what is measurable, and make measurable what is not so.”

Galileo Galilei (Italian physicist, 1564, †1642)

This chapter describes the construction, calibration and operation of an oscil-lating hot-wire anemometer (OHW)17 for the measurement of one-dimensionalbidirectional velocity.

Section 3.1 reviews the literature of other available techniques for measuringbidirectional velocity. Appendix C clarifies the selection of hot-wire anemome-try as the most suitable measurement technique, in spite of its intrinsic insen-sitivity to the velocity direction.

Sections 3.3, 3.4 and 3.5 present respectively the methodology of the ap-proach, the mechanical oscillator designed for this purpose and the hot-wireprobes used during the calibration.

Section 3.6 discusses the calibration approach, which allows to use the OHWon the pulsating flow rig to quantify the time-resolved bidirectional velocity.The OHW is calibrated in a custom-built wind tunnel (Sect. 3.6.1). LaserDoppler anemometry has been used as a reference velocity measurement, phase-locked with the oscillating probe’s motion (Sect. 3.6.2).

Section 3.7 presents and interprets the calibration results. Section 3.7.3formulates general selection and operation criteria for the OHW, based on a

17The abbreviation ‘OHW’ is used throughout this thesis to denote the measurement tech-nique (i.e. oscillating hot-wire anemometry) as well as the mechanical oscillator device de-scribed in Sect. 3.4.

71

72 Chapter 3 Oscillating hot-wire anemometer (OHW)

non-dimensional scaling analysis. Section 3.7.4 discusses the calibration resultsand suggests possible future improvements.

Section 3.8 describes the operation of the OHW system and the selectionof the oscillation frequency for measuring the bidirectional velocity on the iso-choric flow rig with running engine.

3.1 Introduction:Measuring bidirectional velocity

Obtaining high-quality experimental data that captures instantaneous flow re-versal is not straightforward. Optical measurement techniques such as laserDoppler anemometry (LDA) are able to measure bidirectional velocity. How-ever, these techniques require high quality optical access and adequate seed-ing18 in the entire measurement region. LDA-based research in CC catalystsystems is often plagued with spatial or temporal seeding concentration defi-ciency. This makes it very difficult to obtain a sufficiently high data rate formeasuring the time-resolved catalyst velocity distributions. Most studies usingLDA [59, 81, 70, 53] only measure the velocity in a single point or along a singlestraight line in the manifold.

Hot-wire anemometry (HWA) requires neither optical access nor seeding,although obviously, physical access for the hot-wire probe is required. HWAfeatures a number of advantages including high bandwidth, continuous outputsignal and good spatial resolution. The main disadvantage of HWA is its in-ability to discern flow reversal. The amount of heat convected from the wiredepends on the velocity magnitude, and not directly on its direction. Whenusing HWA in a flow featuring flow reversal, rectification or folding errors areencountered (see Fig. 3.1). As such, the measured velocity is always positiveand overestimates the true velocity, and underestimates the turbulence inten-sity. Flow reversal occurs in numerous situations, e.g. recirculating or separatedflow, highly swirling flows in combustion chambers, vortex breakdown, or pe-riodic flow reversal in intake and exhaust piping of reciprocating machinery.Chapter 8 in Bruun [25] presents an overview of techniques used with thermalanemometry to resolve the flow direction ambiguity.

Firstly, a hot-wake probe uses several wires to determine the flow direction,mostly restricted to one-dimensional or near-wall measurements. The probeconsists of a continuously heated or pulse-wise heated central wire with twotemperature sensing wires on either side, operated in constant current mode(CCA). The velocity magnitude is determined from the time-of-flight of a smallheated amount of fluid. Handford and Bradshaw [45] compiled a review onpulsed-wire anemometry (PWA), which has been extensively used for bothmain flow and near-wall measurements. The primary disadvantage of thermalwake anemometry is the limited bandwidth, at most around 100 Hz for PWA

18Appendix C.2 briefly reviews the operation principle of laser Doppler anemometry, in-cluding the seeding requirement.

3.1 Introduction: Measuring bidirectional velocity 73

Time

Vel

ocity

U /

Um

(-)

Example of velocity folding errors using HWA

True velocityHWA velocity

-2

-1

0

1

2

3

4

pdf(U)

Figure 3.1 – Example of rectification or folding errors introduced by standard HWAin reversing flow

probes.Secondly, flying hot-wire anemometry (FHA) has been in use since the

1960’s. FHA consists of a one- or two-dimensional hot-wire probe that movesalong a trajectory with a probe velocity

−→Up, so that the relative velocity seen

by the probe−−→Urel =

−→U −

−→Up remains within the valid acceptance region of the

probe. For the one-dimensional situation, the probe velocity should be negative(i.e. counter to the normal flow direction) and larger in magnitude than thereversing flow velocity. FHA systems are categorized in terms of trajectory. Animportant class uses a bean-shaped trajectory generated by a four-bar linkage(e.g. Thompson and Whitelaw [97], Bruun [25]). Linear FHA systems havealso been used by many authors. Watmuff et al. [106] studied flow separationand recirculation zones behind bluff bodies. Hussein et al. [52] used a linearFHA to minimize hot-wire rectification errors in the mixing layer of a highlyturbulent jet . In each flying hot-wire system, a dead time is incorporated toallow the flow to recover from the probe passage. These systems feature rathercomplicated mechanics and are typically restricted to large-scale surroundingssuch as wind tunnels.

Recently, high-frequency oscillating hot-wire (OHW) systems have beendescribed for use in confined spaces and near-wall measurements. Moulin et al.[78] use a one-dimensional probe mounted onto an inline piezoelectric actuator.The actuator oscillates the probe at frequencies up to 10 kHz and an amplitudeof a few micrometers, comparable to the wire diameter. The actuator is fixedto a high resonance frequency support. Li and Naguib [66] use a bendingbeam-type piezoelectric actuator with a resonance frequency of 110 Hz. Theactuator is used up to 490 Hz, therefore operating in higher order bendingmodes. Prongs are glued to the beam. They protrude through small holesin an acrylic cover, mounted flush with the wall. Li and Naguib [67] discuss


Figure 3.2 – OHW velocity error versus R∗ (Source: [66])

a further development of this OHW. The oscillation frequency is increased to3 kHz. This probe measures bidirectional wall shear stress.

A high-frequency OHW differs from a traditional FHA in that the probevelocity

−→Up cannot be measured. The velocity direction is detected based on

the phase difference between anemometer bridge output and piezo actuatorsignal. As the flow switches direction, the phase difference jumps by 180 .The velocity magnitude is found by calibrating the probe while oscillating.This approach assumes a frozen flow field during one oscillation period, i.e. theoscillation period 1/fo is smaller than the smallest time scale in the flow.

Li and Naguib [66] provide guidelines for selecting the correct oscillationparameters. Figure 3.2 shows the error of the high-frequency OHW approachin terms of R∗ = RURf =

(u′f/u

′p

)(ff/fo), where u′f is the flow r.m.s. veloc-

ity, is the r.m.s. probe velocity (∝ Up,max) and ff is the maximum frequencycontained in the flow. The high-frequency OHW measurement is valid forR∗ < 0.5. Even if the probe oscillation velocity is smaller than typical flowvelocity fluctuations, the method remains valid by sufficiently increasing theoscillation frequency fo. Unlike for FHA and the OHW used in this thesis, themeasurable negative velocity for a high-frequency OHW is not limited by themaximum probe velocity, due to the phase detection technique. However, theselection criteria proposed by Li and Naguib [66] should be kept in mind.

This thesis describes a mechanically driven low-frequency OHW for use inquasi one-dimensional reversing flow in confined geometries, such as an au-tomotive exhaust manifold with close-coupled catalyst. The presented OHWconcept combines aspects of traditional FHA and recent OHW systems. Sec-tions 3.4 and 3.5 describe the OHW and hot-wire probes used in this research.The calibration results in Sect. 3.7 indicate a maximum measurable negativevelocity of approximately −1.0 m/s.

Unlike the piezoelectric-actuated OHW systems by Moulin et al. [78] andLi and Naguib [66, 67], the probe velocity is known for the current system.Therefore, both velocity direction and magnitude can be determined at any

3.1 Introduction: Measuring bidirectional velocity 75

Table 3.1 – Specifications for typical FHA and OHW systems

Authors System Probe Parametersxo fo Up,max

mm Hz m/sThompson andWhitelaw [97]

four-barlinkage

2-D '130 16 −13.5

Watmuff et al. [106] linear sled 2-D - - −4Hussein et al. [52] linear sled 2-D - - −5Moulin et al. [78] inline piezo 1-D 0.004 6000 −0.15Li and Naguib [66] bending

piezo1-D 0.160 490 −0.5

This thesis [83] mechanicaloscillator

1-D 5.5 40 −1.0

given time, as long as the relative velocity seen by the probe is positive. Thereis no requirement that the oscillation period 1/fo be smaller than the smallesttime scale in the flow. On the other hand, oscillation frequency is limited toroughly 50 Hz due to the mechanical drive. The maximum measurable negativevelocity is determined by Up,max ∼ fo,maxxo. To achieve sufficient resolution inthe negative velocity range, the amplitude (xo = 5.5 mm) is quite large. Thisfact combined with the lack of a dead time in between measurements, meansthat the probe is measuring inside its own periodic wake. Phase-locked LDA hasbeen used during the calibration to examine the influence of this periodic wakeon the measurements. For the same reason, three one-dimensional hot-wireprobes have been tested: (i) a straight probe, (ii) a straight probe with extendedprongs and (iii) a probe with 90 angled prongs. Section 3.7.3 discusses thedifferent levels of wake contamination for each probe.

Table 3.1 gives an overview of some typical FHA and OHW systems, in-cluding the OHW system presented in this thesis.

Oscillating a hot-wire probe may cause vibrations of prongs or sensor wire.Wire deflection increases its length, thus altering the wire’s resistance. Thisstrain gauging effect occurs at high oscillation frequencies. The following ex-pression results from an analytical derivation for the first mode resonance fre-quency of a cylindrical wire, rigidly clamped onto the prongs without axialtension:

f (0)res =

12π

λ2

4

√E d2

ρ l4(3.1)

where E and ρ are the material’s Young’s modulus [Pa] and density [kg/m3],d and l are the diameter and length [m] of the wire. The non-dimensionalconstant λ takes the value 4.730 for a double-clamped beam such as the sensorwire. For a 5 mm thick, 1.25 mm long tungsten wire results f (0)

res = 13.2 kHz.A similar derivation yields λ = 1.875 for the resonance frequency of a can-


tilever beam representing a single-clamped prong, shaken perpendicular to itsaxis. The prongs of the OHW by Li and Naguib [66] are 25 mm long and0.55 mm in diameter, resulting in f

(0)res = 620 Hz, quite close to the oscillation

frequency of 490 Hz.Perry and Morrison [82] have experimentally verified the strain gauging ef-

fect by shaking a hot-wire probe in a vacuum chamber, thereby eliminating theconvective heat transfer and isolating the vibration effects in the anemometersignal. For a 4 µm thick, 1.6 mm long platinum wire, they found that straingauging occurs at oscillation frequencies above 4 kHz. Equation (3.1) predictsa resonance frequency of 3.9 kHz for such a wire.

When applying a high oscillation frequency such as proposed by Moulinet al. [78] or Li and Naguib [66], wire rigidity should be verified. Li andNaguib [66] perform a visual check using a microscope and strobe light, re-vealing no wire deflection for an oscillation frequency of 490 Hz. In this study,prong vibration is observed for one probe type in the phase-locked results (seeSect. 3.7).

3.2 Hot-wire anemometer

Hot-wire anemometry is the primary velocity measurement technique usedthroughout this thesis. Its main features and advantages are discussed inApp. C.1. The measurement principle and signal analysis are described byBruun [25].

Figure 3.3 shows a hot-wire sensor placed in a Wheatstone bridge. Besideswire sensors, other elements can be used such as film or fiber sensors. RS rep-resents the resistance of the sensor element (' 3.5 Ω for a wire probe or ' 15 Ωfor a film probe at 20 C). RL is the combined resistance of the prongs, leads,connectors and cable (' 1.5 Ω). The sensor element is heated by the currenti1, which is determined by the bridge top voltage Ebridge and the resistancesR1 + RL + RS and R2 + R3 of each branch of the Wheatstone bridge. Thesensor temperature TS is limited to approximately 300 C for a wire probe.

Neglecting heat radiation to the environment and conduction to the prongs,the conservation of energy for the sensor element is:

RS i21 =

Nu k

lAS (TS − Ta) (3.2)

where Nu is the Nusselt number [-], k is the fluid thermal conductivity[W/(m K)], l is the sensor length [m], AS is the sensor’s surface area exposedto the flow [m2], Ta is the ambient temperature [C]. The sensor resistance RS

and temperature TS are interrelated:

RS = RS,20 (1 + α20 (TS − 20)) (3.3)

where RS,20 is the sensor resistance and α20 is the sensor’s temperature co-efficient of resistance (' 0.0036 K−1 for a typical wire probe), both at the

3.2 Hot-wire anemometer 77

RS

RL

R3

R1 R2

eoff

G Ebridge

ii2i1 e2e1

Figure 3.3 – Constant temperature hot-wire anemometer bridge (CTA)

reference temperature of 20 C. The overheat ratio a [-] is defined as the re-sistance ratio between operating and ambient temperature, or a = RS/RS,20 .Typically, a = 1.8 for a wire probe.

The empirical relationship between the convective heat transfer and thefluid velocity U [m/s] is given by King’s law (Chap. 2 in Bruun [25]):

RS i21 = (TS − Ta) (A+B Un) (3.4)

where A, B and n are correlation parameters determined during a calibrationwith respect to a known velocity.

The left hand side of Eq. (3.4) indicates two possible modes of operation forthe hot-wire anemometer, depending on the bridge configuration. Either RS (∼TS) or i1 is kept constant, corresponding respectively to constant temperatureanemometry (CTA) or constant current anemometry (CCA).

The main limitation of the bandwidth of a CCA system is the wire’s ther-mal inertia ∼ ρScS l d

2, where ρS and cS are the wire’s density [kg/m3] andspecific heat capacity [J/(kg K)] and d is the wire diameter [m]. By keepingthe wire temperature constant, the thermal inertia is excluded from the systemdynamics. As such, the bandwidth of a CTA system is at least an order of mag-nitude greater compared to CCA. CCA is used for temperature measurements,whereas CTA is used for velocity measurements. During this thesis, only CTAis used.

Figure 3.3 shows a basic layout of a CTA electronic circuit. To maximizethe active current i1, the resistance of the passive branch (right hand side inFig. 3.3) is normally larger than the active branch that includes the sensor (lefthand side in Fig. 3.3). The bridge ratio is defined as R2/R1 (here: R2/R1 =20).

Initially, the resistance R3 is set to balance the bridge for a given overheatratio and bridge ratio. When the bridge is in equilibrium, the voltage difference


e1− e2 = 0. The flow conditions are determined by the variables that influencethe right hand side of Eq. (3.4), i.e. mainly the fluid velocity U and ambienttemperature Ta. As U increases, so does Nu and the amount of heat convectedfrom the wire.

An increase in the cooling effect or the convective heat flow rate from thewire is caused by increasing U or decreasing Ta. This decreases the sensor tem-perature TS and therefore its resistance RS . As a result, voltage e1 is reducedand no longer equals e2. The voltage difference e1− e2 < 0 is fed to the invert-ing bridge amplifier, characterized by a large gain G. The resulting increasedoutput voltage Ebridge is supplied to the Wheatstone bridge top junction. Thesensor current i1 increases, which increases the sensor heat dissipation, andconsequently its temperature and resistance until the bridge is again in equilib-rium. As such, the bridge voltage Ebridge is correlated to the convective heatflow rate, and therefore to the fluid velocity.

Peripheral circuitry includes signal conditioning (offset voltage eoff , gain,low-pass and high-pass filter), square wave frequency testing, a precision re-sistance measurement, and a compensation circuit for cable capacitance andinductance.

For this thesis, a Dantec19 StreamlineTM hot-wire anemometer is used with90C10 constant temperature anemometer modules. The maximum bandwidthis roughly 30 kHz for air flow at low velocity (U < 30 m/s), increasing up to200 kHz at high velocity (U > 100 m/s). The HWA is phase-locked with thehot-wire oscillator shaft encoder (see Sect. 3), with the engine crankshaft orwith the pulsator shaft.

The measurement principle is based on the detection of changes in theconvective heat transfer. HWA is therefore insensitive to the direction of theflow passing the wire, only to its magnitude. As a first approximation, theHWA output equals |U |. This phenomenon is denoted rectification or foldingin the literature.

For the same reason, HWA can only be used for flows of low to moderateturbulence. At a turbulence intensity greater than ' 0.30, instantaneous flowreversal occurs. In the presence of such strong fluctuations, the time-averagedvelocity measured by the HWA is overestimated due to folding, and the turbu-lence intensity is underestimated.

Instantaneous flow reversal is known to occur in a close-coupled catalystmanifold on a fired engine, based on the few sources available that use phase-locked laser Doppler anemometry [70, 81, 59].

Given the exhaust stroke flow similarity between the CME flow rig and afired engine, a method for resolving bidirectional one-dimensional flow was pur-sued. Oscillating hot-wire anemometry (see Sect. 3) is one such method, thatis above all compact enough for use in the confined geometry of an automotiveexhaust system.

19Dantec Dynamics A/S, Tonsbakken 16-18, DK-2740 Skovlunde, Denmark(http://www.dantecmt.com)

http://www.dantecmt.com

3.3 Methodology 79

ω t = 2πf to o

xcr

xo

U > 0U > 0U > 0

p rel

arccos α

probe

Figure 3.4 – OHW nomenclature

3.3 Methodology

This section presents the methodology of the OHW approach. A hot-wire probeis oscillated back and forth in a direction parallel to the local flow direction.The flow is assumed virtually one-dimensional (e.g. as is the case downstreama catalyst).

The hot-wire probe is mounted as with traditional hot-wire anemometry,facing the positive direction of flow. The positive direction and nomenclatureis indicated in Fig. 3.4.

The true instantaneous flow velocity is denoted U [m/s]. The OHW velocityU ′ [m/s] is defined as U ′ = Urel +Up, where Urel is the relative velocity as seenby the probe [m/s] and Up is the velocity of the moving probe [m/s]. Theprobe velocity Up is determined from the oscillator device, which is presentedin Sect. 3.4 (Eq. (3.8)). The relative velocity Urel is determined from theanemometer bridge output voltage Ebridge [V]. The relationship between therelative velocity Urel and the bridge output voltage Ebridge is determined inthe stationary calibration. The stationary calibration is performed on a fixedprobe in the positive velocity range from 0.05 m/s to 20 m/s, using a Dantec19

type 90H02 free jet automated calibration unit (see Fig. 3.8). This constitutesthe typical calibration required for traditional hot-wire anemometry.

In reverse flow when U < 0, the OHW provides a valid measurement U ′if the relative velocity Urel > 0, thus if the probe velocity magnitude |Up| issufficiently high and counter to the normal flow direction, or Up < U (< 0).As the probe oscillates, measurements are accepted only in a window aroundthe maximal negative probe velocity Up ' Up,min, or symbolically when Up 6−2πfoxoα = −ωoxoα. Approximating the probe motion as purely sinusoidal(i.e. limxcr→∞ Up = −2πfoxo cosωot), this corresponds to the OHW shaft po-sition interval − arccosα 6 ωot+ 2πn 6 arccosα, where n ∈ Z. The approach


is clarified by the graphical interpretation in Fig. 3.4.Increasing the tolerance factor α reduces the measurement interval and

increases the interval-averaged probe velocity. α is chosen arbitrarily. Duringthe calibration, α is taken α = cos (π/8) ' 0.92. During the measurements,α is taken α = cos (π/4) ' 0.71. The reason for this discrepancy is given inSect. 3.8, which describes the practical operation of the OHW on the isochoricflow rig.

The data reduction uses ensemble averaging (see Sect. 2.5), denoted withangle brackets 〈· · · 〉 in Eqs. (3.5) and (3.6):

〈U (ωot)〉 =1E

E∑e=1

U (ωot, e) (3.5)

where e and E are the index and number of ensembles. In the remainderof the thesis, the brackets denoting ensemble-averaging are mostly omitted.Except for the discussion of phase-locked results during OHW operation (seeSect. 3.7), each reference to a velocity denotes the ensemble-averaged velocity,time-averaged during the interval where Up 6 −2πfoxoα = −ωoxoα. Thevelocity U ′ measured by the OHW is defined as:

U ′ = Urel + Up

=∫

Upωoxo

6−α

〈Urel (ωot) + Up (ωot)〉dt

/∫Up

ωoxo6−α

dt (3.6)

where Up is obtained from Eq. (3.8) and Urel is obtained from the anemometerbridge voltage Ebridge, converted to velocity using the stationary calibration.

The probe oscillates in its own periodic wake, and the presence of the probedisturbs the local flow field in a way which is not a priori known. As such, acustomized calibration is required with the aid of a reference velocity measure-ment technique that allows to determine the influence of the moving probe onthe local flow field. Without such a calibration, no analysis of the accuracy,dynamic range or signal-to-noise ratio can be performed. The calibration isdescribed in Sects. 3.6 and 3.7.

3.4 OscillatorThe oscillator uses a slider-crank mechanism to oscillate a hot-wire probe. Theamplitude of oscillation xo is 5.5 mm. For the calibration, a second amplitudeof 2.85 mm is used. The hot-wire probe fits into a probe holder, guided nearits free end by a brass bushing at the end of a rigid support tube (Figs. 3.5and 3.6). The brass bushing provides tight support close to the probe tip,avoiding transverse vibrations. The probe holder is clamped to the oscillatingprobe holder base, sliding in Teflon guides.

The crankshaft with angular encoder is driven by an electric 70 W DC-motor. The oscillator shaft speed is read by an optical encoder. The current to

3.4 Oscillator 81

probe probe holder oscillating probe holder base

rigid support tube

50 mm

dual balance shafts

U > 0U > 0U > 0

p

rel

opticalencoder

motor

Figure 3.5 – Hot-wire oscillator drawing

the DC-motor is supplied by an amplifier. The input to the amplifier is obtainedfrom a PI (proportional integrative) feedback controller, that regulates the shaftrotational speed ωo = 2πfo to within 0.1 rad/s. The OHW speed controller isimplemented on a dSPACE20 DS1103 real-time data-acquisition system.

Ball bearings are used on all shafts and the crank-connecting rod joint. Twocounter-rotating balance shafts are driven using steel gears by the crankshaft.The balance masses cancel the oscillating mass (i.e. probe holder base, probeholder and probe). During the calibration, the oscillator is mounted on the cal-ibration wind tunnel frame (see Sect. 3.6). The maximum oscillation frequencyfo,max = 50 Hz for xo = 5.5 mm (and fo,max = 80 Hz for xo = 2.85 mm), whichis limited by the DC-motor output.

Figure 3.4 shows the symbol nomenclature and sign convention for the OHWmotion. The probe displacement xp and probe velocity Up are:

20dSPACE GmbH, Technologiepark 25, D-33100 Paderborn, Germany(http://www.dspace.com)

http://www.dspace.com


Figure 3.6 – Hot-wire oscillator

3.5 Hot-wire probes 83

xp (t) = −xo

(sinωot−

sinωot

| sinωot|

(√(xcr/xo)

2 − cos2 ωot

−√

(xcr/xo)2 − 1

))(3.7)

Up (t) = −2πfoxo︸︷︷︸Up,min

cosωot−12

sinωot

| sinωot|sin 2ωot√

(xcr/xo)2 − cos2 ωot

(3.8)

where xo is the crank amplitude (= 5.5 or 2.85 mm), xcr is the connectingrod length (= 50 mm) and ωot = 2πfot is the crankshaft position [rad]. Theminimum velocity Up,min = −2πfoxo occurs at ωot = 2πn.

Since xcr/xo 1, the motion is nearly sinusoidal. However, due to unevenfriction and backlash in the mechanism, the true probe velocity Up,true differsslightly from Eq. (3.8). Up,true and Vp,true are measured using laser Doppleranemometry, by focussing the measuring volume on the blackened side of ahot-wire probe. The same device is used as reference velocity measurementduring the calibration. The deviation of Up,true and Vp,true (i.e. the transversecomponent) are around 1.5% for the highest oscillation frequency. As such, Vp

is considered negligible and Eq. (3.8) is used to determine Up.

3.5 Hot-wire probes

Figure 3.7 shows the three one-dimensional hot-wire probes used during thecalibration of the OHW: (i) 55P11 and (ii) 55P11L are straight probes withdifferent prong lengths, and (iii) 55P14 is a probe with 90 bend prongs. The55P11 and 55P14 probes are manufactured by Dantec19. The 55P11L probe ismanufactured in the TME lab21.

Only one-dimensional probes are used, since the OHW is designed for one-dimensional reversing flow. Table 3.2 lists the probe dimensions and resonancefrequencies. In determining the prong resonance frequency for probe 55P14,Eq. (3.1) is used with a value of λ = 1.399 instead of λ = 1.875. This valueresults from a derivation that considers a single-clamped beam shaped like55P14’s prongs.

As indicated in Fig. 3.7, the base of the prongs is covered by an insulatingpolymer, that slightly extends from the probe body. The difference between hand h′ in Fig. 3.7 is roughly 1 mm.

The sensor wire (5 µm thick Platinum-plated tungsten) is spot-welded tothe flattened ends of the prongs. The stainless steel prongs have a circularcross-section, and slightly tapered toward the end. The flattened end measuresapproximately 100 µm in diameter. All probes can be repaired in the TME

21Katholieke Universiteit Leuven, department of Mechanical Engineering, division TME,Celestijnenlaan 300A, B-3001 Leuven, Belgium (http://www.mech.kuleuven.be/tme)

http://www.mech.kuleuven.be/tme


l, Ød

h' h

ØD

(55P11)

l, Ød

h' h

ØD

(55P11L)

l, Ød

h'

h

ØD

s

(55P14)

Figure 3.7 – Hot-wire probes 55P11, 55P11L and 55P14, used for the OHW cali-bration

3.6 Calibration approach 85

Table 3.2 – Specifications for hot-wire probes

Probe Dimensions Resonanceaccording to Fig. 3.7 frequency

D d l h s wire prongsmm µm mm mm mm kHz kHz

55P11 1.9 5 1.25 5.0 - 13.2 -55P11L 1.9 5 1.50 8.0 - 9.1 -55P14 1.9 5 1.25 3.0 5.5 13.2 5.2

lab21, using a custom-made spot welding power generator, a micromanipulatorand a stereo microscope.

3.6 Calibration approachThe term calibration refers to the relation between actual flow velocity U andthe velocity determined by the OHW U ′ = Urel + Up. The OHW is calibratedfor U between −1.5 and 10 m/s. Note the distinction with the stationarycalibration (see Sect. 3.3), referring to the relation between the relative velocityUrel and the anemometer bridge output voltage Ebridge.

For the negative velocity range (−1.5 6 U < 0 m/s), the wind tunneldescribed below is used, in combination with laser Doppler anemometry asreference velocity measurement.

For the positive velocity range (0 < U 6 10 m/s), the wire is oscillated ina Dantec19 90H02 free jet calibration unit. Figure 3.8 schematically depictsthis system. A free air jet is formed with highly uniform transverse velocityprofile by means of a settling chamber and contraction nozzle. The referencevelocity U is determined from the isentropic expansion equation, in terms of thepressure ratio p0/pambient and temperature T0. The accuracy on the referencevelocity is 1 %. U ′ does not deviate from U by more than 5% for the positivevelocity range. LDA measurements are not possible when using the Dantec19

calibration unit, thus no phase-locked results are discussed for U > 0 m/s.

3.6.1 Calibration wind tunnelFigure 3.9 shows the wind tunnel used for calibrating the OHW in the negativevelocity range. The test section velocity is adjustable between 0 to −10 m/s,following the coordinate convention defined in Fig. 3.9, using a speed-controlledsuction fan with throttle. The fan is vibration isolated from the wind tunnel.Wind tunnel and OHW are mounted on a rigid frame. The acrylic test sectionhas a square cross-section (100×100 mm). The presence of the OHW preventedthe use of a proper settling chamber and contraction, resulting in a radialflow entry into the test section. A bell-mouth inlet seamlessly connects tothe test section. A settling chamber with perforated screens provides uniformflow towards the bell-mouth. The OHW probe support tube enters the inlet


flow controller

p , T

settling chamber

filteredair 8 bar

0 0

U

probe in free jet

pa

Figure 3.8 – Free jet calibrator

honeycomb microscope glass insert

LDA lens perforated screens

inlet settling chamber

bell-mouth inlet

OHW oscillator(mounted onrigid frame)

test section

50 mmy , V

x, U

U < 0

Figure 3.9 – OHW calibration wind tunnel


chamber through a sealed hole and is located along the centreline of bell-mouthand test section.

The hot-wire probe is located 90 mm inside the test section. The calibrationprocedure described in Sect. 3.6 requires that the test section is easily removedfrom the inlet box. High-quality optical access for the LDA is provided by amicroscope glass insert. Only one window is provided, since the LDA is op-erated in backward scattering mode. Operation in forward scattering modecould easily increase the data rate by a factor 10 to 100, and only requires anadditional window on the other side of the test section. Nevertheless, backscat-tering is preferred because the LDA is also used to measure the longitudinaland transverse components of the actual probe velocity Up,true and Vp,true.

The sensor wire is oriented along the vertical y-axis. The wire orienta-tion is important for low velocity behavior since the convective heat trans-fer differs for a vertical and horizontal wire. Bruun [25] mentions a criticalReynolds number below which natural convection becomes significant. Thecritical Reynolds number Recrit = Gr1/3. The Grashof number Gr is definedas Gr = g β d3 (Tw − Ta)

/ν2 , where g is the gravitational acceleration (' 9.81

m/s2), β is the thermal expansion coefficient (K−1), d is the sensor wire diam-eter (= 5 µm), Tw and Ta are the wire and ambient temperature (K) and ν isthe kinematic viscosity [m2/s]. For an ideal gas, the thermal expansion coeffi-cient β = T−1. Here, Gr ' 3.8 · 10−6, yielding Recrit ' 0.016. No influence isexpected since Re varies between 0.51 and 0.08 for −1.50 6 U 6 −0.25 m/s.

Contrary to what Fig. 3.9 depicts, the LDA beams centreline is along thehorizontal z-axis, so that U and V can be measured. In the coordinate sys-tem in Fig. 3.9, x = 0 corresponds to the center of the OHW oscillation rangeand (y, z) = (0, 0) to the center of the wire. The LDA measurement volumeis focussed in the origin (0, 0, 0). As such, the wire passes through the sta-tionary LDA volume. This shows up in the phase-locked LDA velocity (seeSect. 3.7). The LDA reading during the passing of the wire is neglected in thepost-processing.

The LDA measurement volume approximates an ellipsoid with long axis2.2 mm along the z-axis and circular cross-section of diameter 0.165 mm inthe xy-plane.

An axisymmetric boundary layer forms around the probe support tube.Figure 3.10 shows the spanwise distribution of U (y) and turbulence intensityu/U [-]. Note that all references to U refer to U (x = 0, y = 0). In the freestream, turbulence intensity is below 0.8% and the flow non-uniformity is below2% of free stream velocity U∞. The flow becomes turbulent when |U | > 0.75m/s, corresponding to Re > 2000, based on the OHW support tube diameterand the free stream velocity. The turbulent wake features a turbulence intensitybetween 5 to 20%.

Figure 3.11 presents the power spectral density of U for laminar and tur-bulent flow in the wind tunnel. Spectra are shown (i) in the wake center aty = 0 mm, (ii) at the location of the 55P14 sensor wire which corresponds tothe edge of the central wake at y = s = 5.5 mm and (iii) in the free streamat y = 20 mm. The laminar flow spectrum shows evidence of laminar periodic


0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

y =

s (

= 5

.5 m

m)

y =

s (

= 5

.5 m

m)

U(y

)/U

∞ a

nd (

u/U

)(y)

y (mm)

U(0) = 0.37 m/s (light), U(0) = 1.05 m/s (bold)

U(y)/U∞ (-)

(u/U)(y) (-)

Figure 3.10 – Wind tunnel velocity ( ) and turbulence intensity (

) profile for

U = 0.37 m/s (laminar) ( ) and U = 1.05 m/s (turbulent) (

)

101

102

10310

-9

10-8

10-7

10-6

10-5

10-4

10-3

Frequency (Hz)

Ene

rgy

spec

trum

((m

/s)2 /H

z)

U(0) = 0.37 m/s (laminar)

y = 0 mmy = 5.5 mmy = 20 mm

(a)

101

102

10310

-9

10-8

10-7

10-6

10-5

10-4

10-3

Frequency (Hz)

Ene

rgy

spec

trum

((m

/s)2 /H

z)

U(0) = 1.05 m/s (turbulent)

y = 0 mmy = 5.5 mmy = 20 mm

(b)

Figure 3.11 – Wind tunnel velocity frequency spectrum for (a) U = 0.37 m/s(laminar) and (b) U = 1.05 m/s (turbulent), at different spanwise locations


vortex shedding, corresponding to a Strouhal number Sr = f D/U∞ between0.20 and 0.25, where D equals the diameter of the OHW support tube (=10 mm), the probe holder (= 4 mm) or the probe body (= 1.9 mm). Therange of 0.20 < Sr < 0.25 corresponds to typical frequencies of periodic vortexshedding behind bluff bodies.

3.6.2 Laser Doppler anemometeras reference velocity measurement

The LDA serves as reference velocity measurement during the OHW calibra-tion in the negative velocity range. The LDA qualifies as a reference velocitymeasurement for this application because of the following features:

• Direct measurement — LDA measures the velocity of particles (movingwith the flow) directly, requiring no calibration of its own. Of course, thisassumes optimal operating conditions (e.g. correct setting of validationand bandwidth, appropriate seeding type and density, correct opticalalignment, . . . )

• High bandwidth — The maximum OHW oscillation frequency fo,max is80 Hz. As such, a bandwidth of at least 1 kHz is required, which is easilyattained using LDA.

• Non-intrusiveness and directional sensitivity

More details on this measurement technique are given in App. C.2.The two-component LDA is operated in backward scattering mode, with

Bragg cell frequency shifting on both velocity components, and a Dantec19

58N20 Flow Velocity AnalyzerTM to process the raw signals into velocity values.Diethylhexylsebacat (DEHS) seeding is introduced into the settling chamber,taking care not to disturb the flow. Like the HWA, the LDA is phase-lockedwith the oscillator shaft encoder.

3.6.3 Calibration procedure

Using laser Doppler anemometry as a reference velocity measurement has oneimportant drawback: LDA requires that seeding particles are introduced intothe flow (see App. C.2). DEHS is the most practical seeding substance forthis application. However, when a hot-wire is used in a flow contaminatedwith DEHS seeding, liquid gradually deposits onto the sensor wire and prongs,altering its temperature-resistance characteristics. This undesirable effect isdenoted fouling. Fouling increases sensor resistance by 2% or more, whichyields a velocity error of 10 to 20 % below 5 m/s. Since fouling also introducesa strong time dependence, it was decided not to use simultaneous HWA andLDA measurements. Rather, two identical probes are used for each calibration:(i) a dummy probe during the LDA measurements, performed in DEHS seededair flow, and (ii) a reference probe during the HWA measurements, performed


in clean air flow. The calibration procedure involves changing probes in eachset point. For each reference velocity setting, the following actions take place:

(a) With a stationary dummy probe, the test section velocity U (1)stat is adjusted

using the LDA measurement.

(b) While the dummy probe is oscillated at each frequency fo, the phase-locked test section velocity U (ωot) is measured using LDA.

(c) With a stationary dummy probe, the test section velocity U(2)stat is mea-

sured a second time, after which the seeding is turned off.

(d) The test section is removed to replace the dummy with the referenceprobe.

(e) While the reference probe is oscillated at each frequency fo, the phase-locked OHW velocity U ′ (ωot) = Urel (ωot) + Up (ωot) is measured.

(f) The test section is removed to replace the reference with the dummyprobe.

(g) With a stationary dummy probe, the test section velocity U(3)stat is mea-

sured a third time.

The fact that LDA and OHW measurements cannot occur simultaneouslyis an obvious weakness of the calibration method. The repeatability of theabove procedure is verified by comparing the three reference measurements atstationary probe U (1)

stat, U(2)stat and U

(3)stat during each velocity setting. During a

test incorporating 17 velocity settings, the deviation on Ustat is below 1.5 %.

3.7 Calibration results

3.7.1 Calibration chartsFigure 3.12 presents the calibration charts of OHW velocity22 U ′ versus thereference velocity U , expressed in non-dimensional form with the maximumprobe velocity Up,max = ωoxo as scaling factor. For each probe type (seeSect. 3.5), two calibration charts are shown for both oscillation amplitudesxo = 5.5 mm and xo = 2.85 mm. Each chart contains points correspondingto different oscillation frequencies. The estimated uncertainty on each point isbelow 1%.

The measurements in the positive velocity range U > 0 m/s and for astationary probe (f = 0 Hz) are omitted from Fig. 3.12. For positive velocity,U ′ deviates from U by less than 5%. For a stationary probe (f = 0 Hz), thecurves U ′ versus U are asymmetrical about the y-axis, due to the wake formedby probe body and support in case of negative velocity.

22The term ‘velocity’ denotes ensemble-averaged velocity, time-averaged during Up 6−ωoxoα, as defined in Eq. (3.6)

3.7 Calibration results 91

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 0.788, b = 0.5 (R2 = 0.813)

OH

W v

eloc

ity U

/(ω

ox o) (-

)

Reference velocity Uo/(ω

ox

o) (-)

55P11, xo = 5.5 mm

10 Hz20 Hz30 Hz40 Hz

(a)

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 0.862, b = 0.5 (R2 = 0.921)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P11, xo = 2.85 mm

20 Hz40 Hz60 Hz

(b)

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 0.736, b = 0.5 (R2 = 0.949)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P11L, xo = 5.5 mm


(c)

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 0.894, b = 0.5 (R2 = 0.903)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P11L, xo = 2.85 mm

20 Hz40 Hz60 Hz

(d)

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 1.145, b = 0.5 (R2 = 0.940)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P14, xo = 5.5 mm


(e)

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 1.274, b = 0.5 (R2 = 0.976)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P14, xo = 2.85 mm

20 Hz40 Hz60 Hz

(f)

Figure 3.12 – Calibration chart for (a) 55P11, xo = 5.5 mm, (b) 55P11, xo =2.85 mm, (c) 55P11L, xo = 5.5 mm, (d) 55P11L, xo = 2.85 mm, (e) 55P14, xo =5.5 mm, (f) 55P14, xo = 2.85 mm (Note: reference velocity U is measured using LDA, OHWvelocity U ′ is obtained using Eq. (3.6))


-180 -90 0 90 180

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Oscillator shaft angle ωot (ο)

Phas

e-lo

cked

vel

ocity

(m

/s)

55P11, xo = 5.5 mm, U = -0.45 m/s, f

o = 30 Hz

U (ω

ot)

U’ (ω

ot)

Urel

(ωot)

Up (ω

ot)

(a)

-180 -90 0 90 180

-1

-0.5

0

0.5

1

1.5

2

2.5

3


Phas

e-lo

cked

vel

ocity

(m

/s)

55P11, xo = 2.85 mm, U = -0.45 m/s, f

o = 60 Hz

U (ω

ot)

U’ (ω

ot)

Urel

(ωot)

Up (ω

ot)

(b)

-180 -90 0 90 180

-1

-0.5

0

0.5

1

1.5

2

2.5

3


Phas

e-lo

cked

vel

ocity

(m

/s)

55P11L, xo = 5.5 mm, U = -0.46 m/s, f

o = 30 Hz

U (ω

ot)

U’ (ω

ot)

Urel

(ωot)

Up (ω

ot)

(c)

-180 -90 0 90 180

-1

-0.5

0

0.5

1

1.5

2

2.5

3


Phas

e-lo

cked

vel

ocity

(m

/s)

55P11L, xo = 2.85 mm, U = -0.45 m/s, f

o = 60 Hz

U (ω

ot)

U’ (ω

ot)

Urel

(ωot)

Up (ω

ot)

(d)

-180 -90 0 90 180

-1

-0.5

0

0.5

1

1.5

2

2.5

3


Phas

e-lo

cked

vel

ocity

(m

/s)

55P14, xo = 5.5 mm, U = -0.48 m/s, f

o = 30 Hz

U (ω

ot)

U’ (ω

ot)

Urel

(ωot)

Up (ω

ot)

(e)

-180 -90 0 90 180

-1

-0.5

0

0.5

1

1.5

2

2.5

3


Phas

e-lo

cked

vel

ocity

(m

/s)

55P14, xo = 2.85 mm, U = -0.42 m/s, f

o = 60 Hz

U (ω

ot)

U’ (ω

ot)

Urel

(ωot)

Up (ω

ot)

(f)

Figure 3.13 – Phase-locked velocity at U ' −0.45 m/s and ωoxo ' 1.04 m/s, for (a)55P11, xo = 5.5 mm, fo = 30 Hz, (b) 55P11, xo = 2.85 mm, fo = 60 Hz, (c) 55P11L,xo = 5.5 mm, fo = 30 Hz, (d) 55P11L, xo = 2.85 mm, fo = 60 Hz, (e) 55P14,xo = 5.5 mm, fo = 30 Hz, (f) 55P14, xo = 2.85 mm, fo = 60 Hz (Note: referencevelocity U(ωot) is measured using LDA, OHW velocity U ′(ωot) equals Urel(ωot)+Up(ωot), whereUrel is the velocity relative to the probe, obtained from the anemometer bridge reading, and Up

is the probe velocity)


Table 3.3 – OHW calibration chart fit parameters, according to Eq. (3.9)

Probe xo a b R2 Figuremm - - - 3.12

55P11 5.5 0.788 0.5 0.813 (a)55P11 2.85 0.862 0.5 0.921 (b)55P11L 5.5 0.736 0.5 0.949 (c)55P11L 2.85 0.894 0.5 0.903 (d)55P14 5.5 1.145 0.5 0.940 (e)55P14 2.85 1.274 0.5 0.976 (f)

The following function is used to fit U ′/(ωoxo) versus U/(ωoxo) :

Fa,b (u) =

u+ a

(√(u+ 1)2 + b2 − u−

√1 + b2

); u < 0

u ; u > 0(3.9)

where u = U/(ωoxo) [-], a and b are non-dimensional parameters: a determinesthe slope (= 1 − 2a) of the function as u → ∞ and b > 0 yields a smoothtransition around U/(ωoxo) = −1. When b = 0, the function reduces toFa,b (u) = u + a (|u+ 1| − u− 1). A value of b = 0.5 is chosen arbitrarily forall curves.

The non-dimensional calibration curves for different oscillation frequenciescollapse reasonably well. The value of a, b and the coefficient of determinationR2 [-] for each correlation fit with the function Fa,b (u) is given in each plot inFig. 3.12 and in Table 3.3.

For −1 6 U/(ωoxo) 6 0, the calibration curve should ideally be U ′/(ωoxo)= U/(ωoxo) . This region is of highest interest to the calibration, since onlyhere exists an unambiguous relation between U ′/(ωoxo) and U/(ωoxo) .

The behavior is quite different for straight and angled probe types at highand low amplitude. This unexpected difference is investigated below, using anon-dimensional scaling analysis.

3.7.2 Phase-locked results

Figure 3.13 shows the phase-locked reference (U), probe (Up), wire-relative(Urel) and OHW (U ′ = Urel +Up) velocity. All plots represent different probesand different amplitudes, for identical values of U and ωoxo. The number ofensembles taken is sufficiently high to reduce the estimated uncertainty on allensemble-averaged velocities to below 1 %.

Vertical dash-dotted lines indicate where Up 6 −ωoxoα. As indicated inTable 3.2, the 55P11 prong length h is only 5 mm, which is smaller than thegreatest oscillation amplitude (5.5 mm). This causes occasional collapse of theLDA velocity U to the probe velocity Up, when the probe body passes throughthe LDA measurement volume. Due to reflections as the wire passes through


the LDA measurement volume at sinωot = 0 (ωot = πn where n ∈ Z), theLDA velocity around ωot = πn is unreliable (e.g. Fig. 3.13c). These erroneousmeasurements are excluded from the time averaging in Eq. (3.6).

Figure 3.13e shows high-frequency jitter in the HWA signal (Urel and U ′)around ωot ' π + 2πn. Since the jitter shows up after ensemble averaging, itis phase-locked with the probe motion. The peak jitter frequency is 4.3 kHzand is independent of changes in oscillation frequency. The phenomenon islikely caused by prong vibration. The prong resonance frequency of 5.2 kHzlisted in Table 3.2 is apparently somewhat overestimated. The vibrating prongsstrain the sensor wire, which changes its resistance, thereby affecting the ve-locity reading. This is only encountered for the 55P14 probe at high oscillationfrequency (f > 50 Hz).

Figure 3.13 provides insight in the periodic flow around the oscillatingprobe. Since the LDA velocity U is measured at a stationary point (x, y, z) =(0, 0, 0) and the OHW velocity U ′ is measured along the moving wire, LDAand OHW velocity should only be compared at sinωot ' 0 or ωot ' πn. While0 6 ωot < π/2 , the LDA velocity magnitude increases due to the momentumprovided by the passing wire and nearby prongs. While π/2 6 ωot < π, theprobe changes direction and passes through the origin in positive direction,causing a decrease in the LDA velocity magnitude. While −π 6 ωot < 0,the flow around the origin returns to the initial state. The characteristic timeconstant for this recovery is simply the convective time constant xo/U .

3.7.3 Non-dimensional scaling analysis

Figure 3.12 shows a discrepancy in the behavior for −1 6 U/(ωoxo) 6 0.The calibration points collapse reasonably to U ′/(ωoxo) = U/(ωoxo) for the55P11 and 55P11L probes at high amplitude, and for the 55P14 probe at lowamplitude. In all other cases, U ′/(ωoxo) deviates from U/(ωoxo) . For eachcalibration chart in Fig. 3.12, the influence of the oscillation frequency vanisheswhen U ′ and U are scaled with ωoxo. The discrepancy should therefore beinfluenced by xo or other geometrical parameters. To quantify the discrepancy,the velocity deviation ∆U is defined as the difference between the OHW velocityand the expected velocity, which is given by Eq. (3.9) with b = 0:

∆Uωoxo

=U ′

ωoxo− Fa,b

(U

ωoxo

)(3.10)

For each probe, a suitable non-dimensional group is selected that corre-lates the velocity deviation ∆U/(ωoxo) for both amplitudes in the calibrationregion of interest (i.e. −1 6 U/(ωoxo) 6 0). For the angled 55P14 probe,Uangled = (U/(ωoxo) )

(ωox

2o/ν

)is the suitable non-dimensional group. For

the straight 55P11 and 55P11L probes, Ustraight = (U/(ωoxo) )(ωoD

2/ν)

isthe suitable non-dimensional group, where D represents the probe body di-ameter [m]. The correlations between velocity deviation ∆U/(ωoxo) and non-dimensional groups Ustraight and Uangled are presented in Fig. 3.14. For each


-120 -100 -80 -60 -40 -20 0-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

OH

W v

eloc

ity d

evia

tion

∆U

/(ω

ox o) (-

)

Uo /(ω

ox

o) . (ω

o D2/ν) (-)

55P11

10 Hz, 5.5 mm20 Hz, 5.5 mm30 Hz, 5.5 mm20 Hz, 2.85 mm40 Hz, 2.85 mm60 Hz, 2.85 mm

(a)

-120 -100 -80 -60 -40 -20 0-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

OH

W v

eloc

ity d

evia

tion

∆U

/(ω

ox o) (-

)

Uo /(ω

ox

o) . (ω

o D2/ν) (-)

55P11L


(b)

-600 -500 -400 -300 -200 -100 0-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

OH

W v

eloc

ity d

evia

tion

∆U

/(ω

ox o) (-

)

Uo /(ω

ox

o) . (ω

o x

o2 /ν) (-)

55P14


(c)

Figure 3.14 – Correlation of velocity deviation ∆U for (a) 55P11 and (b) 55P11Lversus bUstraight (Eq. (3.11)), and for (c) 55P14 versus bUangled (Eq. (3.12))


probe, ∆U/(ωoxo) collapses roughly to a linear curve versus the appropriatenon-dimensional group for −1 6 U/(ωoxo) 6 0:

∆Uωoxo

∼ U

ωoxo

ωoD2

ν= Ustraight

(55P11, 55P11L) m (3.11)∆UU

∼ ωoxoD

ν

D

xo

∆Uωoxo

∼ U

ωoxo

ωox2o

ν= Uangled

(55P14) m (3.12)∆UU

∼ ωoxoD

ν

xo

D

The expressions for ∆U/U in Eqs. (3.11) and (3.11) indicate that for aconstant value of ωoxo, the velocity deviation decreases for increasing oscillationamplitude xo in case of the straight 55P11 and 55P11L probes. Equivalently,increasing xo yields a better correspondence of U ′/(ωoxo) with U/(ωoxo) for−1 6 U/(ωoxo) 6 0. By contrast, for the angled 55P14 probe, the velocitydeviation decreases for decreasing (instead of increasing) amplitude xo.

When the amplitude xo →∞ for the straight probes, the oscillating motiontends towards a slow moving linear sled. The amplitude xo = 5.5 mm is acompromise between compactness and a small velocity deviation ∆U , whichyields a high negative velocity resolution.

For the angled probe, the amplitude xo should rather be decreased, requiringa higher oscillation frequency to maintain the same value of ωoxo. In this case,the problem of prong vibration shown in Fig. 3.13f has to be considered. Prongvibration can be avoided by raising the prong resonance frequency, either bythickening the prongs or by reducing the prong cantilever length s (Fig. 3.7,right). Reducing s will likely cause the angled probe’s behavior of ∆U toresemble that of the straight probes. In other words, the decrease in velocitydeviation ∆U by decreasing xo (and increasing the oscillation frequency) wouldbe counteracted by reducing the angled prong cantilever length s.

No attempt is made in this thesis to verify the above assumption by de-creasing the amplitude xo for the angled probe below 2.85 mm. Decreasingxo to 0.35 mm and increasing the oscillation frequency to 490 Hz results in asystem similar to Li and Naguib [66]. However, such high oscillation frequencyis unattainable with a mechanical drive. Furthermore, severe prong vibrationwould occur, unless appropriate measures are taken to raise the prong resonancefrequency. Moulin et al. [78] use a straight probe at low oscillation amplitudeand very high frequency. This choice seems in contradiction with the resultsof this study, however extrapolation is difficult. Firstly, the amplitude used byMoulin et al. [78] (= 4 µm) is of the order of the sensor wire diameter (= 5 µm).


Secondly, as discussed in Sect. 3.1, the high-frequency OHW systems [78, 66]use a different approach for detecting the flow direction than the low-frequencyOHW system presented in this thesis. Moulin et al. [78] and Li and Naguib [66]use the phase difference between the anemometer output and the probe motionsignal to detect flow direction.

3.7.4 Discussion of the calibration results

The different behavior of straight and angled probes discussed in Sect. 3.7.3 islikely due to the local flow around the sensor wire. For the angled 55P14, thewire oscillates on the edge of the boundary layer formed around probe bodyand support (Fig. 3.10). For the straight 55P11 and 55P11L, the wire oscillatesin the wake center.

The effect that the periodic wake caused by the moving probe has on thecalibration is difficult to estimate. It is a clear weakness for the low-frequencyOHW approach. Traditional FHA avoids this problem by incorporating a deadtime in the motion, where the probe remains stationary and located sufficientlyfar from the measurement field. However, this seems impossible to achieve ina confined geometry. Phase-locked LDA has been used in the present study tomeasure the time-resolved local flow during wire oscillation.

Wake contamination could be minimized by using a modified version of theangled 55P14 probe, with longer prongs (i.e. increasing s from Table 3.2). AsFig. 3.10 shows, an increase in s by only a few millimeters places the wire in thefree stream. Along with the proposed reduction in the oscillation amplitudexo that follows from the non-dimensional scaling in Sect. 3.7.3, this might besubject for further research.

Simultaneously increasing the prong length and oscillation frequency re-quires a sufficient increase in the resonance frequency to minimize prong vibra-tion. By appropriately shaping the prongs, their stiffness could be increased.Rather than merely thickening the prongs, perhaps a slender airfoil could beused to minimize flow disturbance.

The OHW affects not only the local flow field. A periodic thermal wake iscreated by the moving hot-wire, subject to convection and diffusion. As the wiremoves through a region heated during a previous passage, the convective heattransferred from the wire decreases. This effect is equally present in the high-frequency OHW by Moulin et al. [78] and Li and Naguib [66], perhaps moreso due to the small oscillation amplitude. The effect is difficult to estimate,however it is completely contained within the calibration. No OHW systemcan be used without calibration with oscillating probe.

In summary, the combination of a straight hot-wire probe with long prongs(55P11L) with high oscillation amplitude seems the best option for the pre-sented low-frequency OHW. This combination yields the lowest velocity de-viation ∆U/(ωoxo) for −1 6 U/(ωoxo) 6 0 (Fig. 3.14b). Furthermore, thiscombination results in a maximum measurable negative velocity of −1.0 m/s,and the non-dimensional calibration chart is accurately fitted by Eq. (3.9) with


an R2-value23 of 0.949 (Fig. 3.12c).Further research is required to verify the feasibility of a low-frequency OHW

with minimal wake contamination, based on a modified version of the angled55P14 probe with extended prongs.

3.8 Operation

The current section describes the selection of the OHW oscillation frequencyfo for measuring the bidirectional velocity in the periodic flow in the exhaustsystem.

Based on the calibration results discussed in Sect. 3.7, the 55P11L probeis used with an oscillation amplitude xo = 5.5 mm. The oscillation frequencyfo is kept between 30 and 40 Hz to obtain the maximum resolvable negativevelocity. The oscillation frequency fo is also kept proportional to the enginespeed N [rpm]. The non-dimensional oscillation frequency Rf is defined basedon the ratio of engine cycle period (i.e. two crankshaft revolutions) to theoscillation period:

Rf =fo

N/120=

ωo

ω/2(3.13)

Considering the OHW methodology discussed in Sect. 3.3, the OHW yieldsvalid measurements when the probe velocity Up is large and counter to thenormal flow direction. In terms of the symbols and sign convention establishedin Fig. 3.4, valid measurements are taken when Up 6 −2πfoxoα = −ωoxoα.

The valid measurement window defined by Up 6 −2πfoxoα = −ωoxoα cor-responds to a time interval (i.e. OHW shaft position interval) of approximately:

− arccosα 6 ωot+ 2πn 6 arccosα (n ∈ Z) (3.14)

The approximation in Eq. (3.14) neglects the non-harmonic distortion intro-duced by using a crank-connecting rod mechanism instead of a Scotch yoke.With regard to Eq. (3.8), Up is approximated as limxcr→∞ (Up) = −2πfoxo·cosωot.

Equation (3.14) shows that the valid measurement window represents afraction of 2 arccosα/(2π) of one oscillation period. To clarify the followingdiscussion, the fraction of the valid measurement window per period is definedas 1/A :

1A

=2 arccosα

2π(3.15)

mα = cos (π/A )

23The R2-value represents the coefficient of determination, defined as the square of thecorrelation coefficient between the values and the fitted curve.

3.8 Operation 99

0 180 360 540 720-1

0

1

- α

Engine crankshaft position ω t (ο)

Prob

e ve

loci

ty U

p/ωox o (

-)

N = 2400 rpm, fo = 35.0 Hz, R

f = 1.75

Up/ω

ox

o (cycle 1)

Up/ω

ox

o (cycle 2)

Up/ω

ox

o (cycle 3)

Up/ω

ox

o (cycle 4)

Up = - ω

ox

oα

Figure 3.15 – OHW probe velocity Up, phase-locked with the engine crankshaftposition ωt [ca], for α = cos (π/4) ' 0.71 (as used during the measurements on theCME flow rig)

During the OHW calibration, the non-dimensional tolerance factor α ischosen as α = cos (π/8) ' 0.92. For α = cos (π/8), the valid measurementwindow corresponds to a fraction of 1/A = 1/8 of one oscillation period.For the measurements on the CME flow rig, the tolerance factor α is chosenα = cos (π/4) ' 0.71 instead, corresponding to a fraction of 1/A = 1/4 of theoscillation period. The reason for this arbitrary choice is given in the followingparagraphs.

When the non-dimensional OHW frequency Rf is a whole number (Rf ∈Z), the OHW moves in synchronization with the engine’s crankshaft. In thatcase, the OHW measurements are taken in the same engine crankshaft positionintervals in consecutive engine cycles. In order to cover the entire crankshaftposition range 0 6 ωt 6 720 ca corresponding to a single engine cycle, theOHW motion slightly lags or leads the engine rotation. As such, Rf is chosenas:

Rf = n± 1/A (n ∈ Z) (3.16)

where 1/A corresponds to the above introduced fraction of valid measurementsper oscillation period, or 1/A = (2 arccosα)/(2π) .

Figure 3.15 shows the OHW probe velocity versus crankshaft position fora particular engine speed. The whole number n is maximized, limited by themaximum oscillator frequency fo,max = 40 Hz. For the case of N = 2400 rpmand taking 1/A = 1/4 , this results in fo = 35 Hz for n = 2 or Rf = 2− 1/4 =1.75. In this case, it takes four engine cycles (A = 4) to obtain valid velocitymeasurements for the entire range of crankshaft positions 0 6 ωt 6 720 ca.

Note from Fig. 3.15 that the choice of Rf = n ± 1/A ensures that duringeach next engine crankshaft revolution, the valid OHW measurement window


shifts to the next (higher) crankshaft positions. This is an arbitrary choice; thedifference between Rf and the whole number n may be any number between 0and 1. However, the choice according to Eq. (3.13) ensures the minimum totalmeasuring time.

The different selection of 1/A and α during the OHW calibration and themeasurements on the CME flow rig has the following implications. From thecalibration to the measurements, the value 1/A has been increased from 1/8to 1/4 , thereby decreasing the tolerance factor α from cos (π/8) ' 0.92 tocos (π/4) ' 0.71). This decreases the mean probe velocity magnitude duringa valid measurement window, thus decreasing the resolution in the negativevelocity range.

The main reason for increasing 1/A is that A engine cycles are required tocomplete valid OHW measurements for one engine cycle 0 6 ωt 6 720 ca. Byincreasing 1/A from 1/8 to 1/4 , only four (instead of eight) engine cycles arerequired to complete measurements for one engine cycle.

The magnitude of the loss in negative velocity resolution associated withthe decrease in tolerance factor α from cos (π/8) ' 0.92 to cos (π/4) ' 0.71 isdemonstrated by Fig. 3.16. Figure 3.16 shows two non-dimensional calibrationcharts for the 55P11L probe with oscillation amplitude xo = 5.5 mm. The datareduction for Fig. 3.16a uses α = cos (π/8), which corresponds to the value usedduring the calibration. The data reduction for Fig. 3.16b uses α = cos (π/4),which corresponds to the value used during the measurements on the CMEflow rig.

The resolution in the negative velocity range slightly decreases for the α =cos (π/4) case in Fig. 3.16b, compared to the α = cos (π/8) case in Fig. 3.16a.This can be noted from the increased value of a, which determines the slope ofthe fitted curve according to Eq. (3.9). The parameter a = 0.748 for the casewith low tolerance factor α = cos (π/4) (Fig. 3.16b), compared to a = 0.736for the case with high tolerance factor α = cos (π/8) (Fig. 3.16a).

Several hundred ensembles are required to ensure sufficient accuracy afterensemble-averaging the phase-locked velocity data. A single measurement runthat results in one catalyst velocity distribution takes between two to fourhours when using 1/A = 1/8 . When using 1/A = 1/4 , the slight loss innegative velocity resolution is acceptable given the reduction by 50 % of themeasurement time.

3.9 Conclusion

A novel low-frequency oscillating hot-wire anemometer (OHW) is presentedto measure bidirectional velocity. The OHW is more compact than traditionalflying hot-wire anemometers reviewed by Bruun [25], and less prone to prong orwire vibration and strain gauging than high-frequency OHW systems recentlydescribed by Moulin et al. [78] and Li and Naguib [66]. Unlike high-frequencysystems, the presented OHW does not assume a frozen flow field. Therefore, theoscillation frequency may be well below the maximum frequency contained in

3.9 Conclusion 101

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 0.736, b = 0.5 (R2 = 0.949)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P11L, xo = 5.5 mm, α = cos(π/8)


(a)

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 0.748, b = 0.5 (R2 = 0.947)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P11L, xo = 5.5 mm, α = cos(π/4)


(b)

Figure 3.16 – Calibration chart for 55P11L at xo = 5.5 mm, for tolerance factor(a) α = cos (π/8) ' 0.92 (used during the calibration), and (b) α = cos (π/4) ' 0.71(used during the measurements on the CME flow rig)

the flow. An advantage for the high-frequency approach is that the measurablenegative velocity is not limited, although Li and Naguib [66] provide a criterionrelating minimum negative velocity and oscillation frequency.

A small-scale wind tunnel is used to calibrate the OHW in the negative ve-locity range −1.5 6 U 6 0 m/s. Laser Doppler anemometry is used as referencevelocity measurement. LDA measurements are phase-locked with the OHW.Three hot-wire probe designs are calibrated, examining the influence of pronglength and shape. Calibrations are performed for two oscillation amplitudesand several frequencies.

Based on the calibration charts (Fig. 3.12), the best calibration results areobtained for the 55P11L probe with straight extended prongs, in combinationwith an oscillation amplitude xo = 5.5 mm. This choice results in a maximumresolvable negative velocity of −1.0 m/s.

The non-dimensional analysis indicates in Fig. 3.14 that straight (55P11,55P11L) and angled (55P14) probes behave differently with regard to the cor-respondence between the OHW velocity U ′ and the reference velocity U . Forthe straight probes, increasing the oscillation amplitude xo (and decreasingoscillation frequency fo) reduces the deviation between U ′ and U . For the an-gled probe, the deviation between U ′ and U is reduced by decreasing xo andincreasing fo.

The presented OHW system can be applied to reversing flows in confinedgeometries, such as internal pipe flow. In particular, it has been successfullyapplied during this thesis to measure the phase-locked velocity distributionincluding instantaneous local flow reversal on the CME flow rig (see Chap. 5).

The contents of this chapter have been published in an international journalwith review:

[83] T. Persoons, A. Hoefnagels, and E. Van den Bulck. Calibra-


tion of an oscillating hot-wire anemometer for bidirectional velocitymeasurements. Exp. Fluids, 40(4):555–567, 2006. http://dx.doi.org/10.1007/s00348-005-0095-4

http://dx.doi.org/10.1007/s00348-005-0095-4

http://dx.doi.org/10.1007/s00348-005-0095-4

Chapter 4

Addition principle

“The first principle is that you must not fool yourself and you are theeasiest person to fool.”

Richard Feynman (American physicist, 1918, †1988)

This chapter presents the experimental validation of the addition principle,defined by Eq. (4.1). The relevance of this principle is recalled in Sect. 4.1.

Section 4.3 discusses the elaborate data reduction used to assess the simi-larity between a pair of velocity distributions.

Section 4.4 presents the experimental results for both pulsating flow rigs andboth exhaust manifolds. The combined results are summarized in Sect. 4.4.3and interpreted in Sect. 4.5. The similarity measures introduced in Sect. 4.3 es-tablish a remarkable correlation with a single non-dimensional flow character-istic, the scavenging number S (Eq. (4.42)). The correlations in Fig. 4.29 resultin a critical value for the scavenging number Scrit, which determines the validityrange of the addition principle.

Section 4.6 provides an physical interpretation to the findings of Sect. 4.5in the form of an analogy to a zero-dimensional scalar mixing process. Usingthis analogy, Sect. 4.6.2 introduces the hypothetical concept of a collector effi-ciency ηD, which equals the critical value of the scavenging number Scrit. Thishypothesis warrants further research.

4.1 IntroductionThis chapter discusses the experimental validation of the addition principle.The relevance of the addition principle has already been briefly introduced inthe literature survey in Sect. 1.4.1.

103

104 Chapter 4 Addition principle

The fluid dynamics aspects of the industrial design of exhaust manifoldscomprises mostly stationary CFD studies, using commercially available CFDpackages. The increase of the computational cost associated with transientCFD calculations (relative to stationary calculations) is very high. Within thehighly competitive automotive supplier business, achieving short developmenttimes while maintaining design criteria guarantees is critical for obtaining newcontracts. At present, transient CFD is therefore rarely used for exhaust man-ifold design in industrial practice.

The entire manifold design is based directly and indirectly on the internalflow field and the catalyst velocity distribution. The stationary flow predic-tions are used to estimate the backpressure, the catalyst flow uniformity, anda number of other criteria such as determining the optimal position for the ex-haust gas oxygen (or lambda) sensors so that they receive equal contributionsof exhaust gas from each cylinder. Furthermore, the stationary flow results areused as boundary condition in finite element modeling to predict the surfacetemperatures, the thermal stresses and the related risk of mechanical failuredue to fatigue.

Given the strong pulsating nature of the exhaust flow, the question ariseswhether using stationary predictions is justifiable. For pulsating flow in close-coupled catalyst manifolds, the addition principle states the following:

Addition principle The time-averaged catalyst velocity distri-bution in pulsating flow can be predicted by a linear combination ofvelocity distributions that result from stationary flow through eachof the exhaust runners, with the exhaust valves in the maximumopen position, and for equal volumetric flow rate.

Or symbolically:

U (x, y)puls ' U (x, y)stat =1nr

nr∑r=1

U (x, y)stat,r (4.1)

where Upuls denotes the time-averaged non-dimensional velocity distributionin pulsating flow. Ustat is the linear combination of nr stationary flow velocitydistributions Ustat,r. An overbar (¯ ) denotes a time-averaged quantity. A tilde(˜) represents a non-dimensional velocity, scaled with the time-averaged meanvelocity U = U

/Um .

The comparison between pulsating and stationary flow conditions is per-formed for the equal volumetric flow rate, as indicated by the definition. Fig-ure 4.1 illustrates the importance of this aspect. The top plot in Fig. 4.1 rep-resents the time evolution of the mean catalyst velocity for pulsating flow, fora four-cylinder engine (r = 1 . . . 4). The time-averaged mean velocity Upuls,m

is indicated by the dashed line ( ).

The middle plot in Fig. 4.1 represents the hypothetical case where all run-ners are blocked, except for a single one (r = 3). In this case, the overalltime-averaged velocity Upuls,i=3,m ' Upuls,m/nr (nr = 4).

4.1 Introduction 105

U

t

r = 1 r = 3 r = 4 r = 2

U

tU

tT

120 / Np

Pulsating flowall runnersU

Pulsating flowsingle runnerU

Stationary flowsingle runnerU

puls

puls, r=3

stat, r=3

Upuls, m

Upuls, r=3, m

Ustat, r=3, m

Figure 4.1 – Addition principle: flow rate setting

The addition principle compares the pulsating flow distribution Upuls toa superposition of flow distributions for stationary flow through each runnerseparately. In order to obtain similar flow conditions, stationary flow rateshould equal the time-averaged flow rate in pulsating conditions. Therefore,the stationary flow conditions are as depicted in the bottom plot of Fig. 4.1.The preset velocity Ustat,r,m therefore equals Upuls,m.

Since ideally Ustat,r,m = Upuls,m, it is not strictly necessary in Eq. (4.1) tonon-dimensionalize each velocity distribution by its time-averaged mean value.The reason is rather practical, since there is inevitably some uncertainty insetting the flow rate in the experiment.

The validity of the addition principle means that the pulsating flow in theexhaust manifold behaves quasi-stationary, i.e. that there is no influence ofdynamic effects. Indeed, the linear combination of stationary distributionsUstat may be considered the quasi-stationary limit case for zero engine speed.

Nevertheless, the exhaust manifold of a working engine features a highlytransient, three-dimensional turbulent flow. The flow features a considerabledegree of cycle-by-cycle variability, as illustrated in Sect. 2.5.2. Furthermore,like all fluid dynamic phenomena, the system is nonlinear, due to e.g. internaland external friction, and compressibility effects. For example, as shown inFig. B.1, the discharge coefficient of the exhaust valves even varies nonlinearlyduring the valve lift sequence.

In that sense, it seems a crude approximation to make that any time-varyingeffects are irrelevant in this flow, and that the time-averaged pulsating flowdistribution simply equals a combination of velocity distributions obtained forstationary flow through each runner, with the exhaust valves in the maximumopen position. Therefore, the subject of research of this chapter is to validate


the addition principle and determine its applicability range.The validity of the principle would imply that transient CFD is not required

for designing a manifold with a CC catalyst with respect to the catalyst flowdistribution and that steady state CFD simulations suffice.

This principle carries important practical implications for an industrial ex-haust manifold design team. The computation time for steady CFD is at leastone order of magnitude smaller when compared to transient CFD calculations.This entails a much shorter development time, which is crucial for obtainingcontracts in the fast moving and highly competitive automotive Tier 1 sector.

4.2 Validation approach

A crucial part of the addition principle is the comparison between two spa-tial distributions of the axial catalyst velocity, (i) one representing the time-averaged velocity distribution in pulsating flow conditions, and (ii) one rep-resenting a linear combination of velocity distributions obtained in stationaryflow conditions.

Each distribution is two-dimensional, and given in (x, y) coordinates. Theorthonormal coordinate system (x, y, z) is aligned so that the z-axis coincideswith the catalyst lengthwise axis and the x-axis is along the long axis in caseof an elliptic catalyst. In practice, for a typical four-cylinder engine, the x-axisis (nearly) parallel to the engine crankshaft.

Throughout the field of engineering, a number of similarity measures arein use for comparing two-dimensional distributions. The term ‘distribution’can really denote any two-dimensional collection of scalar data. Much of theresearch into similarity measures is concerned with image processing.

For the present application, a good similarity measure should have the fol-lowing properties:

(a) High sensitivity to the difference in regions of extreme (i.e. high and low)velocity, since these regions are the most critical in terms of catalystdegradation, conversion efficiency and pressure drop.

(b) The measure should allow uncertainty analysis, thereby enabling thequantification of the validity of the addition principle in terms of a rigor-ous statistical hypothesis test.

(c) Low sensitivity to small spatial shifts, of the order of magnitude of0.5 mm, due to errors in positioning the velocity probe.

In the image processing literature [71, 63, 90, 31, 65], there exist a numberof similarity measures: the unweighted and weighted Pearson product-momentcorrelation coefficient, the Moran’s index [29], the earth mover’s distance [90,65], and the untrimmed and trimmed Mallows distance [71, 31].

Out of all these, the weighted Pearson product-moment correlation coeffi-cient corresponds best to the above requirements. This measure corresponds


to the first non-dimensional similarity measure rS used in the remainder of thischapter to validate the addition principle.

The correlation coefficient is sensitive to the difference in shape betweenthe distributions, yet insensitive to the difference in velocity magnitude. How-ever, this latter feature must be included in the comparison, since the velocitymagnitude is related to the flow uniformity.

Therefore, a second similarity measure rM is introduced in Sect. 4.3.2 whichis only sensitive to the difference in velocity magnitude. More specifically, rMcompares the difference in terms of a flow uniformity measure.

4.3 Data reduction

This section describes the particular data reduction used for the validation ofthe addition principle.

4.3.1 Flow uniformity measures

In the field of automotive catalysts, several measures are used to quantify theflow uniformity. The most generally accepted one is the flow uniformity index,introduced by Weltens et al. [108]. However, this thesis mainly uses a differ-ent flow uniformity measure, defined as the mean-to-maximum velocity ratio.This measure is also used with respect to the addition principle validation, tocompare two velocity distributions based on flow uniformity. This is discussedin the Sect. 4.3.2.

Weltens’ flow uniformity index ηw [108]

The flow uniformity index ηw corresponds to a relative ‘variance’ of the velocitydistribution, where the variance is determined using the absolute value, ratherthen the sum of squared deviations:

ηw = 1− 12

1|Um|A

I∑i=1

|Ui − Um|Ai (4.2)

where A is the total cross-sectional area and I is the number of measurementpoints. Ui represents the velocity in point (xi, yi).

Equation (4.2) is actually an adaptation to the original formula proposedby Weltens et al. [108], which does not account for the cross-sectional area Ai

in each grid point.If the velocity U remains positive, the value of ηw varies between zero and

unity. For instance, ηw = 1/2 corresponds to a case where half the cross-section experiences zero flow, and the velocity in the other half is twice themean velocity.


The flow uniformity is usually evaluated on the time-averaged24 veloc-ity distribution, in which case Ui represents the time-averaged local velocityUi = U (x, y). However, it may be useful to evaluate the evolution of the flowuniformity during one engine cycle. In this case, ηw (ωt) is defined based onthe time-resolved velocity U (x, y, ωt) and mean velocity Um (ωt):

ηw (ωt) = 1− 12

1|Um (ωt)|A

I∑i=1

|Ui (ωt)− Um (ωt)|Ai (4.3)

According to the above definitions, the average of the time-resolved uni-formity index ηw (ωt) (4.3) does not equal the time-averaged uniformity indexηw (4.2).

The time-resolved definition according to Eq. (4.3) may result in problemsin case of strong flow reversal, as is the case on the CME flow rig (see Sect. 5.2).The value of ηw (ωt) becomes undefined if Um (ωt) approaches zero.

The statistical inference for Weltens’ flow uniformity index can be deter-mined from the propagation of the uncertainties on the velocity Ui and thecross-sectional area Ai. The uncertainty on Ai is assumed negligible comparedto that on Ui. This is justifiable due to the use of a highly accurate automaticvelocity probe positioning system, featuring a positioning accuracy of betterthan 0.25 mm.

The propagation of errors is based on the following principle, where the vari-able Y is a function of n independent variables Xk, or Y = F (X1, X2, . . . , Xn):

∆Y = δY · Y =

√√√√ n∑k=1

(∂Y

∂Xk∆Xk

)2

(4.4)

where ∆ denotes the absolute error and δ denotes the relative error on a vari-able. This relationship yields the well-known rules ∆ (X1 +X2)

2 = (∆X1)2 +

(∆X2)2 and δ (X1 ·X2)

2 = (δX1)2 + (δX2)

2.Applying the above error propagation principle to ηw according to Eq. (4.2)

results in the following expression for the relative error δηw:

δηw =1− ηw

ηw

√√√√√δU2m +

∑Ii=1 (∆U2

i + ∆U2m)A2

i(∑Ii=1 |Ui − Um|Ai

)2 (4.5)

where, using the same principle, δUm, ∆Ui and ∆Um can be further ex-panded in terms of the uncertainties on individual ensemble-averaged velocitiesU (xi, yi, ωt). The uncertainty on U (xi, yi, ωt) is defined in Sect. 2.5.1.

24As mentioned in Sect. 2.5, the overline x (indicating time-averaging) and the tilde ex(indicating non-dimensionalizing with the time-averaged mean velocity) are usually omittedfor the sake of clarity. Time-resolved quantities are specified with the crankshaft position(ωt).


Mean-to-maximum velocity ratio ηm

In spite of the general use of the Weltens’ index, a different non-dimensionalflow uniformity measure is used throughout this thesis. ηm is defined as theratio of mean to maximum velocity. The following expressions define ηm forthe time-averaged and time-resolved case:

ηm =|Um|Umax

(4.6)

ηm (ωt) =|Um (ωt)|Umax (ωt)

(4.7)

where Umax = maxi∈[1,I] (|Ui|) = maxi∈[1,I]

(∣∣U (xi, yi)∣∣) and Umax (ωt) =

maxi∈[1,I] (|Ui (ωt)|) = maxi∈[1,I] (|U (xi, yi, ωt)|). Alternatively, ηm can bedefined based on the non-dimensional velocity U [-], where U = U/Um :

ηm =1

Umax

(4.8)

ηm (ωt) =1

Umax (ωt)(4.9)

where Um = Um/Um = 1, Umax = maxi∈[1,I] (|Ui/Um |) and Umax (ωt) =maxi∈[1,I] (|Ui (ωt)/Um (ωt) |).

The use of the absolute value ensures that 0 6 ηm 6 1. By contrastto the definition of ηw (ωt) (4.3), the mean velocity does not appear in thedenominator in the definition of ηm. As such, ηm (ωt) can be used to quantifythe time-resolved flow uniformity in case of strong reversing flows.

Hald [44] discusses the sampling distribution of the largest observation ina population. This approach is used to determine the sampling distribution ofthe non-dimensional maximum velocity Umax:

PUmax

=

(PU)n

and pUmax

= n

(PU)n−1

pU

(4.10)

where p · · · and P · · · represent the probability and the cumulative prob-ability density function, respectively. Here, n denotes the maximum numberof spatially independent points, determined with the approach using Moran’sindex (see Sect. 4.3.2).

Eq. (4.10) assumes that the n velocity observations are stochastically in-dependent and have the same probability density function. The probabilitydensity function can be determined directly from the histogram of the non-dimensional velocity U .


4.3.2 Distribution similarityShape similarity measure rS

The Pearson product-moment correlation coefficient ρ is an obvious choiceto quantify the comparison between two distributions, in terms of their non-dimensional shape.

The unbiased estimator25 r for the Pearson product-moment correlationcoefficient ρ is defined as:

r =

n∑i=1

(zi,1 − zm,1) (zi,2 − zm,2)√√√√ n∑i=1

(zi,1 − zm,1)2 ·

n∑i=1

(zi,2 − zm,2)2

(4.11)

where zm,k = 1n

∑ni=1 zi,k, i and n are the index and number of data points.

In light of the validation of the addition principle, the correlation coefficientis named rS . It forms the principal similarity measure used for quantifying theshape similarity :

rS =

I∑i=1

(Ui,1 − Um,1) (Ui,2 − Um,2)√√√√ I∑i=1

(Ui,1 − Um,1)2 ·

I∑i=1

(Ui,2 − Um,2)2

(4.12)

where Um,k = 1A

∑Ii=1 Ui,kAi, i and I are the index and number of measure-

ment points. Ai and A represent the local and the total cross-sectional area inthe measurement points (A =

∑Ii=1Ai). In practice, the area weighting using

Ai does not affect the value of rS , since the measurement grid points are apriori arranged so that each grid point has the same cross-sectional area.

Detailed information on the statistical inference of the Pearson product-moment correlation coefficient can be found in Hald [44], Spiegel [94], McPher-son [72] and Guttmann et al. [42].

The sampling distribution of the correlation coefficient ρ is very skewed,unless for the case ρ = 0. The confidence interval for r can be determinedusing Fisher’s Z transformation. The statistic Z defined as [44]:

Z =12

log(

1 + r

1− r

)(4.13)

features an approximately normal (i.e. normalized Gaussian) distribution witha standard deviation equal to 1

/√n− 3 . The normal approximation is accept-

able if n exceeds 20.

25For the sake of clarity, the statistical terminology such as ‘unbiased estimator’ will bediscarded throughout most of the discussion.


0 0.25 0.5 0.75 10

2

4

6

8

10

12

Correlation coefficient ρ (-)

Prob

abili

ty d

ensi

ty f

unct

ion

(-)

PDF of ρ using Fisher’s Z transformation

ρ = 0.9ρ = 0.75ρ = 0.5ρ = 0

Figure 4.2 – Probability density function of the correlation coefficient ρ, usingFisher’s Z transformation in Eq. (4.13) with n = 30

Therefore, the confidence interval for a significance level26 α is:

Z − z1−α/21√n− 3

< Z < Z + z1−α/21√n− 3

(4.14)

where z1−α/2 is the critical value for the normal distribution corresponding toa two-sided confidence interval at a significance level α (e.g. z1−α/2 = 1.96 forα = 0.05). Transformation from Z to r uses the inverse of Eq. (4.13):

r =e2Z − 1e2Z + 1

(4.15)

Fig. 4.2 gives some examples of the probability density function for differentvalues of ρ, for n = 30.

Spiegel [94] provides the clearest explanation for using a hypothesis testbased on the Pearson product-moment correlation coefficient.

The hypothesis HS,1 tests for totally dissimilar distributions:

HS,1

H0 : ρ = 0H1 : ρ > 0 (4.16)

For ρ = 0, the sampling distribution of the estimator r is symmetric, and rmay be transformed into a statistic t which features a Student’s t distributionwith n− 2 degrees of freedom (see Hald [44]):

t =r√n− 2√

1− r2(4.17)

On the basis of a one-sided test of Student’s t distribution at a significancelevel α, one would reject H0 if t > t1−α;n−2.

26The significance level α is equivalent to the confidence level 1 − α. In this thesis, theconfidence level is 95% or α = 0.05.


The P-value P of an observation with respect to a hypothesis test is definedas the probability that, given that the null hypothesis H0 is true, the testvariable assumes a more extreme value than the observation. The P-valuequantifies the statistical evidence for rejecting the null hypothesis H0. If theP-value is smaller than the significance level α, H0 is rejected.

For the above hypothesis HS,1, the P-value PS,1 is defined as:

PS,1 = Pt;n−2

r√n− 2√

1− r2< t

(4.18)

where Pt;n−2 t0 < t is the probability that t exceeds t0 in a Student’s t dis-tribution with n − 2 degrees of freedom. The value of PS,1 can be obtainedfrom the corresponding cumulative probability density function.

Recalling the definition of the hypothesis test HS,1 in (4.16), if PS,1 issmaller than α = 0.05, then H0 is rejected and the correlation coefficient rbetween the two distributions is significantly positive. The smaller PS,1, thestronger is the evidence for correlation.

The statistical strength of the hypothesis test HS,1 is somewhat limited dueto the fact that the sampling distribution of r becomes increasingly skewed asr is closer to unity.

Whereas HS,1 tested for dissimilar distributions, the hypothesis HS,2 testsfor highly similar distributions:

HS,2

H0 : ρ = ρcrit (> 0)H1 : ρ < ρcrit

(4.19)

where ρcrit can be any arbitrary ‘high’ correlation coefficient value. Becauseof the exponential correlation between rS and S found during the experiments(see Sect. 4.5), the value of ρcrit is taken equal to 1 − e−1 ' 0.63. Referringto Sect. 4.5, the value of ρcrit corresponds to the critical value of rS when thescavenging number equals the critical scavenging number. It is shown belowthat ρcrit should be strictly smaller than unity. The sampling distribution forthe hypothesis test H0: ρ = ρcrit 6= 0 features a skewed sampling distributionin r (see Fig. 4.2). Therefore, Fisher’s Z transformation according to Eq. (4.13)can be applied to transform the skewed r distribution into a symmetric one.The statistic Z defined by Eq. (4.13) is approximately normal distributed withmean value µz = 1/2 log ((1 + ρcrit)/(1− ρcrit) ) and standard deviation σz =1/√

n− 3 .With reference to Hald [44], the mean value µz actually equals µz = 1/2 ·

log ((1 + ρcrit)/(1− ρcrit) ) + ρcrit/2 (n− 1) . However, for n > 24, the secondterm is more than 10 times smaller then the standard deviation, and as such, itis omitted. This procedure cannot be performed unless ρcrit is strictly smallerthan unity.

For the hypothesis HS,2, the P-value PS,2 is defined as:

PS,2 = Pz

z <

(12

log(

1 + r

1− r

)− µz

)/σz

(4.20)


where Pz z < z0 is the probability that z is smaller than z0 in a normaldistribution, and µz and σz are defined above.

If PS,2 is smaller than α = 0.05, then H0 is rejected and the correlationcoefficient r between the two distributions is significantly different from ρcrit.

Since the hypotheses HS,1 (4.16) and HS,2 (4.19) are each other’s inverse, soare the corresponding P-values. The smaller PS,1, the stronger is the evidencefor correlation. However, the smaller PS,2, the stronger is the evidence againstcorrelation.

The choice of ρcrit is quite arbitrary. The only restriction is that ρcrit issmaller than unity for using the Fisher transformation.

The number of samples n in the above discussion does not necessarily cor-respond to the number of velocity measurement points. Instead, n correspondsto the largest number of spatially independent points of the distributions. Spa-tial dependence is determined using Moran’s index, which is introduced in thefollowing section.

Spatial autocorrelation

Moran’s index M is a measure of spatial autocorrelation. It is one of the oldestavailable measures, introduced by Moran [77] in 1950, yet remains the standardspatial autocorrelation measure. M is defined according to Cliff and Ord [29]:

M =

n

N∑i=1

N∑j=1

wij (zi − zm) (zj − zm)

WN∑

i=1

(zi − zm)2(4.21)

where wij are weighting factors, W =∑N

i=1

∑Nj=1 wij . According to the above

definition, M compares the value of the variable z (here: z = U , the catalystvelocity) at any one location with the value at all other locations. Like thecorrelation coefficient, M varies between −1 and 1. M ' 0 indicates no spatialautocorrelation, M ' 1 indicates strong positive spatial autocorrelation.

The N -by-N weighting matrix wij can be determined in different ways.Moran [77] originally introduced the index M in combination with wij = δij ,where δij is a binary adjacency measure (not the Kronecker δ):

δij =

1 if elements i and j are adjacent, yet i 6= j ,0 otherwise. (4.22)

Alternatively, instead of a binary (0,1) connection matrix, wij can be a prox-imity measure, based on the inverse of the Euclidean distance or any otherdistance measure. More information on alternative weighting is given by Cliffand Ord [29]. In this thesis, the above adjacency definition is used accordingto Moran [77].


0 50 100 150 200-0.5

0

0.5

1

α = 0.05

n = 30

Number of points N (-)

Mor

an’s

inde

x M

(-)


Moran’s M (-)P-value (-)

(a)

0 50 100 150 200-0.5

0

0.5

1

α = 0.05

n = 45

Number of points N (-)

Mor

an’s

inde

x M

(-)


Moran’s M (-)P-value (-)

(b)

Figure 4.3 – Determining the number of spatially independent points in the catalystvelocity distribution, for manifold (a) A and (b) B

If the sample size n is sufficiently large, Moran’s index M is approximatelynormally distributed, with a mean value and variance defined in Cliff andOrd [29] by Eqs. (2.24) and (2.28), respectively. Based on the mean value,variance and normality assumption, a confidence interval can be establishedfor M .

Moran’s index can now be applied to determine the number of spatially in-dependent points in a measured velocity distribution. A spatial autocorrelationhypothesis test H is constructed based on M :

HH0 : M = 0 no spatial autocorrelationH1 : M > 0 (4.23)

The P-value P for this hypothesis test is based on the normality assumptionforM and the mean value µM and variance σ2

M defined by Eqs. (2.24) and (2.28)in Cliff and Ord [29]:

P = Pz

M − µM

σM< z

(4.24)

For any given velocity distribution, Moran’s index can be determined, alongwith P . According to the definition of the hypothesis test H, there is a signif-icant spatial autocorrelation if P is smaller than the significance level α. Thenumber of data points in the velocity distribution N is gradually decreaseduntil P becomes greater than α. Decreasing the number of points is performedby two-dimensional linear interpolation of the original data on a mesh withincreasingly larger spacing.

Figure 4.3 gives an example of determining the number of spatially inde-pendent points n for velocity distributions obtained on manifolds A and B. The


values for n are relatively insensitive to changes in flow conditions. As such,the number of spatially independent points are assumed n = 30 for manifoldA, and n = 45 for manifold B. These values are used e.g. in the statisticalinference for the correlation coefficient, as discussed in the preceding section.

Since the number of spatially independent points is relatively constant foreach of the manifolds, critical limits for rS indicating significant similarity canbe derived based on the hypothesis test HS,1. For a 95% confidence level, onecan derive that two velocity distributions are significantly correlated when:

rS > 0.317 for manifold A (n = 30)rS > 0.254 for manifold B (n = 45) (4.25)

The difference between the limits is solely due to the different spatial depen-dence of the distributions of manifolds A and B.

At first sight, these limits appear quite low. Strictly statistically speaking,the limits apply. However, the discussion on the validation of the additionprinciple in Sect. 4.5 yields a more intuitively correct similarity limit, rS >rS,crit = 1− e−1 ' 0.63.

Magnitude similarity measure rM

The correlation coefficient rS (4.12) is used to quantify the similarity betweentwo velocity distributions based on differences in shape. This section explainsthe selection procedure for a second similarity measure, based on differencesin magnitude. Two analytical examples are provided to clarify and justify thisselection.

Example 1 (using a cosine velocity distribution) show that rS , by natureof its definition, is insensitive to differences in magnitude between two velocitydistributions with identical shape. Following Example 1, the magnitude simi-larity measure rM is introduced, based on the ratio of the flow uniformity inpulsating and stationary conditions.

Example 2 (using a non-negative velocity distribution) clarifies the choiceof ηm as a flow uniformity measure for the magnitude similarity measure rM .

Example 1: Cosine distribution Consider a simple one-dimensionalcase, comparing two velocity distributions U1 (x) and U2 (x), defined as:

U1 = Um,1 (1 + a1 cos (2πx))

U2 = Um,2 (1 + a2 cos (2πx)) (4.26)

where x is the coordinate (−1/2 6 x 6 1/2 ), a1 and a2 are non-dimensional numbers (a > 0) that determine the magnitude of the veloc-ity variations in U1 and U2 (see Fig. 4.4a).

The continuous version of the discrete definition of rS (4.12) is:


rS =

Z 1/2

x=−1/2

(U1 − Um,1) · (U2 − Um,2) dxsZ 1/2

x=−1/2

(U1 − Um,1)2 dx ·

Z 1/2

x=−1/2

(U2 − Um,2)2 dx

(4.27)

Substituting the expressions for U1 and U2 in Eq. (4.27) yields rS = 1.Thus, rS is insensitive to changes in mean velocity Um or changes invelocity magnitude a.

In light of the insensitivity of rS to differences in magnitude of the velocitydistributions, a second similarity measure rM is introduced. Ideally, rM shouldcomplement rS in terms of its sensitivity. In other words, rM should be sensitiveto differences in magnitude, yet insensitive to differences in the shape of thedistribution.

As such, the magnitude similarity measure rM is defined as the ratio of theflow uniformity measures for each velocity distribution, based on the mean-to-maximum velocity ratio ηm to quantify the flow uniformity:

rM =ηm,puls

ηm,stat(4.28)

Substitution of the definition of ηm (4.6) into Eq. (4.28) yields:

rM =(Um/Umax )puls

(Um/Umax )stat

=

(1/Umax

)puls(

1/Umax

)stat

=Umax,stat

Umax,puls

(4.29)

Unlike the definition of rS (4.12), the above definition of rM is not sym-metrical (ηm,puls/ηm,stat 6= ηm,stat/ηm,puls ). For the validation of the addi-tion principle, the subscript puls in Eqs. (4.28) and (4.29) denotes pulsatingflow conditions and stat denotes the linear combination of stationary flow con-ditions. Therefore, rM quantifies the relative increase in flow uniformity inpulsating flow, compared to the averaged stationary distribution. If rM > 1,the pulsating flow has a better flow uniformity than the stationary averagedflow. As discussed in Sect. 4.4.3, this is actually the case for all flow conditionsencountered.

Example 1: Cosine distribution (cont’d) Continuing the simpleanalytical example described above, this example examines the behaviorof the flow uniformity measures ηw and ηm, and the magnitude similaritymeasure rM .


The continuous version of the definition of Weltens’ flow uniformity indexηw (4.2) is:

ηw = 1− 1

2

1

|Um|

Z 1/2

x=−1/2

|U (x)− Um| dx (4.30)

whereR 1

x=−1dx = 1 vanishes. Substituting Eqs. (4.26) into Eq. (4.30)

yields:

ηw = 1− 1

2

|Uma||Um|

Z 1/2

x=−1/2

|cos (2πx)| dx

= 1− a

π(4.31)

The mean-to-maximum velocity ratio ηm (4.6) is simply:

ηm =Um

Umax

=Um

Um (1 + a)

=1

1 + a(4.32)

The following table summarizes the behavior of the flow uniformity mea-sures ηw and ηm for the velocity distribution in this simple example, fordifferent values of the magnitude parameter a (see Fig. 4.4a). Both mea-sures reach a maximum value of unity for a perfectly uniform distribu-tion. Figure 4.5a shows the evolution of ηw and ηm versus the magnitudeparameter a.

ηw ηm

Eq. (4.31) Eq. (4.32)a = 0 1 1a = 1 0.682 0.5a = π 0 0.242a →∞ −∞ 0

Substituting Eqs. (4.26) into the definition of the magnitude similaritymeasure rM (4.28) yields (assuming subscript 1 and 2 correspond to pulsand stat, respectively):

rM =ηm,1

ηm,2

=1 + a2

1 + a1(4.33)

Since ηm varies between zero and unity, rM varies between zero and +∞.


-0.5 0 0.5

-2

-1

0

1

2

3

4

x (-)

U /

Um

(-)

Example: Cosine distribution

a = 0a = 1a = π

(a)

-0.5 0 0.50

0.5

1

1.5

2

2.5

x (-)

U /

Um

(-)

Example: Non-negative distribution

a = 0a = 1a = 2a = 4

(b)

Figure 4.4 – Velocity distributions, for (a) cosine (see Example 1) and (b) non-negative (see Example 2) distributions

In Example 1, Eq. (4.33) shows that the definition of rM based on ηm yieldsa straightforward and intuitive interpretation, at least for this simple one-dimensional test case. Example 2 presents a derivation analogous to Example 1,yet for a non-negative velocity distribution.

Example 2: Non-negative distribution This example discussesthe behavior of rS , ηw, ηm and rM for a simple yet non-negative one-dimensional velocity distribution, for −1/2 6 x 6 1/2 .

Consider two velocity distributions U1 (x) and U2 (x), defined as:

U1 = Um,1e−(a1x)2

√π/a1 erf(a1/2)

U2 = Um,2e−(a2x)2

√π/a2 erf(a2/2)

(4.34)

where a1 and a2 are non-dimensional numbers (a > 0) that determine themagnitude and (to a lesser extent) the shape of the velocity variations inU1 and U2. The error function erf is defined as erf(z) = 2/

√π

R z

t=0e−t2dt.

These distributions correspond to the normalized Gaussian distributionfunction, scaled such that the mean velocity over the interval −1/2 6x 6 1/2 equals Um.

By contrast to Example 1 using the cosine distribution, the parameters aaffect both the magnitude and the shape of the distributions. As shownin Fig. 4.4b, the Gaussian bell shape is relatively insensitive to smallvariations in a. Since the shape is altered by changes in a, rS is nolonger constant as is the case in Example 1 with the cosine distribution.Taking into account that

R 1/2

x=−1/2e−(ax)2dx =

√π/a erf(a/2), rS yields:


0 1 6 8 100

0.2

0.4

0.6

0.8

1

Magnitude parameter a (-)

Flow

uni

form

ity (

-)


Flow uniformity measures ηw

and ηm

ηw

ηm

π

(a)

0 1 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Magnitude parameter a (-)Fl

ow u

nifo

rmity

(-)


Flow uniformity measures ηw

and ηm

ηw

ηm

(b)

Figure 4.5 – Flow uniformity measures for different velocity magnitude, for (a)cosine (see Example 1) and (b) non-negative (see Example 2) distributions

0 1 2 3 40

0.5

1

1.5

2

2.5

Pulsating case (1) is more uniform

than stationary case (2) for a2 > a

1

Magnitude parameter ratio a2/a

1 (-)

Sim

ilari

ty m

easu

res

(-)


Similarity measures rS and r

M

rS

rM

(a)

0 1 2 3 40

0.5

1

1.5

2

2.5

Pulsating case (1) is more uniform

than stationary case (2) for a2 > a

1

Magnitude parameter ratio a2/a

1 (-)

Sim

ilari

ty m

easu

res

(-)


Similarity measures rS and r

M

rS

rM

(b)

Figure 4.6 – Similarity measures for different velocity magnitude ratios, for (a)cosine (see Example 1) and (b) non-negative (see Example 2) distributions


rS =

26664 2a1a2

a21 + a2

2

erf

„√a21+a2

22

«2

erf“

a1√2

”erf

“a2√

2

”37775

12

(4.35)

For typical velocity distributions, a varies between zero (i.e. perfectlyuniform) and four (see Fig. 4.4b). Taking a1 as unity and varying a2

between zero and four, yields a variation of rS between 0.83 and unity,according to Eq. (4.35). This is shown in Fig. 4.6b as well.

No analytical solution can be found for Weltens’ flow uniformity indexηw (4.2).

The mean-to-maximum velocity ratio ηm (4.6) is:

ηm =Um

Umax

=

√π

aerf

“a

2

”(4.36)

ηw ηm

Eq. (4.36)a = 0 1 1a = 1 0.968 0.923a = 2 0.881 0.747a = 4 0.649 0.441a →∞ 0 0

The table above summarizes the behavior of the flow uniformity mea-sures ηw and ηm for the velocity distribution in this simple example.Both measures reach a maximum value of unity for a perfectly uniformdistribution. Figure 4.5b shows the evolution of ηw and ηm versus themagnitude parameter a.

Substituting Eqs. (4.34) into the definition of the magnitude similaritymeasure rM (4.28) yields (assuming subscript 1 and 2 correspond to pulsand stat, respectively):

rM =ηm,1

ηm,2

=a2

a1

erf`

a12

´erf

`a22

´ (4.37)

The above examples for a cosine velocity distribution and a non-negative veloc-ity distribution provide some reference values for the flow uniformity measuresηw and ηm, and the related magnitude similarity measure rM . For a varyingratio of the magnitude parameter a, Fig. 4.6 presents the variation of rS andrM for both examples.

In the definition of rM (4.28), the mean-to-maximum velocity ratio ηm (4.6)is chosen over Weltens’ flow uniformity index ηw (4.2) for the following reasons:


• Boundedness — In case of a not strictly positive velocity distribution (e.g.see cosine distribution in Example 1), only ηm remains bounded betweenzero and unity. For distributions with strong flow reversal, ηw can assumenegative values with an unbounded amplitude (see Fig. 4.5a).

Since rM is to be defined as the ratio of two flow uniformity measures, auniformity measure whose value may become zero (such as ηw) is unde-sirable.

• Sensitivity — As shown in Fig. 4.5, ∂ηm/∂a (i.e. the derivative of ηm

with respect to the magnitude parameter a) is greater in absolute valuethan ∂ηw/∂a . At least, this is true in the region of typical magnitudeparameter values, between zero and four.

In other words, ηm is more sensitive to changes in the magnitude of thevelocity distribution than ηw, yet still ηm is the only measure that remainsbounded.

The statistical significance of rM is based on (i) the sampling distribution ofηm according to Eq. (4.10), and (ii) on the Mellin convolution. The Mellinconvolution is a technique described e.g. in Springer [95] (Sect. 4.1). Equa-tion (4.1.7) in [95] presents the probability density function of the quotienty = z1/z2 of two non-negative independent random variables with probabilitydensity functions p1 z1 and p2 z2, expressed as the Mellin convolution:

p

y =

z1z2

=∫ ∞

z2=0

z2 · p1 y z2 · p2 z2 dz2 (4.38)

Equation (4.38) represents the probability density function of the magnitudesimilarity measure rM . Symbolically, p rM = p y = z1/z2 , where z1 andz2 correspond to ηm,puls and ηm,stat, respectively. The probability densityfunctions p1 and p2 are determined according to Eq. (4.10).

An example of the probability density function for one particular combi-nation of two velocity distributions is given by Fig. 4.7. The irregular shapeof p rM results from the Mellin convolution and the irregular shape of thedistributions for each ηm.

Since this method provides the entire estimated probability density for rM ,no assumptions are required as to the nature of the distribution, in order todetermine the statistical inference.

The (1− α) 100 % confidence interval[rM,α/2, rM,1−α/2

]is defined as:

PrM

rM,α/2 6 rM 6 rM,1−α/2

= 1− α (4.39)

where the confidence limits rM,α/2 and rM,1−α/2 result directly from the cumu-lative probability density function PrM

rM, which is obtained by integratingp rM (4.38).

Similar to rS , a hypothesis test HM is defined as:

HM

H0 : rM = 1H1 : rM 6= 1 (4.40)


0.5 1 1.5 2

Magnitude similarity measure y (-)

Prob

abili

ty d

ensi

ty f

unct

ion

(-)

PDF of magnitude similarity measure rM

py

y = rM

rM

Figure 4.7 – Probability density function for rM , based on Eq. (4.10) and the Mellinconvolution (4.38)

The P-value PM for this hypothesis test is based on the probability density forrM obtained as described above:

PM = PrM|rM − y| > |rM − 1| (4.41)

where the right hand side represents the probability of an observation y witha greater deviation to unity than the actual value rM − 1, in the assumptionthat the null hypothesis is true.

Figure 4.7 shows an example of the probability density function of rM ,obtained using the above described approach. The combined area to eitherside of the dotted vertical lines, below the function p (rM ), corresponds to theP-value PM defined by Eq. (4.41).

4.3.3 Flow characteristic

The pulsating flow in the exhaust manifold with close-coupled catalyst enforcesa periodic scavenging of the diffuser or pre-cat chamber. The scavenging processis determined by the diffuser volume Vd [m3], the exhausted gas volume percylinder and per cycle [m3], the number and layout of the exhaust runnersissuing into the diffuser, and the flow pulsation period Tp [s].

These quantities are combined into a non-dimensional number S [-] to char-acterize the scavenging process. The scavenging number S is used in Sect. 4.4to correlate the similarity measures rS and rM introduced in Sect. 4.3.2. S isdefined as the ratio of two time scales involved in the scavenging process:

S =Tp

Ts(4.42)

where Ts is the scavenging time scale [s] or the residence time scale of the gas


passing through the diffuser. Ts is defined as the ratio of diffuser volume Vd totime-averaged volumetric flow rate Q [m3/s] through the catalyst:

Ts =Vd

Q(4.43)

The volumetric flow rate Q can be (i) calculated from the time-averagedvelocity distribution or (ii) obtained from a reference flow rate reading. Thereference flow rate reading corresponds to a standardized orifice for the isother-mal flow rig (see Sect. 2.4.1) and a laminar flow meter for the CME flow rig(see Sect. 2.4.2).

During the initial experiments on the isothermal flow rig, Tp was based onlyon the engine speed N [rpm]:

T oldp =

120/Nnr

(4.44)

where nr is the number of runners issuing into the catalyst. The true flowperiod is one engine cycle (i.e. two crankshaft revolutions) or 120/N . Eachengine cycle features nr exhaust pulses or exhaust gas passing through thecatalyst. Thus Tp represents the apparent flow pulsation period experiencedby the manifold.

Figure 4.8 indicates the two basic time scales involved in this process: (i) theapparent flow pulsation period (Tp), which should not be confused with theengine cycle period 120/N , and (ii) the scavenging or residence time scale ofthe diffuser Ts. The dotted area represents the remaining exhaust gas fromthe previous exhaust stroke, which is being scavenged from the diffuser by thefresh incoming exhaust gas.

The statistical inference for S with the above definition of T oldp is obtained

using the principle of propagation of errors, as defined by Eq. (4.4):

δSold =√δT old

p2 + δT 2

s

'√δN2 + δQ2

' δQ (4.45)

where the uncertainties on geometrical parameters (e.g. δVd) and the enginespeed are negligible compared to the flow rate error (typically about 5 to 10 %).

The definition of the apparent pulsation period Tp according to Eq. (4.44)is no longer valid for the pulsating flow generated by the isochoric (CME) flowrig, or indeed for fired engine conditions.

The exhaust stroke in the CME flow rig consists of blowdown and displace-ment phases. This two-stage nature in combination with strong Helmholtzresonances during the displacement phase results in a smaller apparent flowpulsation period. Therefore, the following new definition of Tp is introduced:

Tp =1

fPSD(Um),max(4.46)


U #1 #3 #4 #2

T120 / N

p

a b c d

(a) (b) (c) (d)

Figure 4.8 – Periodic scavenging of the diffuser

where the frequency fPSD(Um),max [Hz] corresponds to the maximum in thepower spectral density of the time-resolved mean velocity Um (ωt). The ap-parent flow pulsation period experienced by the catalyst is better described byEq. (4.46) than by the old definition (4.44).

Figure 4.9 gives an example of the mean velocity power spectral densityfor both flow rigs, for identical engine speed and a volumetric flow rate corre-sponding to part load conditions. For the isothermal flow rig, Fig. 4.9a showsthat the peak frequency in the spectrum corresponds to fPSD,max ' nr N/120 .This is generally true for all experiments on the isothermal flow rig. As such,the value of Tp according to the new definition in Eq. (4.46) corresponds to thevalue of the old definition in Eq. (4.44). The results of Persoons et al. [88] aretherefore not undermined. As shown in Fig. 4.9b, the frequency content of theflow in the CME flow rig is much higher.

The statistical inference on Tp = f−1PSD,max is difficult to obtain. It is

assumed that, similar to the old definition of S, the greatest uncertainty isdue to Ts and not Tp. As such, δS is estimated equal to δQ, regardless of thedefinition of Tp.

The behavior of S may be summarized as follows. A high scavenging num-ber S (e.g. low engine speed and/or high flow rate) means that the diffuserscavenging occurs faster than the flow pulsation period, therefore the catalystflow distribution should be relatively unaffected by changes in S, or indeedchanges in engine speed or flow rate. A low scavenging number S (e.g. highengine speed or low flow rate) results in the opposite, meaning more interfer-ence of exhaust flow pulses from individual runners. Consequently, the flowdistribution should be more sensitive to changes in S in the lower range of S.

Other researchers use equivalent dimensionless numbers for characterizing

4.4 Experimental results 125

0 100 200 300 400 50010

-6

10-5

10-4

10-3

10-2

10-1

Frequency (Hz)

Ene

rgy

spec

tral

den

sity

of

Um

((m

/s)2 /H

z)

nr N / 120 = 40.0 Hz

fPSD,max

= 40.5 Hz

(a)

0 100 200 300 400 50010

-6

10-5

10-4

10-3

10-2

10-1

Frequency (Hz)

Ene

rgy

spec

tral

den

sity

of

Um

((m

/s)2 /H

z)

nr N / 120 = 40.0 Hz

fPSD,max

= 118.9 Hz

(b)

Figure 4.9 – Power spectral density of the time-resolved mean velocity Um (ωt) on(a) isothermal and (b) CME flow rig, for N = 1200 rpm and part load

pulsating flow in a close-coupled catalyst manifold. Benjamin et al. [17] defineJ as the ratio of pulsation period to diffuser residence time. Benjamin et al.[17] use an axisymmetric isothermal flow rig. The residence time is definedin terms of the length of the diffuser and the mean velocity in the inlet pipe,which corresponds to a single exhaust runner. J is proportional to S, definedusing Eq. (4.44) as definition for Tp.

Bressler et al. [22] define GEN or ‘gas exchange number’ as the ratio ofexhausted gas volume per cylinder per cycle to the diffuser volume. Bothpapers present relationships between flow uniformity in pulsating flow and thisdimensionless number.

In a numerical study on the conversion efficiency of a catalyst subjected topulsating flow, Tsinoglou and Koltsakis [99] non-dimensionalize the pulsationfrequency with the catalyst residence time. The pulsation index is inverselyproportional to S.

Regarding the validation of the addition principle, the results of this thesisare compared to the findings of Benjamin et al. [17] and Bressler et al. [22] inSect. 4.5.

4.4 Experimental results

Recalling the definition of the addition principle (4.1), the time-averaged di-mensionless catalyst velocity distribution in pulsating flow conditions(= U (x, y)puls) is compared to a linear combination of nr dimensionless veloc-ity distributions (= U (x, y)stat,r, where r = 1 . . . nr), obtained for stationaryflow through each of the exhaust runners.


Table 4.1 – Summary of experimental campaign

Flow rig Pulsator Stationary flow Pulsating flow OHWIsothermal RV A A 2

CH A + B A + B 2Isochoric (CME) CH B 4

The time-averaged velocity distribution obtained in pulsating conditionsU (x, y)puls is usually abbreviated to pulsating flow distribution or Upuls.

The velocity distributions obtained for stationary flow through each of theexhaust runners U (x, y)stat,r is usually abbreviated to Ustat,r.

The velocity distribution resulting from the linear combination defined byEq. (4.1) is usually abbreviated to stationary (averaged) flow distribution orUstat.

Two flow rigs are used to generate pulsating flow. The (i) isothermal flowrig set up is described in Sect. 2.2.1. The (ii) isochoric or charged motoredengine (CME) flow rig is described in Sect. 2.2.2.

The stationary flow distributions Ustat,r cannot be obtained on the iso-choric flow rig. Therefore, these measurements are always performed on theisothermal flow rig. For the rotating valve pulsator (see Sect. 2.2.1), the Ustat

measurements are performed with the valve blocked in the maximum flow rateposition. For the cylinder head pulsator (see Sects. 2.2.1 and 2.2.2), the Ustat

measurements are performed with the exhaust camshaft blocked in the positionof maximum valve lift. For each of the nr stationary flow cases, flow is onlyallowed through a single exhaust runner.

The addition principle is validated by examining the similarity between theaveraged stationary distribution Ustat defined by Eq. (4.1) and the pulsating ve-locity distribution, for identical time-averaged volumetric flow rate. Typically,the flow rate is set to the same value throughout pulsating flow experimentswith different engine speeds. These are then all compared to the same station-ary flow experiment.

Table 4.1 gives a brief overview of the experimental campaign. ‘RV’ and‘CH’ denote rotating valve and cylinder head pulsator, respectively. ‘A’ and ‘B’indicate the use of the three-runner manifold A without exhaust valve overlap,and the four-runner manifold B with exhaust valve overlap (see Sect. 2.1). Thefinal column indicates where the oscillating hot-wire anemometer (see Chap. 3)has been applied for measuring bidirectional velocity.


Each of the velocity distributions are plotted as dimensionless velocity U =U/Um , so as to better compare the distributions at different flow rate. Theactual reference volumetric flow rate Qref [m3/h] and the mean time-averagedvelocity Um [m/s] are indicated on each plot. For the isothermal flow rig,the reference flow rate corresponds to the orifice flow rate measurement (see


Sect. 2.4.1). Also indicated are: the exhaust runner (in case of a stationaryvelocity distribution), and the flow uniformity measures ηm and ηw, accordingto Eqs. (4.6) and (4.2) respectively.

The velocity distribution itself is plotted using contour lines, where the‘elevation’ U of each contour line is indicated in the vertical scale on the rightside of the plot. The unity contour U = 1 is plotted as a dashed line (

). The

x- and y-coordinates are presented in mm and correspond to the actual size ofthe catalyst cross-section. As mentioned in Sect. 2.1, all velocity measurementsare performed in a plane 25 mm downstream of the catalyst, to avoid the small-scale mixing region of the laminar jets issuing from individual catalyst substratechannels.

Below each two-dimensional plot is a one-dimensional cross-sectional plotof the velocity along the line y = 0 mm.

Manifold A (see Table 2.1)

Figures 4.10 and 4.11 show examples of velocity distributions Ustat,r obtainedon the isothermal flow rig, for stationary flow through each of the three runnersof manifold A (see Table 2.1). The rotating valve is used for the case in Fig. 4.10,and the cylinder head is used for the case in Fig. 4.11.

The linearly combined velocity distributions Ustat according to Eq. (4.1) arepresented in Fig. 4.12. For Ustat, the values for flow rate and mean velocity areonly indicative. Each corresponds to the mean of the values for the stationarydistributions Ustat,r.

For the isothermal flow rig measurements in pulsating flow conditions, theterm ‘engine speed’ N is used to quantify the flow pulsation frequency, al-though the flow rig contains no crankshaft. For each runner, the rotating valveprovides two openings per valve revolution. As such, the rotating valve speedcorresponds to N/4 [rpm]. For the cylinder head experiments, the exhaustcamshaft is driven at a speed N/2 [rpm].

Figures 4.13 and 4.14 provide comparisons between time-averaged velocitydistributions Upuls obtained in pulsating flow conditions and stationary aver-aged distributions Ustat at the same volumetric flow rate. Both are obtainedusing the rotating valve, at a comparable flow rate Qref ' 75 m3/h, yet fordifferent values of the engine speed N . Figure 4.13 corresponds to a highscavenging number (S ' 2.0) and Fig. 4.14 to a very high scavenging number(S ' 4.2). There are no cases available for low scavenging number for mani-fold A, since the relationship between the scavenging number and the additionprinciple’s validity has only been established during the experiments on man-ifold B. These occurred chronologically much later than the experiments onmanifold A.

Figures 4.15 and 4.16 provide similar comparisons between Upuls and Ustat

for the cylinder head as pulsator. Based on a visual inspection of Figs. 4.13through 4.16, the similarity is very good. This is due to the high scavengingnumber (S > 2). If S is sufficiently greater than unity, the scavenging timescale is smaller than the flow pulsation period. In that case, one would expect


0

0.5

1

1.5

2

2.5

3

3.5

4

-30 -15 0 15 300123

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.2

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1

1

1

1

1.4

1.4

1.4

1.8

1.8

1.8

2.2

2.2

2.2

2.63

Runner 1, Qref

= 74.5 m3/h

Um

= 5.465 m/s, ηm

= 0.342, ηw

= 0.689

(a)

0

0.5

1

1.5

2

2.5

3

3.5

4

-30 -15 0 15 300123

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.2

0.4 0.4

0.4

0.40.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

1

1

1

1.4

1.4

1.4

1.8

1.8

2.2

2.2

2.62.6

3

3.4

Runner 2, Qref

= 73.2 m3/h

Um

= 5.215 m/s, ηm

= 0.307, ηw

= 0.645

(b)

0

0.5

1

1.5

2

2.5

3

3.5

4

-30 -15 0 15 300123

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.2

0.4

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1

1

1

1.4

1.4

1.4

1.8

1.8

1.8

2.2

2.2

Runner 3, Qref

= 73.0 m3/h

Um

= 5.355 m/s, ηm

= 0.441, ηw

= 0.702

(c)

Figure 4.10 – Stationary velocity distributions Ustat,r for flow through each runner(a, b, c: r = 1 . . . 3) for manifold A on the isothermal flow rig with rotating valve(Qref ' 75 m3/h)


0

0.5

1

1.5

2

2.5

3

3.5

4

-30 -15 0 15 300123

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.2

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1

1

1

1.4

1.4

1.4

1.8 1.8

1.8

2.2

2.2

2.2

2.6

Runner 1, Qref

= 73.4 m3/h

Um

= 4.738 m/s, ηm

= 0.393, ηw

= 0.719

(a)

0

0.5

1

1.5

2

2.5

3

3.5

4

-30 -15 0 15 300123

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.2

0.4

0.4 0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.6

0.80.8

0.8

11

1

1

1.4

1.4

1.4 1.8

1.8

2.2

2.2

2.22.6

2.63

Runner 2, Qref

= 76.9 m3/h

Um

= 4.826 m/s, ηm

= 0.344, ηw

= 0.658

(b)

0

0.5

1

1.5

2

2.5

3

3.5

4

-30 -15 0 15 300123

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.2

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.6

0.6

0.8

0.8

0.8

1

1

1

1.4

1.4 1.4

1.8

1.8

1.8

2.22.2

Runner 3, Qref

= 77.1 m3/h

Um

= 4.891 m/s, ηm

= 0.459, ηw

= 0.723

(c)

Figure 4.11 – Stationary velocity distributions Ustat,r for flow through each runner(a, b, c: r = 1 . . . 3) for manifold A on the isothermal flow rig with cylinder head(Qref ' 75 m3/h)


0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30

Stationary averaged velocity U (-)

y (m

m)

0.3

0.4

0.4

0.4

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.8

N = 0 rpm, Qref

~ 73.6 m3/h

Um

~ 5.221 m/s, ηm

= 0.613, ηw

= 0.873

(a)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.4

0.4

0.5

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.6

1.8

N = 0 rpm, Qref

~ 75.8 m3/h

Um

~ 5.254 m/s, ηm

= 0.581, ηw

= 0.879

(b)

Figure 4.12 – Stationary averaged velocity distributions Ustat according to Eq. (4.1)for manifold A on the isothermal flow rig with (a) rotating valve and (b) cylinder head(Qref ' 75 m3/h)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30

Time-averaged velocity U (-)

y (m

m)

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1.2

1.2

1.2

1.4

1.4

1.4

N = 2810 rpm, Qref

= 75.7 m3/h

Um

= 5.400 m/s, ηm

= 0.686, ηw

= 0.902

(a)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.3

0.4

0.4

0.4

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.8

N = 0 rpm, Qref

~ 73.6 m3/h

Um

~ 5.221 m/s, ηm

= 0.613, ηw

= 0.873

(b)

Figure 4.13 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold A on isothermal flow rig with rotating valve, at high scavenging number(S = 2.134, rS = 0.960, rM = 1.119)


0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

N = 1440 rpm, Qref

= 77.3 m3/h

Um

= 5.633 m/s, ηm

= 0.690, ηw

= 0.900

(a)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.3

0.4

0.4

0.4

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.8

N = 0 rpm, Qref

~ 73.6 m3/h

Um

~ 5.221 m/s, ηm

= 0.613, ηw

= 0.873

(b)

Figure 4.14 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold A on isothermal flow rig with rotating valve, at very high scavenging number(S = 4.252, rS = 0.965, rM = 1.126)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

1

1

1

11.2

1.2

1.21.4

1.4

N = 2810 rpm, Qref

= 76.6 m3/h

Um

= 5.559 m/s, ηm

= 0.745, ηw

= 0.916

(a)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.4

0.4

0.5

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.6

1.8

N = 0 rpm, Qref

~ 75.8 m3/h

Um

~ 5.254 m/s, ηm

= 0.581, ηw

= 0.879

(b)

Figure 4.15 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold A on isothermal flow rig with cylinder head, at high scavenging number(S = 2.158, rS = 0.944, rM = 1.282)


0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.80.8

0.9

0.9

0.9

0.91

1

1

1

1.21.2

1.2

1.21.4

1.4

1.4

1.6

N = 1440 rpm, Qref

= 77.4 m3/h

Um

= 5.399 m/s, ηm

= 0.670, ηw

= 0.897

(a)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 300

1

2

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.40.4

0.5

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1.2

1.2

1.21.2

1.4

1.4

1.4

1.41.4

1.6

1.8

N = 0 rpm, Qref

~ 75.8 m3/h

Um

~ 5.254 m/s, ηm

= 0.581, ηw

= 0.879

(b)

Figure 4.16 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold A on isothermal flow rig with cylinder head, at very high scavenging number(S = 4.334, rS = 0.971, rM = 1.153)

only a minor influence of the flow conditions (engine speed, flow rate) on thevelocity distribution. This is shown by the relatively constant values for the flowuniformity (0.64 < ηm < 0.75, 0.89 < ηw < 0.92) in Figs. 4.13 through 4.16.Furthermore, a good agreement is expected between pulsating distributionsand the limit case of zero engine speed, which corresponds to the stationaryaveraged distribution. This is confirmed by the high values of rS in Table 4.3 formanifold A. Table 4.3 quantifies the similarity using the shape and magnitudesimilarity measures rS and rM , defined in Sect. 4.3.2. In addition, Table 4.3provides the 95 % confidence intervals for rS and rM , as well as the P-valuesfor the hypothesis tests HS,1 (4.16), HS,2 (4.19) and HM (4.40) described inSect. 4.3.2.

The velocity distributions show no substantial difference resulting from us-ing the rotating valve or the cylinder head. This is true for both the time-averaged velocity distribution in pulsating flow Upuls and the stationary flowdistributions Ustat,r and Ustat. This resemblance is quantified in Table 4.2,using the correlation coefficient defined as Eq. (4.12).

Manifold B (see Table 2.1)

Figures 4.17 and 4.18 show velocity distributions Ustat,r for manifold B, ob-tained for stationary flow through each of the four runners, for two different flowrates Qref . The stationary averaged distributions Ustat according to Eq. (4.1)are shown in Fig. 4.19. For manifold B, only the cylinder head has been usedas pulsator. The reason for this is twofold. (i) There is a good agreement


0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.5

1

1

1

1 1

1

1

2

2

34

Runner 1, Qref

= 65.4 m3/h

Um

= 1.667 m/s, ηm

= 0.213, ηw

= 0.808

(a)

0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.51

1

1

1 1

1

111

1

1

1

22

3

Runner 2, Qref

= 65.1 m3/h

Um

= 1.658 m/s, ηm

= 0.304, ηw

= 0.863

(b)

0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

1

1

1

1

1

11 2

Runner 3, Qref

= 63.9 m3/h

Um

= 1.627 m/s, ηm

= 0.376, ηw

= 0.911

(c)

0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

1

11

1

1

1

1

1

1

1

1

1

1

2

Runner 4, Qref

= 63.8 m3/h

Um

= 1.626 m/s, ηm

= 0.372, ηw

= 0.923

(d)

Figure 4.17 – Stationary velocity distributions Ustat,r for flow through each runner(a, b, c, d: r = 1 . . . 4) for manifold B on the isothermal flow rig with cylinder head(Qref ' 65 m3/h)


0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.51

1

1

1

1

2

2

3

3

4 5

6

Runner 1, Qref

= 130.1 m3/h

Um

= 3.288 m/s, ηm

= 0.167, ηw

= 0.736

(a)

0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.50.5

0.5

1

1

1

1

1

1

11

2

2

2

3

3 4

Runner 2, Qref

= 134.2 m3/h

Um

= 3.392 m/s, ηm

= 0.244, ηw

= 0.798

(b)

0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

1

1

1

1

2

2

3

Runner 3, Qref

= 130.7 m3/h

Um

= 3.304 m/s, ηm

= 0.269, ηw

= 0.850

(c)

0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.51

1

1

1

1

1

2

2

3 4

Runner 4, Qref

= 131.8 m3/h

Um

= 3.331 m/s, ηm

= 0.234, ηw

= 0.858

(d)

Figure 4.18 – Stationary velocity distributions Ustat,r for flow through each runner(a, b, c, d: r = 1 . . . 4) for manifold B on the isothermal flow rig with cylinder head(Qref ' 130 m3/h)


0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8 0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.90.9

0.9

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.61.8

22.

2

N = 0 rpm, Qref

~ 64.6 m3/h

Um

~ 1.645 m/s, ηm

= 0.445, ηw

= 0.919

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.60.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.2 1.4

1.4

1.4

1.4

1.6

1.61.61.6

1.8 2 2.2 2.4

N = 0 rpm, Qref

~ 131.7 m3/h

Um

~ 3.329 m/s, ηm

= 0.407, ηw

= 0.877

(b)

Figure 4.19 – Stationary averaged velocity distribution Ustat according to Eq. (4.1)for manifold B on the isothermal flow rig with cylinder head, for (a) Qref ' 65 m3/hand (b) Qref ' 130 m3/h

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1 1

1

1

1

1

1

1

1

1

1.2

1.21.2

1.4

N = 4400 rpm, Qref

= 72.2 m3/h

Um

= 1.826 m/s, ηm

= 0.696, ηw

= 0.964

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8 0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.90.9

0.9

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.61.8

22.

2

N = 0 rpm, Qref

~ 64.6 m3/h

Um

~ 1.645 m/s, ηm

= 0.445, ηw

= 0.919

(b)

Figure 4.20 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isothermal flow rig with cylinder head, at very low scavenging number(S = 0.349, rS = 0.448, rM = 1.547)


0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.4

N = 1200 rpm, Qref

= 43.3 m3/h

Um

= 1.093 m/s, ηm

= 0.694, ηw

= 0.958

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.80.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.90.9

0.9

0.9

1

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2 1.4

1.6

N = 0 rpm, Qref

~ 41.9 m3/h

Um

~ 1.060 m/s, ηm

= 0.576, ηw

= 0.945

(b)

Figure 4.21 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isothermal flow rig with cylinder head, at low to moderate scavengingnumber (S = 0.806, rS = 0.741, rM = 1.205)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

11

1.2

1.2

1.2

1.2

1.2

1.4

1.61.8

N = 1200 rpm, Qref

= 68.6 m3/h

Um

= 1.670 m/s, ηm

= 0.549, ηw

= 0.940

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8 0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.90.9

0.9

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.61.8

22.

2

N = 0 rpm, Qref

~ 64.6 m3/h

Um

~ 1.645 m/s, ηm

= 0.445, ηw

= 0.919

(b)

Figure 4.22 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isothermal flow rig with cylinder head, at moderate scavenging number(S = 1.202, rS = 0.782, rM = 1.233)


0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

11

1

1

1

1.2

1.2

1.21.2

1.4

1.4

1.4

1.41.6

1.6

1.8

22.2

2.4

N = 1200 rpm, Qref

= 117.1 m3/h

Um

= 2.961 m/s, ηm

= 0.412, ηw

= 0.895

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m) 0.6

0.7

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

11

1

1

1

1.2

1.21.2

1.2

1.4

1.4

1.4

1.41.6

1.6

1.822.22.4

N = 0 rpm, Qref

~ 110.9 m3/h

Um

~ 2.826 m/s, ηm

= 0.382, ηw

= 0.879

(b)

Figure 4.23 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isothermal flow rig with cylinder head, at high scavenging number(S = 2.090, rS = 0.965, rM = 1.076)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.60.7

0.7

0.70.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.90.9

11

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.6

1.6

1.8

22.22.4

N = 600 rpm, Qref

= 116.4 m3/h

Um

= 2.941 m/s, ηm

= 0.417, ηw

= 0.891

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m) 0.6

0.7

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

11

1

1

1

1.2

1.21.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.822.22.4

N = 0 rpm, Qref

~ 110.9 m3/h

Um

~ 2.826 m/s, ηm

= 0.382, ηw

= 0.879

(b)

Figure 4.24 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isothermal flow rig with cylinder head, at very high scavenging number(S = 4.142, rS = 0.974, rM = 1.091)


Table 4.2 – Comparison between velocity distributions for manifold A using rotatingvalve (left values) and cylinder head (right values)

Case N ηm ηw rS Figurerpm - - -

Ustat 0/0 0.61/0.58 0.87/0.88 0.957 4.12Upuls, S ' 4 1440/1440 0.69/0.67 0.90/0.90 0.948 4.14, 4.16Upuls, S ' 3 2150/2010 0.69/0.69 0.90/0.90 0.952Upuls, S ' 2 2810/2810 0.69/0.75 0.90/0.92 0.949 4.13, 4.15

between the velocity distributions obtained for manifold A with rotating valveand cylinder head (see Table 4.2). This demonstrate that there is little ex-tra information to be obtained from using the rotating valve. (ii) Using thecylinder head on the isothermal flow rig poses no appreciable difficulty, otherthan the need for forced lubrication and a more powerful electric motor (seeSect. 2.2.1).

Figures 4.20 through 4.24 show comparisons between the time-averaged ve-locity distributions Upuls and the corresponding stationary averaged distribu-tions Ustat at the same volumetric flow rate. Figures 4.20 through 4.24 rangefrom low to high scavenging number. The scavenging number for Figs. 4.23(S ' 2) and 4.24 (S ' 4) correspond to the values for Figs. 4.13 through 4.16.The similarity measure rS exhibits comparable high values. The values for rMagree not so well. It will be shown in Sect. 4.5 that the statistical evidenceprovided by rM is not as strong as rS .

As shown in Table 4.3 summarizing the isothermal flow rig experiments, agreater variation of the scavenging number S is obtained during the measure-ments on manifold B: S varies between 0.23 and 4.5, whereas S varies onlybetween 2 and 4.5 for manifold A. The cases for low (S < 0.5) and moderatescavenging number (0.75 < S < 1.5) are discussed in Sect. 4.4.2, where theseare compared to measurements on the isochoric flow rig.

4.4.2 Isochoric flow rig

Manifold B (see Table 2.1)

Figures 4.25 through 4.27 present comparisons between time-averaged velocitydistributions obtained on the isochoric (CME) flow rig (see Sect. 2.2.2) and thestationary averaged distribution for the same volumetric flow rate.

All experiments on the CME flow rig use the oscillating hot-wire anemome-ter discussed in Chap. 3. This is important due to the occurrence of flowreversal. Without the use of the OHW, the velocity would be significantlyoverestimated using standard hot-wire anemometry. The OHW is validated inSect. 5.2.1.

For Figs. 4.25 through 4.27, the scavenging numbers respectively corre-sponds to the scavenging numbers of Figs. 4.20 through 4.22 obtained on theisothermal flow rig, using the same manifold B.


0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8

0.8

0.80.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

11

111

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4 1.6 1.8

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

= 1.388 m/s, ηm

= 0.536, ηw

= 0.923

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8 0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.90.9

0.9

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.61.8

22.

2

N = 0 rpm, Qref

~ 64.6 m3/h

Um

~ 1.645 m/s, ηm

= 0.445, ηw

= 0.919

(b)

Figure 4.25 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isochoric (CME) flow rig, at very low scavenging number (S = 0.316,rS = 0.341, rM = 1.192)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m) 0.7

0.7

0.8

0.80.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.8

2

N = 1800 rpm, Qref

= 137.0 m3/h, pi = 2.15 atm

Um

= 3.449 m/s, ηm

= 0.491, ηw

= 0.892

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.60.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.2 1.4

1.4

1.4

1.4

1.6

1.61.6

1.61.8 2 2.2 2.

4

N = 0 rpm, Qref

~ 131.7 m3/h

Um

~ 3.329 m/s, ηm

= 0.407, ηw

= 0.877

(b)

Figure 4.26 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isochoric (CME) flow rig, at moderate scavenging number (S = 0.819,rS = 0.661, rM = 1.206)


0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.6

0.7

0.7

0.8

0.8

0.8 0.80.8

0.8

0.9 0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2 1.4

1.41.4

1.4

1.6

1.6

1.6

1.8

N = 2400 rpm, Qref

= 234.6 m3/h, pi = 2.00 atm

Um

= 4.207 m/s, ηm

= 0.516, ηw

= 0.882

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.6

0.60.7

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.80.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.91

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.2 1.4

1.41.4

1.4 1.6

1.6

1.61.6 1.822.2

2.4

N = 0 rpm, Qref

~ 227.3 m3/h

Um

~ 3.717 m/s, ηm

= 0.412, ηw

= 0.866

(b)

Figure 4.27 – Comparison of (a) Upuls and (b) Ustat according to Eq. (4.1), formanifold B on isochoric (CME) flow rig, at moderate to high scavenging number(S = 1.036, rS = 0.646, rM = 1.252)

In spite of the different flow rigs, the different engine speeds and flow rates,each pair of figures with comparable scavenging number (S ' 0.3 for Figs. 4.25and 4.20, S ' 0.7 for Figs. 4.26 and 4.21, S ' 1 for Figs. 4.27 and 4.22)yield comparable values of the shape similarity measure (rS = 0.341 and 0.450,rS = 0.661 and 0.781, rS = 0.646 and 0.782). For the magnitude similaritymeasure, the agreement is less convincing (rM = 1.192 and 1.549, rM = 1.206and 1.205, rM = 1.252 and 1.233).

4.4.3 Summary of the resultsTables 4.3 and 4.4 summarize the experiments on the isothermal and isochoricflow rig, respectively. These experiments are used for the validation of theaddition principle.

Tables 4.3 and 4.4 provide the 95% confidence limits for rS and rM . Therespective confidence intervals are [rlow

S , rhighS ] and [rlow

M , rhighM ]. Due to the spe-

cific statistical inference discussed in Sect. 4.3.2, these limits are asymmetrical.Furthermore, the table gives the P-values for the hypothesis tests describedin Sect. 4.3.2. Recall from the definition of the hypothesis tests (Eqs. (4.16),(4.19) and (4.40)) that the interpretation for the P-values differs:

• PS,1 < 0.05 (= α) corresponds to a significantly positive correlation co-efficient.

• PS,2 < 0.05 corresponds to a significantly lower correlation coefficientthan the arbitrary high value ρcrit (= 0.9).


• PM < 0.05 corresponds to a value of rM significantly different from unity.

In summary, significant similarity corresponds to a low value of PS,1, a highvalue of PS,2 and a low value of PM . The P-values in Tables 4.3 and 4.4 thatbear evidence against similarity are printed in italic.

Background: How to interpret P-values For a general statisticalhypothesis test H, the P-value P quantifies the strength of the statisticalargument against the null hypothesis H0 and in favor of the alternativehypothesis H1. The smaller P , the stronger the evidence. The P-value isa continuous measure, and the hypothesis tests should not be regardedas discrete (similarity versus no similarity) tests. Instead, the followinginterpretation may be used:

0.10 < P No evidence against the null hypothesis.0.05 < P < 0.1 Weak evidence against the null hypothesis, in

favor of the alternative.0.01 < P < 0.05 Moderate evidence against the null hypothesis, in

favor of the alternative.0.001 < P < 0.01 Strong evidence against the null hypothesis, in

favor of the alternative.P < 0.001 Very strong evidence against the null hypothesis,

in favor of the alternative.

The values listed in Tables 4.3 and 4.4 should be regarded with this inmind.

Tables 4.3 and 4.4 do not explicitly mention the relative uncertainties for theother variables (N , Qref and S). The uncertainty on the engine speed δN isnegligible. As mentioned in Sect. 4.3.3, δS ' δQref , which is approximately5% as derived in Sect. 2.4.1.

Tables 4.3 and 4.4 list both the old and new versions of the scavenging num-ber (Sold and S), using the different definitions of the apparent pulsation periodTp according to Eq. (4.44) and Eq. (4.46), respectively. Since the isothermalflow rig lacks a blowdown phase, the new and old definitions of Tp yield nearlyidentical results in Table 4.3. The deviation on S is below 0.1, except in onecase featuring strong Helmholtz resonances, as discussed in Sect. 5.3. Since theCME flow rig features a two-stage (instead of a single pulse) exhaust stroke,the new definition of Tp according to Eq. (4.46) is typically half of the old valueaccording to Eq. (4.44), which explains the approximate difference by a factortwo between Sold and S in Table 4.3.

Based on Table 4.3, some observations can be made with regard to thegeometrical differences of manifolds A and B. The catalyst cross-section ofmanifold B is considerably greater than for manifold A. For the same flowrate, the mean velocity is inversely proportionally smaller for manifold B. Dueto the lower velocity and the longer substrate (see Table 2.1), the residencetime of the exhaust gas in manifold B’s catalyst is greater. Consequently, sois its conversion efficiency. On the other hand, the greater cross-section makesit more difficult to obtain a good flow uniformity. This is clearly shown inFigs. 4.24 and 4.23. The difference in scavenging number is partly due to the


Tab

le4.

3–

Sum

mar

yof

expe

rim

ents

onth

eis

othe

rmal

flow

rig

Cas

e†N

pi

Qref

Sold

Sr S

rlow

Srh

igh

SP

S,1

PS

,2r M

rlow

Mrh

igh

MP

MFig

ure

rpm

atm

m3/h

--

--

--

--

--

A,R

V14

40-

77.3

4.21

74.

264

0.96

50.

926

0.98

30.

000

1.00

01.

126

0.77

71.

176

0.60

94.

1421

50-

78.2

2.95

32.

996

0.96

60.

930

0.98

4"

"1.

135

0.76

31.

188

0.58

028

10-

75.7

2.11

82.

134

0.96

00.

917

0.98

1"

"1.

119

0.80

31.

195

0.53

84.

13A

,CH

1440

-77

.44.

279

4.33

40.

971

0.93

90.

986

""

1.15

30.

760

1.22

20.

558

4.16

2010

-76

.83.

053

3.10

00.

957

0.91

10.

980

""

1.19

00.

800

1.25

10.

445

2810

-76

.62.

178

2.15

80.

944

0.88

40.

973

""

1.28

20.

824

1.28

10.

353

4.15

B,C

H60

0-

43.8

1.56

11.

561

0.88

20.

793

0.93

4"

"1.

056

0.64

31.

350

0.80

161

0-

61.5

2.16

32.

158

0.88

40.

797

0.93

5"

"1.

154

0.59

51.

595

0.65

560

0-

98.3

3.49

83.

498

0.96

50.

938

0.98

1"

"1.

055

0.56

71.

687

0.86

660

0-

116.

44.

142

4.14

20.

974

0.95

30.

986

""

1.09

10.

590

1.68

40.

780

4.24

1200

-43

.30.

770

0.80

60.

741

0.57

10.

849

"0.

910

1.20

50.

725

1.35

60.

476

4.21

1200

-68

.01.

211

1.20

20.

782

0.63

30.

875

"0.

976

1.23

30.

633

1.63

00.

491

4.22

1200

-99

.61.

772

1.77

70.

956

0.92

00.

976

"1.

000

1.06

80.

569

1.67

10.

835

1200

-11

7.1

2.08

52.

090

0.96

50.

937

0.98

1"

1.00

01.

076

0.58

61.

716

0.82

04.

2320

00-

67.2

0.71

80.

748

0.72

40.

547

0.83

9"

0.87

01.

444

0.70

41.

633

0.36

828

10-

64.1

0.49

50.

520

0.62

80.

410

0.77

8"

0.48

31.

600

0.80

31.

657

0.23

636

00-

73.3

0.44

00.

220

0.46

30.

196

0.66

60.

001

0.05

71.

584

0.81

41.

712

0.18

244

00-

72.2

0.35

10.

349

0.44

80.

178

0.65

60.

001

0.04

41.

547

0.76

91.

679

0.22

04.

20†

Sym

bols

‘A’an

d‘B

’de

note

man

ifold

sA

and

B;‘R

V’an

d‘C

H’de

note

the

use

ofth

ero

tating

valv

ean

dcy

linde

rhe

adas

puls

ator

s.T

heva

lue

ofp

iis

not

appl

icab

leto

the

isot

herm

alflo

wri

g.


Tab

le4.

4–

Sum

mar

yof

expe

rim

ents

onth

eis

ocho

ric

(CM

E)

flow

rig

Cas

e†N

pi

Qref

Sold

Sr S

rlow

Srh

igh

SP

S,1

PS

,2r M

rlow

Mrh

igh

MP

MFig

ure

rpm

atm

m3/h

--

--

--

--

--

B,C

H12

000.

9850

.20.

893

0.18

30.

122

-0.1

780.

401

0.21

30.

000

1.15

10.

780

1.30

10.

468

1200

1.55

70.9

1.26

10.

316

0.34

10.

053

0.57

70.

011

0.00

61.

192

0.61

31.

428

0.63

84.

2518

000.

9779

.70.

946

0.47

80.

334

0.04

50.

572

0.01

20.

005

1.20

10.

627

1.50

40.

575

1200

2.21

97.3

1.73

10.

583

0.55

40.

311

0.72

90.

000

0.21

81.

180

0.57

11.

547

0.64

918

001.

5611

0.6

1.31

20.

439

0.51

40.

260

0.70

2"

0.12

71.

223

0.55

31.

525

0.65

818

001.

5510

4.1

1.23

50.

413

0.52

50.

274

0.71

0"

0.14

81.

228

0.59

81.

587

0.58

518

002.

1513

7.0

1.62

50.

819

0.66

10.

456

0.79

9"

0.62

61.

206

0.66

81.

472

0.49

718

002.

2014

6.5

1.73

90.

879

0.64

90.

439

0.79

2"

0.57

40.

998

0.58

81.

378

0.99

24.

2624

001.

5318

7.7

1.67

00.

830

0.61

50.

392

0.76

9"

0.42

61.

147

0.63

41.

466

0.63

724

002.

0023

4.6

2.08

81.

036

0.64

60.

435

0.79

0"

0.55

91.

252

0.70

11.

469

0.41

04.

2730

001.

5323

7.4

1.69

00.

838

0.59

80.

369

0.75

80.

000

0.36

11.

267

0.71

41.

449

0.40

2


large diffuser volume of manifold B. Furthermore, manifold B features fourinstead of three runners, which implies a smaller pulsation period Tp for thesame engine speed.

Table 4.3 demonstrates a monotonous behavior of rS versus S in the isother-mal flow rig experiments. This is not entirely present in the isochoric flow rigexperiments (see Table 4.4). As a particular example, since the scavengingnumber is greater for Fig. 4.27 (S = 1.036) than for Fig. 4.26 (S = 0.819), onewould expect the value of rS to be equally greater. This is not the case. How-ever, as indicated in Table 4.4, the confidence limits for rS become increasinglywide as the value of rS decreases. This is due to the skewed sampling distribu-tion of a positive correlation coefficient (see Sect. 4.3.2). Given the fact thatrS decreases for decreasing S, the confidence limits on rS inevitably increaseas S decreases.

Overall, the combined results presented in Sects. 4.4.1 and 4.4.2 indicatethat the scavenging number S is correlated to the degree of similarity betweensteady and pulsating distributions, and thus to the addition principle’s validity.Upon comparing the stationary averaged and pulsating distributions Ustat andUpuls in Figs. 4.13 through 4.27, it shows that the magnitude similarity measurerM is consistently greater than unity. Given its definition (4.28), the flowuniformity is consistently higher for pulsating than for stationary flow. Thequantification and statistical significance of the similarity based on shape (rS)and magnitude (rM ) are presented in Table 4.3 for the isothermal flow rig andTable 4.4 for the isochoric (CME) flow rig.

In the CME flow rig experiments (see Table 4.4), the scavenging numbervaries roughly between 0.2 and 1, whereas the scavenging number in the isother-mal flow rig experiments (see Table 4.3) varies roughly between 0.2 and 4.5.Both for a fired engine and the CME flow rig, the catalyst volumetric flow rateQ increases linearly with the engine speedN , the intake manifold density ρi andthe exhaust gas temperature Te, at least as a first approximation. Combiningthis with Eqs. (4.43), (4.44) and (4.42) shows that S is nearly independent of Nand varies mainly with engine load. S increases for a variation from zero to fullengine load. By contrast, the isothermal flow rig allows the pulsation frequency(i.e. the engine speed) and flow rate (i.e. the engine load) to be controlled inde-pendently, thus enabling a wider range of scavenging number than physicallypossible in a fired engine. The scavenging number does not differ significantlybetween fired engine conditions and the CME flow rig (see Sect. 2.3).

4.5 Interpretation of the results

The data used in Figs. 4.28 and 4.29 correspond to the values in Tables 4.3and 4.4. Figure 4.28 shows the non-dimensional correlation of both similaritymeasures rS and rM versus the old definition of the scavenging number Sold,using Eq. (4.44). The CME flow rig experiments are plotted as crosses (

),

whereas the other markers ( ,

,

) represent experiments on the isother-

mal flow rig. In the figure legends, ‘A’ and ‘B’ denote manifold types A and B,

4.5 Interpretation of the results 145

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

rS’ = 1 - exp(- Sold / 0.621)

(R2 = 0.96)

Scavenging number Sold

(-)

Shap

e si

mila

rity

mea

sure

rS (

-)

ISOT, A, RVISOT, A, CHISOT, B, CHCME, B, CHrS’

(a)

0 1 2 3 4 51

1.1

1.2

1.3

1.4

1.5

1.6

rM

’ = 1.104 + 0.879 exp(- Sold / 0.621)

(R2 = 0.82)

Scavenging number Sold

(-)

Mag

nitu

de s

imila

rity

mea

sure

rM

(-)

ISOT, A, RVISOT, A, CHISOT, B, CHCME, B, CHrM

’

(b)

Figure 4.28 – Correlations of similarity measures (a) rS and (b) rM versus scaveng-ing number Sold, using the old definition of T old

p (4.44)

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

rS’’ = 1 - exp(- S / 0.723)

(R2 = 0.91)

Scavenging number S (-)

Shap

e si

mila

rity

mea

sure

rS (

-)

ISOT, A, RVISOT, A, CHISOT, B, CHCME, B, CHrS’’

(a)

0 1 2 3 4 51

1.1

1.2

1.3

1.4

1.5

1.6

rM

’’ = 1.118 + 0.337 exp(- S / 0.723)

(R2 = 0.30)


Mag

nitu

de s

imila

rity

mea

sure

rM

(-)


’’

(b)

Figure 4.29 – Correlations of similarity measures (a) rS and (b) rM versus scaveng-ing number S, using the new definition of Tp (4.46)


and ‘RV’ and ‘CH’ denote rotating valve or cylinder head as pulsator.The exponential correlation fits r′S = 1 − exp

(−Sold

/S′crit,S

)and r′M =

r′M,∞ + c′M exp(−Sold

/S′crit,M

)are least square fitted to the isothermal flow

rig experiments, excluding the experiments on the CME flow rig.Figure 4.29 shows the correlation versus the new definition of the scavenging

number S, using Eq. (4.46). The points corresponding to the isothermal flowrig experiments remain roughly unchanged with respect to Fig. 4.28. However,the crosses (

) representing the CME flow rig experiments now correlate very

well with the isothermal flow rig experiments. Correspondence is remarkablygood for rS yet only moderate for rM . Indeed, the correspondence seems toeven slightly deteriorate for rM .

In Fig. 4.29b, the crosses ( ) representing the CME flow rig cases appear

to deviate from the isothermal flow rig cases. Due to the greater uncertaintyon rM and the limited range of S obtained of the CME flow rig, the deviationmay not be considered very significant. Nevertheless, further experiments areclearly required to explain this deviation.

The form of the exponential correlation fits is altered into r′′S = 1−exp (−S/Scrit ) and r′′M = r′′M,∞ + c′′M exp (−S/Scrit ). The critical value Scrit

for the rM correlation is set equal to the value obtained from the rS correlation.The resulting correlations for the similarity measures rS and rM versus the

scavenging number S are: r′′S = 1− exp (−S/0.723) ; R2 = 0.91

r′′M = 1.118 + 0.337 exp (−S/0.723) ; R2 = 0.30(4.47)

where the critical value of the scavenging number Scrit = 0.723. These cor-relations combine the CME flow rig experiments with the isothermal flow rigexperiments, obtained for two types of exhaust manifold with and withoutexhaust valve overlap, and for a rotating valve and cylinder head as pulsator.

Regarding the statistical significance of rS , the limits in Eq. (4.25) for signif-icant similarity based on hypothesis test HS,1 (4.16) hold for most experimentslisted in Tables 4.3 and 4.4. Indeed, the P-values PS,1 are smaller than thesignificance level α = 0.05, with one exception.

The hypothesis test HS,2 (4.19) tests whether the observed value of rS issignificantly smaller than a ‘high’ correlation value ρcrit. In Sect. 4.3.2, thiscritical value is arbitrarily chosen as ρcrit = 1 − e−1 ' 0.63. This choicebecomes clear in light of the remarkable correlation fit between rS and S. ρcrit

corresponds to the expected correlation coefficient when the scavenging numberS equals its critical value Scrit.

The P-values PS,2 in Tables 4.3 and 4.4 are mostly larger than 0.05, indi-cating weak or no evidence against the null hypothesis, i.e. the values of rS arenot significantly lower than ρcrit. For a very low scavenging number (S . 0.3,rS . 0.5) PS,2 is smaller than the significance level, which indicates evidenceagainst similarity.

Concerning the P-values PM of hypothesis test HM (4.40), a value of PM

greater than 0.05 indicates there is no statistically significant deviation between

4.5 Interpretation of the results 147

Table 4.5 – Monte Carlo-based 95% uncertainty estimate for the fit parameters inEq. (4.47) and Figs. 4.29 and 4.28

Parameter Value Error Figure- -

Using the new definition of Tp (4.46):Scrit 0.723 ± 0.052 4.29r′′M,∞ 1.118 ± 0.057c′′M 0.337 ± 0.149Using the old definition of Tp (4.44):S′crit 0.621 ± 0.069 4.28r′M,∞ 1.104 ± 0.061c′M 0.879 ± 0.284

the value of rM and unity. In other words, if PM > 0.05, similarity cannot beoverruled. In Tables 4.3 and 4.4, values for PM are consistently greater than0.05. On the other hand, rM is always larger than unity (with one exception),indicating that the flow uniformity is higher in pulsating than in steady flowconditions. Nevertheless, the HM (4.40) hypothesis test does not indicate asignificant difference between steady and pulsating flow distributions.

The virtual absence of statistical evidence based on rM is a problem which isdifficult to overcome. Instead of the present definition of rM in Eq. (4.28) whichis based on the mean-to-maximum velocity ratio ηm (4.6), other definitionshave been tried without success. In particular, defining rM as the ratio of twoWeltens’ uniformity indices ηw (4.2) leads to much worse results in terms ofthe correlation fit in Fig. 4.29b and the statistical strength.

The evidence based on rM is weaker when compared to rS . Yet strictlystatistically speaking, the addition principle is valid for almost the entire rangeof S. Taking into account Eq. (4.47), it seems however more appropriate tostate that the addition principle is valid when S exceeds the critical valueScrit = 0.723, corresponding roughly to rS > 1− e−1 = 0.63 and rM < 1.24.

The dashed lines in Figs. 4.29 and 4.28 correspond to the 95 % confidencebounds on the fitted curve. The estimated uncertainties on the fit parametersare shown in Table 4.5. These errors are determined using a Monte Carlo-like simulation. A total of 1024 sets of

[S, Sold, rS , rM

]are constructed using

a normally distributed random number generator. Each set is a collection ofrandomized observations of S + ∆S, Sold + ∆S, rS + ∆rS and rM + ∆rM ,as listed in Tables 4.3 and 4.4. According to Sect. 4.3.3, the uncertainty ∆Sis assumed constant, and equal to 0.05. The uncertainties ∆rS and ∆rM aredetermined according to the sampling distribution of each quantity, as discussedin Sects. 4.3.2 and 4.3.2.

For each of the 1024 randomized sets, the corresponding curves are fitted.This results in a collection of 1024 values for each fit parameter Scrit, r

′′M,∞, c

′′M

and S′crit, r′M,∞, c

′M . Based on these sampling distributions, the uncertainty on

each parameter is estimated, resulting in the values in Table 4.5.


flow path is closed resulting in intermittent wall jets athigher frequencies.

The reasons for the increase in flow uniformity athigher frequencies are possibly two fold. First, it wouldseem that at high frequency the flow does not have suffi-cient time to establish the inertia dominated steady flowregimes associated with high Reynolds number flows, thatis separation at the throat and large recirculation zoneswithin the diffuser volume. At low frequency, separation atthe diffuser inlet may be more likely at the peak of thepulse as the flow is quasi-steady and hence the flow mal-distribution may be expected to be similar to that understeady flow conditions as shown in Fig. 6. Second, theenhanced mixing within the diffuser at higher frequenciescould also produce flatter profiles. At low values of J thereis the possibility of more than one pulse residing in thediffuser volume at any one time leading to pulse interac-tion and increased mixing. Increasing the residence timein the diffuser (say by increasing the diffuser length)would increase the probability of such an occurrence.There is also a possibility that wave dynamics could becontributing to the increased mixing at higher frequencies.However, pressure measurements recorded 30 mmdownstream of the rear face of the catalyst (P2 in Fig. 11a)do not indicate any strong reflections from the open end ofthe sleeve and it is therefore concluded that such effectsare probably secondary.

3.5Non-dimensional correlationsThe observation of improved flow profiles as Re reducesand frequency increases suggests that there is a functionalrelationship between the maldistribution index and thesevariables. Clearly the length of the diffuser is also impor-tant as mentioned above. To examine if general relation-ships could be derived two additional 180 diffusers weretested. The standard diffuser length (L0) is 61.5 mm longand the additional diffusers were of lengths 79.85 (L1) and119.15 mm (L2). Velocity profiles for L1 and L2 were takenfor high Re in the range of 70,000–110,000 for all thefrequencies. The results have been plotted in Fig. 14a asnon-uniformity index against the non-dimensional pa-rameter, J. The results collapse reasonably well whenplotted in this form. Figure 14b shows the data for the 60diffuser and 152 mm substrate plotted similarly. Suchcorrelations could form a useful basis for design engineersfaced with the task of reducing flow maldistribution inautocatalyst systems.

4ConclusionThis study has examined the effect of pulsating flow withinautomotive catalyst systems. The flow distribution as ex-hibited by velocity profiles at the substrate exit has been

Fig. 13. a Inlet pulse shape from ensemble averaged velocity andb velocity profiles at the rear of the substrate at 100 Hz

Fig. 14a, b. Non-uniformity index against non-dimensional param-eter, J for a 180 diffuser and b 60 diffuser using 152 mm substrate

638

Figure 4.30 – Non-uniformity index versus J (Note: cases (a) and (b) are fordifferent diffusers) (Source: [17])

As mentioned in the literature survey (Sect. 1.4.1), the present results areconfirmed to some extent by findings from other researchers. Benjamin et al.[17] define the non-dimensional number J as the ratio of pulsation period todiffuser residence time. By contrast to the definition in this thesis (4.43), theresidence time is defined based on the mean runner velocity Urun

m and thediffuser length Ld:

J =1/f

Ld/Urunm

Benjamin et al. [17] (4.48)

As such, this definition assumes that a free jet is established in the ‘diffuser’, andthat no actual diffusion takes place. J is nevertheless very similar to the scav-enging number S (4.42). Figure 4.30 shows a correlation of a non-uniformitymeasure versus J . Upon inverting the y-axis values from a non-uniformityinto a uniformity measure, Fig. 4.30 compares qualitatively to the evolutionof rM in Fig. 4.29b. Indeed, rM equals by definition (4.28) a flow uniformitymeasure (based on the mean-to-maximum velocity ratio ηm) in pulsating flow,relative to the corresponding uniformity measure in steady flow. Therefore, theincreasing flow uniformity in pulsating flow for decreasing S is confirmed byFig. 4.30.

Bressler et al. [22] define GEN [-] as the ratio of exhausted gas volume percylinder per cycle Vexh [m3] to the diffuser volume Vd [m3]. Upon dividingnumerator and denominator of this ratio by the engine speed N , it becomesclear that GEN is proportional to S, at least according to the old definition of

4.6 Discussion: A physical interpretation 149

T oldp (4.44):

GEN =Vexh

Vd=

1/NVd/(N Vexh)

∼ S Bressler et al. [22] (4.49)

Although no correlation is given by Bressler et al. [22], their conclusions indi-cate that the flow uniformity in pulsating flow is unaffected by engine speedwhen GEN remains constant. Also, the authors [22] conclude that the flowuniformity in pulsating flow is always higher than for steady flow. Further-more, the deviation between the flow uniformity in pulsating flow and steadyflow is minimal for high values of GEN (i.e. high values of S) and increases fordecreasing GEN (i.e. low values of S).

4.6 Discussion: A physical interpretation

4.6.1 Scalar mixing analogy

Figure 4.29 and the correlations in Eq. (4.47) provide substantial evidence thatthe addition principle remains valid under various conditions. The elegance ofEq. (4.47), at least for rS , further supports that the scavenging number is thecorrect choice of non-dimensional group to describe this flow.

A remarkable analogy seems to hold between the current problem and thescavenging of a volume with a scalar quantity, e.g. a species concentration. Forinstance, assume incompressible flow through a perfectly stirred volume V [m3]with one inlet and one outlet, containing a volumetric concentration φ (vol %)of some compound. The following partial differential equation describes theconcentration evolution in time inside the perfect mixing volume:

∂ (V φ)∂t

= V∂φ

∂t= Qφi −Qφ (4.50)

where Q is the volumetric flow rate [m3/s] and φi is the inlet concentra-tion (vol%). This corresponds to the following transfer function in the Laplacedomain:

φ

φi(s) =

1τs s+ 1

(4.51)

where s is the Laplace variable (s = jω) [s−1] and τs is the scavenging timeconstant [s], defined as τs = V /Q . The scavenging time τs may be regarded asthe mean residence time of fluid in the mixing volume. Assuming a stepwisechange in the inlet concentration φi at time t = 0, and an initial concentrationφ(t = 0) = 0, the solution to the above partial differential equation is:

φ

φi(t) = 1− exp (−t/τs ) (4.52)

Equation (4.52) expresses to what extent the volume is scavenged, as afunction of the non-dimensional time t/τs . If t/τs is sufficiently large, the


solution becomes independent of t/τs . The non-dimensional time correspondsto the scavenging number S used to characterize the pulsating flow in theexhaust manifold.

The remarkable correlation fit in Eq. (4.47) for rS suggests that this complexmulti-dimensional flow behaves essentially like a first order zero-dimensionalscavenging process of a scalar quantity.

The flow conditions in the mixing volume may be such that only part ofthe volume takes part in the mixing process. For instance, the trace speciesintroduced at the inlet may not penetrate into recirculation zones that areformed in corners or near a sudden expansion inlet. In that case, the meanresidence time τs,eff = Veff/Q decreases with respect to the perfect mixingcase, where τs = V /Q . The ratio of the residence time scales τs,eff/τs variesbetween zero and unity, and is a measure of the quality of the mixing process.The ratio τs,eff/τs can also be regarded as the ratio of effective to geometricvolume τs,eff/τs = Veff/V .

4.6.2 Hypothesis: Collector efficiency

In light of the above introduced analogy with a scalar mixing process, the criti-cal scavenging number Scrit = 0.723 < 1 suggests that only part of the diffuservolume may be active during the scavenging process. From the introduction ofan alternate scavenging number S′:

S′ =S

Scrit=

Tp

Scrit Vd/Q=

Tp

Vd,eff/Q(4.53)

follows an effective diffuser volume Vd,eff = Scrit Vd. The velocity distributionsin Figs. 4.20 through 4.27 indeed indicate that some parts of the catalyst inmanifold B are subject to a very low flow rate, particularly the leftmost andcentral areas. Since rM increases for decreasing S and S is inversely propor-tional to the diffuser volume Vd, the flow uniformity in pulsating flow increasesfor an increasing diffuser volume. As such, the ratio of the effective to actualdiffuser volume Vd,eff/Vd could be interpreted as a collector efficiency withrespect to catalyst flow uniformity:

ηD =Vd,eff

Vd= Scrit (4.54)

The term collector efficiency should be regarded as the effectiveness of theuse of the diffuser volume in distributing the flow across the catalyst cross-section. It is inappropriate to denote this effectiveness as the ‘diffuser’ efficiency,since the shape of the exhaust runners plays a major role in the flow distributionas well. Therefore, the term ‘collector’ is used, comprising the exhaust runnersand diffuser.

The collector efficiency ηD equals the critical scavenging number. In otherwords, the higher the critical scavenging number Scrit, the more efficiently thediffuser distributes the exhaust gas throughout the catalyst cross-section.

4.6 Discussion: A physical interpretation 151

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

rS’’ = 1 - exp(- S / 0.722)

(R2 = 0.88)


Shap

e si

mila

rity

mea

sure

rS (

-)

ISOT, B, CHCME, B, CHrS’’

(a)

0 1 2 3 4 51

1.1

1.2

1.3

1.4

1.5

1.6

rM

’’ = 1.084 + 0.403 exp(- S / 0.722)

(R2 = 0.32)


Mag

nitu

de s

imila

rity

mea

sure

rM

(-)

ISOT, B, CHCME, B, CHrM

’’

(b)

Figure 4.31 – Correlations of similarity measures (a) rS and (b) rM versus scaveng-ing number S, for experiments on manifold B

Table 4.6 – Monte Carlo-based 95% uncertainty estimate for the fit parameters inEq. (4.55) and Fig. 4.31

Parameter Value Error Figure- -

Using the new definition of Tp (4.46):Scrit 0.722 ± 0.056 4.31r′′M,∞ 1.084 ± 0.097c′′M 0.403 ± 0.207

The correlation in Eq. (4.47) and the resulting value for the critical scav-enging number Scrit = 0.723 are obtained for the combined experiments onmanifolds A and B, using two pulsator devices and two types of flow rigs. Ifthe above assumption is correct, the critical scavenging number is a manifoldgeometry-dependent measure, which should differ from manifold A to mani-fold B.

Unfortunately, the scavenging number range (2 < S < 4.5) for the availableexperiments on manifold A is, in retrospect, inappropriately chosen. Based onthe experiments on manifold A, no critical scavenging number can be obtained.

Since the scavenging number range is much wider for manifold B, the exper-iments on manifold B contribute the most to the value of the critical scavengingnumber obtained from the correlation in Eq. (4.47).

Figure 4.31 shows the correlations of the similarity measures rS and rMversus the scavenging number using the new definition of Tp (4.46), similar toFig. 4.29, yet only including the experiments on manifold B. The fitted curvesare:


r′′S = 1− exp (−S/0.722) ; R2 = 0.88

r′′M = 1.084 + 0.403 exp (−S/0.722) ; R2 = 0.32(4.55)

Using the same Monte Carlo simulation approach as used previously inSect. 4.5, the uncertainty on the fit parameters is estimated and given in Ta-ble 4.6.

For the experiments performed on manifold B, including the isothermaland isochoric (CME) flow rig experiments, the collector efficiency ηD (= Scrit)equals 0.722, with an estimated 95% uncertainty of 0.056.

Further studies are needed to confirm the hypothesis of the existence ofa collector efficiency. In particular, the effect of the collector geometry (e.g.shape of the exhaust runners, entrance angle of the runners in the diffuser)on the critical scavenging number should be investigated using a number ofgeometrical variants. This might be the focus of future research.

4.7 ConclusionChapter 4 investigates the validity of the addition principle (4.1) for pulsatingflow in two close-coupled catalyst manifolds A and B (see Sect. 2.1). Theaddition principle states that the time-averaged catalyst velocity distributionin pulsating flow Upuls equals a linear combination of velocity distributionsobtained for steady flow through each of the exhaust runners Ustat, accordingto Eq. (4.1).

The results obtained on an isothermal and isochoric (CME) flow rig arein good agreement, in spite of the appreciable difference in the pulsating flowgenerated by both flow rigs (see Sect. 2.3.

The CME flow rig generates cold pulsating flow that resembles fired engineconditions better than the isothermal flow rig, featuring a two-stage exhauststroke consisting of blowdown and displacement phases. The exhaust strokeflow similarity between CME and fired conditions is incomplete. Nevertheless,combined with Helmholtz resonances (see Sect. 5.3) intrinsic to the manifold,the pulsating flow features a similar frequency content to fired engines [70, 81,59]. The increased frequency content compared to the isothermal flow rig leadsto a introduction of a new definition of the apparent flow pulsation period Tp

in Eq. (4.46).For the experiments on the isochoric flow rig, an oscillating hot-wire anemo-

meter (OHW) is used to measure bidirectional velocity, with a maximum mea-surable negative velocity of −1 m/s. The effect of using the OHW cannotbe directly observed in the time-averaged velocity distributions shown in thischapter. Nevertheless, the accuracy of the velocity measurements is greatlyimproved over using standard hot-wire anemometry. The beneficial aspects ofthe OHW for the isochoric flow rig experiments are discussed in Sect. 5.2.1.

The scavenging number S defined in Eq. (4.42) using the new apparent pul-sation period Tp definition in Eq. (4.46) forms the appropriate non-dimensional

4.7 Conclusion 153

number to characterize the pulsating flow. The non-dimensional measuresrS (see Sect. 4.3.2) and rM (see Sect. 4.3.2) quantify the similarity betweenthe Ustat and Upuls distributions based on shape and magnitude, respectively.These measures are used to quantify the validity of the addition principle.

The results from the entire measurement campaign are combined in Fig. 4.29and Tables 4.3 and 4.4. Figure 4.29 shows the good correlation between thesimilarity measures rS and rM and the scavenging number S. The validityof the addition principle is quantified in Tables 4.3 and 4.4 in terms of thestatistical significance of rS and rM , as discussed by Sect. 4.3.2.

The correlations in Eq. (4.47) are least-square fitted to the values of rS , rMand S:

r′′S = 1− exp (−S/0.723) ; R2 = 0.91

r′′M = 1.118 + 0.337 exp (−S/0.723) ; R2 = 0.30

Strong statistical evidence is given in support of the addition principle, fornearly the entire range of S. However, no clear validity limit can be derivedbased on the statistical significance of rS and rM . Therefore, the practical limitof the addition principle’s validity is when S exceeds the critical scavengingnumber Scrit = 0.723 (± 0.052), corresponding roughly to rS > 1− e−1 = 0.63and rM < 1.24.

Other authors [17, 22, 99] have used non-dimensional numbers similar toS to characterize the pulsating flow in close-coupled catalyst manifolds. How-ever, the original contribution of this work is to relate S to the flow distributionsimilarity between pulsating and stationary flow conditions using rS and rM ,and furthermore to derive the validity of the addition principle from that rela-tionship.

Based on the elegance of the rS correlation in Eq. (4.47), this complexmulti-dimensional flow behaves essentially like a zero-dimensional scalar mixingprocess. In that respect, the critical scavenging number Scrit may be consideredthe ratio of the effective to actual diffuser volume. As such, the hypothesisis formulated that Scrit corresponds to a collector (i.e. runners and diffuser)efficiency ηD with respect to catalyst flow uniformity. By maximizing thecollector efficiency ηD, the flow uniformity is optimized, and consequently so isthe catalyst durability, conversion efficiency and exhaust system backpressure.The correlations in Eq. (4.47) are valid for two different exhaust manifolds. InSect. 4.6.2, the correlations in Eq. (4.55) are obtained only for the experimentson manifold B. Based on these correlations, the critical scavenging number orhypothesized collector efficiency ηD yields 0.722 (± 0.056).

Further investigations are required to determine (i) whether Scrit indeedcorresponds to a collector efficiency, and (ii) to what extent the collector effi-ciency depends on the manifold geometry.

The contents of this chapter have been published in two international jour-nals with review:


[86] T. Persoons, A. Hoefnagels, and E. Van den Bulck. Exper-imental validation of the addition principle for pulsating flow inclose-coupled catalyst manifolds. J. Fluids Eng.-Trans. ASME,128(4):656–670, 2006. http://dx.doi.org/10.1115/1.2201646.

[88] T. Persoons, E. Van den Bulck, and S. Fausto. Study of pul-sating flow in close-coupled catalyst manifolds using phase-lockedhot-wire anemometry. Exp. Fluids, 36(2):217–232, 2004. http://dx.doi.org/10.1007/s00348-003-0683-0

http://dx.doi.org/10.1115/1.2201646

http://dx.doi.org/10.1007/s00348-003-0683-0

http://dx.doi.org/10.1007/s00348-003-0683-0

Chapter 5

Flow dynamics

“A theory is something nobody believes, except the person who made it.An experiment is something everybody believes, except the person whomade it.”

Albert Einstein (German-born American physicist, 1879, †1955)

This chapter focuses on the time-resolved27 aspects of the flow in exhaust sys-tems with close-coupled catalyst, whereas Chap. 4 is more concerned with thetime-averaged velocity distribution.

Using cold pulsating flow rigs in combination with hot-wire anemometryyields detailed whole-field time-resolved velocity distributions in the close-coupled catalyst. Section 5.1 discusses the resulting time-resolved distributionsfor different pulsating flow rigs, exhaust manifolds and operating conditions.

Section 5.2 focuses on the spatial and temporal occurrence of periodic flowreversal in the close-coupled catalyst. The bidirectional velocity measurementsare performed using the oscillating hot-wire anemometer (OHW) (see Chap. 3).Sect. 5.2.1 validates the OHW in conditions where catalyst flow reversal isknown to occur. The validation is performed with respect to integral flow ratemeasurements. Using a bidirectional velocity measurement technique such asthe OHW proves crucial for obtaining accurate measurements in the event offlow reversal. All velocity measurements on the isochoric pulsating flow rig areperformed using the OHW.

The experimental data in Sect. 5.2.2 reveal the time-resolved velocity distri-bution throughout the entire catalyst cross-section, including areas of negativevelocity.

27The term ‘time-resolved’ denotes the (ensemble-averaged) time variation during one en-gine cycle, or two crankshaft revolutions (i.e. 720 ca).

155

156 Chapter 5 Flow dynamics

Section 5.2.3 describes the use of a one-dimensional gas dynamic modelof the exhaust system to simulate the occurrence of flow reversal in terms ofthe mean velocity. Appendix D discusses the gas dynamic model in detail.Through numerical simulation, Sect. 5.2.3 establishes the influence on catalystflow reversal of the presence of the exit cone and cold end.

Section 5.3 analyzes the ubiquitous resonance phenomenon observed in bothflow rigs. The phenomenon is explained as a Helmholtz-type resonance, usingan analytical explanation in Sect. 5.3.2.

Section 5.3.4 uses the same one-dimensional gas dynamic model (seeApp. D) to explain the resonance phenomenon numerically. Gas dynamic fre-quency response functions of the exhaust manifold are determined, revealingthe nature of the resonating system responsible for these strong velocity fluc-tuations in the catalyst.

5.1 Time-resolved flow distributions

This section describes the time-evolution of the catalyst velocity distribution.The difference between the isothermal and isochoric flow rig is demonstratedby plots of the time-resolved mean velocity Um (ωt), flow uniformity ηm (ωt),and the time-resolved velocity distribution U (ωt) during the exhaust stroke ofthe first cylinder.

The pulsating flow in the isothermal flow rig exhibits a much lower fre-quency content compared to the isochoric flow rig, because of the single-stageexhaust stroke. As such, the experiments on the isothermal flow rig revealsome interesting details of the flow evolution, e.g. the phase lead by the flowuniformity with respect to the pulsator device.

Resonance fluctuations are observed in the isothermal flow rig, using thecylinder head as pulsator. Similar yet much stronger fluctuations are observedon the isochoric flow rig. These are discussed in detail in Sect. 5.3.

The oscillating hot-wire anemometer (OHW) is used for all experiments onthe isochoric flow rig, thus enabling bidirectional velocity measurements. Thephenomenon of flow reversal in the catalyst is discussed in detail in Sect. 5.2.


Manifold A

Figures 5.1 and 5.2 show in the top plots the time-resolved dimensionless meancatalyst velocity Um (ωt), where ωt is the crankshaft position. As noted earlier,in case of the isothermal flow rig, this corresponds to the imaginary crankshaftposition corresponding to the position of the pulsator device (i.e. rotating valveor cylinder head). The bottom plots in Figures 5.1 and 5.2 show the correspond-ing time-averaged velocity distribution.

The crankshaft position ωt = θ (ca) is defined relative to top dead centerof cylinder 1, prior to the intake stroke. As such, and taking into account thefiring order, the time-resolved mean velocity plots show the consecutive exhaust

5.1 Time-resolved flow distributions 157

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1440 rpm, Qref

= 77.3 m3/h

Um

ηm

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 2810 rpm, Qref

= 75.7 m3/h

Um

ηm

0

0.5

1

1.5

2

2.5

-30 -15 0 15 30

-30

-15

0

15

30


x (mm)

y (m

m)

0.6

0.6

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

1

11

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

N = 1440 rpm, Qref

= 77.3 m3/h

Um

= 5.633 m/s, ηm

= 0.690, ηw

= 0.900

(a)

0

0.5

1

1.5

2

2.5

-30 -15 0 15 30

-30

-15

0

15

30


x (mm)

y (m

m)

0.6

0.6

0.7

0.7

0.7

0.80.8

0.8

0.8

0.9

0.9

0.9

0.9

1

1

1

1

1.2

1.2

1.2

1.4

1.4

1.4

N = 2810 rpm, Qref

= 75.7 m3/h

Um

= 5.400 m/s, ηm

= 0.686, ηw

= 0.902

(b)

Figure 5.1 – Time-resolved mean velocity Um (ωt) [-] (top) and corresponding time-averaged distribution U [-] (bottom) for manifold A on the isothermal flow rig withrotating valve, for (a) N = 1440 rpm and (b) N = 2810 rpm


0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1440 rpm, Qref

= 77.4 m3/h

Um

ηm

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 2810 rpm, Qref

= 76.6 m3/h

Um

ηm

0

0.5

1

1.5

2

2.5

-30 -15 0 15 30

-30

-15

0

15

30


x (mm)

y (m

m)

0.6

0.6

0.6

0.70.7

0.7

0.8

0.8

0.8

0.8 0.80.9

0.9

0.9

0.91

1

1

1

1.21.2

1.2

1.21.4

1.4

1.4

1.6

N = 1440 rpm, Qref

= 77.4 m3/h

Um

= 5.399 m/s, ηm

= 0.670, ηw

= 0.897 0

0.5

1

1.5

2

2.5

-30 -15 0 15 30

-30

-15

0

15

30


x (mm)

y (m

m)

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1

1

1

11.2

1.2

1.2

1.41.4

N = 2810 rpm, Qref

= 76.6 m3/h

Um

= 5.559 m/s, ηm

= 0.745, ηw

= 0.916

Figure 5.2 – Time-resolved mean velocity Um (ωt) [-] (top) and corresponding time-averaged distribution U [-] (bottom) for manifold A on the isothermal flow rig withcylinder head, for (a) N = 1440 rpm and (b) N = 2810 rpm


strokes of cylinders 2, 3 and 1. The same convention is applied throughout thethesis. The exhaust stroke of cylinder 1 therefore always corresponds to therightmost pulse in the time-resolved mean velocity plots, and varies roughlybetween 480 and 720 ca.

In the upper plots, the solid line ( ) is the mean catalyst velocity Um (ωt).

The dashed line ( ) is the time-resolved flow uniformity ηm (ωt), as defined

by Eq. (4.9). The light solid line ( ) represents the dimensional exhaust valve

lift. For the rotating valve, this lift equals the valve open cross-sectional area,divided by the maximum open area. Close examination of the sawtooth-likelift curves show a small inter-cylinder28 exhaust valve overlap, corresponding tothe valve timing and the three exhaust runners per catalyst for manifold A. Thesame valve overlap is present in the cylinder head (see Fig. 5.2). A significantlylarger overlap can be noted for manifold B (see Fig. 5.8 and 5.9).

Although the vertical scale varies between −1 and 3, no negative velocitycan be measured in this case, since the oscillating hot-wire anemometer (seeChap. 3) has not been used on the isothermal flow rig, only for the measure-ments on the isochoric (CME) flow rig (see Sect. 5.1.2).

Figures 5.1a and b are for two different engine speeds. The time-resolvedplots (Fig. 5.1, top) are rather similar for both engine speeds. The same holdstrue for the time-averaged plots (Fig. 5.1, bottom), which may be explainedby the high scavenging number S for these flow conditions (S > 2). In bothcases, the mean velocity is quite sinusoidal. This is due to the sawtooth-likecharacteristic of the rotating valve open area. This remark is important in lightof the explanation of the resonance phenomenon in Sect. 5.3.

Figures 5.2a and b are for corresponding flow conditions, yet with the cylin-der head as pulsator. The dimensionless exhaust valve lift is again plotted aslight solid lines (

), yet now represents the cosine-like evolution of the exhaust

valve lift.The time-resolved mean velocity Um (ωt) behaves very differently compared

to using the rotating valve (Fig. 5.1). This is due to the combination of (i) adifferent cross-sectional area evolution (i.e. sawtooth versus cosine) and (ii) adifferent discharge coefficient Cd for both geometries. For compressible flowthrough a restriction, Eq. (B.6) gives the mass flow rate for a given restrictionand upstream and downstream flow conditions. The mass flow rate m ∼ CdA,where A is the variable cross-sectional area of the restriction, and the dischargecoefficient Cd for exhaust valves is based on Fig. B.1 from Heywood [47]. For arotating valve, Cd can be obtained based on the loss coefficient for a ball valve,as given e.g. by Fig. B.2 from Miller [74].

Figure 5.3 shows the product of discharge coefficient and cross-sectionalarea Cd · A, as it evolves during the course of a single exhaust stroke. For therotating valve (

), Cd · A = Amax in the maximum open position, since Cd

becomes unity (see Fig. B.2b). By contrast, for the cylinder head (( ), Cd ·A

remains smaller, yet quite constant around the maximum open position, due

28See the comment on p. 35 concerning the difference between intra-cylinder and inter -cylinder valve overlap.


0

0.2

0.4

0.6

0.8

1

Cd ⋅

A /

Am

ax (

-)

Crankshaft angle θ

Rotating valveCylinder head

θe

θe + ∆θ

Figure 5.3 – Difference between rotating valve and cylinder head in terms of theproduct CdA (θ)

to the fact that Cd decreases for increasing lift (see Fig. B.1). As such, Fig. 5.3clarifies the different behavior between both pulsators in Figs. 5.1 and 5.2.

From Fig. 5.2b, the mean velocity Um (ωt) clearly exhibits strong fluctu-ations. Due to the phase-locked measurement technique and the ensemble-averaging data reduction (see Sect. 2.5.1), these cannot be caused by randomphenomena, such as noise or turbulence. The fluctuations occur only whileusing the cylinder head and not while using the rotating valve, as shown bycomparison of Figs. 5.2b and 5.1b. This phenomenon is discussed in detail inSect. 5.3.

Both cases shown in Fig. 5.2a and b are for a high scavenging numberS. The time-averaged distributions appear similar, although the high enginespeed distribution is notably more uniform compared to the low engine speeddistribution (ηm = 0.75 for Fig. 5.2b versus ηm = 0.67 for Fig. 5.2a). The sameis not true for the rotating valve cases in Fig. 5.1a and b. Since the flow rate iscomparable (Qref ' 75 m3/h), the geometry is identical and the engine speedsdiffer by a factor of two, the scavenging numbers differ by the same factor oftwo. For Figs. 5.1a and 5.2a, S ' 4, compared to S ' 2 for Figs. 5.1b and 5.2b.

The difference in flow uniformity between Figs. 5.2a and b can be explainedin terms of the different frequency content of the mean velocity. Referring to thesecond definition of the apparent pulsation period Tp in Eq. (4.46) based on thepeak frequency in the mean velocity spectral density, and the conclusions in thepreceding chapter concerning the validity of the addition principle, the energyspectral density of Um in the case of Fig. 5.2b is increased due to the occurrenceof the resonance phenomenon. If the fluctuations were any stronger, the valueof Tp according to Eq. (4.46) would be lower compared to the value based on theold definition in Eq. (4.44). In that case, the value of the scavenging numberS = Tp/Ts would decrease. In light of the conclusions of the preceding chapterand in particular Fig. 4.29, a decrease in scavenging number by any means


(e.g. increasing frequency content in Um) entails an increase in flow uniformity(see rM versus S in Fig. 4.29b) and a decrease in correlation between pulsatingand stationary flow conditions (see rS versus S in Fig. 4.29a). This is all inaccordance with the observed difference.

Unlike the mean velocity, the flow uniformity ηm (ωt) in Figs. 5.4 and 5.2(

) is clearly out of phase with (and leading) the rotating valve motion. This

becomes more clear in Figs. 5.4 and 5.5.Figures 5.4 and 5.5 show some time-resolved velocity distributions U (ωt)

during the exhaust stroke of cylinder 1. The distributions are taken at fivecrankshaft positions between 480 ca and 720 ca. According to Table 2.1, thevalve timing for the engine corresponding to manifold A is −12 | 242 | −246 | 10.As such, the exhaust stroke for cylinder 1 occurs between −246 = 474 ca and10 ca. The five crankshaft positions are chosen arbitrarily, for the sake ofsimplicity as (a) 480 ca, (b) 540 ca, (c) 600 ca, (d) 660 ca and (e) 720 ca.The middle position (c) corresponds roughly to the maximum lift position,= (−246 + 10)/2 = −118 = 602 ca.

Each velocity distribution is obtained using linear interpolation from the Javailable distributions for the entire engine cycle. As defined in Sect. 2.5.1, Jcorresponds to the number of samples per engine cycle. For the isothermal flowrig experiments, a constant value of J = 80 is taken. This corresponds to atemporal resolution of 720/J ' 9 ca. For the isochoric flow rig measurements,a higher value of J = 256 is taken to better resolve the higher frequencycontent in the time-resolved velocity, corresponding to a temporal resolution of720/J ' 3 ca.

Similar to the time-averaged velocity distribution plots in the precedingchapter, the time-resolved velocity distributions in Figs. 5.4 and 5.5 are plottednon-dimensionally, dividing the velocity by the time-averaged mean velocityUm =

∫ωtUm (ωt) d (ωt)/(4π) . Contour lines of equal velocity are plotted,

with a dashed contour at unity. A cross-sectional plot is added below eachfigure, indicating the dimensionless velocity along the straight line y = 0 mm.The top left of each figure indicates the engine speed N and time-averagedreference flow rate Qref , whereas the bottom left indicates the time-resolvedmean velocity Um (θ)/Um and the time-resolved flow uniformity measure ηm (θ)according to Eq. (4.9). The bottom right of each figure indicates the crankshaftposition θ = ωt (ca) and the time (ms) during the engine cycle. For clarity,the position of the camshaft29 is indicated by the clockwise rotating marker.The upright position corresponds to 0 = 720 crankshaft angle. The numbers1, 2 and 3 indicate the exhaust strokes of each cylinder, which corresponds tothe firing order for manifold A (1–4–2–6–3–5).

The out-of-phase evolution of the flow uniformity notable in Fig. 5.1a isobserved in Fig. 5.4 as well. During the initial phase of the exhaust stroke(from Figs. 5.4a to b), the flow distribution becomes more uniform. This maybe explained by the following hypothesis:

29For the experiments using the rotating valve, this position corresponds to twice the valueof the rotating valve position, since the rotating valve features two openings per revolution.


0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30

Time-resolved velocity U (ω t) (-)

y (m

m)

0.5

0.5

0.5

0.5

0.5

1

1

1

t = 55.6 msθ = 480.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.3 m3/h

Um

(θ)/Um

= 0.609, ηm

(θ) = 0.447

(a) (b)

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

1

1

1

t = 62.5 msθ = 540.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.3 m3/h

Um

(θ)/Um

= 1.043, ηm

(θ) = 0.634

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.5

0.5

0.5

0.5

1

1

1

1

1

1

2

2

2

3

t = 69.4 msθ = 600.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.3 m3/h

Um

(θ)/Um

= 1.286, ηm

(θ) = 0.385

(c) (d)

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30

Time-resolved velocity U (ω t) (-)y

(mm

)

0.5

0.5

0.5

0.5

0.5

1

1

1

2

2

2

3

t = 76.4 msθ = 660.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.3 m3/h

Um

(θ)/Um

= 0.957, ηm

(θ) = 0.309

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

t = 83.3 msθ = 720.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.3 m3/h

Um

(θ)/Um

= 0.621, ηm

(θ) = 0.377

(e)

Figure 5.4 – Time-resolved velocity distributions U (ωt) [-] for crankshaft positions(a) 480 ca through (e) 720 ca, for manifold A on the isothermal flow rig with rotatingvalve, at N = 1440 rpm (see Fig. 5.1a)


0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m) 0.5

0.5

0.5

0.5

0.5

0.5

0.5

1

1

11

t = 56.3 msθ = 480.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.4 m3/h

Um

(θ)/Um

= 0.670, ηm

(θ) = 0.363

(a) (b)

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

1

1 1

1 1

1

1

1

t = 63.3 msθ = 540.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.4 m3/h

Um

(θ)/Um

= 1.080, ηm

(θ) = 0.704

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.5

0.5

0.5

0.5

0.5

0.5

0.5

1

11

1

1

2

2

2

3

t = 70.3 msθ = 600.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.4 m3/h

Um

(θ)/Um

= 1.109, ηm

(θ) = 0.361

(c) (d)

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


(mm

)

0.5

0.5

0.5

0.5

0.5

1

1

1

2

2

2

33

t = 77.3 msθ = 660.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.4 m3/h

Um

(θ)/Um

= 1.121, ηm

(θ) = 0.367

0

1

2

3

4

5

6

-30 -15 0 15 300

2

4

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

t = 84.4 msθ = 720.0 °ca 1 2

3

N = 1440 rpm, Qref

= 77.4 m3/h

Um

(θ)/Um

= 0.641, ηm

(θ) = 0.324

(e)

Figure 5.5 – Time-resolved velocity distributions U (ωt) [-] for crankshaft positions(a) 480 ca through (e) 720 ca, for manifold A on the isothermal flow rig with cylinderhead, at N = 1440 rpm (see Fig. 5.2a)


0

1

2

3

4

5

6

-30 -15 0 15 30 0 1

3

5

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.5

0.5

0.5

0.5

0.5

1

1

1

1

2

2

2

3

Runner 1, Qref

= 74.5 m3/h

Um

= 5.465 m/s, ηm

= 0.342, ηw

= 0.689

(a)

0

1

2

3

4

5

6

-30 -15 0 15 30 0 1

3

5

Uy=

0 (-)

x (mm)

-30

-15

0

15

30


y (m

m)

0.5

0.5

0.5

0.5

0.5

1

1

1

2

2

2

Runner 1, Qref

= 73.4 m3/h

Um

= 4.738 m/s, ηm

= 0.393, ηw

= 0.719

(b)

Figure 5.6 – Stationary velocity U [-] for flow through runner 1 on manifold Amounted on isothermal flow rig, using (a) rotating valve and (b) cylinder head, atcomparable flow rate to Figs. 5.4 and 5.5

Hypothesis: Diffuser flow attachment evolution As the gasin the open runner and the diffuser starts to move during the ini-tial stage of the exhaust stroke, the flow in the diffuser appears toremain attached to the walls. At some point (see Figs. 5.4b to c),the flow in the diffuser separates and the flow uniformity decreasessignificantly.

The peak velocity occurs in the region of the catalyst where theopen runner issues. The time-resolved velocity distribution (c) atmaximum lift (ωt = 600 ca) is quite similar to (yet slightly moreuniform than) the stationary flow distribution shown in Fig. 5.6afor steady flow through runner 1, with the rotating valve fixed inthe maximum flow position.

During the remainder of the exhaust stroke (from Figs. 5.4c to e),the gas decelerates, although the high velocity region remains vis-ible. The velocity in the rest of the cross-section is very low. Al-though the value of the time-resolved mean velocity is the samein Figs. 5.4b and d (Um (ωt) ' 1), one can hypothesize that noreattachment occurs in the diffuser. As such, the flow uniformityremains low throughout the remainder of the exhaust stroke, untilthe beginning of the exhaust stroke of the following cylinder.

Literature exists on the flow patterns (Fig. 5.7) and pressure recov-ery performance of diffusers [10, 74, 105]. However, the geometryof the exhaust manifolds under investigation is quite complex and


(a)(b)

Figure 5.7 – Diffuser flow patterns for (a) small and (b) wide divergence(Source: [74])

differs too much from the simple geometries described in literature.Nevertheless, even simple diffusers exhibit complex separation, de-pending on the divergence angle and inlet conditions. For a nearlyuniform inlet distribution, Miller [74] identifies five regimes of tran-sitory separation for an axisymmetric diffuser, ranging from steadyflow (for small angle diffusers) to violent fluctuations in the flow pat-tern and pressure recovery (for wide angle diffusers, comparable tothose found in close-coupled catalyst manifolds). For a non-uniformor skewed inlet velocity profile or containing secondary flows (e.g.in an exhaust manifold), separation is extensive yet stationary [74].Separation patterns are determined by the location of low energyfluid, e.g. downstream of the inside of a bend.

Figure 5.7b shows the typical flow pattern in a wide angle diffuser.When the divergence angle is greater than a few degrees, separationoccurs, causing a distorted outlet velocity distribution with outerregions of flow reversal. Flow reversal exists up to the reattachmentpoint in the downstream pipe. However, the influence of the pres-ence of a catalyst substrate on this flow pattern is unknown. Noliterature is available on this subject.

The same observations can be made in Fig. 5.5. The flow uniformity attainsa maximum during the initial phase of the exhaust stroke (Fig. 5.5b), andremains low throughout the remainder of the exhaust stroke. At maximum lift(Fig. 5.5c), the velocity distribution is similar to the stationary flow case shownin Fig. 5.6b.

Manifold B

Figure 5.8 (top) shows the time-resolved dimensionless mean catalyst velocityUm (ωt), for manifold B mounted on the isothermal flow rig, for a constantengine speed yet (a) Qref ' 45 m3/h and (b) Qref ' 115 m3/h. The bottomplots show the corresponding time-averaged velocity distributions.

As for manifold A, the crankshaft position ωt is defined relative to top dead


0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 43.3 m3/h

Um

ηm

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 117.1 m3/h

Um

ηm

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.8 0.8

0.8

0.9

0.90.9

0.9

0.9

0.9

1

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.4

N = 1200 rpm, Qref

= 43.3 m3/h

Um

= 1.093 m/s, ηm

= 0.694, ηw

= 0.958

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.7

0.70.8

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9 0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.61.61.82 2.2

2.4

N = 1200 rpm, Qref

= 117.1 m3/h

Um

= 2.961 m/s, ηm

= 0.412, ηw

= 0.895

(b)

Figure 5.8 – Time-resolved mean velocity Um (ωt) [-] (top) and corresponding time-averaged distribution U [-] (bottom) for manifold B on the isothermal flow rig, forN = 1200 rpm and (a) Qref ' 45 m3/h and (b) Qref ' 115 m3/h


0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 68.0 m3/h

Um

ηm

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 2810 rpm, Qref

= 64.1 m3/h

Um

ηm

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.7

0.80.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.90.9

1

1

1

1

1

1

1

1

1.2

1.21.2

1.2

1.21.41.61.8

N = 1200 rpm, Qref

= 68.0 m3/h

Um

= 1.670 m/s, ηm

= 0.549, ηw

= 0.940

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1

1

1

11

1.2

1.2

1.4

N = 2810 rpm, Qref

= 64.1 m3/h

Um

= 1.586 m/s, ηm

= 0.712, ηw

= 0.952

(b)

Figure 5.9 – Time-resolved mean velocity Um (ωt) [-] (top) and corresponding time-averaged distribution U [-] (bottom) for manifold B on the isothermal flow rig, forQref ' 70 m3/h and (a) N = 1200 rpm and (b) N = 2810 rpm


center of cylinder 1, prior to the intake stroke. As such, the time-resolved meanvelocity plots show the consecutive exhaust strokes of cylinders 3, 4, 2 and 1.

Some distinct differences may be noted between Figs. 5.8a and b, which dif-fer only in terms of flow rate while the engine speed remains constant. Firstly,the peak mean velocities corresponding to each of the maximum valve lift in-stants do not agree. The maximum valve lifts occur roughly at 75 + n 180 ca,where n = 0 . . . 3. For a low flow rate (Fig. 5.8a), the highest peak velocityoccurs during the exhaust stroke of cylinder 4. For a high flow rate (Fig. 5.8b),the highest peak velocity occurs during the exhaust stroke of cylinder 2. Thedifference is likely due to the Reynolds number-dependence of the flow patternin the runners, although this cannot be verified experimentally.

Secondly, the flow uniformity ηm (ωt) ( ) also behaves differently depend-

ing on the flow rate. For a high flow rate (Fig. 5.8b), the flow uniformityexhibits a time evolution which is very similar to that observed on manifold A.The flow uniformity increases during the initial phase of the exhaust stroke.At some point prior to the maximum valve lift, the flow in the diffuser de-taches and the flow uniformity remains low and relative constant throughoutthe remainder of the exhaust stroke.

However, this changes dramatically for a low flow rate (Fig. 5.8a). On thetime-averaged level, the flow uniformity is much higher. On the time-resolvedlevel, the flow uniformity shows no clear sign of flow detachment in the diffuser.Instead, the flow uniformity ηm increases monotonously during the exhauststroke, reaching a maximum after the maximum valve lift event. Possibly,the flow in the diffuser remains attached at such low flow rate. However, thishypothesis cannot be supported based on the literature. Miller [74] indicatesthat the diffuser pressure loss increases for decreasing Reynolds number.

More likely, the effect is due to interfering effects in the diffuser. Indeed, thecondition in Fig. 5.8a corresponds to low engine load conditions and therefore,a low scavenging number S. As such, successive exhaust pulses interfere to ahigher degree in the diffuser.

For the same engine speed, an intermediate flow rate of Qref ' 70 m3/his shown in Fig. 5.9a. In this case, the flow detachment can already be noted,although not as clear as for the high flow rate case of Fig. 5.8b.

Figure 5.9 shows a comparison for the same flow rate yet different enginespeed. The main difference between the two cases is the resonance phenomenonwhich was already observed on manifold A using its cylinder head as pulsator.This phenomenon is discussed in detail in Sect. 5.3.

Figure 5.10 shows some time-resolved velocity distributions U (ωt) duringthe exhaust stroke of cylinder 1, for manifold B. The distributions are takenat five crankshaft positions between 525 ca and 705 ca. These positions differslightly compared to those for manifold A, due to (i) the later exhaust valveopening for manifold B (EO equals -220 ca instead of -246 ca, see Table 2.1),and (ii) the significant interference of the exhaust pulses, which results fromthe higher inter-cylinder valve overlap.

The overlap ∆θ between consecutive exhaust strokes equals ∆θ =(EC− EO) − 720/nr , where EO and EC represent the exhaust valve open


0

1

2

3

4

5

6

-60 -30 0 30 600

2

4

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.50.5

0.5

0.5

0.50.5 0.5

0.5

1

1

1

22

t = 72.9 msθ = 525.0 °ca 1 3

2 4

N = 1200 rpm, Qref

= 68.0 m3/h

Um

(θ)/Um

= 0.626, ηm

(θ) = 0.244

(a) (b)

0

1

2

3

4

5

6

-60 -30 0 30 600

2

4

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m) 0.5

0.5

1

1

1

1

1

11

11

1

2

2

t = 79.2 msθ = 570.0 °ca 1 3

2 4

N = 1200 rpm, Qref

= 68.0 m3/h

Um

(θ)/Um

= 0.977, ηm

(θ) = 0.477

0

1

2

3

4

5

6

-60 -30 0 30 600

2

4

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

1

1 1

1

1

11

11

1

1

11

1

2

t = 85.4 msθ = 615.0 °ca 1 3

2 4

N = 1200 rpm, Qref

= 68.0 m3/h

Um

(θ)/Um

= 1.041, ηm

(θ) = 0.498

(c) (d)

0

1

2

3

4

5

6

-60 -30 0 30 600

2

4

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


(mm

)

0.5

1

1

1

1

1

1

1

1

1

2

2

3

4

t = 91.7 msθ = 660.0 °ca 1 3

2 4

N = 1200 rpm, Qref

= 68.0 m3/h

Um

(θ)/Um

= 1.042, ηm

(θ) = 0.272

0

1

2

3

4

5

6

-60 -30 0 30 600

2

4

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

23

t = 97.9 msθ = 705.0 °ca 1 3

2 4

N = 1200 rpm, Qref

= 68.0 m3/h

Um

(θ)/Um

= 0.617, ηm

(θ) = 0.186

(e)

Figure 5.10 – Time-resolved velocity distributions U (ωt) [-] for crankshaft positions(a) 525 ca through (e) 705 ca, for manifold B on the isothermal flow rig, at N =1200 rpm and Qref ' 70 m3/h (see Fig. 5.9a)


and close crankshaft angles (see Table 2.1) and nr is the number of exhaustrunners per catalyst (i.e. nr = 3 for manifold A and nr = 4 for manifold B).This corresponds to an overlap of ∆θA = 16 ca and ∆θB = 53 ca. Althoughthese values differ only 37 ca, the difference is significant, due to the non-linearrelationship between the crankshaft position and the exhaust valve flow rate(see App. B, Eq. (B.6)).

In Fig. 5.10, the five crankshaft positions are chosen as (a) 525 ca,(b) 570 ca, (c) 615 ca, (d) 660 ca and (e) 705 ca. Similar to Figs. 5.4 and 5.5,the middle position (c) 615 ca corresponds roughly to the maximum lift posi-tion, = (−220 + 13)/2 ' −104 = 616 ca. The start position (a) 525 ca andthe end position (e) 705 ca are chosen where the exhaust valve lift of cylinder 1equals that of the preceding and following cylinder (2 and 3, respectively).

The out-of-phase evolution of the flow uniformity notable in Fig. 5.9a isagain observed in Fig. 5.10.

Although the first position (a) in Fig. 5.10a occurs at 525 ca, whereas theexhaust valves for cylinder 1 start to open at 500 ca, the velocity distributionsshows that the gas is still flowing from runner 2. The same observation can bemade for the end position (e), where the gas is still flowing from runner 1 whilethe exhaust valves of cylinder 3 are already opening.

The peak velocity occurs in the region of the catalyst where runner 1 issues.Contrary to the case for manifold A, the time-resolved velocity distributionat maximum lift in Fig. 5.10c significantly differs from the stationary flowdistribution shown in Fig. 4.17a for steady flow through runner 1, with thevalves blocked in the maximum lift position. The correspondence is betterwith the velocity distributions in Figs. 5.10d and e.

5.1.2 Isochoric flow rigMean velocity

Only manifold B has been used during the experiments on the isochoric (CME)flow rig (see Sect. 2.2.2). These measurements are all performed using theoscillating hot-wire anemometer (OHW) presented in Chap. 3. This systemfeatures a maximum measurable negative velocity of −1 m/s. This limit valueis adequate at low engine speed N < 1500 rpm, yet it proves insufficient toresolve the strong flow reversal at low engine load and higher engine speed (seeSect. 5.2).

With reference to Sects. 2.2.2 and 2.3, the isochoric CME flow rig generatesa cold pulsating flow in the exhaust system which closely resembles fired en-gine flow conditions. In that sense, the flow conditions are denoted somewhatdifferently from the isothermal flow rig. For the isothermal flow rig, the enginespeed N is determined by the pulsator frequency, and the flow rate Qref isdetermined independently from the engine speed. Thus, a broad scavengingnumber range could be tested in Chap. 4. On the other hand, the CME flowrig and a fired engine are volumetric (hence: isochoric) machines. The flowrate Qref is in first approximation proportional to the engine speed N , andis furthermore determined by the engine load. The correct interpretation of


0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

ηm

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

ηm

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.7

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1 1

1

1

1

11

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.6 1.8

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

= 1.388 m/s, ηm

= 0.536, ηw

= 0.923

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1 1

1

1.2

1.2

1.2

1.2

1.41.4

1.6

1.6

1.8

2

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

= 2.356 m/s, ηm

= 0.467, ηw

= 0.903

(b)

Figure 5.11 – Time-resolved mean velocity Um (ωt) [-] (top) and correspondingtime-averaged distribution U [-] (bottom) on the CME flow rig, for N = 1200 rpmand (a) Qref ' 70 m3/h (part load) and (b) Qref ' 100 m3/h (high load)


‘engine load’ is given by Footnote 6. Both for the fired engine and for theCME flow rig, the intake manifold pressure pi (or more precisely: the densityρi = pi/(r Ti) ) determines the engine load. As such, the intake system pressurepi is shown for experiments obtained on the CME flow rig. The reference flowrate Qref is also shown, to compare with the isothermal flow rig experiments.

Figure 5.11 presents the time-resolved mean velocity Um (ωt) and corre-sponding time-averaged velocity distributions U obtained on the CME flowrig, in pulsating flow conditions.

Upon examination of Fig. 5.11, some striking features are noted. Firstly, themean velocity exhibits very strong resonance fluctuations. On the isothermalflow rig (see Sect. 5.1.1), these occur when using the cylinder head as pulsator,yet only for an engine speed in excess of 2500 rpm. The resonance phenomenonis further discussed in Sect. 5.3.

Secondly, periodic backflow occurs through the catalyst, in particular atlow engine load (i.e. low intake system pressure pi, low flow rate Qref , lowscavenging number S). Flow reversal is most pronounced immediately follow-ing the blowdown phase. This is quite remarkable, given that Fig. 5.11 plotsthe mean velocity. As such, more extensive local flow reversal is expected.This is confirmed by the time-resolved velocity distribution plots in Figs. 5.16through 5.18.

In terms of the time-resolved flow uniformity ηm (ωt), no clear conclusioncan be drawn from Fig. 5.11. The flow uniformity is strongly affected by themean velocity fluctuations. Presumably, the flow detachment and reattachmentprocess in the diffuser is equally affected by the velocity and pressure transients.

In the evolution of the mean velocity in Fig. 5.11, the blowdown phase can bediscerned as the velocity peak immediately following each exhaust valve opening(e.g. the highest peak in Fig. 5.11b at ωt ' 540 ca). The displacement phasefollows the blowdown, and is generally characterized by a lower peak flow rateand lower transients. However, in case of this close-coupled catalyst manifold,the resonance phenomenon greatly amplifies the velocity fluctuations. Thisyields a time-resolved mean velocity during the displacement phase which isvery dissimilar to e.g. the simulated velocity evolution plotted in Fig. 2.10. Thesimulation is performed using a zero-dimensional filling-and-emptying model,which does not take the gas dynamics in the exhaust manifold into account. Asa very crude approximation, the mean velocity evolution for the CME flow rigshown in Fig. 2.10 can be regarded as a low-pass filtered average of the actualvelocity evolution. However, non-linearities in the gas dynamics ensure thatthis comparison does not necessarily hold.

For the part load case (Fig. 5.11a), the magnitude of the blowdown peakvelocity is of the same level as the subsequent peaks during the displacementphase. Only for the high load case (Fig. 5.11a), the blowdown peaks can beclearly discerned at approximately 0, 180, 360, 540 ca for cylinders 3, 4, 2 and1, respectively.

Figure 5.12 shows a similar comparison as Fig. 5.11, yet for N = 1800 rpm.The time-resolved mean velocity and flow uniformity are quite comparable tothe N = 1200 rpm case. Since the eigenfrequency of the resonance phenomenon


0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1800 rpm, Qref

= 104.1 m3/h, pi = 1.55 atm

Um

ηm

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1800 rpm, Qref

= 146.5 m3/h, pi = 2.20 atm

Um

ηm

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m) 0.

8

0.80.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.8

2

N = 1800 rpm, Qref

= 104.1 m3/h, pi = 1.55 atm

Um

= 2.288 m/s, ηm

= 0.486, ηw

= 0.908

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.6

0.7

0.7

0.8

0.8

0.80.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.91

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.6

1.6

1.8

1.8

22.2

2.4

N = 1800 rpm, Qref

= 146.5 m3/h, pi = 2.20 atm

Um

= 3.458 m/s, ηm

= 0.406, ηw

= 0.871

(b)

Figure 5.12 – Time-resolved mean velocity Um (ωt) [-] (top) and correspondingtime-averaged distribution U [-] (bottom) on the CME flow rig, for N = 1800 rpmand (a) Qref ' 100 m3/h (part load) and (b) Qref ' 145 m3/h (high load)


0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 2400 rpm, Qref

= 234.6 m3/h, pi = 2.00 atm

Um

ηm

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 3000 rpm, Qref

= 237.4 m3/h, pi = 1.55 atm

Um

ηm

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m)

0.6

0.7

0.70.8

0.80.8

0.8

0.8

0.80.9

0.9

0.9

0.9

0.9

0.91

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.8

N = 2400 rpm, Qref

= 234.6 m3/h, pi = 2.00 atm

Um

= 4.207 m/s, ηm

= 0.516, ηw

= 0.882

(a)

0

0.5

1

1.5

2

2.5

-60 -30 0 30 60

-60

-30

0

30

60


x (mm)

y (m

m) 0.

7

0.7

0.8

0.8

0.8

0.8

0.8

0.80.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1

11

1.2

1.21.2 1.

2

1.2

1.4

1.4

1.4

1.4

1.6

1.6

1.6

1.6

1.8

N = 3000 rpm, Qref

= 237.4 m3/h, pi = 1.55 atm

Um

= 3.997 m/s, ηm

= 0.522, ηw

= 0.877

(b)

Figure 5.13 – Time-resolved mean velocity Um (ωt) [-] (top) and correspondingtime-averaged distribution U [-] (bottom) on the CME flow rig, for Qref ' 235 m3/hand (a) N = 2400 rpm (high load) and (b) N = 3000 rpm (part load)

is unaffected by engine speed or flow rate (see Sect. 5.3), fewer peaks are shownduring the displacement phase, due to the increased engine speed.

The time-averaged velocity distributions in Fig. 5.12a and 5.11b show a verygood resemblance. This may be attributed to the fact that the flow rates cor-respond (Qref ' 100 m3/h) and that the scavenging numbers are comparable(S = 0.58 for Fig. 5.11b and S = 0.41 for Fig. 5.12a).

Figure 5.13 shows two additional cases at high engine speed. Due to thehigher engine speed, Fig. 5.13a shows only a single blowdown and displacementpeak in the mean catalyst velocity. The same is observed at N = 3000 rpm inFig. 5.13b. Since Fig. 5.13b is obtained in part load conditions (pi = 1.55 atm),the blowdown peak is smaller than the displacement peak.


Velocity distributions

For the experiments on the isochoric flow rig, some selected time-resolved veloc-ity distributions are shown for a constant engine speed N = 1200 rpm and high,part and low engine loads. This corresponds to an intake system pressure pi ofapproximately 2.2, 1.55 and 1 atm, respectively. As a reference, Fig. 5.14 (left)provides the corresponding time-averaged velocity distributions, where the en-gine load varies from high to low from top to bottom.

Figure 5.14 (left) show that the flow uniformity decreases as the engine loadincreases (i.e. from bottom to top in Fig. 5.14 left), or equivalently the flowrate and scavenging number increase.

The plots in Fig. 5.14 (right) show the stationary velocity distribution forflow through runner 1, at comparable flow rates to each of the engine load cases.These are obtained on the isothermal flow rig, with the exhaust valves blockedin the position of maximum lift. The stationary distributions for runner 1 areshown as reference, since the time-evolution of the velocity distributions areinspected only during the exhaust stroke of cylinder 1 (see Figs. 5.16, 5.17and 5.18).

For each engine load case (high to low load from top to bottom), Fig. 5.15shows the time-resolved mean velocity Um (ωt) and flow uniformity ηm (ωt).The six vertical lines in each plot indicate the crankshaft positions θi (i =1 . . . 6) at which the time-resolved velocity distributions are shown.

By contrast to the isothermal flow rig, the crankshaft positions θi are se-lected differently for each engine load case. This is due to the stronger fluc-tuations in the mean velocity. Simply selecting a number of fixed crankshaftpositions would complicate a good comparison between the engine load cases.As such, six consecutive crankshaft positions (a) θ1 through (f) θ6 are selectedduring the exhaust stroke of cylinder 1 for each individual case, according tothe following rules:

(a) θ1 corresponds to the maximum Um during the blowdown phase (firstvertical line in Fig. 5.15).

(b) θ2 corresponds to the minimum Um immediately following the blowdownphase (second vertical line in Fig. 5.15).

(c) θ3 corresponds to the first occurrence of Um = 1 during the displacementphase (third vertical line in Fig. 5.15).

(d) θ4 corresponds to the first local maximum of Um during the displacementphase (fourth vertical line in Fig. 5.15).

(e) θ5 corresponds to the second occurrence of Um = 1 during the displace-ment phase (fifth vertical line in Fig. 5.15).

(f) θ6 corresponds to the first local minimum of Um during the displacementphase (sixth vertical line in Fig. 5.15).


0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

1

1

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.61.

6

1.8

2

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

= 2.356 m/s, ηm

= 0.467, ηw

= 0.903

(a) (b)

0

1

2

3

4

5

6

-60 -30 0 30 60 0 1

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.5

1

1

1

1

1

1

2

2

33 45

Runner 1, Qref

= 94.5 m3/h

Um

= 2.388 m/s, ηm

= 0.178, ηw

= 0.762

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.7

0.8

0.8

0.80.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

1

1

1

1

1

1

11

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4 1.6 1.8

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

= 1.388 m/s, ηm

= 0.536, ηw

= 0.923

(c) (d)

0

1

2

3

4

5

6

-60 -30 0 30 6001

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60

Stationary velocity U (-)y

(mm

)

0.5

0.5

1

11

1 1

1

1

2

2

34

Runner 1, Qref

= 65.4 m3/h

Um

= 1.667 m/s, ηm

= 0.213, ηw

= 0.808

0

0.5

1

1.5

2

2.5

-60 -30 0 30 600

1

2

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.8

0.9

0.9 0.9

0.9

0.9

1

1

1

1

1

1

1

1.2 1.2

1.2

1.2

1.4

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

= 1.177 m/s, ηm

= 0.631, ηw

= 0.945

(e) (f)

0

1

2

3

4

5

6

-60 -30 0 30 60 0 1

3

5

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

1

1

1

1 1

1

1

23

Runner 1, Qref

= 42.2 m3/h

Um

= 1.067 m/s, ηm

= 0.332, ηw

= 0.876

Figure 5.14 – Time-averaged velocity distributions U [-] (left) and stationary ve-locity distributions for flow through runner 1 (right), for (a, b) high load, (c, d) partload, (e, f) low load


0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

ηm

(a)

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

ηm

(b)

0 180 360 540 720-1

-0.5

0

0.5

1

1.5

2

2.5

3Time-resolved


Mea

n ve

loci

ty, f

low

uni

form

ity (

-)

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

ηm

(c)

Figure 5.15 – Time-resolved mean velocity Um (ωt) [-], for (a) high load, (b) partload, (c) low load; six vertical lines indicate crankshaft positions θi (i = 1 . . . 6) inFigs. 5.16, 5.17 and 5.18


-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

2

3

3

33

3

3

3

33

t = 74.0 msθ = 533.0 °ca 1 3

2 4

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

(θ)/Um

= 2.728, ηm

(θ) = 0.818

(a) (b)

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.5

11

2

2

3

3

4

4

0

0

0

t = 78.5 msθ = 565.4 °ca 1 3

2 4

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

(θ)/Um

= 0.295, ηm

(θ) = 0.061

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

2

2

2

2

2

2

2

2 2

t = 73.4 msθ = 528.8 °ca 1 3

2 4

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

(θ)/Um

= 1.920, ηm

(θ) = 0.699 -1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


(mm

)

-0.5

-0.5

-0.5

-0.50

t = 78.5 msθ = 565.2 °ca 1 3

2 4

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

(θ)/Um

= -0.617, ηm

(θ) = 0.638

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m) 0.5

0.5

0.5

0.5

0.5

0.5

1

t = 74.6 msθ = 537.2 °ca 1 3

2 4

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

(θ)/Um

= 0.393, ηm

(θ) = 0.366 -1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0

0

0

0

t = 76.2 msθ = 548.4 °ca 1 3

2 4

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

(θ)/Um

= -0.294, ηm

(θ) = 0.583

Figure 5.16 – Time-resolved velocity distributions U (ωt) [-], for (top) high load,(middle) part load, (bottom) low load, at crankshaft positions (a) θ1 and (b) θ2 (othercrankshaft positions: see Figs. 5.17 and 5.18)


-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

1

1

1

1

2

2

2

33

4

0

t = 82.0 msθ = 590.2 °ca 1 3

2 4

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

(θ)/Um

= 1.000, ηm

(θ) = 0.213

(c) (d)

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

2

2

2

2

2

2

2

3

3

4

4

t = 83.6 msθ = 601.8 °ca 1 3

2 4

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

(θ)/Um

= 1.895, ηm

(θ) = 0.438

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

1

1

1

1

1

1

1

1

1

1

1

t = 80.4 msθ = 579.2 °ca 1 3

2 4

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

(θ)/Um

= 1.000, ηm

(θ) = 0.600 -1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


(mm

)

2

2

2

2

2

2

2

2

2

2

t = 82.0 msθ = 590.6 °ca 1 3

2 4

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

(θ)/Um

= 1.962, ηm

(θ) = 0.722

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

1

1

1

1

1

1

1

1

t = 77.2 msθ = 555.6 °ca 1 3

2 4

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

(θ)/Um

= 1.000, ηm

(θ) = 0.499 -1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

2

2

2

2

2

222

2

2

t = 78.5 msθ = 565.2 °ca 1 3

2 4

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

(θ)/Um

= 2.022, ηm

(θ) = 0.701

Figure 5.17 – Time-resolved velocity distributions U (ωt) [-], for (top) high load,(middle) part load, (bottom) low load, at crankshaft positions (c) θ3 and (d) θ4 (othercrankshaft positions: see Figs. 5.16 and 5.18)


-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

1

1

1

1

1

1

11

2

23

t = 85.3 msθ = 614.1 °ca 1 3

2 4

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

(θ)/Um

= 1.000, ηm

(θ) = 0.317

(e) (f)

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.5

0.5

1 1

00

0

0

0

0

t = 87.1 msθ = 627.2 °ca 1 3

2 4

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

(θ)/Um

= 0.295, ηm

(θ) = 0.172

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0.5

0.5

1

11

1

1

1

1

1

1

1

t = 83.8 msθ = 603.2 °ca 1 3

2 4

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

(θ)/Um

= 1.000, ηm

(θ) = 0.562 -1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


(mm

)

0.5

0.5

0.50.5

0.5

0.5

0.5

0.5

0.5

11

1

0

0

0

t = 85.6 msθ = 616.0 °ca 1 3

2 4

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

(θ)/Um

= 0.336, ηm

(θ) = 0.301

-1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

1

1

1

1

1

1

1

1 1

1

1

1

1

t = 80.1 msθ = 576.4 °ca 1 3

2 4

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

(θ)/Um

= 1.000, ηm

(θ) = 0.592 -1

0

1

2

3

4

5

6

-60 -30 0 30 60024

Uy=

0 (-)

x (mm)

-60

-30

0

30

60


y (m

m)

0

0

00

t = 82.0 msθ = 590.6 °ca 1 3

2 4

N = 1200 rpm, Qref

= 49.9 m3/h, pi = 1.00 atm

Um

(θ)/Um

= -0.179, ηm

(θ) = 0.370

Figure 5.18 – Time-resolved velocity distributions U (ωt) [-], for (top) high load,(middle) part load, (bottom) low load, at crankshaft positions (e) θ5 and (f) θ6 (othercrankshaft positions: see Figs. 5.16 and 5.17)


Figures 5.16, 5.17 and 5.18 show the time-evolution of the velocity distri-bution for each engine load case (high to low load from top to bottom), forcrankshaft positions (a) θ1 and (b) θ2 (Fig. 5.16), (c) θ3 and (d) θ4 (Fig. 5.17)and (e) θ5 and (f) θ6 (Fig. 5.18). As before, the velocity distributions areplotted as contour lines, where the dashed and dotted contour lines representunity and zero velocity respectively. Regions of flow reversal below the dottedcontour line (

) of zero velocity are shaded gray.

During the first part of the blowdown phase (θ1: Fig. 5.16a), the velocityincreases while the flow uniformity remains quite high. The second part of theblowdown (θ2: Fig. 5.16b) differs according to the engine load. For high engineload, the distribution is characterized by a sharp velocity peak where runner 1issues into the catalyst, and extensive backflow throughout the remainder ofthe cross-section. Backflow occurs even for high load conditions.

The engine load clearly affects the magnitude and nature of the flow rever-sal. As discussed in the hypothesis concerning diffuser flow attachment (seep. 161), for low load conditions, the scavenging number S is low, which meansthat successive exhaust pulses interact to a higher degree in the diffuser. ForFig. 5.16, the three load cases correspond respectively to (top) S = 0.58, (mid-dle) S = 0.32 and (bottom) S = 0.18.

During the subsequent displacement phase, the mean velocity increases asthe piston starts expelling the cylinder charge (θ3: Fig. 5.17c). The peakvelocity at high engine load decreases only gradually (Fig. 5.17, top). Dueto the resonance phenomenon in the manifold, the mean velocity continues tofluctuate throughout the displacement phase. Figures 5.17d and 5.18e,f showthe evolution from the first maximum Um to the first minimum Um during thedisplacement phase.

Remarkably, the sixth crankshaft position θ6 corresponding to the first min-imum Um occurs roughly simultaneously to the point of maximum piston ve-locity (at 630 ca). In spite of the high piston velocity, flow reversal still occurs(θ6: Fig. 5.18f). It is however less pronounced when compared to the post-blowdown flow reversal (θ2: Fig. 5.16b).

Park et al. [81] present phase-locked velocity results obtained using LDA ina close-coupled catalyst manifold on a fired engine. Figure 5.19 shows periodicflow reversal in the order of −1 to −2 m/s. The backflow occurs following eachblowdown.

Also using LDA, Liu et al. [70] show flow reversal occurring downstreamof a close-coupled catalyst in motored engine conditions. These conditionscorrespond exactly to the CME flow rig with atmospheric intake pressurepi = 1 atm. Transient simulations show flow reversal in motored and firedconditions. Equivalently, flow reversal is most pronounced following blowdown.The maximum backflow varies between −1 and −5 m/s in motored and firedconditions.


Figure 5.19 – Single-point velocity in the catalyst of a fired engine (Source: [81])

5.2 Flow reversal

This section focuses on the occurrence of flow reversal throughout the catalystcross-section. Section 5.2.1 describes the validation of the oscillating hot-wireanemometer (OHW) on the isochoric flow rig, in conditions where extensiveflow reversal is known to occur. The OHW proves crucial for obtaining accuratemeasurements on the isochoric flow rig.

Section 5.2.2 discusses the experimental time-resolved velocity data ob-tained on the CME flow rig, using the OHW for measuring the bidirectionalvelocity (see also Sect. 5.1.2).

Section 5.2.3 discusses numerical results obtained using a one-dimensionalgas dynamic model of the exhaust system. The numerical results are comparedto the measured mean catalyst velocity.

Based on the numerical model, the influence of an exit cone and exhaust pipewith muffler is investigated on the flow dynamics in the manifold, in particularon the catalyst flow reversal.

5.2.1 OHW validation

For the experiments on the CME flow rig, the oscillating hot-wire anemometer(OHW) is used for measuring the bidirectional phase-locked velocity. Theconstruction and calibration of the OHW are described in Chap. 3.

To assess the effectiveness of the OHW in measuring the bidirectional veloc-ity, a number of engine operating points that feature flow reversal are selected.In these operating points, the oscillator frequency Rf [-] defined by Eq. (3.13)is increased from zero for a stationary probe to the maximum attainable. AsRf increases, so does the resolution in the negative velocity range, and conse-quently the correspondence improves between the exhaust flow rate calculatedas the area-averaged OHW velocity Q = UmA and the reference flow rate Qref

measured using the laminar flow meter (see Sect. 2.4.2).Figure 5.20a shows the non-dimensional flow rate deviation δQ = Q/Qref −

1 [-]. The reference exhaust flow rate Qref [m3/s] is calculated as Qref =ρs (Qs,in −Qs,bb)/ρ , where ρs and ρ are the density of air at standard condi-tions (i.e. 0 C, 1 atm) and exhaust conditions, respectively. The intake stan-

5.2 Flow reversal 183

0 1 2 3 4 5 6 7-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

OHW frequency Rf (-)

Flow

rat

e er

ror

δQ

= Q

/Qre

f - 1

(-)

pi = 1.0 atm, N = 600 rpm

pi = 1.0 atm, N = 1200 rpm

pi = 1.0 atm, N = 1800 rpm

pi = 1.5 atm, N = 600 rpm

pi = 1.5 atm, N = 1200 rpm

pi = 1.5 atm, N = 1800 rpm

pi = 2.2 atm, N = 1200 rpm

pi = 2.2 atm, N = 1800 rpm

(a)

0 180 360 540 720-1

-0.5

0

0.5

1

1.5Time-resolved

Crankshaft angle ωt (°)

Mea

n ve

loci

ty U

m (

m/s

)

Rf = 0

Rf = 6.75

N = 600 rpm, pi = 1.00 atm

(b)

Figure 5.20 – Influence of OHW frequency Rf on (a) the flow rate deviation and(b) the (dimensional) time-resolved mean velocity Um (ωt) [m/s]

dard flow rate Qs,in (Nm3/s) is determined by means of a laminar flow meterin the intake system. This measurement is further verified using a cylinderpressure sensor, by calculating the cylinder charge per cycle from the pressurerise during the compression stroke (see Sect. 2.4.3).

The blow-by leakage standard flow rate Qs,bb (Nm3/s) is estimated basedon a correlation as a function of the engine speed N and the intake manifoldpressure. Figure 5.21 shows the ratio of blow-by standard flow rate Qs,bb tothe intake system standard flow rate Qs,in. These data are obtained on theisochoric flow rig. The blow-by mass flow rate is determined using low rangerotameters30 connected to the crankcase ventilation outlet. A correlation ofthe following form is fitted to the data:

Q′s,bb = (Cd δc)bb (4πb)pi√rTi

√γ

(2

γ + 1

) γ+12(γ−1)

(5.1)

where b is the cylinder bore [m], pi is the intake manifold pressure [Pa], Ti isthe intake manifold temperature [K], γ is the ratio of specific heats [-]. Thefactor (Cd δc)bb represents the product of a discharge coefficient and an equiv-alent clearance width between the cylinder wall and the piston rings. Thefactor (Cd δc)bb is fitted to match the experimental data, resulting in a value of(Cd δc)bb = 0.934 µm.

Equation (5.1) is established based on the assumption that choked flowoccurs within the cylinder-to-piston clearance. This seems a fair assump-tion, since the averaged cylinder pressure during the compression and expan-sion stroke pcyl,m (when blow-by leakage is most pronounced) is greater than

30Kobold low range precision rotameters, ranges 50 to 500 Nl/h and 300 to 3000 Nl/h inair at 20 C, 1.2 atm.


0 1000 2000 30000

0.01

0.02

0.03

0.04

0.05

Qs,

bb /

Qs,

in (

-)

Blow-by leakage correlation

Engine speed N (rpm)

pi / p

a = 1.0

pi / p

a = 1.5

pi / p

a = 2.0

pi / p

a = 2.5

Qs,bb

’ / Qs,in

Figure 5.21 – Experimental correlation for the blow-by leakage on the isochoric flowrig

the critical pressure, or symbolically pcyl,m > pa ((γ + 1)/2)γ/(γ−1) (see alsoEq. (B.6)).

The correlation Q′s,bb ( ) in Fig 5.21 is determined according to Eq. (5.1).

Figure 5.21 demonstrates that the blow-by leakage at most amounts to 5 % ofthe intake flow rate, at low engine speed.

The data in Fig. 5.20a represent experiments at engine speeds of 600, 1200and 1800 rpm. At low engine load (pi = 1 atm), strong backflow occurs (seeSect. 5.2). This situation is not physically possible with fired engine conditions,as discussed in Sect. 2.3. However, local occasional backflow occurs also athigher engine load (pi = 1.5 . . . 2.2 atm).

Figure 5.20a shows that for increasing OHW oscillation frequency Rf , thevelocity measurement becomes increasingly more accurate. Traditional HWAusing a stationary probe corresponds in Fig. 5.20a to the points at Rf = 0.The flow rate error δQ amounts to anywhere between 0 and 50 %. The OHWreduces δQ to within the uncertainty margins on Qref , which corresponds toapproximately 10 % (see Sect. 2.4).

The maximum attainable dimensionless frequency Rf depends on the enginespeed, since Rf = fo/(N/120) and the maximum oscillation frequency fo isabout 50 Hz for xo = 5.5 mm. This explains why the curves in Fig. 5.20a havea different range, depending on the engine speed N .

Figure 5.20b shows the influence of using the OHW with different frequencyRf on the time-resolved mean velocity Um (ωt) [m/s]. Contrary to above fig-ures, the mean velocity is plotted dimensional in m/s, so as to better distinguishthe effect of using the OHW at different oscillation frequencies.

The dashed line ( ) in Fig. 5.20b uses a stationary probe (Rf = 0), whereas

the solid line ( ) uses an oscillating probe at Rf = 6.75. This experiment

corresponds to the rightmost circular marker ( ) in Fig. 5.20a. The mean

velocity using traditional HWA (Rf = 0) exhibits the typical rectification or


-60 -30 0 30 60

-60

-30

0

30

60

Characteristic catalyst regions

x (mm)

y (m

m) A

B D C

E

Figure 5.22 – Characteristic catalyst regions for manifold B

folding when flow reversal occurs. This is due to the inherent insensitivity ofHWA to the velocity direction (see Sect. 3.2).

The mean velocity fluctuations in Fig. 5.20b during the displacement phasesare due to Helmholtz resonances in the exhaust runners and collector volume.This is explained in Sect. 5.3. No significant flow reversal occurs during thelatter part of the displacement phase. During those periods, Fig.5.20b demon-strates that the mean velocity at Rf = 0 and Rf = 6.75 yield identical results.

In conclusion, the OHW seems an appropriate measurement for determiningthe time-resolved velocity in case of occasional flow reversal. Further improve-ments to the OHW approach can be made based on the discussion in Sect. 3.7.4.The present system features a maximum measurable negative velocity of ap-proximately −1 m/s, which is sufficient for the CME flow rig at low enginespeed, yet insufficient at higher engine speed (N > 2000 rpm) and low loadconditions. Nevertheless, as demonstrated by Fig. 5.20a the accuracy on the ve-locity measurements is significantly improved compared to traditional hot-wireanemometry with a stationary probe.

5.2.2 Experimental results

Upon examination of the time-averaged velocity distributions in Figs. 5.11, 5.12and 5.13 for manifold B on the CME flow rig, one can discern five characteristicregions in the catalyst cross-section.

These are indicated in Fig. 5.22. The flow rate in regions A and B ishigh, since runners 1 and 2, respectively 3 and 4 issue into the diffuser at thoselocations. This is shown in Fig. 2.1. The central region C and the outer regionsD and E are most prone to backflow.

The time evolution of the catalyst flow distribution during the exhauststroke of cylinder 1 is examined up-close in Figs. 5.16, 5.17 and 5.18. Basedon the mean velocity evolution in Fig. 5.15, six crankshaft positions θi, i =


0 180 360 540 720-1

0

1

2

3

4

5

6Time-resolved


Vel

ocity

(-)

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

UA(θ)

UB(θ)

(a)

0 180 360 540 720-1

0

1

2

3

4

5

6Time-resolved


Vel

ocity

(-)

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

UC

(θ)U

D(θ)

UE(θ)

(b)

Figure 5.23 – Time-resolved velocity for 1200 rpm and high load, locally averagedin (a) regions A and B and (b) regions C, D and E

1 . . . 6 are determined for each engine load case. These positions are defined inSect. 5.1.2.

Figs. 5.16, 5.17 and 5.18 show the evolution from crankshaft positions (a) θ1through (f) θ6, for (top) high, (middle) part and (bottom) low engine load.Flow reversal is indicated by a dotted contour at zero (U = 0) and particularlyby the shaded region, representing negative velocity.

During peak blowdown flow rate (Fig. 5.16a), the flow remains relativelyuniform. At the end of the blowdown, the cylinder pressure has dropped to thelevel of the exhaust manifold. The inertia of the gas in runners and catalystcauses it to keep flowing in region A (Fig. 5.16b). The cylinder and manifoldpressure drop below atmospheric pressure and cause backflow in the remainderof the cross-section, even at high engine load. Backflow is most pronounced inregions C and E, although at lower engine load, the entire catalyst cross-sectionexperiences flow reversal.

During the beginning of the displacement phase (Fig. 5.17), the piston ismoving upwards, thereby expelling the remaining expanded gas from the cylin-der. Due to the resonance phenomenon, the mean velocity fluctuates as shownin Fig. 5.15. The resonance effect is strong enough to cause further backflowduring the displacement phase (Figs. 5.17 and 5.18). Although the piston veloc-ity is roughly at a maximum in Fig. 5.18f, backflow is still observed, primarilyin region D. It is increasingly more pronounced at lower engine load.

Figure 5.23 depicts the time evolution of the velocity, locally averaged ineach of the five regions A through E of the catalyst cross-section, defined inFig. 5.22.

Regions C, D and E (Fig. 5.23b) are subject to a low time-average flowrate. The velocity behaves very similar in those areas. The strongest flowreversal occurs following each cylinder’s blowdown.


The velocity in the high flow rate regions A and B behaves rather differ-ently (Fig. 5.23a). Peak velocities correspond to the opening of each cylinder.Runners 1 (540 to 720 ca) and 2 (360 to 540 ca) issue near A. Runners 3 (0to 180 ca) and 4 (180 to 360 ca) issue near B. Flow reversal also occurs inregions A and B following blowdown phases of neighboring cylinders.

Experiments have been performed for several engine load conditions andengine speeds ranging between 600 and 3000 rpm. The maximum flow rate de-livered by the lab screw compressor prevented measurements at higher speeds.Very similar flow patterns are observed throughout the engine operating range.

5.2.3 Numerical analysisThe numerical results discussed in this section are obtained using a one-dimensional gas dynamic model of the exhaust system. The model uses a sec-ond order total variation diminishing flux difference splitting scheme and fourthorder Runge-Kutta time integration. The model is implemented in Simulink11,and briefly described below. Appendix D gives more details and validates themodel using benchmark problems.

Subsequently, the numerical results are discussed. Firstly, the results forthe exhaust manifold without cold end are described, i.e. with free discharge tothe atmosphere downstream of the catalyst. This situation is identical to theexperimental set up. Secondly, the results for an exhaust system are describedincluding a cold end, which consists of a single expansion chamber muffler anda straight exhaust pipe.

Model description

Model basis: One-dimensional gas dynamics The one-dimensional Eu-ler equations express the conservation of mass, momentum and energy in thelengthwise z-direction. For unsteady, one-dimensional flow in a duct with vari-able cross-section, including wall friction and heat transfer, the Euler equationsin conservative form are (Eq. (D.1)):

∂ (ρA)∂t

+∂ (ρUA)∂z

= 0

∂ (ρUA)∂t

+∂(ρU2A

)∂z

= −∂ (pA)∂z

+ p∂A

∂z− f

4Ad

U

|U |ρU2

2∂ (ρEA)

∂t+∂ (ρUEA)

∂z= −∂ (pUA)

∂z+ ρqA

where the quantities ρ [kg/m3], U [m/s], E [J/kg], p [Pa] denote average valuesacross the duct cross-section such that the conservation laws are fulfilled.

The duct is discretized in the streamwise z-direction by a n nodes, such thatthe node spacing ∆z = L/(n− 1) (mm). Figure 5.24 shows the discretizationused by the model, which is of the cell-vertex type, i.e. the nodes coincidewith the edges of the control volumes. The Euler equations are solved in each


1 2 j j +1 n

∆zL

A

Figure 5.24 – One-dimensional gas dynamic model: Discretization

node j, for each time step. Although the implemented model can handle non-equidistant nodes, the node spacing is kept constant within each duct. Also,only fixed time stepping is applied for the integration. The local cross-sectionalarea A of the duct can vary along the duct length, as is e.g. the case for thecold end with expansion chamber muffler.

To solve the Euler equations numerically, these coupled partial differentialequations should be transformed into an uncoupled set of scalar differentialequations. Appendix D.1.1 describes this procedure, resulting in the charac-teristic Euler equations (Eq. (D.14)).

Appendix D.1.2 describes the discretization procedure that is applied to thecharacteristic Euler equations. For this model, a second order total variationdiminishing (TVD) discretization scheme is applied, which is developed byVandevoorde [101]. Since the model is cell-vertex based, the flux balances arefulfilled in the nodes and the conservation laws are better satisfied in case ofchanges in the cross-sectional area A [101, 103]. The algorithm is given byEq. (D.23).

Appendix D.2 validates this model using some benchmark problems, similarto the approach of Vandevoorde [101]. Appendix D.3 examines the spatial andtemporal resolution of the model in terms of the node spacing ∆z.

Model assembly: Hot end Figure 5.25 shows a diagram of the gas dy-namic model of the exhaust system. The leftmost dashed box corresponds toexhaust manifold B as depicted in Fig. 2.1. The model features four exhaustrunners, where runners 1 and 3 are longer than 2 and 4. Table 5.1 gives therelevant geometrical specifications. Runners 1 and 2, and likewise 3 and 4 jointo form the two ‘joined runners’ in Fig. 5.25, each 60 mm long and with across-sectional area twice that of a single runner. All runners are cell-vertexdiscretized, according to the specifications in Table 5.1. The gas dynamics aresolved using the second order TVD model as described above.

As indicated in Table 5.1, the node spacing for each duct (except the ex-haust pipe) is ∆z = 10 mm. According to each ducts length, this corresponds

31The runner lengths given in Table 2.1 correspond to the distance between the cylinderhead flange and the diffuser. Each runner extends 100 mm into the cylinder head, up to theexhaust valves seats. In the numerical model, this length is added to the values in Table 2.1.


exhaust runner 1

exhaust runner 2

exhaust runner 3

exhaust runner 4

joined runner 1-2

joined runner 3-4

diffuser and catalyst exit conecold end

exhaust manifold B

cold end (and exit cone)

Figure 5.25 – One-dimensional gas dynamic model of exhaust manifold B includingcold end

respectively to 27, 19 and 7 nodes for runners 1 and 3, runners 2 and 4 and thejoined runners.

As indicated in App. D.3.2, the required number of nodes per minimumwavelength nλ = 16. Based on Eq. (D.31), the maximum resolved frequency isfmax ' (c/∆z )/16 ' 2000 Hz for cold flow conditions (i.e. CME flow rig), orfmax ' 4000 Hz for fired engine conditions.

The calculations are performed with wall friction, yet without heat transferor chemical reactions. The internal wall roughness k = 0.05 mm, correspond-ing to welded steel pipes [74]. The friction factor f is determined using theColebrook-White relationship between f , Re and k/d (see Eq. (1.3)) for fully

Table 5.1 – Numerical model geometry

Component Diameter Length31 Nodes ∆zmm mm - mm

Exhaust runners 1 and 3 28.0 260 27 10Exhaust runners 2 and 4 28.0 180 19 10Joined runners 1–2 and 3–4 39.6 60 7 10Exhaust pipe 40.0 4000 200 20


developed turbulent flow.Besides the wall friction losses, an additional pressure loss due to the runner

curvature is taken into account. This additional pressure loss K = ∆p/pdyn

is distributed throughout the runner length by increasing the friction factorfeff = f+Kd/(4L) , since this local bend loss is difficult to assign to a particulararea of the runner.

The values for the interacting bend pressure loss are obtained fromMiller [74]. Runners 1 and 3 are considered as two interacting 90 bendswith radius of curvature rc = 2d at an out-of-plane combination angle of 90 ,which yields a total pressure loss coefficient K ' 0.48. Runners 2 and 4 areconsidered as single 90 bends with radius of curvature rc = 1d, which yieldsK ' 0.50. The joined runner 1–2 is considered as a single 75 bend withradius of curvature rc = 1d, which yields K ' 0.45. The joined runner 3–4is considered as a single 90 bend with radius of curvature rc = 0.8d, whichyields K ' 0.78.

The cylinders, diffuser and exit cone are modeled as zero-dimensional com-pressible volumes with conservation of mass and energy. The working fluid(air) is assumed an ideal gas. As such, the following equations are solved inthese volumes (Eq. (D.24)):

∂m

∂t=

∑min −

∑mout

∂ (mcvT )∂t

=∑

(mH)in −∑

(mH)out −mrT1V

∂V

∂t

The volume and exhaust valve lift for each cylinder is time-dependent.Equations (2.11) and (B.7) give the instantaneous cylinder volume Vcyl (ωt)and exhaust valve lift h′e (ωt), where the crankshaft position for each cylinderis phased to correspond to the engine firing order (see Table 2.1).

The states in each cylinder are only computed while the exhaust valves areopen. In that case, the inlet boundary condition to the runner corresponds to arestricted flow end. The discharge coefficient Cd for the exhaust valves is takenaccording to Heywood [47] (see Eq. (B.6) and Fig. B.1). When the valves areclosed, the runner is terminated by a closed end. The initial conditions of thecylinder are set to the residual cylinder pressure and temperature correspondingto the experimental case.

The diffuser and exit cone were originally modeled as one-dimensional pipeswith a high aspect ratio (d/L > 1), forming tapered cross-sectional area transi-tions between the catalyst monolith and the connecting pipes. To speed up thesimulation, these blocks are instead modeled as zero-dimensional compressiblevolumes, with conservation of mass and energy. This does not noticeably affectthe results.

The flow in the catalyst substrate is modeled as incompressible gas. Theinertia of the gas is taken into account, although this effect is small due tothe large cross-sectional area ratio associated with the catalyst (see Table 2.1).The wall friction inside the catalyst corresponds to developing laminar flow,including the entrance and exit losses, as described in App. A.2.


Time integration uses a fourth order Runge-Kutta scheme with fixed timestepping. The fixed time step ∆t [s] is determined a priori, based on a CFL-number of 0.5 (see comment below) and assuming a maximum characteristiceigenvalue λmax = 2c, which results in the expression ∆t = CFL∆z/(2c) .After the simulation, the maximum actual CFL number is verified over all thenodes.

Courant-Friedrichs-Lewy (CFL) number The CFL number is adimensionless time step applied to integrate the equations. It followsfrom the Courant-Friedrichs-Lewy (1928) stability condition which ap-plies to finite difference schemes for hyperbolic partial differential equa-tions. The CFL condition states that the numerical dependence domainshould contain the physical dependence domain. In terms of the eigen-value discussion in App. D.1.1, the time step ∆t should be smaller thanthe time it takes the characteristic of the largest eigenvalue λmax to travelalong one node spacing ∆z. Symbolically, this yields:

CFL = max (|λ|) ∆t

∆z= max (|U ± c|) ∆t

∆z< 1 (5.2)

Figure 5.25 shows the exhaust system model including cold end. A secondmodel has been used that corresponds to the experimental set up. In that case,the rightmost dashed box in Fig. 5.25 is not modeled, and only the exhaustmanifold is modeled without exit cone and cold end, i.e. with free discharge tothe atmosphere.

Model assembly: Cold end As shown in Fig. 5.25, the entire cold endis modeled as a single exhaust pipe (4 m long, 40 mm in diameter), witha single expansion chamber muffler which corresponds to Muffler 2 in Daviset al. [33] (24 inch long chamber, area ratio m = 16). The muffler is located inthe center of the exhaust pipe. The cold end is modeled as such a simple caseinstead of the actual exhaust system, since the purpose is merely to determinethe significance of the cold end’s influence on the catalyst velocity distribution.

The exhaust pipe is terminated with an open end boundary condition at at-mospheric conditions. No spherical radiation boundary condition is consideredfor simplicity, since for low frequencies (f < 500 Hz) the reflection coefficientof a spherical radiator approximates unity, similar to the open end boundarycondition [20, 33].

The exhaust pipe is modeled using 200 nodes, corresponding to a nodespacing ∆z = 20 mm. Using Eq. (D.31), this amounts to a frequency resolutionfmax = 1000 Hz. For reasons of calculation time, the cold end node spacing islarger than the spacing in the hot end.

The exhaust pipe wall roughness k = 0.025 mm, corresponding to smoothsteel pipe [74]. The maximum pressure drop in the exhaust pipe (for firedengine conditions, full load and 6000 rpm) is approximately 100 mbar, whichagrees with typical exhaust systems.

Figure 5.26 shows the numerically determined admittance Y /Y0 of the ex-haust pipe, (a) with and (b) without muffler. The admittance is defined in


0 80 160 240 320 400 480 560 640 720−40

−20

0

20

40

Am

plitu

de (

dB)

of ρ

cUi/p

i

Admittance of exhaust pipePipe: ∅ 40 mm x 4 m, Muffler: m = 16, L = 24"

Frequency f (Hz)

Theoretical (L1)Numerical

(a)

0 80 160 240 320 400 480 560 640 720−40

−20

0

20

40

Am

plitu

de (

dB)

of ρ

cUi/p

i

Admittance of exhaust pipePipe: ∅ 40 mm x 4 m, No muffler

Frequency f (Hz)

TheoreticalNumerical

(b)

Figure 5.26 – Admittance of the cold end (a) with muffler and (b) without muffler

0 720 1440 2160−6

−4

−2

0

2

4

6

8

10N = 1200 rpm, Q

ref = 97.3 m3/h, p

i = 2.20 atm


Cat

alys

t vel

ocity

dev

iatio

n U

− U

∞ (

m/s

)

Periodicity

1st cycle 2nd cycle 3rd cycle

Figure 5.27 – Periodicity of the numerical solution, based on the catalyst meanvelocity deviation U − U∞

App. D by Eq. (D.28). Figure 5.26b shows the same behavior as observedin App. D.2.2. Upon introducing the muffler, Fig. 5.26a shows that the ad-mittance corresponds roughly to the admittance of the pipe upstream of themuffler, measuring L1 = (2− 24 · 0.0254)/2 ' 1.7 m in length.

Periodicity Figure 5.27 shows the difference between the calculated meancatalyst velocity U (ωt) at an increasing simulation time t and the mean catalystvelocity obtained after several engine cycles U∞ (ωt). Figure 5.27 demonstratesthat a periodic solution is attained after two engine cycles. In the followingsections, simulations have been performed on an exhaust model including acold end. For those simulations, a periodic solution is only attained after fourengine cycles, due to the larger residence time scale.


Results without cold end: Free discharge

Isochoric flow rig The results discussed in this section are obtained for afree atmospheric discharge after the catalyst (i.e. without cold end), as is thecase for the experiments on the CME flow rig. The following section discussesthe influence of the absence of the cold end, based on numerical simulations.

Figures 5.28 and 5.29 compare the numerical results obtained with thegas dynamic exhaust system model to the experimental results. Each plotshows the numerical catalyst velocity Um,num (ωt) as a dashed line (

), and

the corresponding experimental catalyst velocity Um,exp (ωt) as a solid line(

). These experiments are obtained on the isochoric (CME) flow rig, and

correspond to those discussed in Sect. 5.1.2.The one-dimensional model seems to give an adequate prediction of the

flow dynamics in the catalyst, even though the flow in the actual manifold (seeFig. 2.1b) may be expected to be significantly three-dimensional.

The magnitude of the flow reversal following each blowdown is generallygreater than the one observed experimentally. However, one should keep inmind the limitations of the oscillating hot-wire anemometer (see Chap. 3).The OHW features a maximum measurable negative velocity of approximately−1 m/s. If the local time-resolved velocity U (x, y, ωt) drops below −1 m/s,the resulting measured mean velocity Um (ωt) deviates from the actual value.These measurement errors are denoted rectification or folding errors. Whenusing standard hot-wire anemometry, the folding occurs at zero velocity. Inthe case of OHW, the folding occurs at −1 m/s. This folding effect may benoted in Fig. 5.28b, c and d (

).

Figure 5.30 illustrates this problem for two hypothetical cases with identicalmean velocity Um = −0.5 m/s. For the uniform distribution in Fig. 5.30a, theOHW obtains the correct mean velocity, whereas for the peak distribution inFig. 5.30b, errors occur in the outer region where U < −1 m/s. In the lattercase, the OHW overestimates the actual mean velocity. This causes the localunphysical increases in the measured mean velocity (

) in Fig. 5.28b, c and d

when the simulated mean velocity ( ) becomes negative.

The flow uniformity ηm (ωt) in combination with the mean velocity Um (ωt)in Figs. 5.11a and 5.15b, shows that the OHW errors occur mostly followingthe blowdown phase, when the flow uniformity is quite low for high engine load.This effect also shows up in the velocity distribution in Fig. 5.16b (top), whichexhibits a very low flow uniformity value.

Based on the numerical results, the magnitude of the flow reversal doesnot decrease for increasing engine load. In fact, the opposite is true uponcomparison of Figs. 5.28b,c,d for N = 1200 rpm, and Figs. 5.29a,b for N =1800 rpm. The magnitude of the flow reversal does decrease for increasingengine speed (compare Figs. 5.28d, 5.29b and c).

The velocity fluctuations during the displacement phase are well capturedby the simulation. Upon close examination of Fig. 5.28a, the fluctuation fre-quency corresponds very well, yet the magnitude of the fluctuations does notentirely agree. However, judging by the excellent agreement of the fluctua-


0 180 360 540 720−2

−1

0

1

2

3

4

5N = 600 rpm, Q

ref = 26.5 m3/h, p

i = 1.00 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(a)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 49.9 m3/h, p

i = 1.00 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(b)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 70.9 m3/h, p

i = 1.55 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(c)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 97.3 m3/h, p

i = 2.20 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(d)

Figure 5.28 – Time-resolved numerical and experimental catalyst velocityUm (ωt) [-], for (a) N = 600 rpm (zero load), (b) N = 1200 rpm (zero load),(c) N = 1200 rpm (part load), (d) N = 1200 rpm (high load)


0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1800 rpm, Q

ref = 110.6 m3/h, p

i = 1.55 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(a)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1800 rpm, Q

ref = 137.0 m3/h, p

i = 2.15 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(b)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 2400 rpm, Q

ref = 234.6 m3/h, p

i = 2.00 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(c)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 3000 rpm, Q

ref = 237.4 m3/h, p

i = 1.55 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(d)

Figure 5.29 – Time-resolved numerical and experimental catalyst velocityUm (ωt) [-], for (a) N = 1800 rpm (part load), (b) N = 1800 rpm (high load),(c) N = 2400 rpm (high load), (d) N = 3000 rpm (part load)


-2

-1

0

1

2

3

4

5

U (

m/s

)

Cross-section

Um

= -0.5 m/s, Um

’ = -0.5 m/s

U (true)U’ (measured)

(a)

-2

-1

0

1

2

3

4

5

U (

m/s

)

Cross-section

Um

= -0.5 m/s, Um

’ > -0.5 m/s

U (true)U’ (measured)

(b)

Figure 5.30 – OHW error for velocity distributions with small area of extensive flowreversal

tion frequencies, the numerical model may be expected to be quite helpful inexplaining this resonance phenomenon. The same model is therefore used inSect. 5.3.

For most conditions in Figs. 5.28 and 5.29, the magnitude of the displace-ment phase fluctuations in the numerical catalyst velocity is greater than themeasured fluctuations. However, for the particular case of Fig. 5.28b, the re-verse is true. In the numerical model, the fluctuations may be decreased byincreasing the damping due to wall friction and additional pressure losses. Inparticular, the pressure loss due to the runner curvature is difficult to predict.In the numerical model, the bend losses are distributed throughout the runnerlengths. Furthermore, the loss coefficients are based on correlations [74]. Theseincorporate the effect of bend-to-bend interactions, yet they also assume thatthe bend combinations are connected to upstream and downstream pipes ofquasi-infinite length. An improved agreement might be obtained between sim-ulations and measurements by experimentally determining the loss coefficientsof the individual runners using a stationary flow bench. However, this has notbeen attempted within the scope of this work.

In conclusion, the correspondence between numerical and experimental re-sults seems satisfactory, and of similar quality to results obtained by otherresearchers using commercially available one-dimensional gas dynamic codes.Benjamin et al. [14] present LDA measurements downstream of a close-coupledcatalyst, in a fired engine at 2000 rpm and high load. The experimental re-sults are compared to a transient CFD simulation, coupled with a commercialone-dimensional gas dynamics code.

Figure 5.31a shows a comparison between measured ( ) and calculated

( ) runner velocity. Figure 5.31b shows the correspondence between numer-

ical and experimental results for the velocity at a single point in the catalyst.


(a) (b)

Figure 5.31 – Measured and simulated (a) runner and (b) catalyst velocity for firedengine (Source: [14])

The simulation results predict much stronger backflow than the experimentalobservations. Upon assessing the results in Fig. 5.31b, one should take intoaccount that these are single-point results. Benjamin et al. [14] show no plotof the time-resolved mean velocity, for which the results are likely in betteragreement.

Fired engine Figure 5.32 shows a comparison of the numerical results for(a) fired engine conditions and (b) CME flow rig conditions, both with freedischarge to atmosphere after the catalyst (i.e. without cold end). Both casesare for identical engine speed (N = 1200 rpm) and high engine load. For thefired engine case, the residual cylinder pressure and temperature is 3 atm and800 C, resulting in a temperature of approximately 600 C in the hot end. Forfired engine conditions, air is used as working fluid instead of exhaust gas. Noheat transfer from the gas to the walls and surroundings is modeled.

There is quite some difference in the flow dynamics between both cases,which is mainly due to the difference in temperature. Firstly, the ratio of peakblowdown flow rate to peak displacement flow rate (respectively denoted M1

and M2 in Sect. 2.3.2) is significantly greater for fired engine conditions. Thisalso resulted from the exhaust stroke flow similarity, analyzed in Sect. 2.3 andApp. B. The limitations of the CME flow rig with regard to the maximumintake system pressure have been indicated in Sect. 2.3.3.

The magnitude of the flow reversal following blowdown is greater for firedconditions. This is due to the higher peak blowdown flow rate M1. The blow-down exhaust gas pulse contains more momentum compared to cold flow condi-tions, thereby creating a stronger expansion wave near the end of the blowdown,which in turn causes the increased flow reversal.

Secondly, the velocity fluctuations during the displacement phase are char-acterized by a frequency which is approximately twice the value observed onthe CME flow rig. This is simply the temperature effect on the speed of sound.As explained in Sect. 5.3, the resonance phenomenon is caused by a Helmholtzresonance in the hot end. The resonance frequency f0 is proportional to the


0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q = 99.3 m3/h, high load (fired conditions)


Mea

n ve

loci

ty (

−)

Time−resolved

Um,num

(a)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 97.3 m3/h, p

i = 2.20 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(b)

Figure 5.32 – Time-resolved numerical catalyst velocity Um (ωt) [-] for N =1200 rpm (high load) without cold end, in (a) fired engine and (b) CME flow rigconditions

speed of sound c ∝√T . As such, the ratio of resonance frequencies is expected

to be f0,fired/f0,cold =√Tfired/Tcold ' 1.72. According to the numerical sim-

ulation, the observed frequency ratio varies between 1.54 and 1.70, which is ingood agreement with the above assumption.

Results with cold end

The purpose of this section is to assess the influence of the absence of thecold end on the manifold flow dynamics in general, and the occurrence of flowreversal in the catalyst in particular.

The first paragraph discusses the influence of including a numerical cold endmodel into the one-dimensional exhaust model, for the cold flow conditionsexperienced on the isochoric (CME) flow rig. The second paragraph showsthe effect of fired engine conditions on the flow dynamics, determined using thenumerical model. No experimental data are available for comparison. However,the numerical model has proven its validity, based on the good agreementbetween numerical and experimental results observed in Sect. 5.2.3.

Isochoric flow rig Figure 5.33 compares the time-resolved catalyst velocityobtained using the numerical model, with and without cold end. The casewithout cold end (

) corresponds to a free discharge to the atmosphere after

the catalyst, the same situation as for the experiments on the isochoric flowrig. In the case with cold end (

), the exhaust pipe described in Sect. 5.2.3

is included in the model.As shown in Fig. 5.33, the presence of the cold end influences the catalyst

velocity to some extent, albeit rather limited. In terms of the flow reversal


0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 70.9 m3/h, p

i = 1.55 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,num

Um,num (with cold end)

(a)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 97.3 m3/h, p

i = 2.20 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,num


(b)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1800 rpm, Q

ref = 110.6 m3/h, p

i = 1.55 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,num


(c)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1800 rpm, Q

ref = 137.0 m3/h, p

i = 2.15 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,num


(d)

Figure 5.33 – Time-resolved numerical catalyst velocity Um (ωt) [-], with and with-out cold end, for (a) N = 1200 rpm (part load), (b) N = 1200 rpm (high load),(c) N = 1800 rpm (part load), (d) N = 1800 rpm (high load)


0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1800 rpm, Q

ref = 137.0 m3/h, p

i = 2.15 atm


Mea

n ve

loci

ty (

−)

Time−resolved


Um,num (with cold end, increased friction)

(a)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1800 rpm, Q

ref = 137.0 m3/h, p

i = 2.15 atm


Mea

n ve

loci

ty (

−)

Time−resolved


Um,num (with cold end, without muffler)

(b)

Figure 5.34 – Time-resolved numerical catalyst velocity Um (ωt) [-] for N =1800 rpm (high load) with cold end, (a) with increased (×2.5) wall friction, (b) withexhaust pipe excluding muffler

observed without cold end, the presence of the cold end does not seem toreduce the backflow magnitude. In case of Fig. 5.33a and b, the opposite iseven true. During the displacement phase, the velocity fluctuations are slightlyaffected by the presence of the cold end, mostly in terms of the fluctuationfrequency and not so much for the amplitude.

In general, the cold end does not significantly affect the flow dynamics in thecatalyst. However, this conclusion is based only on the simulations performedusing the present gas dynamic model of the exhaust system, with the simpleexpansion chamber muffler. In truth, a more complex exhaust system will bepresent in the real engine configuration, although no attempt was made tosimulate a realistic cold end in this thesis.

Figure 5.34 demonstrates the effect of varying parameters of this simple coldend model. Figure 5.34a shows the effect on the catalyst velocity of increasingthe wall friction factor f by a factor of 2.5 (

) with respect to the reference

case ( ), at least for the governing flow conditions at N = 1800 rpm and high

engine load. The increased friction factor is obtained by artificially increasingthe wall roughness from a value k = 0.025 mm to k = 1 mm, corresponding toa heavily rusted steel pipe [74].

By increasing the wall friction, the stationary (i.e. low frequency, f → 0)flow resistance of the cold end is increased without changing its reactivity athigher frequency. In terms of the admittance Y /Y0 , the DC-component isreduced, while the higher frequency characteristics are unchanged.

Figure 5.34b shows the effect on the catalyst velocity of removing the mufflerfrom the cold end, resulting in a 4 m long straight exhaust pipe. In this case, thehigher frequency characteristics of the admittance Y /Y0 are changed withoutsignificantly changing the DC-component.


0 180 360 540 720-2

-1

0

1

2

3

4

5N = 1200 rpm, Q = 93.7 m3/h, high load (fired conditions)


Mea

n ve

loci

ty (

-)

Time-resolved


(a)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 97.3 m3/h, p

i = 2.20 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,num


(b)

Figure 5.35 – Time-resolved numerical catalyst velocity Um (ωt) [-] for N =1200 rpm (high load) with cold end, in (a) fired engine and (b) CME flow rig condi-tions

As demonstrated by Figs. 5.34a and b, the influence of altering the cold endcharacteristics is most significant during the displacement phase, affecting boththe fluctuation frequency and amplitude. Neither the backpressure of the coldend, nor the higher frequency reactivity significantly affect the flow dynamicsin terms of the magnitude of the flow reversal following the blowdown phase.

Fired engine A comparison between Figs. 5.35a and 5.32a reveals an ap-preciable influence of the presence of the cold end in fired engine conditions,in particular during the displacement phase. This contrasts with Fig. 5.35bobtained in cold flow conditions, where only a small influence can be detectedbetween the dashed line (

) (with cold end) and the solid line (

) (without

cold end).As indicated by Fig. 5.32, in the absence of a cold end, the velocity fluc-

tuations appear at a higher frequency in fired engine conditions. The ratio offluctuation frequencies between fired and cold conditions is determined by thesquare root of the temperature ratio (see Sect. 5.2.3).

This is not true upon introducing the cold end. In this case, the hot endinteracts with the cold end, resulting in very different gas dynamics and dif-ferent resonance frequencies. Based on Fig. 5.35b, one might have concludedthat the hot end gas dynamics can be considered decoupled from the cold enddynamics. However, the difference between Figs. 5.35a and 5.32a shows thatthis is not a valid assumption, at least not in fired engine conditions.

Park et al. [81] present phase-locked velocity results obtained using LDA ina close-coupled catalyst manifold on a fired engine. Figure 5.19 shows periodicflow reversal in the order of −1 to−2 m/s, that occurs following each blowdown.

Also using LDA, Liu et al. [70] show flow reversal occurring downstream of


a close-coupled catalyst in motored engine conditions, albeit not in fired engineconditions. Transient simulations do show flow reversal in motored and firedconditions. Equivalently, flow reversal is most pronounced following blowdown.The maximum backflow varies between −1 and −5 m/s in motored and firedconditions.

Conclusion

Reviewing the numerical results discussed in the preceding sections, the gasdynamic model has improved the understanding of the flow dynamics in theclose-coupled catalyst manifold. Particularly, (i) the effect of the cold end and(ii) the effect of fired engine conditions have been studied numerically.

In cold flow conditions (corresponding to the isochoric CME flow rig), nosignificant influence is noted between the flow dynamics in hot end and coldend. However, the influence proves much stronger in fired engine conditions.

Based on these numerical results for the time-resolved catalyst velocity, theexperiments appear to be valid in cold flow conditions, regardless of the pres-ence of the cold end, or the related backpressure. In fired engine conditions, thetemperature and speed of sound is higher, which invariably increases the res-onance frequencies. Therefore, a straightforward extrapolation to fired engineconditions cannot be made based on these measurements.

Finally, periodic flow reversal following the blowdown phase is noted inall operating conditions, (i) fired engine or cold flow conditions, (ii) with andwithout cold end, (iii) for two typical variations in the cold end characteristics(i.e. backpressure and attenuation). For the examined cases, the magnitudeof the flow reversal is minimal corresponding to the experimental conditionson the CME flow rig. Therefore, in realistic conditions (i.e. fired engine withcold end), the periodic flow reversal is expected to be stronger than observedexperimentally on the CME flow rig.

5.2.4 Discussion: Physical relevance of catalyst flow re-versal

Catalytic reactions in automotive catalysts are exothermic. In fired engineconditions, the temperature of the gas downstream of the catalyst is thereforehigher than upstream. Periodic backflow is observed on the CME flow rig, andis also reported in fired engine conditions by other authors [4, 70, 81, 59]. Incase of backflow, part of the hot processed gas is recycled through the catalyst,into the collector-diffuser upstream of the catalyst.

As pointed out in Sect. 1.2.1, thermal degradation of the catalyst is a com-plex process that mainly involves loss of catalytic surface area by sintering,due to excessive catalyst temperature [11, 38]. Sintering rate increases expo-nentially with temperature, so even a small temperature change may signifi-cantly affect local catalyst degradation. Regions of high flow rate (A and B inFig. 5.22) are subject to higher chemical degradation due to poisoning. Flowreversal in these regions (Fig. 5.23a) may impose an additional thermal load.


The walls of the exhaust manifold are already subject to severe cyclic ther-mal loads. Manifold design aims to avoid local hot spots, especially on sensitiveareas such as welds. Catalyst flow reversal in near-wall regions (D and E inFig. 5.22 and Fig. 5.23b) may raise the time-averaged gas temperature, therebyadding to the existing thermal load on wall materials immediately upstream ofthe catalyst.

Background: Reverse flow catalytic reactors The chemical pro-cess industry has recently seen the introduction of so-called reverse flowcatalytic reactors (RFCR). These are mainly applied for endothermic orslightly exothermic reactions (for air purification: e.g. oxidation of hy-drocarbons, carbon monoxide and sulphur dioxide; for synthesis: partialoxidation of methane, synthesis of methanol and ammonia).

A standard unidirectional catalytic reactor requires preheating for suchreactions. By applying periodic reversal of inlet and outlet sides, the endsections of the catalyst act as regenerative heat exchangers. The cata-lyst itself therefore does part of the preheating. If operating conditionsare well controlled, the catalyst center may obtain much higher temper-atures compared to unidirectional operation. The RFCR has not beenin widespread use. Its complex dynamics require an advanced controlsystem to prevent extinction of the reaction.

Mitri et al. [76] discuss experimental results of thermal deactivation inRFCR operation, for partial oxidation of methane. The average catalysttemperature is 300 to 400 C higher compared to unidirectional opera-tion. A significant increase in thermal deactivation is noted.

Eigenberger and Nieken [35] discuss the influence of several parametersincluding the reversal frequency on the maximum catalyst temperatureand reactor stability. The reactor temperature increases for increasingreversal frequency.

Results from these studies [76, 35] cannot be extrapolated to the presentcase. Flow reversal observed in the automotive catalyst is characterizedby (i) higher reversal frequencies (50 to 200 Hz, compared to 0.01 to1 Hz), (ii) lower reverse flow magnitude. Furthermore, (iii) the processedgas is recycled yet contains less reactants, whereas an RFCR is fed withfresh mixture in both forward and reverse flow.

Based on the observed velocity magnitude of the flow reversal in the close-coupled catalyst manifold, the traveled distance of the hot exhaust gas may beestimated as it passes through the catalyst. For a negative velocity magnitude|Urev| ' 1 m/s and a catalyst length of L = 137 mm, the space velocity V =U/L equals 7.3 s−1, corresponding to a characteristic travel time of 137 ms.Thus, this is a rather large timescale compared to the flow pulsation period Tp.The traveled distance is proportional to the product of the negative velocitymagnitude |Urev| and the flow pulsation period Tp, which yields values in theorder of 10 mm for the traveled distance. This is small compared to the catalystmonolith length of 137 mm.

Nevertheless, an automotive close-coupled catalyst operates at the outeredge of permissible material constraints. Exhaust gas temperatures reach in


excess of 1000 C during high engine load. Any process causing even a minorincrease or decrease in thermal load is worth investigating. Further research isneeded to establish the effect of flow reversal as observed in the current researchon the catalyst and manifold wall temperatures.

5.3 Helmholtz resonance

5.3.1 Introduction

Figure 5.2b shows the first encounter with an unexpected and initially unex-plained phenomenon. Due to the high bandwidth of the hot-wire anemometerand the applied phase-locked measurement technique, strong fluctuations areobserved in the time-resolved mean catalyst velocity.

Except for the isothermal flow rig with rotating valve, this phenomenon isobserved for both exhaust manifolds A and B, and for both isothermal andisochoric flow rigs. For the isochoric (CME) flow rig, the fluctuations are muchstronger compared to the same manifold mounted on the isothermal flow rig.

Upon the first encounter with these fluctuations, the possibility of mechani-cal vibrations was considered. The hot-wire probe is mounted on an automatedtraversing system, which is mounted on the lab floor, adjacent to the flow rig.Both flow rig and traversing system are mounted as rigidly as possible to thefloor, using thick threaded supports. These threaded supports are also used tolevel the flow rig and traversing system perfectly horizontally.

Any significant relative motion between the velocity probe and the exhaustmanifold results in an error velocity ∆U . Using directionally sensitive ac-celerometers32, the accelerations of the flow rig, exhaust manifold and travers-ing system were measured, phase-locked with the flow pulsation. The relativevelocity ∆U is determined from the integrated difference of the accelerationsignals, or ∆U =

∫t(a− a0) dt, where the probe acceleration a0 is negligible

compared to the exhaust manifold acceleration a a0 ' 0.For the rotating valve, the operation is virtually vibrationless, due to the

absence of any inertial forces. The cylinder head exhibits some detectable vi-bration, although completely insignificant compared to an engine with movingpistons. For both pulsator devices, the resulting error velocity ∆U correspond-ing to the relative motion between manifold and hot-wire probe is found to besmaller than 10 mm/s, with peak frequencies not exceeding 25 Hz. As such,∆U is marginal compared to the observed mean velocity fluctuations, whichare of the order of 1 m/s and higher.

The following sections explore the origin of the observed fluctuations. Sec-tion 5.3.2 provides an analytical description of the low-frequency character-istics of a gas dynamic system, introducing the Helmholtz resonance. Sec-tion 5.3.3 discusses the velocity fluctuations observed experimentally on theisothermal and isochoric (CME) flow rigs. Section 5.3.4 discusses the frequency

32PCB Piezotronics type 356B08 three-dimensional accelerometer and ICP amplifier.

5.3 Helmholtz resonance 205

response function of the close-coupled catalyst manifold, by means of the one-dimensional gas dynamic model used in Sect. 5.2.3 and described in App. D.

5.3.2 Analytical modelA Helmholtz33 resonator [20, 33] consists of a volume connected to a pipe (asdepicted in Fig. 5.36), filled with a compressible fluid. At low frequencies(f < c/(2L) , where c is the speed of sound and L is the pipe length), thisgas dynamic system behaves approximately as a second order spring-and-massmechanical system. The gas in the pipe behaves as an incompressible oscillatingplug, with a mass m [kg] equal to:

m = ρAL (5.3)

where A and L are the cross-sectional area [m2] and the length [m] of the pipe.The compressible gas in the volume V [m3] is characterized by a mechanicalspring constant k [N/m] equal to:

k = γpA2/V (5.4)

where γ is the ratio of specific heats [-]. In Eqs. (5.3) and (5.4), p, ρ and γare evaluated at a mean reference condition. This system features an eigenfre-quency fH [Hz]:

fH =12π

√k

m=

12π

c

L

√AL

V(5.5)

where c =√γrT is the speed of sound [m/s].

In acoustics, the term ‘Helmholtz resonator’ denotes a cavity consisting ofa closed volume and a pipe (or ‘neck’) which is perpendicular to the main duct(see e.g. Beranek [20], Davis et al. [33], Boonen [21]). While the duct mayexperience a net flow, the cavity neck experiences only an oscillating flow withzero mean. Such resonators are used as narrow-band acoustic dampers (e.g.in silencers for reciprocating machinery, such as the simple muffler shown inFig. 5.37), or as reference tone sound sources in musical instruments (by meansof some aero-acoustic or aero-elastic sound generation).

As noted by Davis et al. [33], the effective oscillating mass in the resonatorneck is increased by a certain amount, due to the entrainment of surroundingnearby gas on either side of the neck (see Fig. 5.36). This effect is taken intoaccount by using an effective length in Eq. (5.3), usually defined as:

Leff = L+ 2β d (5.6)

33Hermann Ludwig Ferdinand von Helmholtz ( 31 Aug. 1821 –† 8 Sept. 1894) was a German physician and physicist. Besides im-portant contributions to thermodynamics (e.g. Über die Erhaltung derKraft, 1847), Helmholtz is famous for his 1863 book Die Lehre von denTonempfindungen als physiologische Grundlage für die Theorie der Musikand of course, for inventing the Helmholtz resonator to show the heightof various tones. (Source: Wikipedia, Universität Heidelberg)


L Leff A

V

p, T

Figure 5.36 – Helmholtz resonatornomenclature

Figure 5.37 – Helmholtz resonator asexhaust muffler (Source: [33])

where d is the diameter of the neck pipe and β is an empirical constant, typicallyin the range 0.3 < β < 0.43 [20, 33].

In close-coupled catalyst manifolds, the same resonating behavior is ob-served, yet with net flow through the resonator. In general, the Helmholtzfrequency fH denotes the zeroth order resonance frequency of a gas dynamicsystem. This is the interpretation that should be kept in mind when the termHelmholtz resonance is used in this thesis.

Considering the complexity of the exhaust system, several resonating com-binations of masses and springs may be identified. For instance, any volumewith negligible momentum may be considered as a spring (e.g. cylinders, dif-fuser and exit cone, closed exhaust runners), and any pipe with a significantmomentum may be considered as a mass (open exhaust runners, exhaust pipe).The combined exhaust system features multiple connections, which are furthercomplicated by damping components (e.g. exhaust valves, catalyst substrate,pipe bends and junctions).

Figure 5.38 shows an equivalent mechanical spring and mass system for thelow frequency gas dynamics in the close-coupled catalyst exhaust manifold.The diagram shows the volumes as springs kcyl, kd, and the pipes as massesmr, mcat. The factors σd and σe represent the area ratios of the diffuserand exit cone. Figure 5.38a represents a free discharge, corresponding to theexperimental set up. Figure 5.38b includes the exit cone and the cold end as a‘black box’ impedance Zcold end (f).

For each spring, an effective volume should be considered. Typically, kcyl

corresponds to the cylinder volume at mid position in between bottom and topdead center (see Boonen [21]), or:

Vcyl,eff =(

12

+1

%− 1

)πb2

4s (5.7)

where b and s are the bore and stroke [m], and % is the volumetric compres-sion ratio [-]. The factor 1/(%− 1) is the relative dead volume. The volumecorresponding to kd may be considered the diffuser volume Vd along with partof the combined volume of the closed runners, or:


p cyl

Ur U

mr kdkcyl

V cyl Ar, Lr V d

1/σd

mcat

closed runner

open runner

closed runner

closed runner

p d

(a)

p cyl

Ur U

mr kdkcyl

V cyl Ar, Lr V d

1/σd σe

mcat

closed runner

open runner

closed runner

closed runner

Zcold end

ke Zcold end

p d

(b)

Figure 5.38 – Equivalent lumped parameter model of the low frequency gas dy-namics in a close-coupled catalyst exhaust manifold, (a) without and (b) with coldend


Vd,eff = Vd + α (nr − 1)ArLr (5.8)

where nr is the number of runners and 0 6 α 6 1.Similarly, effective lengths should be used for each mass, by introducing

a correction factor β as described above [33]. Not shown in the mechanicaldiagram of Fig. 5.38 are the different damping components corresponding toflow resistances (e.g. exhaust valves, catalyst substrate friction, pipe bends andwall friction).

In Fig. 5.38, the quantity of interest is the catalyst velocity U [m/s]. Thedriving quantity is the piston displacement, which creates a volume velocityQcyl = −dVcyl/dt [m3/s]. In Sect. 5.3.4, the frequency response functionfrom ‘input’ Qcyl to ‘output’ U is determined numerically, by means of theone-dimensional gas dynamic model of the exhaust system previously used inSect. 5.2.3.

To establish which system components are in resonance, and cause the ob-served velocity fluctuations, simultaneous phase-locked velocity and/or pressuredata are required at more than one location, thereby revealing the phase dif-ference between the signals. In the experimental set up, besides the catalystvelocity, also the velocity at the entrance to runner 1 has been measured, aswell as the pressure in cylinder 1 and the diffuser pressure.

The following section describes the experimental observations, and the ac-tions taken to identify the resonating components.

5.3.3 Experimental results

Figure 5.39 gives a comparison at equal engine speed (N = 1200 rpm) betweenthe time-resolved mean velocity on (a,b,c) the CME flow rig and (d) the isother-mal flow rig. Only a minor difference can be observed in Fig. 5.39d betweenminimum and maximum flow rate (Qref ' 50 . . . 115 m3/h). This comparisonis presented here since an isothermal flow rig approach is used by numerousauthors [88, 17, 69, 22, 53] for studying pulsating flow in exhaust systems withclose-coupled catalyst, in spite of the appreciably different flow dynamics.

Figure 5.39 shows the time-resolved velocity in runner 1 Ur=1 (ωt) [-] as adashed line (

). Top dead center of cylinder 1 corresponds to 0 ca. Consid-

ering the engine’s firing order (see Table 2.1), the plots show the consecutiveexhaust strokes of cylinders 3, 4, 2 and 1, respectively. The runner velocityis measured at the inlet of runner 1 using a hot-film sensor, mounted flushwith the inner wall. Ur=1 (ωt) is measured in a single point, and as such itis only indicative of the mean runner velocity. It is only used to determinethe phase lag between runner and catalyst velocity, with respect to the reso-nance phenomenon. The runner velocity measurement is not available for allexperiments, which explains why it is only shown in Fig. 5.39a and b.

Background: Measuring the runner velocity Initially, the runnervelocity has been measured using a hot-wire probe, which could be tra-versed along a straight line. However, such a probe is very prone to wire


0 180 360 540 720-1

0

1

2

3

4

5

6

7Time-resolved


Mea

n ve

loci

ty (

-)

N = 1200 rpm, Qref

= 97.3 m3/h, pi = 2.20 atm

Um

(θ)U

r=1(θ)

(a)

0 180 360 540 720-1

0

1

2

3

4

5

6

7Time-resolved


Mea

n ve

loci

ty (

-)

N = 1200 rpm, Qref

= 70.9 m3/h, pi = 1.55 atm

Um

(θ)U

r=1(θ)

(b)

0 180 360 540 720-1

0

1

2

3

4

5

6

7Time-resolved


Mea

n ve

loci

ty (

-)

N = 1200 rpm, Qref

= 50.2 m3/h, pi = 1.00 atm

Um

(θ)

(c)

0 180 360 540 720-1

0

1

2

3

4

5

6

7Time-resolved


Mea

n ve

loci

ty (

-)

N = 1200 rpmQ

ref = 117.1 m3/h

Qref

= 43.3 m3/h

(d)

Figure 5.39 – Time-resolved velocity observed on (a,b,c) CME and (d) isothermalflow rig, for N = 1200 rpm and different flow rates


breakage. According to the manufacturer19, wire breakage may occurin strong pulsating flows of near sonic peak velocity. Furthermore, asexplained in Sect. 2.3, the temperature of the exhaust gas stream dropsbelow 0 C at high intake pressure pi > 2.5 atm. This is due to the heatloss from the gas to the combustion chamber walls during the compres-sion and expansion strokes, and due to the blow-by leakage through thepiston-cylinder clearance. Subzero temperatures in the exhaust system(in combination with the absence of a dehumidifier in the compressed airsupply) yields tiny ice particles in the exhaust flow. These particles mayimpact the wire and further promote breakage. Downstream of the cata-lyst, this problem is not encountered, likely due to the warming of the airas it passes through the exhaust runners and catalyst. The metal man-ifold parts ensure a good heat conduction away from the engine block,which is heated internally due to viscous friction of the moving parts, toaround 100 C (depending on the engine speed).

The mean velocity fluctuations during the displacement phases in Figs. 5.39a,b and c have also been observed with manifold B mounted on the isothermalflow rig, although to a much lesser extent and only at higher engine speed(see Fig. 5.9b). For manifold A mounted on the isothermal flow rig, similarfluctuations have been observed, yet only when using the cylinder head aspulsator. For the rotating valve, such fluctuations were not observed. Thepeak fluctuation frequencies for manifold A are between 200 and 280 Hz (seeFig. 5.2b).

For manifold B, the fluctuation frequencies observed on CME and isother-mal flow rig are nearly identical, varying between 140 and 200 Hz. The fre-quency is independent of engine speed and flow rate, as shown in the summaryin Table 5.2. Table 5.2 shows the peak frequency in the catalyst velocity duringthe displacement phase of individual exhaust strokes, for runner r = 1 . . . 4 (seeTable 2.1 and Fig. 2.1b). The peak frequencies are determined from the energyspectrum, as shown in Fig. 5.40.

Figure 5.40 shows frequency spectra of the time-resolved mean catalyst ve-locity Um during each cylinder’s exhaust stroke for N = 600 rpm. As Table 5.2indicates, the peak frequency remains unchanged at higher engine speeds. How-ever, the spectral resolution decreases as the engine speed increases (due to thedecreasing period), which leads to increasing uncertainty on the peak frequen-cies.

Table 5.2 demonstrates that the length of the open runner can be detectedfrom the fluctuation frequency of the catalyst velocity during individual exhauststrokes. Longer runners (e.g. 1 and 3) result in lower resonance frequenciesthan shorter runners (e.g. 2 and 4). The same is observed in measurementsand simulations by other authors (see Sect. 5.3.5).

Table 5.3 demonstrates the prediction of the resonating system, based onthe lumped parameter model in Fig. 5.38. Two possible resonating systems areconsidered, that result in resonance frequencies close to the observed values inTable 5.2. Note that the runner length, cylinder volume and diffuser volumeused to predict the values in Table 5.3 are the effective values, defined byEqs. (5.6), (5.7) and (5.8), respectively, with α = 1 and β = 0.43.


10 20 50 100 200 50010

-6

10-5

10-4

10-3

Frequency f (Hz)

Ene

rgy

spec

tral

den

sity

of

Um

((m

/s)2 /H

z)

fpeak = 160.6 Hz (r = 3)fpeak = 183.1 Hz (r = 4)fpeak = 181.9 Hz (r = 2)fpeak = 157.5 Hz (r = 1)

Figure 5.40 – Frequency spectra of the catalyst velocity during individual exhauststrokes for manifold B on the CME flow rig, for N = 600 rpm

Table 5.2 – Catalyst mean velocity peak fluctuation frequencies during individualexhaust strokes, for manifold B on the CME flow rig

N pi Qref Peak frequencyr = 1 r = 2 r = 3 r = 4

rpm atm m3/h Hz Hz Hz Hz600 1.00 26.5 158 182 161 183

1200 1.00 46.6 164 181 166 1781200 1.55 67.7 141 153 126 1611800 1.00 75.1 148 158 143 1441200 2.23 93.3 125 173 141 1581800 1.58 97.4 152 165 141 1691800 2.23 136.6 143 146 139 1442400 1.55 192.1 135 193 125 1952400 2.03 238.8 140 193 153 178fH,1, see Table 5.3 166 188 166 188fH,2, see Table 5.3 182 205 182 205


The gas in the open exhaust runner oscillates as incompressible plug. Eitherthe cylinder volume Vcyl act as a single compressible spring (fH,1), or thediffuser volume Vd and cylinder volume Vcyl act as two compressible springsin series (fH,2). The resulting spring constant for two springs in series is thesum of the individual spring constants kcyl + kd. In terms of Eq. (5.4), theequivalent volume corresponds to V −1 = V −1

cyl,eff + V −1d,eff , where Vcyl,eff and

Vd,eff are given by Eqs. (5.7) and (5.8).Up-close examination of Figs. 5.39a and b reveals that the velocity in

runner 1 Ur=1 (ωt) ( ) leads the mean catalyst velocity Um (ωt) (

) by

∆ϕ = π/2 radians. Although the time-resolved cylinder pressure pcyl (ωt)is not shown in Fig. 5.39, it also leads the catalyst velocity by π/2 radians.

This phase lead of π/2 rad is quite surprising. Considering the lumpedparameter model in Fig. 5.38, two possible cases may arise in terms of thephase difference ∆ϕ between runner and catalyst velocity. (i) Firstly, the phasedifference ∆ϕmay be zero, if the diffuser volume acts as an infinitely stiff springkd kcyl. (ii) Secondly, the phase difference ∆ϕ may equal π rad. In thatcase, the gas mass in the open runner and the catalyst substrate oscillate inantiphase, and the diffuser volume acts as a spring of finite stiffness kd ∼ kcyl.

However, the observed phase difference of ∆ϕ = π/2 suggests that thelumped parameter model in Fig. 5.38 is incorrect. The phase lead becomes π/2if the inertia of the gas contained in the catalyst substrate mcat is negligible.Taking into account the laminar flow friction in the substrate (see App. A.2),the catalyst velocity U is then in phase with (and roughly proportional to) thepressure difference across the catalyst, which reduces to pd for a free discharge.As such, the runner velocity Ur may lead the catalyst velocity by ∆ϕ = π/2 rad.

This explanation for the resonance frequency seems acceptable for the CMEflow rig conditions. However, when manifold B is mounted on the isothermalflow rig, nearly the same fluctuation frequencies are observed (between 140and 200 Hz). Similarly, frequencies between 200 and 280 Hz are observed whenmanifold A is mounted on the isothermal flow rig with the cylinder head aspulsator. As noted earlier, the fluctuations are (i) weaker compared to theones observed on the CME flow rig, and (ii) occur only at higher engine speed(e.g. see Figs. 5.9b, 5.2b).

For the isothermal flow rig, Fig. 2.2 demonstrates that the surge vesselmimics an infinite cylinder volume at quasi constant pressure. Given the 450 lsurge vessel volume, the spring stiffness associated with the surge vessel isnegligible, according to Eq. (5.4). For a free discharge set up, the only eligiblevolume to act as a compressible spring is the diffuser volume Vd.

According to Beranek [20] and Davis et al. [33], there is a considerableuncertainty on the parameter β used in Eq. (5.6) for correcting the pipe length.The same holds true for the parameter α in Eq. (5.8). In fact, these parametersare only known a priori for very basic applications (e.g. a circular orifice inan infinite plane [33]). In engineering applications, the parameters should bedetermined through empirical testing or model fitting.

It is therefore not surprising that by ‘fitting’ these parameters, Eq. (5.5)may yield the observed fluctuation frequencies not only for the CME flow rig,


102

103

-60

-50

-40

-30

-20

-10

02nd order TVD

δx = 5 mm

Mag

nitu

de (

dB)

of ρ

cU/p

cyl

FRFFrom: Cylinder pressure p

cyl, To: Catalyst velocity ρcU

L = 150 mm (234 Hz)L = 90 mm (274 Hz)L = 120 mm (249 Hz)

102

103

-180

-90

0

90

180

Frequency f (Hz)

Phas

e (°

)

(a)

102

103

-60

-50

-40

-30

-20

-10

02nd order TVD

δx = 5 mm

Mag

nitu

de (

dB)

of ρ

cU/p

cyl

FRFFrom: Cylinder pressure p

cyl, To: Catalyst velocity ρcU

L = 160 mm (131 Hz)L = 80 mm (181 Hz)

102

103

-180

-90

0

90

180

Frequency f (Hz)

Phas

e (°

)

(b)

Figure 5.41 – Frequency response function between ‘cylinder’ pressure and catalystvelocity, for (a) manifold A and (b) manifold B on the isothermal flow rig

but also for the isothermal flow rig.In conclusion, a significant uncertainty remains in identifying the resonating

system by means of the experiments alone. Therefore, the following sectiondescribes the use of the one-dimensional gas dynamic model to estimate thefrequency response function of the exhaust system.

5.3.4 Numerical results

Isothermal flow rig

Figure 5.41 shows the numerically determined frequency response functions forboth manifolds, mounted on the isothermal flow rig. The response function isdefined as:

FRF (f) =ρcU

pcyl(5.9)

where the cylinder pressure pcyl is relative to the atmospheric pressure [Pa] andthe characteristic impedance ρc (see App. D.2) is included to non-dimensionalize FRF (f).

The numerical model shown in Fig. 5.25 is simplified by replacing the cylin-ders with constant pressure boundary conditions. Thus, the ‘cylinder’ pressureis simply the surge vessel pressure. The dynamics of the surge vessel are entirely


neglected. For manifold A, three runners are simulated, without junctions priorto issuing into the diffuser volume (see Fig. 2.1a).

The usual approach to determine the frequency response function is de-scribed in App. D.4, and uses a multisine signal as input disturbance. Thisapproach is used throughout the thesis, except for determining the responsefunctions in Fig. 5.41. Instead, these responses are determined by linearizingthe model about a steady-state operating point, and subsequently determiningthe FRF for the linear model. This is easily accomplished using the built-inSimulink11 functionality. However, this approach is not used further in this the-sis, because of its poor resolution in the higher frequency range (f > 500 Hz).

Nevertheless, the numerically determined FRFs in Fig. 5.41 still providesuseful information in the lower frequency range (f < 500 Hz).

The steady state range (f → 0) of the response function behaves as ex-pected, with zero phase difference between the surge vessel pressure pcyl andthe resulting flow rate UA. The response level (between −25 and −30 dB) ismainly influenced by the catalyst wall friction and the cross-sectional area. Atincreasing frequency, the response magnitude increases and the phase drops. Atthe resonance frequency, the magnitude is limited by the damping components(e.g. exhaust valves, catalyst friction).

The first resonance peaks correspond to the open runner mass oscillatingon the diffuser volume. This resonating system is here denoted Helmholtzresonances. The frequencies agree with the experimental observations on theisothermal flow rig. The Helmholtz resonance frequencies range from 234 to274 Hz for manifold A (from longest to shortest runner), and from 131 to181 Hz for manifold B (long runners 1 and 3 versus short runners 2 and 4).The peaks between 500 < f < 1000 Hz are due to the gas mass inside thecatalyst oscillating on the diffuser volume. The higher frequency peaks andphase changes (f > 1000 Hz) are due to standing waves in the runners.

Isochoric flow rig: Without cold end

For the isochoric flow rig, the numerical model as presented in Fig. 5.25 isused to numerically determine several frequency response functions presentedin this section. By contrast to Sect. 5.3.4, these functions are obtained usingthe approach described in App. D.4, rather than by linearizing the model. Theresponse function is determined by applying a multisine disturbance to thecylinder volume and monitoring the response of the model. The mean cylindervolume corresponds to the mid position between bottom and top dead center,as discussed in Sect. 5.3.2 for Eq. (5.7).

Figure 5.42a shows the frequency response function between the cylin-der volumetric velocity Qcyl and the catalyst velocity U . The cylinder vol-umetric velocity is determined by the piston rate of displacement, or Qcyl =−dVcyl/dt [m3/s]. Numerator and denominator both have the dimensions ofa volumetric flow rate by multiplying U with the catalyst cross-sectional areaA. As such, the FRF equals the ratio of two volumetric flow rates at differ-ent locations in the model, i.e. at the cylinder of the open runner and at the


102

103

−40

−20

0

20

40 f

0,r=1 = 146.5 Hz

Am

plitu

de (

dB)

of U

A/Q

cyl

FRFFrom: Cylinder volume velocity Q

cyl, To: Catalyst velocity U A

f0,r=2

= 170.9 Hz

Runner 1Runner 2

102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

(a)

102

103

−40

−20

0

20

40

Am

plitu

de (

dB)

of U

A/U

r Ar

FRFFrom: Runner velocity U

r A

r, To: Catalyst velocity U A

Runner 1Runner 2

102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

f1,r=1

= 236.0 Hz f1,r=2

= 236.0 Hz

(b)

102

103

−40

−20

0

20

40

Am

plitu

de (

dB)

of ρ

cU/p

FRFFrom: Catalyst pressure p, To: Catalyst velocity ρcU

Runner 1Runner 2

102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

f0,r=2

= 172.9 Hz f0,r=1

= 148.5 Hz

(c)

Figure 5.42 – Frequency response function between (a) cylinder volume velocity,(b) runner velocity, (c) downstream catalyst pressure and catalyst velocity, for man-ifold B on the CME flow rig (free discharge)


catalyst.The magnitude and phase of the FRF in Fig. 5.42a behaves as expected.

For low frequencies (f → 0), the numerator and denominator have the samemagnitude and zero phase difference. For increasing frequency, the catalystvelocity magnitude increases and its phase lags with respect to the piston dis-placement velocity. At the resonance frequency f0, the phase lag between Qcyl

and U is −π/2 rad.Figure 5.42b shows the frequency response function between the open run-

ner velocity (near the exhaust port) Ur and the catalyst velocity U . At theresonance frequency f0 obtained from Fig. 5.42a, the phase difference betweenrunner and catalyst velocity is still negligible. Therefore, this numerical simu-lation does not confirm the experimental observation that the runner velocityleads the catalyst velocity by π/2 rad. The reason for this discrepancy is notimmediately clear.

Corresponding to the two runner lengths, two resonance frequencies are ob-tained in Fig. 5.42a, f0 = 146.5 and 170.9 Hz (for long runner 1 and shortrunner 2). These are in good agreement with the observed fluctuation fre-quencies in Table 5.2. The resonance peaks for the remaining runners 3 and 4coincide with these for 1 and 2. The magnitude at resonance is slightly differentfor runners 3 and 4. This is due to the different pressure drop coefficient injoined runner 3–4 compared to joined runner 1–2 (see Fig. 5.25). As shown inFig. 2.1b, the joined runner 3–4 features a stronger bend angle.

The next resonance peak in Fig. 5.42a is due to the oscillation of gas insidethe catalyst on the diffuser volume. This is demonstrated in Fig. 5.42b. Theresonance frequency f1 = 236 Hz, which is independent of the open runnerlength. At this resonance, the catalyst velocity lags the runner velocity byπ/2 . This phase difference corresponds to the observations in Sect. 5.3.3, yetat a higher resonance frequency.

As an alternative, Fig. 5.42c shows the transfer function between the pres-sure downstream of the catalyst and the catalyst velocity. This correspondsto the admittance of the manifold and engine, at the measurement locationimmediately downstream of the catalyst. The admittance Y /Y0 is defined inApp. D.2.2.

The response function in Fig. 5.42c is determined by applying a multisinedisturbance to the pressure downstream of the catalyst and monitoring theresponse of the model. Again, the open cylinder volume is set to the midposition. Figure 5.42c shows approximately the same resonance frequencies asFig. 5.42a, corresponding to the runner mass oscillating on the cylinder volume.The low frequency (f → 0) behavior is characteristic of the combined volumeof cylinder, runners and diffuser. The magnitude slopes at +20 dB/decade andthe velocity lags the pressure by π/2 rad.

Figure 5.42c is shown here, partly because of the comparison to the doc-toral work of Boonen [21]. Figure 5.43 shows the acoustic impedance of a smallcombustion engine, where Fig. 5.43c is obtained for a stationary engine andFigs. 5.43a and b are obtained for motored conditions with blocked intake ports(i.e. without net flow). The figures show the load impedance Z/Z0 = (Y /Y0 )−1


(a) (b)

(c) (d)

Figure 5.43 – Measured (a, b and c) and simulated (d) acoustic impedance ofan engine with exhaust manifold, motored at (a) 1000 rpm, (b) 2000 rpm and (c,d) stationary (Source: [21])

at the four-in-one junction of the exhaust runners. No catalyst is present. Theimpedance functions are obtained through two simultaneous pressure measure-ments at different locations in a long exhaust pipe, as developed by Boonen [21].

Upon inverting the impedance shown in Fig. 5.43, there is an obvious qual-itative correspondence between the response functions. The first zero in theimpedance (between 100 and 150 Hz) corresponds to the pole or resonancepeak in the admittance function shown in Fig. 5.42c, and is due to the runnermass oscillating on the cylinder volume.

Interestingly, there is some discrepancy between the measured impedancefor the stationary engine (Fig. 5.43c) and the motored engine (Fig. 5.43a and b).Neglecting the low frequency errors in Fig. 5.43c, the magnitude and phase tendto vary in the vicinity of the first resonance. In particular, a substantial differ-ence is noted in the frequency range from 150 to 300 Hz. The running engineseems to exhibit a larger damping in this region compared to the stationaryengine.

The same engine setup is simulated using an electrical equivalent scheme ofthe gas dynamics in the exhaust manifold. Figure 5.43d shows the numericallydetermined impedance. The model captures the first resonance around 150 Hzwell, yet some deviation is observed for higher frequencies.

Although the setup used by Boonen [21] does not include a close-coupled


102

103

−40

−20

0

20

40

Am

plitu

de (

dB)

of ρ

cU/p

FRFFrom: Junction pressure p, To: Junction velocity ρcU

Runner 1Runner 2

102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

f0,r=1

= 170.9 Hz f0,r=2

= 203.5 Hz

(a)

102

103

−40

−20

0

20

40

Am

plitu

de (

dB)

of ρ

cU/p

FRFFrom: Runner pressure p, To: Runner velocity ρcU

Runner 1Runner 2

102

103

−90

0

Phas

e (°

)

Frequency f (Hz)

(b)

Figure 5.44 – Frequency response function (a) between junction pressure and junc-tion velocity, (b) between runner pressure and runner velocity, for manifold B on theCME flow rig (free discharge)

catalyst, the presented results indicate some uncertainty in the frequency rangearound the Helmholtz resonance, comparable to the discrepancy noted in thisthesis between the experimental and numerical results.

Figure 5.44 shows two additional frequency response functions that maybe interpreted as the admittance at two locations: (a) at the inlet to thejoined runner 1–2 and (b) at the inlet to the open exhaust runner. Most ofthe manifold dynamics are still visible in the admittance near the runner 1–2junction (Fig. 5.44a), although the Helmholtz resonance peaks are reduced inmagnitude and slightly shifted to higher frequencies. Figure 5.44b shows theadmittance near the open exhaust ports. As such, only the cylinder volume andthe exhaust valve damping can be discerned in this graph. The +20 dB/decadeslope and −π/2 phase are characteristic for the cylinder volume compressibility.At very high frequency (f > 1000 Hz), the exhaust valve damping causes themagnitude to level off and the phase to increase towards zero.

Isochoric flow rig: With cold end

All transfer functions shown in Sect. 5.3.4 are for a free discharge, i.e. with-out cold end attached to the catalyst, which is the same situation as for theexperiments. Figure 5.45a shows the effect of including the cold end on thefrequency response function between the cylinder volume velocity and catalystvelocity. The simulated cold end is identical to the one used in Sect. 5.2.3, and


Table 5.3 – Prediction of the resonating system and corresponding frequency fH ,for manifold B on the CME flow rig

Resonance frequency k m Resonating system,according to Eq. (5.5) see Fig. 5.38afH,1 kcyl mrun Open runner on cylinder

volumefH,2 kcyl + kd mrun Open runner on cylinder

and diffuser volumeNote: kcyl, kd and mrun are determined using the effective volumes inEqs. (5.7) and (5.8) with α = 1 and the effective length in Eq. (5.6) withβ ' 0.43

102

103

−40

−20

0

20

40 f

0,r=1 = 154.6 Hz

Am

plitu

de (

dB)

of U

A/Q

cyl



Runner 1Runner 2

102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

f0,r=2

= 179.0 Hz

(a)

102

103

−40

−20

0

20

40 f

0,r=1 = 146.5 Hz

Am

plitu

de (

dB)

of U

A/Q

cyl



f0,r=2

= 170.9 Hz

Runner 1Runner 2

102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

(b)

Figure 5.45 – Frequency response function between cylinder volume velocity andcatalyst velocity, for manifold B on the CME flow rig, (a) with and (b) without coldend


Figure 5.46 – Simulated runner velocity for fired engine (Source: [4])

is described in Sect. 5.2.3.The response function in Fig. 5.45a exhibits little difference compared to

the case without cold end. The Helmholtz resonance peaks are slightly shiftedto higher frequencies, and some additional smaller peaks are introduced by thecoupling between hot end and cold end. Overall, the influence of the cold endseems limited. This is also observed in the numerical simulation of the time-resolved catalyst velocity in Fig. 5.33, where the dashed and solid lines are thesimulated catalyst velocity with and without cold end, respectively.

5.3.5 Discussion

As already indicated in the literature survey in Sect. 1.4.2, this type of cat-alyst velocity fluctuations has been found by other researchers as well, bothexperimentally and numerically.

Adam et al. [4] present numerical results for a one-dimensional gas dynamicmodel of a close-coupled catalyst exhaust manifold, mounted on a fired engine.Figure 5.46 shows the velocity in each exhaust runner for 3000 rpm at partload. The velocity fluctuations during the displacement phases are very similarto the time-resolved catalyst velocity observed on the CME flow rig. However,fluctuations in their catalyst velocity are much less pronounced compared tothe CME flow rig.

The fluctuation frequencies during each cylinder’s exhaust stroke differ,depending on the runner length. Based on visual inspection of the data inFig. 5.46, the estimated fluctuation frequency is 450 Hz for the long runners 1and 4 and 580 Hz for the short runners 2 and 3. From Eq. (5.5) follows that theresonance frequency fH ∝ 1/

√L. As such, based on these frequency estimates,

the ratio of the length of long to short runners is 1.6, which seems plausiblefrom their paper [4].

Park et al. [81] present experimental results using LDA for a close-coupledcatalyst exhaust manifold, mounted on a fired engine. Figure 5.47 shows thevelocity in runner 3 for 2000 rpm at part load. Substantial backflow occursfollowing blowdown, as is observed on the CME flow rig. The estimated fluctu-ation frequency is 300 Hz. This frequency is too low to be caused by pressure


Figure 5.47 – Measured runner ve-locity for fired engine (Source: [81])

Figure 5.48 – Simulated runner ve-locity for fired engine (Source: [70])

waves as explained by the authors [81], yet the value corresponds well with aHelmholtz resonance of the manifold.

Liu et al. [70] present numerical results for a close-coupled catalyst mani-fold in fired engine conditions, obtained using a combined one-dimensional andthree-dimensional numerical approach similar to Adam et al. [4]. Figure 5.48shows the runner velocity at 3000 rpm and full load. The estimated frequencyof the fluctuations during the displacement phase is 310 Hz. Simulation resultsby [70] indicate no fluctuations in motored engine conditions. This is ratherunexpected, assuming the Helmholtz resonance explanation stated above is cor-rect. Perhaps the motored and fired cases do not exhibit the same excitationrequired to invoke the resonance effect, although similar flow conditions on theCME flow rig are found to exhibit the same velocity fluctuations, regardlessof the engine load. Figure 1.18 shows numerical and experimental results us-ing LDA, downstream of the catalyst. Although no actual positive blowdownoccurs in motored conditions at atmospheric intake pressure, flow reversal isnonetheless detected in experiments and simulations. For fired conditions, onlythe simulations show flow reversal.

For fired engine conditions, the temperature is much higher compared tothe CME flow rig. From Eq. (5.5) follows that the resonance frequency fH ∝c ∝

√T . Since the temperature ratio between cold flow conditions and fired

engine conditions is approximately Tfired/Tcold ' 1073/273 ' 4, the resonancefrequency (for the same geometry) will be twice as large for a fired enginecompared to the CME flow rig. This seems to correspond in the literature [4, 81]to the values observed for fired engines, ranging between 300 and 600 Hz.

Benjamin et al. [14] present LDA measurements downstream of a close-coupled catalyst, in a fired engine at 2000 rpm and high load. Similar to Liuet al. [70], the experimental results are compared to a transient CFD simulation,coupled with a commercial one-dimensional gas dynamics code. The simulationpredicts a catalyst velocity between −5 and 22 m/s. The measured velocityresults at the same location exhibit significantly lower amplitude and reducedbackflow magnitude.

Figure 5.31a shows a comparison between measured ( ) and calculated


Table 5.4 – Overview of the resonance frequencies observed in the literature

Author Flow rig Resonance frequency (Hz) FigureNumerical Experimental

Park et al. [81] Fired engine 300∗ 5.47Adam et al. [4] Fired engine 450∗∗ – 580∗ 5.46Adam et al. [4] Fired engine 450∗∗ – 580∗ 5.46Liu et al. [70] Fired engine 310∗∗ 5.48

Motored " no resonanceBenjamin et al.[14]

Fired engine 376∗∗ 197∗∗ 5.31a

This thesis CME flow rig 130∗∗ – 180∗ 160∗∗ – 180∗Fired engine 330∗∗ – 360∗

∗, ∗∗ These frequencies correspond to a long∗∗ or short∗ runner.

( ) runner velocity. The simulation exhibits strong backflow following the

blowdown, and significant velocity fluctuations during the displacement phase.The fluctuation frequency is about 376 Hz for the numerical model, which is ingood agreement with the frequencies observed in other fired engine setups [4, 81,70]. However, the measured runner velocity exhibits a fluctuation frequency ofapproximately 197 Hz, which is 1.9 times smaller than the calculated frequencyfor the same conditions. This cannot be readily explained based on the detailsgiven in the manuscript [14]. Figure 5.31b shows a qualitative correspondencebetween numerical and experimental results for the velocity at a single point inthe catalyst. The simulation results predict much stronger backflow than theexperimental observations.

Table 5.4 summarizes the resonance frequency values observed in the lit-erature, through numerical and experimental methods. Since most manifoldsfeature runners of different lengths, each mentioned frequency is marked byasterisks, denoting the corresponding runner length compared to the otherrunners. Typically for a four-cylinder engine, the outer runners (1, 4) arelonger than the middle runners (2, 3). The resonance frequency values foundin this thesis are quite consistent: the numerical simulations agree with theexperimental measurements for the CME flow rig.

For fired engine conditions, the simulations using the one-dimensional gasdynamics code yield a resonance frequency that is higher compared to the CMEflow rig, which is readily explained by the ratio of absolute temperatures. Thevalues found for manifold B in this thesis are consistent with values foundby other authors [81, 4, 70, 14] in fired engine conditions, for similar exhaustmanifolds, taking into account the given variability in manifold geometry andconditions.

5.4 Conclusion 223

5.4 Conclusion

The characteristic flow dynamics have been investigated in a close-coupled cat-alyst exhaust manifold. Using phase-locked hot-wire anemometry, Sect. 5.1comments on the time-resolved catalyst velocity distribution measured in coldflow conditions, using an (i) isothermal flow rig and an (ii) isochoric or chargedmotored engine (CME) flow rig. The exhaust stroke flow similarity with respectto fired engine conditions has been discussed previously in Sect. 2.3.

The oscillating hot-wire anemometer discussed in Chap. 3 has been suc-cessfully applied to measure the instantaneous local bidirectional velocity inthe entire catalyst cross-section, yielding velocity data with high spatial andtemporal resolution. The OHW has been validated in Sect. 5.2.1 against a ref-erence flow rate measurement. It improves the effect of rectification or foldingerrors associated with using standard hot-wire anemometry. The high resolu-tion in space and time, as well as the ability to measure bidirectional velocityconstitute unique features of this experimental approach, making this work anoriginal contribution to the present state-of-the-art concerning flow in exhaustsystems.

The combination of the OHW approach and the phase-locked measurementtechnique has revealed significant periodic flow reversal in the catalyst, undervarying engine operating conditions. This has been previously described in theliterature for close-coupled catalyst manifolds under fired engine conditions.The spatial and temporal occurrence of backflow is studied in Sect. 5.2.2 on theisochoric flow rig in cold flow conditions. Strong flow reversal occurs followingeach blowdown phase.

A numerical one-dimensional gas dynamic model of the entire exhaust sys-tem has been implemented. The model uses a second order total variationdiminishing scheme developed by Vandevoorde [101], as described in App. D.The model is extensively validated in App. D.2, using several benchmark prob-lems relevant to exhaust systems.

Section 5.2.3 compares the experimental velocity data to the simulationresults of the numerical gas dynamic model. Given the good agreement, thenumerical model is used to predict the influence of the cold end (i.e. exit cone,exhaust pipe and a reference single expansion chamber muffler) on the flowdynamics. For cold flow conditions corresponding to the isochoric flow rig,the presence of the cold end does not appreciably influence the time-resolvedcatalyst velocity.

Furthermore, the numerical model has been used to predict the correspond-ing flow conditions in fired engine operation, with and without cold end. Theexhaust stroke flow similarity is not perfect, as indicated in Sect. 2.3. However,flow reversal is also observed in fired engine conditions, even more so than incold flow conditions.

The catalyst velocity fluctuations observed on the isochoric flow rig havebeen analyzed and may be explained as zeroth order gas dynamic resonancesor Helmholtz resonances in Sect. 5.3. By determining the frequency responsefunction of the numerical exhaust model, the understanding of the phenomenon


is greatly facilitated.In summary, the relevant flow dynamics in a close-coupled catalyst exhaust

manifold have been studied in cold flow conditions, similar to fired engineoperation. The study is performed using a combination of (i) a high resolutionexperimental approach including the ability to quantify bidirectional velocity,and (ii) a one-dimensional numerical gas dynamic model of the exhaust system.

Parts of this chapter have been published in international journals withreview:


[86] T. Persoons, A. Hoefnagels, and E. Van den Bulck. Exper-imental validation of the addition principle for pulsating flow inclose-coupled catalyst manifolds. J. Fluids Eng.-Trans. ASME,128(4):656–670, 2006. http://dx.doi.org/10.1115/1.2201646.

[88] T. Persoons, E. Van den Bulck, and S. Fausto. Study of pul-sating flow in close-coupled catalyst manifolds using phase-lockedhot-wire anemometry. Exp. Fluids, 36(2):217–232, 2004. http://dx.doi.org/10.1007/s00348-003-0683-0

http://dx.doi.org/10.1115/1.2201646

http://dx.doi.org/10.1007/s00348-003-0683-0

http://dx.doi.org/10.1007/s00348-003-0683-0

Chapter 6

Design considerations

This brief chapter provides some considerations for the design of close-coupledcatalyst exhaust manifolds, based on the experiences gained within this thesis.Section 6.2 discusses the relationship between the manifold flow dynamics andthe addition principle’s validity, thereby linking the findings in Chap. 4 and 5.

6.1 Addition principle

Some manifold design criteria may be formulated based on Fig. 4.29 andEq. (4.47). Based on the correlation for rS (4.47), a good correspondencebetween numerical simulations or measurements in stationary and pulsatingflow conditions is obtained for a high scavenging number, S > Scrit. The criti-cal value equals Scrit = 0.723±0.052 when taking into account the experimentson manifolds A and B combined, or Scrit = 0.722 ± 0.056 when only takinginto account the experiments on manifold B.

Recall the definition of the scavenging number as S = Tp/Ts , where Tp

is the flow pulsation time scale (4.46), and Ts is the diffuser residence timescale (4.43). Ts is determined by the diffuser volume Vd and the time-averagedvolumetric flow rate Q through the catalyst, or Ts = Vd/Q .

Figure 6.1 summarizes the findings concerning the validity of the additionprinciple. For a given engine geometry and operating range, decreasing thediffuser volume Vd increases the scavenging number S, thereby improving thecorrespondence between stationary and pulsating flow. In the validity regionof the addition principle (S > Scrit), stationary flow CFD simulations canbe used instead of time-consuming transient simulations for the design of anexhaust manifold with close-coupled catalyst, resulting in significantly shorterdevelopment times.

Based on the correlation for rM (4.47), the flow uniformity is always higherin pulsating flow compared to stationary flow. A manifold that is designed

225

226 Chapter 6 Design considerations

0 1 2 3 4 50

0.5

1

1.5


Sim

ilari

ty m

easu

res

(-)

Validity of the addition principle

rS

rM

S ∼ Q

N V

d low engine load

high engine speedlarge diffuser volume

addition principle not valid (and high flow uniformity)

high engine loadlow engine speed

small diffuser volume

addition principle valid

low Scrit

low Scrit

high Scrit

high Scrit

Figure 6.1 – Validity of the addition principle

based on stationary CFD simulations, and that satisfies the preset criteria forflow uniformity, will likely feature a better flow uniformity in pulsating flowconditions.

Flow uniformity in pulsating flow is higher for a small scavenging number,S < Scrit. Increasing the diffuser volume Vd decreases the scavenging numberS, and consequently increases the flow uniformity. This unsurprising conclusionwill be subject to compromise in terms of geometrical and thermal packagingconstraints within the engine compartment. However, Sect. 6.2 provides aninteresting addition to this conclusion, with regard to the Helmholtz resonancein the manifold.

6.2 Flow dynamics: Helmholtz resonance

The flow dynamics discussed in Chap. 5 are indirectly related to the additionprinciple’s validity derived in Chap. 4. In particular, the Helmholtz resonancewhich is intrinsic to the manifold geometry, causes strong fluctuations in themean catalyst velocity. These fluctuations are strong enough to cause extensiveflow reversal or otherwise periods of near standstill of the gas in the catalyst.This has been observed experimentally on the CME flow rig, using the OHW for

6.2 Flow dynamics: Helmholtz resonance 227

measuring bidirectional instantaneous local velocity. Furthermore, numericalsimulations described in Sect. 5.2.3 show that these velocity fluctuations andthe related flow reversal are even stronger in a fired engine. This fact hasbeen observed experimentally and numerically by some authors in fired engineconditions [4, 81, 70].

Due to the Helmholtz resonance effect, the frequency spectrum of the meancatalyst velocity contains more energy in the higher frequency range, e.g. whencompared to the isothermal flow rig experiments. Considering the definition ofthe apparent flow pulsation period Tp in Eq. (4.46) used in the expression forthe scavenging number S = Tp/Ts , the higher frequency content of the catalystvelocity influences Tp and consequently S.

Although S is mainly a function of the collector geometry (diffuser volumeVd, number of runners nr) and the engine operating conditions (engine speed Nand engine load, which determines Q), the strong catalyst velocity fluctuationsduring the displacement phase may alter the effective value of S as ‘experienced’by the catalyst. In other words, S is quasi independent of the engine speed Nin the presence of the Helmholtz resonances. As such, the distinction in Fig. 6.1with respect to engine speed no longer applies and the validity of the additionprinciple is governed predominantly by the engine load and diffuser volume.

Section 4.5 gives the summarized results on the validity of the additionprinciple. Figure 4.29 and the correlations in Eq. (4.47) demonstrate the strongrelationship between S and (i) the validity of the addition principle (based on rSand rM ), as well as (ii) the relative increase of the flow uniformity in pulsatingflow compared to stationary flow (based on rM ).

Example As a thought experiment, assume that the exhaust sys-tem features no gas dynamics at all. In that case, the catalyst veloc-ity during the exhaust stroke is expected to behaves as indicated bythe solid line (

) in Fig. 2.10, which is a numerical result obtained

from a zero-dimensional filling-and-emptying engine model.

In that case, a given engine operating point corresponds to a certainvalue of S. Assume, with loss of generality, that e.g. S = 1.1.

When the exhaust system gas dynamics are now considered, themean catalyst velocity will exhibit the fluctuations as observed dur-ing the displacement phase, thereby decreasing the flow pulsationperiod Tp apparent to the manifold and catalyst, and consequentlythe value of S will decrease to e.g. S = 0.4.

Based on Fig. 4.29 and the correlations in Eq. (4.47), the decreasein S will cause:

• Based on rM : The flow uniformity in pulsating flow conditionswill increase with respect to stationary flow conditions.

• Based on rS : The correspondence in shape between the veloc-ity distribution in pulsating flow conditions will decrease withrespect to stationary flow conditions.


As indicated in Sect. 5.3.2, the Helmholtz resonance frequency fH correspondsvery well to the observed catalyst velocity fluctuations. fH is defined byEq. (5.5):

fH =12π

c

Lr

√ArLr

Vd

As such, fH features the following dependencies:

(i) fH ∝ c ∝√Texh

(ii) fH ∝ 1√Lr

(iii) fH ∝√Ar

(iv) fH ∝ 1√Vd

(6.1)

Section 1.2.1 provided some aspects of manifold design, related to the optimaluse of the catalyst. Catalyst flow uniformity is found to be of major impor-tance for minimizing local catalyst deactivation, minimizing backpressure andmaximizing the conversion efficiency.

The above example indicates that the observed velocity fluctuations duringthe displacement phase are not at all undesirable, in terms of the catalystflow uniformity. In fact, based on Fig. 4.29b and the correlation for rM inEq. (4.47), the flow uniformity can be maximized in pulsating flow conditionsby decreasing the scavenging number S for a given engine operating range.

As already indicated in Sect. 6.1, increasing the diffuser volume Vd effec-tively decreases the range of S, yet this opposes packaging constraints. Rather,S = Tp/Ts can be decreased by decreasing the apparent flow pulsation periodTp, defined as Eq. (4.46):

Tp =1

fPSD(Um),max

Since the frequency spectrum of the catalyst velocity Um (ωt) is governedlargely by the Helmholtz resonance frequency fH :

S ∝ Tp =1

fPSD(Um),max∝ 1fH

(6.2)

where the statement fPSD(Um),max ∝ fH is only an approximation, given thenon-linear nature of the ‘max’ function.

Based on the dependencies in Eq. (6.1) of the Helmholtz resonance fre-quency, the scavenging number S features the following dependencies:

S =TpQ

Vd∝ 1Vd

√LrVd

TexhAr=√

Lr

VdArTexh(6.3)

As such, S may be decreased (i.e. flow uniformity may be increased) by:

6.3 Summary 229

(i) higher exhaust gas temperature (Texh 1)

(ii) shorter exhaust runners (Lr %),

(iii) larger diameter exhaust runners (Ar 1)

(iv) larger resonating volume (Vd 1).

Particularly conditions (i) and (ii) are in agreement with the general trends thatare observed in exhaust systems. Rapid catalyst warmup is obtained by usingrunners with small length-to-diameter ratio, in combination with heat shieldsand thermal insulation to decrease enthalpy losses in the hot end. As such, theflow dynamics which are governed by the Helmholtz resonance appear to befavorable in terms of the catalyst flow uniformity. Of course, this derivationis made based upon the results for only two manifolds. Further research isrequired to verify this statement.

Although the Helmholtz resonance phenomenon seems beneficial for the flowuniformity, the mean velocity fluctuations also causes strong pressure transientswhich are favorable for the occurrence of flow reversal. This may be noted inFigs. 5.16 through 5.18, where the flow reversal occurs mainly following theblowdown yet also during the displacement phase, when the piston is alreadymoving fast towards top dead center. The relation between flow reversal andcatalyst ageing is unknown, yet also warrants further research due to the strongtemperature dependence of the ageing process (see Sect. 1.2.1 and Sect. 5.2.4).

6.3 SummaryIn summary, the following practical considerations are formulated based onthe findings of this thesis. When faced with the task of designing an exhaustmanifold for a close-coupled catalyst, two stages are discerned:

(1) During the conceptual stage, the optimal manifold geometry is selectedbased on the given range of operating conditions that influence the scav-enging number S (e.g. engine speed, engine displacement, intake systemcharging) and the critical value of the scavenging number Scrit:

Firstly, since the flow uniformity in pulsating conditions increases withrespect to the stationary flow uniformity, the scavenging number S de-creases in case of (see above):

(i) high exhaust gas temperature (Texh 1)

(ii) short exhaust runners (Lr %),

(iii) large diameter exhaust runners (Ar 1)

(iv) large diffuser volume (Vd 1).

Secondly, referring to the hypothetical collector efficiency ηD introducedin Sect. 4.6.2, the critical scavenging number Scrit should be maximized.


With reference to Eq. (4.54), maximizing ηD = Scrit is equivalent tomaximizing the effectively used diffuser volume in the flow distributionprocess (ηD = Scrit = Vd,eff/Vd ).

However, further studies are needed to confirm the collector efficiencyhypothesis, and the influence of the manifold geometry (e.g. the shapeof the exhaust runners, the entrance angle of the runners in the diffuser)on the critical scavenging number. This might be the focus of futureresearch.

(2) For a given exhaust manifold geometry, the following rules apply for inter-preting stationary CFD predictions of the catalyst velocity distribution:

(i) The addition principle is valid for high engine load and low enginespeed (S > Scrit). The engine speed is of lesser importance giventhe inevitable resonance phenomenon which reduces the influenceof N on the flow pulsation period Tp. In these conditions, the sta-tionary velocity distribution Ustat obtained according to Eq. (4.1)corresponds to the actual velocity distribution in pulsating condi-tions.

(ii) The addition principle is not valid for low engine load and high en-gine speed (S < Scrit). In these conditions, the stationary velocitydistribution Ustat does not correspond to the pulsating velocity dis-tribution. However, the flow uniformity in pulsating conditions ishigher than in stationary conditions.

Based on the results in this thesis, one may conclude that an exhaustmanifold for which the stationary flow distribution meets the uniformitydesign criterion, will also meet the design criterion in actual pulsatingflow conditions. However, the accuracy of the velocity distribution itself(e.g. location of maximum velocity and flow reversal, overall shape of thedistribution) is only guaranteed in the region of validity of the additionprinciple, i.e. S > Scrit.

Chapter 7

Conclusion

7.1 Conclusion

Recalling the goals specified in Sect. 1.6, this thesis aimed to further the under-standing of pulsating flow in modern compact close-coupled catalyst exhaustmanifolds for internal combustion engines. Instead of using a fired engine fea-turing a hot corrosive exhaust gas environment, two cold pulsating flow rigshave been used. This enables the use of velocity measurement techniques thatyield a high spatial and temporal resolution. Other authors [59, 81, 70, 53, 14]encountered serious problems in measuring velocity distributions in the exhaustsystem of a fired engine, using optical anemometry. Their findings are discussedin App. C.2.

The thesis has focused on the most relevant flow-related aspect to the de-sign of the exhaust manifold: the catalyst velocity distribution. As discussedin Sect. 1.2, obtaining a uniform catalyst velocity distribution is crucial foran optimal manifold design, in terms of minimal local catalyst degradation,minimal pressure drop and maximal conversion efficiency.

• Section 2.2 describes two experimental flow rigs. The isothermal flow rig(Sect. 2.2.1) is commonly used by a number of authors [88, 58, 18, 69,17, 16, 15, 43, 22], because of its simplicity to use. However, the ex-haust system flow similarity between the isothermal flow rig and a firedengine is quite poor. Section 2.2.2 describes the isochoric or charged mo-tored engine (CME) flow rig, developed within this thesis. The CMEflow rig mimics the exhaust system flow in fired engine conditions asbest as possible, while still operating at ambient temperature. The ex-haust stroke features blowdown and displacement phase, typical of a firedengine. Section 2.3 discusses a thermodynamic analytical derivation ofthe exhaust stroke flow similarity between CME and fired engine condi-tions [88, 87, 86, 84, 85].

231

232 Chapter 7 Conclusion

• Chapter 3 presents a novel low-frequency oscillating hot-wire anemome-ter (OHW) that enables bidirectional velocity measurements in the ex-haust system. The OHW is more compact than traditional flying hot-wireanemometers [25], and less prone to prong or wire vibration and straingauging than recent high-frequency OHW systems [78, 66].The OHW is calibrated in a small-scale wind tunnel, in the negativevelocity range −1.5 6 U 6 0 m/s. Laser Doppler anemometry is used asreference velocity measurement, phase-locked with the OHW. Three hot-wire probe designs are calibrated, examining the influence of prong lengthand shape. Calibrations are performed for two oscillation amplitudesand several frequencies. The best calibration results are obtained for astraight probe with extended prongs (55P11L), in combination with anoscillation amplitude xo = 5.5 mm. This choice results in a maximumresolvable negative velocity of −1.0 m/s.A non-dimensional scaling analysis reveals that straight (55P11, 55P11L)and angled (55P14) probes behave differently with regard to the corre-spondence between the OHW velocity U ′ and the reference velocity U .For the straight probes, increasing the oscillation amplitude xo (and de-creasing oscillation frequency fo) reduces the deviation between U ′ andU . For the angled probe, the deviation between U ′ and U is reduced bydecreasing xo and increasing fo.The presented OHW system has been successfully applied within thisthesis to measure the phase-locked velocity distribution including instan-taneous local flow reversal on the CME flow rig [83, 84, 85].

• Chapter 4 investigates the validity of the addition principle (4.1) for pul-sating flow in close-coupled catalyst manifolds. The addition principlestates that the time-averaged catalyst velocity distribution in pulsatingflow Upuls equals a linear combination of velocity distributions obtainedfor steady flow through each of the exhaust runners Ustat, according toEq. (4.1).The scavenging number S defined in Eq. (4.42) forms the appropriatenon-dimensional number to characterize the pulsating flow. The non-dimensional measures rS (see Sect. 4.3.2) and rM (see Sect. 4.3.2) quantifythe similarity between the Ustat and Upuls distributions based on shapeand magnitude, respectively. These measures are used to quantify thevalidity of the addition principle.The results from the entire measurement campaign are combined inFig. 4.29 and Tables 4.3 and 4.4. Figure 4.29 shows the correlation be-tween the similarity measures rS and rM and the scavenging number S,resulting in the correlation fits (4.47):

r′′S = 1− exp (−S/0.723) ; R2 = 0.91

r′′M = 1.118 + 0.337 exp (−S/0.723) ; R2 = 0.30

7.1 Conclusion 233

where the correlation is excellent for rS and not quite so convincing forrM (for reasons explained in Sect. 4.5).

Strong statistical evidence is given in support of the addition principlein Tables 4.3 and 4.4, for nearly the entire range of S. Since no clearvalidity limit can be derived from the statistical significance of rS and rM ,the practical limit of the addition principle’s validity is when S exceedsthe critical scavenging number Scrit = 0.723 (± 0.052), correspondingroughly to rS > 1− e−1 = 0.63 and rM < 1.24.

The validity of the addition principle in terms of S carries two importantconsequences for the industrial design of these systems:

(i) Based on the correlation for rM (4.47), the flow uniformity is alwayshigher in pulsating flow compared to stationary flow. A manifoldthat is designed based on stationary CFD simulations, and thatsatisfies the preset criteria for flow uniformity, will likely feature ahigher flow uniformity in pulsating flow conditions.

(ii) In the validity region of the addition principle (S > Scrit), steady-state CFD simulations can be used instead of time-consuming tran-sient simulations for the design of an exhaust manifold with close-coupled catalyst, resulting in a significantly shorter developmenttime.

Other authors [17, 22, 99] have used non-dimensional numbers similar toS to characterize the pulsating flow in close-coupled catalyst manifolds.However, the original contribution of this work is to relate S to the flowdistribution similarity between pulsating and stationary flow conditionsusing rS and rM , and furthermore to derive the validity of the additionprinciple from that relationship [88, 86].

• Based on the elegance of the rS correlation in Eq. (4.47), this complexmulti-dimensional flow behaves essentially like a zero-dimensional scalarmixing process. In that respect, the critical scavenging number Scrit

may be considered the ratio of the effective to actual diffuser volume.As such, the hypothesis may be formulated that Scrit corresponds to acollector (i.e. runners and diffuser) efficiency ηD with respect to cata-lyst flow uniformity. By maximizing the collector efficiency ηD, the flowuniformity is optimized, and consequently so is the catalyst durability,conversion efficiency and exhaust system backpressure. The correlationsin Eq. (4.47) are valid for two different exhaust manifolds. In Sect. 4.6.2,the correlations in Eq. (4.55) are obtained only for the experiments onmanifold B. Based on these correlations, the critical scavenging numberor hypothesized collector efficiency ηD yields 0.722 (± 0.056).

• The characteristic flow dynamics are discussed in Chap. 5. Section 5.1demonstrates the potential of the experimental approach in determiningthe time-resolved catalyst velocity distribution in cold flow conditions,using an (i) isothermal flow rig and an (ii) isochoric or charged motored


engine (CME) flow rig. The oscillating hot-wire anemometer introducedin Chap. 3 has been successfully applied to measure the instantaneouslocal bidirectional velocity in the entire catalyst cross-section, yieldingvelocity data with high spatial and temporal resolution. The OHW hasbeen validated in Sect. 5.2.1 against a reference flow rate measurement.The OHW reduces the effect of rectification or folding errors associatedwith using standard hot-wire anemometry in strong pulsating flows. Thehigh resolution in space and time, as well as the ability to measure bidirec-tional velocity constitute unique features of this experimental approach,making this work an original contribution to the present state-of-the-artconcerning flow in exhaust systems.

Significant periodic flow reversal is observed in the catalyst, under vary-ing engine operating conditions. This has been previously described inthe literature for close-coupled catalyst manifolds under fired engine con-ditions. The spatial and temporal occurrence of backflow is studied inSect. 5.2.2 on the isochoric flow rig in cold flow conditions. Strong flowreversal occurs following each blowdown phase [84, 85].

• A numerical one-dimensional gas dynamic model of the entire exhaust sys-tem has been implemented. The model uses a second order total variationdiminishing scheme [101], as described in App. D. The model is exten-sively validated in App. D.2, using several benchmark problems relevantto exhaust systems. Section 5.2.3 compares the experimental velocitydata to the simulation results of the gas dynamic model. Given the goodagreement, the numerical model is used to predict the influence of the coldend (i.e. exit cone, exhaust pipe and a reference single expansion chambermuffler) on the flow dynamics. For cold flow conditions corresponding tothe isochoric flow rig, the presence of the cold end does not appreciablyinfluence the time-resolved catalyst velocity. Furthermore, the numericalmodel has been used to predict the corresponding flow conditions in firedengine operation, with and without cold end. The exhaust stroke flowsimilarity is imperfect. However, flow reversal is also observed in firedengine conditions, even more so than in cold flow conditions [84, 85].

• Strong catalyst velocity fluctuations during the displacement phase areobserved on the isochoric flow rig. These fluctuations have been analyzedand explained as zeroth order gas dynamic resonances or Helmholtz res-onances in Sect. 5.3. By determining the frequency response function ofthe numerical exhaust model, the understanding of the phenomenon isgreatly improved [84, 85].

• The flow dynamics discussed in Chap. 5 are indirectly related to the addi-tion principle’s validity derived in Chap. 4. This relationship is illustratedin Chap. 6.

Equation (6.3) presents the dependencies of the scavenging number Staking into account the strong Helmholtz resonances that occur in the

7.2 Suggestions for future research 235

manifold. These resonance velocity fluctuations reduce the apparent pul-sation period and therefore reduce the scavenging number. In terms ofthe validity of the addition principle (Fig. 4.29), this causes a higher flowuniformity in pulsating flow conditions.Therefore, the observed catalyst velocity fluctuations seem beneficial forincreasing the flow uniformity. Furthermore, the Helmholtz resonancefrequency range increases for shorter exhaust runners and higher exhaustgas temperature, two factors that agree with the tendency to place thecatalyst close to the engine and reduce the enthalpy loss in the hot end.Although the Helmholtz resonance phenomenon seems beneficial for theflow uniformity, it also promotes catalyst flow reversal due to strong pres-sure transients. The relation between flow reversal and catalyst ageing isunknown, yet also warrants further research due to the strong tempera-ture dependence of the ageing process (see Sect. 1.2.1 and Sect. 5.2.4).

In summary, this thesis has improved the understanding of the flow dynamicsin close-coupled catalyst exhaust manifolds in general, and the catalyst velocitydistribution in particular. The experimental approach has yielded high resolu-tion bidirectional velocity data that would be otherwise very difficult to obtainin fired engine conditions. The validity of the addition principle in terms of thescavenging number S carries important consequences for the optimal design ofthese systems. And finally, the governing flow dynamics have been analyzedand explained, with the aid of a one-dimensional gas dynamical model of theexhaust system.

7.2 Suggestions for future research• The main subject of future research concerns the hypothesis that has been

formulated in Sect. 4.6.2, stating that the critical value of the scavengingnumber Scrit can be interpreted as a collector efficiency with regard tothe catalyst flow uniformity.This hypothesis has been formulated based on the experimental resultsobtained in this thesis, using only two manifold geometries. Further inves-tigations are required to determine (i) whether Scrit indeed correspondsto a collector efficiency, and (ii) to what extent the collector efficiencydepends on the manifold geometry.To determine whether Scrit corresponds to a collector efficiency, the crit-ical scavenging number should be determined based on the correlationsin Sect. 4.5 for several geometrical variants of a single manifold. Mani-fold parameters expected to influence the collector efficiency are (i) theentrance of the runners into the diffuser, (ii) the shape of the exhaustrunner centerlines and (iii) the diffuser volume. During the course of anIWT project [2] in cooperation with an industrial partner, experience hasbeen gained with regard to the influence of swirl induced by the runnercurvature on the catalyst velocity distribution. This effect proves to be


of major importance, and is usually not captured by RANS-CFD calcu-lations.

• Section 4.6.1 presents a remarkable analogy between the pulsating flowin a close-coupled catalyst manifold and a zero-dimensional scalar mixingprocess. Based on this analogy, a fast method might be established todetermine the critical scavenging number (i.e. collector efficiency). Thefast method might use a fast concentration measurement which shouldbe capable of detecting the time-resolved concentration of a trace gasspecies in the diffuser, following a stepwise change in the concentrationupstream of the exhaust manifold. By determining the time constant ofthis mixing process, and comparing it to the expected time constant inthe assumption of perfect mixing, the collector efficiency can be obtained.The time constants in question range between 5 and 50 ms. Therefore, thetrace gas injection and detection should be performed with reaction timesof 1 ms or less. This should be possible e.g. by means of a fast responseflame ionization detector (FID) hydrocarbon measurement device.

• The oscillating hot-wire anemometer (OHW) developed during this thesismay be further improved according to the recommendations in Sect. 3.7.4.These recommendations follow from the non-dimensional scaling analysisperformed in Sect. 3.7.3.Wake contamination by the moving wire could be minimized by usinga modified version of the angled 55P14 probe, with longer prongs (i.e.increasing s from Table 3.2). As Fig. 3.10 shows, an increase in s byonly a few millimeters places the wire in the free stream. Along with theproposed reduction in the oscillation amplitude xo that follows from thenon-dimensional scaling in Sect. 3.7.3, this might be subject for furtherresearch.The challenge lies in simultaneously increasing the prong length and theoscillation frequency. In order to avoid prong vibration, this requires asufficient increase in the prong’s mechanical resonance frequency. By ap-propriately shaping the prongs, their stiffness could be increased. Ratherthan merely thickening the prongs, perhaps a slender airfoil could be usedto minimize flow disturbance.

• This thesis has demonstrated that significant flow reversal occurs in largeportions of the catalyst, for a broad range of operating conditions in firedengine operation. However, the relevance of flow reversal with respect tocatalyst ageing is unknown. Although some literature exists on reverseflow catalytic reactors (see Sect. 5.2.4), it does not apply to the condi-tions of automotive catalysts with periodic flow reversal at a much fasterfrequency. Nevertheless, Sect. 1.2.1 indicates the strong temperature de-pendence of thermal ageing. For future research, an experimental set upmight be conceived to generate a known uniform periodic flow reversaland verify the gradual deterioration in the catalyst conversion under ac-celerated ageing conditions. Alternatively, a numerical model based on

7.2 Suggestions for future research 237

the heterogenous catalytic kinetics described in App. A.3 can be used toestimate the importance of flow reversal.

Appendices

239

Appendix A

Catalyst substrate flow

“The catalytic converter gets hotter than any of the other under-car com-ponents.”

Jeff Beck (English rock guitarist, 1944)

A.1 IntroductionAn automotive catalyst substrate consists of a large number of small parallelchannels. The channel cross-sectional shape depends on the substrate material,which can be either (i) ceramic or (ii) metal. Metal substrates are usually madeup of honeycomb-like sheets, wound into a circular shape. The cross-section canbe represented as a sine function. A ceramic substrate (or: monolith, brick) isextruded and subsequently baked, resulting in a quasi perfect array of channelswith square, circular, or other cross-section.

The ability to produce channels with low tolerances on cross-sectional areais a clear advantage of ceramic substrates. Furthermore, the washcoat is easierto apply on ceramic than on metal substrates, because of the porous structure.Ceramics like cordierite (2MgO · 2Al2O3 · 5SiO2) are stronger than earlier ce-ramics, making it possible to reduce wall thickness and thus increase geometricsurface area of the catalyst.

However, metals have a higher thermal conductivity and lower specific heatcapacity compared to ceramics, making a metal substrate better suited forrapid warm-up applications, such as a close-coupled catalyst. On the otherhand, metal also has a larger thermal expansion coefficient, which increasesits sensitivity to thermal shock, and causes packaging problems. The channelsof metal and ceramic substrates differ not only in shape. In metal substrates,‘bumps’ may be indented in the channels, thereby increasing the mass transfer.

241

242 Appendix A Catalyst substrate flow

The noble metal particles enabling the catalytic reactions are embedded inthe washcoat. The washcoat, a porous metal oxide such as aluminum oxide(Al2O3), is applied onto the substrate in liquid form. The liquid adheres to theinner walls of the substrate, leaving a layer of washcoat with active metals as itdries. The washcoated substrates are heated to dry and harden the washcoat.

From the nature of the washcoating process, it is clear that the washcoatlayer thickness is not uniform throughout the channel. More liquid will accu-mulate in sharp corners, rounding off the original unwashcoated cross-section.For instance, where unwashcoated ceramic substrates have square channels,washcoated ceramic substrate channels are often modeled as a circle-in-squarecross-section.

The porous washcoat enlarges the catalytic surface to reduce the diffusionresistance and increasing the reaction rate. Therefore, the substrate channelwalls are significantly rough. However, since the flow regime is laminar, thisdoes not directly affect the pressure drop, nor the heat and mass transfer.

Sect. 1.2.1 gives more details on deactivation of automotive catalysts. Thefollowing sections provide background information on the transfer of momen-tum (i.e. pressure drop) and mass (i.e. catalytic reaction kinetics).

A.2 Momentum transfer

The Reynolds number Re is based on the catalyst channel hydraulic diameter34d and the mean channel velocity U = U0/ε , where U0 is the upstream axialvelocity and ε is the open frontal area ratio or porosity (see Sect. 1.2.1). Thisassumes incompressible flow, which is fulfilled in automotive catalysts since theMach number is typically Ma < 0.1.

For stationary flow and a smooth surface, the flow is laminar for Re < 2300and turbulent for Re > 4000. According to Çengel [27], the surface roughnessand flow fluctuations have a considerable influence on these limits.

Numerical example The typical velocity in a catalyst substratechannel varies between 0 and 20 m/s. A ceramic substrate of cell den-sity 600 cpsi (cells per square inch) and wall thickness of 3 mil (1 mil= 1/1000 inch), results in a hydraulic diameter d = 0.96 mm (taking intoaccount a porosity ε = 0.85). Assuming a temperature of 500 C, the dy-namic viscosity is approximately 3.5× 10−5 Pa·s. At 1.2 bar, the densityequals 0.54 kg/m3, so Re varies between 0 and 300. These is the typicalrange for Re inside an automotive catalyst.

The cross-sectional area ratio between the catalyst and the upstreamconnecting pipe is around 4 : 1 to 10 : 1, making the upstream averagevelocity in a pipe of diameter 50 mm roughly 40 to 100 m/s. At thesame conditions of temperature and pressure this yields an upstreamReynolds number between 30 000 and 80 000.

34The hydraulic diameter is defined as d = 4S/P , where S and P are the cross-sectionalarea and the perimeter of the channel. For square channels, d corresponds to the width. Forcircular channels, d corresponds to the diameter.

A.2 Momentum transfer 243

The above numerical example demonstrates that the flow in a channel islaminar, while the upstream flow is turbulent. This means that the flow willrelaminarize upon entering the channel.

The pressure drop over a channel is defined as the difference in total pressurebetween in- and outlet:

∆p0 = p0,in − p0,out

= pin − pout +ρU2

0

2

∣∣∣∣in

− ρU20

2

∣∣∣∣out

(A.1)

where p0 and p represent total and static pressure [Pa], respectively andU0 [m/s] is the velocity outside of the catalyst.

A.2.1 Fully developed laminar flowThe preferred measure to quantify the dimensionless pressure drop is the fric-tion factor f , here defined as the Fanning friction factor, which equals 1/4 ofthe Darcy friction factor:

∆p = 4fL

d

ρU2

2(A.2)

where L is the length of the channel [m] and U is the channel velocity (U =U0/ε ).

The pressure drop in a fully developed laminar flow is caused by viscousshear forces, acting on the fluid laminae. For this regime, the Navier-Stokesequations can be solved analytically for a number of geometries, yielding typ-ically a parabolic velocity profile, known as the Hagen-Poiseuille profile. Theviscous shear stress at the wall is proportional to the fluid dynamic viscosity µand the velocity gradient normal to the wall (y-direction):

τw = −µ∂U (y)∂y

(A.3)

The shear stress, integrated over the channel length is proportional to thepressure drop ∆p. For fully developed laminar flow this yields the followingexpressions for the friction factor f (Shah and London [92]):

f Re = 16 for a circular cross-sectionf Re = 14.227 for a square cross-section (A.4)

The effect of wall roughness is negligible for laminar flow.

A.2.2 Developing laminar flowNear the catalyst entrance, a complex flow field is established as the flow con-tracts due to the finite thickness of the catalyst substrate walls t. The porosity


ε is a measure of the contraction of the flow field. The contribution of thiseffect to the overall pressure drop is discussed in Sect. A.2.3.

Immediately following the first entrance region, the velocity profile insidethe channels is roughly uniform. At this point, the hydrodynamic boundarylayer starts to develop. After some distance (denoted the entrance length Le),the parabolic velocity profile is established, corresponding to fully developedflow.

The hydrodynamic entrance length Le is defined as the lengthwise coordi-nate where the maximum velocity reaches 99% of the maximum velocity in thefully developed regime. Shah and London [92] give a correlation by Chen (1973)based on numerical results by Friedmann (1968):

Le

d=

0.60.035Re+ 1

+ 0.056Re ' 0.056Re (A.5)

which yields Le ' 11 mm for d = 1 mm and Re = 200.In the near-wall region, viscous shear forces slow down the fluid, causing

the velocity profile to exhibit a drop in velocity near the wall, and a regionof higher velocity in the center of the pipe. This momentum transfer acrossthe fluid laminae causes the pressure to increase as the fluid flows furtherthrough the pipe. The developing flow thus causes an extra pressure drop.The total pressure drop caused by a developing laminar flow is characterizedby the apparent friction factor fapp:

∆p = ∆pfully developed + ∆pdeveloping = 4fappL

d

ρU2

2(A.6)

where fapp is always greater than the fully developed friction factor f given byEq. (A.4).

There is no analytical expression for laminar developing flow. Either numer-ical or experimental techniques are used to estimate fapp. Shah and London [92]present numerical results for a circular and a square channel as a function ofthe dimensionless lengthwise coordinate z+, defined as z+ = z/(dRe) .

Shah and London [92] give a relation for fappRe, which is fitted to numericalresults by Liu (1974) and Hornbeck (1964). This is an approximate numericalsolution, where as the correlation by Schmidt (1971) is obtained by solving theNavier-Stokes equations exactly:

fappRe(z+)

=3.44√z+

+f Re+K∞/z+ − 3.44

/√z+

1 + C/z+2

(A.7)

For a circular cross-section, f Re = 16, C = 0.000 212 and K∞ = 0.3125 (Shahand London [92]). For a square cross-section, f Re = 14.227, C = 0.000 290and K∞ = 0.3575 (Shah [91]).

Equation (A.7) can be used to evaluate the local friction factor along thelength of the channel. To obtain the pressure drop over the entire length,Eq. (A.7) is evaluated at z+ = L+ = L/(dRe) .


The incremental contribution to the pressure drop of the boundary layerdevelopment can be singled out from the fully developed pressure drop bysubtracting f Re from fappRe given by Eq. (A.7). The resulting pressure dropis written as a friction factor:

fdev =fappRe− f Re

Re(A.8)

Numerical example The contribution of the boundary layer devel-opment to the overall pressure drop cannot be neglected, in particularfor short catalysts, or at a relatively high Reynolds number. For squarechannels, the following table gives the relative increase in pressure dropdue to the boundary layer development, as a function of the dimensionlesscatalyst length L+:

L+ fdev/f- -∞ 0

100 0.000310 0.00251 0.0250.1 0.240.01 1.70 ∞

For a 50 mm long catalyst, with square channels measuring d = 1 mm andat Re = 200, L+ = 0.25. From Eq. (A.7), fapp Re = 15.617. Therefore,the pressure drop is fdev Re/f Re ' 10 % greater than the pressure dropfor fully developed laminar flow.

A.2.3 Entrance and exit losses

Chapter 5 in Kays and London [57] deals entirely with contraction (i.e. en-trance) and expansion (i.e. exit) loss in heat exchangers.

The flow entering the channel experiences a cross-sectional change quanti-fied by the porosity ε. A separation zone appears at the entrance, causing astatic pressure drop ∆pc which can be split up into two parts: a (i) reversiblepressure drop caused by the area change and the resulting flow accelerationand (ii) an irreversible pressure drop, which is characterized by the entrancepressure loss coefficient Kc:

∆pc = (1− ε)ρU2

2︸︷︷︸i

+KcρU2

2︸︷︷︸ii

(A.9)

At the channel exit the flow expands, creating a static pressure rise ∆pe

which again consists of a (i) reversible part due to the flow deceleration and an(ii) irreversible part, characterized by the exit pressure loss coefficient Ke:


∆pe = (1− ε)ρU2

2︸︷︷︸i

−KeρU2

2︸︷︷︸ii

(A.10)

The combined irreversible pressure drop (Kc +Ke) ρU2/2 equals the totalpressure drop. Kc and Ke are a function of the area ratio ε, and to a lesserextent of the channel Reynolds number Re.

Kays and London [57] provide charts of Kc and Ke indicating the influenceof ε and Re for various geometries. The following correlations have been fittedbased on [57] by Van den Bulck [100] to incorporate the influence of ε and Rein a functional form. For turbulent flow:

Kc = 0.4

(1− ε2

)+ 1.16Re−1/4

Ke = (1− ε)2 − 1.16 εRe−1/4 (A.11)

and for laminar flow:

Kc = 0.4

(1− ε2

)+ 0.78

Ke = (1− ε)2 − 0.756 ε(A.12)

The curves for Kc and Ke in Fig. A.1 are plotted using Eqs. (A.11) and (A.12).

Numerical example Assuming laminar flow (Eq. (A.12)) and a typ-ical porosity of ε = 0.85 (see Table 1.2), the entrance (i.e. contraction)and exit (i.e. expansion) pressure drop coefficients are Kc ' 0.89 andKe ' −0.62. The overall pressure drop of the combined entrance andexit loss is Kc + Ke ' 0.27.

Wendland et al. [110] estimate the contribution of entrance and exit lossesas a whole to be around 5 % of the total catalyst pressure loss for a typical400 cpsi monolith.

A.2.4 Flow accelerationWhen the temperature of the flow inside the channel changes from inlet tooutlet, the density is not constant. For an operating catalytic converter, heatis produced by the exothermic catalytic reactions (see Sect. 1.2.1). As such,the density decreases and the velocity increases along the length of the catalystchannel. This flow acceleration causes an additional pressure difference betweeninlet and outlet.

Kays and London [57] (Eq. 2.26a) present a general formula for static pres-sure drop in a heat exchanger, incorporating the term accounting for flow accel-eration. The factor 2 in Eq. 2.26a is an approximation of 1 + ε2, thus yieldingthe correct term to account for flow acceleration:

∆pacc =(1 + ε2

)( ρin

ρout− 1)ρU2

2(A.13)


0 0.5 1-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Kc, K

e (-)

ε (-)

Laminar

Kc (-)

Ke (-)

Laminar

Re = 2000

Re = 10 000

Re → ∞

Re → ∞

Re = 10 000

Re = 2000

Figure A.1 – Contraction (Kc) and expansion (Ke) pressure drop coefficients as afunction of open frontal area ε and Re (adapted from Kays and London [57], usingEqs. (A.11) and (A.12))

Note that U here represents the velocity inside the channel yet near the en-trance, where the density is still unchanged. In the expression for total pressuredrop, the factor 1 + ε2 disappears:

∆p0,acc =(ρin

ρout− 1)ρU2

2(A.14)

A.2.5 Oblique entrance

When the upstream velocity vector is not in line with the channel centerline,an additional pressure drop occurs. The velocity vector misalignment causesan enlarged recirculation zone at the channel entrance, reinforcing the entranceeffect discussed in Sect. A.2.3.

The doctoral research of Haimad [43] proves that this effect greatly influ-ences the CFD-predicted catalyst flow distribution. Since the flow field expandsin the diffuser, one can imagine that only the region of the catalyst inlet facewhich is aligned with the upstream runner experience velocity vectors with a


low angle-of-attack (provided the runner is in line to the catalyst axis). Nearthe edges of the catalyst, high entrance angles may occur, due to the diffusioneffect, recirculation zones and vortices generated by the curved runners. Ac-cording to Haimad [43] and Benjamin et al. [15], this may explain why CFDoften overpredicts the flow uniformity compared to experimental data.

Küchemann and Weber [32] propose an upper limit to the pressure losscaused by oblique entry:

∆pobl,max =ρU2

t

2(A.15)

where Ut is the transverse velocity component.This upper limit is based on the idea that for an ideal unseparated flow,

the force exerted per unit frontal area by the oblique flow on a series of par-allel plates equals F = ρU2

t /2 (N/m2). For ‘real’ oblique flow over a non-aerodynamically streamlined body (e.g. a series of parallel plates or a mono-lith) and assuming that no suction can be sustained without flow separation,F should equal zero. Equation (A.15) follows directly from this assumption.

Written as a pressure drop coefficient, based on the dynamic pressure,Eq. (A.15) becomes:

Kobl,max = ∆pobl,max

/(ρU2

2

)=

(Ut

U

)2

=(U0

U

)2(Ut

U0

)2

= ε2 tan2 β (A.16)

where β is the angle-of-attack, corresponding to the angle between the catalystaxis and the upstream velocity vector [U0, Ut].

A.2.6 Overall

The overall total pressure drop, referenced to the dynamic pressure inside thechannel (yet near the entrance) is:

∆p0 =[4fapp

L

d

ρin

ρm+Kc +Ke

ρin

ρout+(ρin

ρout− 1)

+Kobl

]ρU2

2(A.17)

where the factors ρin/ρ take the change in density with respect to the en-trance conditions into account. fapp,m is evaluated at a mean temperature andρm represents a mean density, defined so that fapp,m ρin/ρm =

∫ L

z=0

[fapp (z)·

(ρin/ρ (z) )]dz/L .

The following expression gives the difference in static pressure from a loca-tion upstream to a location downstream of the monolith, which incorporatesthe reversible static pressure changes and in- and outlet:

A.3 Mass transfer 249

∆p =[4fapp

L

d

ρin

ρm+(Kc +

(1− ε2

))+(Ke −

(1− ε2

)) ρin

ρout

+(1− ε2

)( ρin

ρout− 1)

+Kobl

]ρU2

2(A.18)

where U still represents the velocity inside the channel yet near the entrance,where the density equals the upstream density. In the absence of densitychanges as is the case on the isochoric flow rig, Eqs. (A.18) and (A.17) re-duce to the same expression for static and total pressure drop:

∆p0 = ∆p =[4fapp

L

d+Kc +Ke +Kobl

]ρU2

2(A.19)

The expressions described in the above sections have been used to describethe relation between the flow rate and pressure drop in the laminar flow ele-ment meter (LFE) (see Sect. 2.4.2). The LFE is used as reference flow ratemeasurement during the measurements on the isochoric (CME) flow rig (seeSect. 2.2.2).

A.3 Mass transfer

A.3.1 General

The equations of conservation of mass and species for a three-dimensional sys-tem are:

∂ρ

∂t= −∇ ·

(ρ ~U)

(A.20)

∂Ci

∂t= −∇ ·

(Ci

~U)

︸︷︷︸convection

+∇ ·(Di~∇ (Ci)

)︸︷︷︸

diffusion

+Ri (A.21)

where ρ is the density [kg/m3], ~U is the velocity [m/s], Ci is concentration ofspecies i [kmol/m3], Di is the molecular diffusivity [m2/s] and Ri is the reactionrate for species i [kmol/m3s].

Given the strong anisotropic catalyst geometry (§1.2.1), the convection anddiffusion terms in Eq. (A.21) can be split into axial and transversal components.Three time scales can be defined based on the splitted version of Eq. (A.21):

• convection time or residence time τU = L/U

• axial diffusion time τD,a,i = L2/Di

• transversal diffusion time τD,t,i = d2/Di


where d is the channel hydraulic diameter [m]. These three time scales combineinto two dimensionless Peclet numbers:

• axial Peclet number Pea = τU/τD,a,i

• transversal Peclet number Pet = τU/τD,t,i

For an automotive catalyst, the axial diffusion time is much larger thanthe typical residence time of 10 ms (Pea 1). Axial diffusion is thereforeneglected. Because of the small channel size, the transverse diffusion time issmaller than the residence time (Pet 1). As such, the transverse concentra-tion distribution within a single channel is considered uniform.

The time scale that limits the chemistry depends on the catalyst tempera-ture: at a low temperature, transverse diffusion between gas and surface phasesis faster than the time scale of the catalytic reactions occurring in the surfacephase. This process is denoted mass transfer-limited. At a high temperature,the reactions occur faster than the diffusion time scale, and the process is ratelimited or kinetically limited.

The catalytic reactions can be modeled using (i) a homogeneous approx-imation, or (ii) a lumped-parameter heterogeneous model. The latter bestdescribes the reaction kinetics and is generally used in the literature.

A.3.2 Homogeneous reaction kineticsThe homogeneous first order model assumes that all reactions take place in thegas phase, leading to a reaction rate Ri = −Ki Ci. For the one-dimensionalstationary case, this reduces Eq. (A.21) to:

∂ (Ci U)∂z

= −Ki Ci (A.22)

where z is the lengthwise coordinate [m]. Assuming U constant35, this yieldsan exponential lengthwise concentration distribution:

Ci (z) = Ci,0 exp(−Ki z

U

)(A.23)

Based on Eq. (A.23), the conversion efficiency can be defined as the ratio oftotal converted amount of species i given a certain (non-uniform) catalyst veloc-ity distribution, to the converted amount given a uniform velocity distributionwith the same mean velocity:

ηC,i =

∮A

(1− exp

(− Ki L

U (x, y)

))ρU (x, y) dA(

1− exp(−Ki L

Um

))m

(A.24)

35Catalyst flow is incompressible (Ma < 0.3), however because of the generated reactionheat, the density decreases and the gas accelerates as it passes through the catalyst.

A.3 Mass transfer 251

This equation is used in Sect. 1.2.1 in Fig. 1.5 to demonstrate the influenceof the flow uniformity on the catalyst conversion efficiency.

A.3.3 Heterogeneous reaction kineticsAlternatively, a catalyst channel can be modeled as a one-dimensional lumped-parameter system with gas and surface phases. In such heterogeneous reactionmodel, all reactions occur in the surface phase. Transverse diffusion betweengas and surface phase is modeled by a mass transfer coefficient km [m/s]. km

represents the ratio of diffusive flux to the surface [kmol/m2s] to the concentra-tion difference between bulk and surface phase C−Cs [kmol/m3]. Multiplyingthis diffusive flux J = km (C − Cs) with the geometric surface area of thechannel av = 4/d [m−1], this yields a reaction rate expression −kmav (C − Cs)[kmol/m3s]. Upon substitution in Eq. (A.21), the one-dimensional stationary film model for mass transfer becomes:

∂ (Ci U)∂z

= −km,i av (Ci − Cs,i) (A.25)

The Sherwood number is the non-dimensional mass transfer coefficient, de-fined as Sh = km d/Dm. Sh is the mass transfer analogous of the Nusseltnumber Nu. Sh and Nu can be determined analytically for fully developedlaminar flow [92]. Numerical and experimental correlations exist which takethe developing flow region into account.

The surface phase species concentration is determined by its own conserva-tion equation. In steady state this equation becomes:

km,i (Ci − Cs,i) = Rs,i (Ts, Xs,1 . . . Xs,I) (A.26)

where Ts is the surface temperature [K], X denotes species molar fraction[kmol/kmol], I is the number of species. The reaction rate expressions Rs,i aredetermined experimentally. Catalytic reactions rate expressions are typicallyof the following form, including inhibition factors in the denominator:

Rs,i (Ts, Xs,1 . . . Xs,I) = ks,i (Ts)∏

r Xαrr∏

r (1 + βr Xr)γr

(A.27)

and the rate coefficients have an Arrhenius-type temperature dependence:

ks,i (Ts) = Ai exp(−Ea,i

RTs

)(A.28)

Numerical values for the rate equations can found in the literature (e.g.Mezaki and Inoue [73]). The set of partial differential equations Eqs. (A.25)and (A.26) for heterogeneous reactions cannot be solved analytically in thesame way as Eq. (A.22) for homogeneous reactions. It should be solved usingnumerical integration.

Appendix B

Exhaust stroke flow similarity

The analytical derivation below yields expressions for the peak mass flow ratesduring the blowdown (Eq. (2.1)) and the displacement phase (Eq. (2.2)) for afired engine, as well as for the CME flow rig used in this thesis. These expres-sions are used in the discussion of exhaust stroke flow similarity in Sect. 2.3between the CME flow rig and a fired engine.

For this derivation, in-cylinder heat loss and blow-by leakage are neglected.Air is taken as working fluid, with thermodynamic properties evaluated at afixed mean temperature.

From the conservation of mass and energy (and assuming isentropic com-pression and expansion, and isochoric combustion) result the following expres-sions describing the relation between intake and residual state:

ρe

ρi=Vi

Ve;

pe

pi=(Vi

Ve

)γ(

1 +∆Tc

Ti

(V0

Vi

)γ−1)

(B.1)

where ρ is the density [kg/m3], p is the pressure [Pa], V is the cylinder vol-ume [m3], T is the temperature [K] and the subscripts i, e, 0 respectively denoteintake valve closing, exhaust valve opening and top dead center. The adiabatictemperature rise due to combustion equals ∆Tc = φSf/ (cvLf ), where φ isthe product of the equivalence ratio and the combustion efficiency [-], Sf isthe lower heating value of the fuel (J/kg), cv is the specific heat capacity atconstant volume (J/(kg K)) and Lf is the theoretical air-to-fuel ratio [kg/kg].

Equation (B.1) can easily be derived in three steps: (i) isentropic compres-sion between Vi and the dead volume V0:

p0

pi=(Vi

V0

)γ

;T0

Ti=(Vi

V0

)γ−1

(B.2)

(ii) isochoric combustion at V0, assuming no change occurs in the working fluidcomposition and incorporating Eq. (B.2):

253

254 Appendix B Exhaust stroke flow similarity

p1

p0=

T1

T0; T1 = T0 + ∆Tc

⇔ p1

p0= 1 +

∆Tc

T0

⇔ p1

p0= 1 +

∆Tc

Ti

(V0

Vi

)γ−1

(B.3)

(iii) isentropic expansion from V0 to Ve, before exhaust valve opening:

pe

p1=(V1

Ve

)γ

;Te

T1=(V1

Ve

)γ−1

(B.4)

Combining Eqs. (B.2), (B.3) and (B.4) yields Eq. (B.1).The exhaust stroke is divided into blowdown and displacement phases. The

blowdown phase is regarded as the expansion of the residual cylinder pres-sure under constant cylinder volume. The displacement phase is regarded asvolumetric expulsion of gas at quasi-constant pressure.

Assuming a constant cylinder volume and adiabatic sudden transition, thestate evolution with respect to the residual state (denoted with subscript e) isdescribed by:

ρ (θ)ρe

=m (θ)me

;p (θ)pe

=(m (θ)me

)γ

(B.5)

where θ (= ωt) is the crankshaft angle [rad] and m is the gas mass containedin the cylinder [kg].

Approximating the exhaust manifold pressure with the atmospheric pres-sure pa, the following expression (see e.g. Heywood [47], App. C) gives the massflow rate over the exhaust valves assuming compressible restricted flow:

m (θ) = Cd neπdeh′e (θ)

p (θ)√rT (θ)

· f(

pa

p (θ)

)= −dm (θ)

dt(B.6)

f

(pa

p (θ)

)=

(

pa

p

) 1γ

√2γ

γ−1

(1−

(pa

p

) γ−1γ

); pa

p >(

2γ+1

) γγ−1

(a)

√γ(

2γ+1

) γ+12(γ−1)

; pa

p 6(

2γ+1

) γγ−1

(b)

where conditions (a) and (b) respectively denote subsonic and sonic (choked)regime. Cd is the exhaust valve discharge coefficient [-], r is the specific gas con-stant [J/(kgK)], ne and de are the number per cylinder [-] and the diameter [m]of the exhaust valves. The discharge coefficient Cd for poppet exhaust valvesis based on Fig. B.1, compiled from empirical data by Heywood [47]. Sincethe flow pattern depends on the lift height, so does the discharge coefficient.Figure B.2a shows the pressure loss coefficient K [-] for a rotating valve, based

255

Flow patternat low lift

Flow patternat high lift

Figure B.1 – Discharge coefficient Cd for exhaust valves (Source: [47])

(a)

0 30 60 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cd (

-)

Valve angle (°)

(b)

Figure B.2 – (a) Pressure loss coefficient K and (b) discharge coefficient Cd forrotating valve (Source: [74])


on Miller [74]. Figure B.2b shows the discharge coefficient Cd as a function ofthe valve angle, determined from K using the relation K =

(C−1

d − 1)2

.The lift height h′e [m] in Eq. (B.6) is approximated by:

h′e (θ) = he12

(1− cos

(2πθ − θe

∆θ

))(B.7)

where he is the maximum valve lift height [m], θe is the start of exhaust valveopening [rad] and ∆θ is the exhaust valve opening duration [rad]. The expres-sion for h′e (θ) is further approximated using a Taylor expansion for small valuesof (θ − θe) /∆θ, and substituting θ−θe = ωt results in h′e (t) = he (π/∆θ)2 ω2t2,where 2πω/60 equals the engine speed N [rpm]. Note that p and T actuallyrepresent total conditions, although this is neglected in the remainder of theanalytical derivation in order to keep the equations solvable.

Substituting Eq. (B.5) in Eq. (B.6) and incorporating the above approxi-mation for h′e results in:

d

dt

(m

me

)= −Cd

neπ3dehe

∆θ2ω2t2

√rTe

Ve

(m

me

) γ+12

f

(pa

pe

(m

me

)−γ)

(B.8)

For this partial differential equation to be solvable, the function f is ap-proximated using the following expression:

f ' f ′ = cf

(m

me

(pe

pa

) 1γ

)− γ+12 (

pe

pa

) γ−32γ

(m

me

(pe

pa

) 1γ

− 1

)(B.9)

where cf is a dimensionless fit constant. The exponents −(γ + 1)/2 and(γ − 3)/(2γ) in Eq. (B.9) have no physical meaning. They are selected with thesole purpose of rendering Eq. (B.8) solvable. Figure B.3 shows f and f ′ accord-ing to Eq. (B.9), as a function of the gas mass remaining in the cylinder m/me .Note that initially, m/me = 1, until the cylinder pressure equalizes with theatmospheric pressure (p = pa) and m/me = (pa/pe )1/γ (from Eq. (B.5)).

Substituting Eq. (B.9) in Eq. (B.8) yields a solvable partial differentialequation that describes the approximate evolution of m, the gas remaining inthe cylinder:

d

dt

(m

me

)= −Cd

neπ3dehe

∆θ2ω2t2

√rTe

Ve

(pe

pa

)− 2γ

(m

me

(pe

pa

) 1γ

− 1

)

= −Kt2(

1A

m

me− 1)

(B.10)

The solution to this partial differential equation is:

257

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

f (−

)

m/me (−)

f (pe/p

a= 5)

f ’(pe/p

a= 5)

f (pe/p

a= 2)

f ’(pe/p

a= 2)

Figure B.3 – Approximation of f ac-cording to Eq. (B.9)

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t / tmax

= t / (2A/K)1/3 (−)

M /

M1 (

−)

analytical, Eq. (20)experimental

Figure B.4 – Flow rate predicted byEq. (B.12) compared to measured run-ner flow rate

m

me(t) = A+ (1−A) exp

(− K

3At3)

(B.11)

where K = Cdneπ3dehe

∆θ2 ω2√

rTe

Ve

(pe

pa

)− 2γ

[s−3] and A =(

pa

pe

) 1γ

[-]. The flow rateyields:

m (t) = −dmdt

(t) = me K

(1A− 1)t2 exp

(− K

3At3)

(B.12)

The maximum mass flow rate during blowdown m1 [kg/s] occurs when thederivative of Eq. (B.12) is zero. This corresponds to a time after the exhaustvalve opening that is equal to:

t1 = (2A/K )1/3 (B.13)

t1 [s] represents the characteristic time scale for the blowdown process, whereK [s−3] and A [-] are the variables defined above. The peak mass flow rate att1 equals:

m1 = mmax = me (2/e)2/3 (K/A)1/3 (1−A) (B.14)

Figure B.4 shows the good correspondence between the analytically pre-dicted mass flow rate according to Eq. (B.12) and the experimentally deter-mined flow rate in an exhaust runner on the CME flow rig.

Substituting Eq. (B.1) and choosing the fit constant in Eq. (B.9) cf =2 (2/e)−2 ' 3.695 yields:


m1 = ρiViω

(2Cd

neπ3dehe

∆θ2

√rTi

ωVi

) 13(Vi

Ve

) γ−76

·

(1 +

∆Tc

Ti

(V0

Vi

)γ−1)

︸︷︷︸ii

γ−86γ

·(pi

pa

)︸︷︷︸

i

− 43γ

·

(pi

pa

)︸︷︷︸

i

1γ(Vi

Ve

)(1 +

∆Tc

Ti

(V0

Vi

)γ−1)

︸︷︷︸ii

1γ

− 1

(B.15)

During the displacement phase, cylinder pressure and density are assumedconstant. From the conservation of mass results the following expression forthe peak mass flow rate m2 [kg/s] during displacement:

m2 = ρi

(πb2

4s

)ω

2

(pi

pa

)︸︷︷︸

i

− 1γ

(1 +

∆Tc

Ti

(V0

Vi

)γ−1)

︸︷︷︸ii

1γ

(B.16)

Equations (B.15) and (B.16) correspond respectively to Eqs. (2.1) and (2.2)in Sect. 2.3.

Elaborating Eq. (B.13) with substitution of Eqs. (B.1) yields:

ωt1 =(

12Cdneπ

3dehe

∆θ2

√rTi

ωVi

)− 13(Vi

Ve

) 1−γ6

·(pi

pa

)︸︷︷︸

i

13γ

(1 +

∆Tc

Ti

(V0

Vi

)γ−1)

︸︷︷︸ii

2−γ6γ

(B.17)

Equation (B.17) is used to plot the analytical values of the blowdown time scalein Fig. 2.16 in Sect. 2.3.

Parts of this appendix have been published in an international journal withreview:


Appendix C

Velocity measurementtechniques

Several experimental techniques exist for measuring the local instantaneousfluid velocity. For research in most turbulent gas flows where velocity fluctua-tions are of interest, two velocity measurement approaches are in competition:thermal anemometry and optical anemometry.

The following is an overview of the applicability of these techniques, specif-ically to exhaust system flows.

C.1 Thermal anemometry

Thermal anemometry measures the local fluid velocity indirectly, based on theconvective heat transferred from an electrically heated sensor element (wire,film, fiber, . . . ). Typically, the sensor’s resistance (and consequently its tem-perature) is kept constant by incorporating it in a Wheatstone bridge withfeedback amplifier. This mode of operation is referred to as constant tem-perature anemometry (CTA), and is characterized by a very high bandwidth.Further details are given in Sect. 3.2.

Any change in the fluid flow that changes the amount of heat transferredfrom the sensor is detected by the CTA. As such, not only velocity can bemeasured but also temperature, changes in fluid mixture composition or phasechanges in multi-phase flow.

Excellent historical reviews of thermal anemometry are given by Frey-muth [39] and Fingerson and Freymuth [37]. Freymuth [40] comprises a detailedbibliography of thermal anemometry. The main reference work by Bruun [25]provides a detailed background of hot-wire and hot-film anemometry, and selec-tion criteria for different flow conditions. Data reduction methods for obtaining

259

260 Appendix C Velocity measurement techniques

velocity values from raw anemometer bridge voltages (e.g. velocity calibration,temperature correction) used in this thesis are all according to Bruun [25].

The most widely used application is hot-wire anemometry (HWA) in con-stant temperature mode. Advantages of HWA include:

• High bandwidth — A typical hot-wire probe operated in gas using a con-stant temperature anemometer bridge features a flat frequency responseup to approximately 30 kHz at velocities between 0.5 and 50 m/s. Mea-surements at several hundred kilohertz are possible for higher velocities.

• Spatial resolution — A standard hot-wire sensor is 5 µm in diameter and1.25 mm long. Even smaller sensors can be used in boundary layer flows.The small sensor size yields a good spatial resolution in comparison toother techniques.

• Signal analysis — By contrast to an optical anemometer, the outputsignal of the HWA is a time-continuous signal, which enables the use ofconventional time-domain and frequency-domain analysis.

• Low-velocity sensitivity — The sensitivity of the output voltage versusvelocity is high at low velocity. Given the small sensor dimensions, HWAis therefore ideally suited for boundary layer research.

• Signal-to-noise ratio — High quality constant temperature anemometerbridges exhibit a very low noise level (−40 dB or 1/10 000 ), when comparedto LDA (−30 dB or 1/1000 ).

Section 3.2 discusses the hot-wire anemometer used during this thesis.

C.2 Optical anemometryOptical anemometry comprises mainly laser Doppler anemometry (LDA) andparticle image velocimetry (PIV). A reference book by Albrecht et al. [6] givesan overview of LDA measurement principles, signal processing and applicationissues.

In its most typical form, LDA uses a pair of intersecting laser beams, wherethe measuring volume is defined by the intersection of both beams. As shownin Fig. C.2, an interference pattern of successive light and dark planes (orfringes) is formed by the intersecting beams, according to regions of positiveand negative interference. The planar fringes are directed along the beambisector and the normal to the beam plane. The inter-fringe spacing ∆x =λb/ (2 sin θ), where λb is the laser light wavelength (m) and 2 θ is the intersectingbeam angle.

If the flow is seeded using sufficiently small tracer particles (e.g. oil mistdroplets, fine solid powders,. . . ), a particle traveling through the fringe pat-tern at a velocity

−→U (Ux, Uy, Uz) scatters the laser light, which is picked up by

a photo-detector. The scattered light intensity varies as the seeding particle

C.2 Optical anemometry 261

Particle-seeded flow

∆x (known)

Velocity = distance/time

∆t (measured)

Signal

Time

Figure C.1 – Schematic diagram of LDA working principle and resulting Dopplersignals

travels through the light or dark regions. Assume the beam bisector is alongthe y-direction, and the fringe planes are parallel to the y-z plane. The mag-nitude of the projection of the velocity normal to the fringe plane |Ux| can bedetermined based on the known fringe spacing ∆x, the amount of fringe pulsescaught on the detector and the measured time ∆t between individual fringepulses (see Fig. C.2).

The seeding particles should be (i) small enough to accurately follow thefluctuating flow, (ii) smaller than the fringe spacing to yield an optimal detec-tor signal, yet (iii) not too small to still scatter enough light to the detector.Furthermore, light is scattered in all directions, yet at a different intensitydepending on the angle to the beam bisector. The intensity of backward scat-tered light (i.e. towards the laser beam source) is ' 100 times smaller than theforward scattered light intensity. The highest sensitivity is therefore achievedusing a the detector that picks up the forward scattering light signals.

Introducing seeding into the flow under investigation has some practicaldrawbacks. Depending on the type of seeding substance, periodic cleaning ofthe test set up is required. Particularly, the viewing windows should be free ofdeposits to ensure optimal optical access. In gas flows, oil mist aerosol seedingis typically preferred over solid seeding.

The direction or the sign of the velocity Ux/|Ux| can only be determinedif the intersecting beams have slightly different wavelengths. Applying a fre-quency shift fsh to one of the beams causes the fringes themselves to move ata velocity of ±fshλb/ (2 sin θ). Thus, a stationary particle (Ux = 0) scatterslight at a frequency corresponding to the frequency shift fsh. Particles with


Umin

0 Umin

Umax

Umax

fmin

fshift

fmax

Velocity

Freq

uenc

y f

(=

∆t-

1 )

LDA frequency shifting

U (unshifted)U (shifted)

Figure C.2 – Principle of frequency shifting for resolving the directional ambiguityin LDA

negative velocity (Ux < 0) scatter light at a frequency fsh − |Ux| (2 sin θ) /λb.In conclusion, bidirectional velocity can be measured using frequency shift-ing, where the minimum measurable velocity is proportional to the frequencyshift, or Umin = −fshλb/ (2 sin θ). For a typical LDA system with a maximumfrequency shift of 40 MHz and λb ' 500 nm, Umin is around −100 m/s.

To measure two or three velocity components, additional intersecting beampairs are required. Each beam pair has a different wavelength (i.e. differentcolor). Note that the difference in wavelength between beam pairs is manyorders of magnitude larger than the wavelength shift corresponding to thefrequency shifting. Using color filters, the scattered light is split into eachcomponent and directed to one photo-detector for each velocity component.

Advantages of a LDA system with frequency shifting include:

• Non-intrusiveness — The main advantage with respect to thermal anemo-metry is that optical measurement techniques do not disturb the flow.Nevertheless, the introduction of seeding and the need for high-qualityoptical access may require some flow disturbance.

As a consequence of the non-intrusive nature of LDA measurements, thereis no temperature limit to the flow. LDA can be used e.g. in fired burnerresearch, provided that adequate seeding is used.

• Directional sensitivity — An LDA system with frequency shifting resolvesthe velocity with a very large minimum measurable velocity. By contrast,thermal anemometry as such is incapable of detecting the flow direction.

• High accuracy — Both LDA and HWA systems feature a similar accuracyup to 0.1. . . 0.2 % in carefully controlled experiments, or most likely 1%in practical applications.


• Spatial resolution — The spatial resolution is determined by the size ofthe measuring volume. For a typical LDA set up, the volume is 150 µmby 2 mm, compared to 5 µm by 1.25 mm or less for HWA. Clearly, LDAis less suited for near-wall flow investigation than HWA.

However, there are some important disadvantages to LDA which make itdifficult to use for measuring the velocity distribution in a catalyst, and ingeneral any internal flow in a confined geometry with curved boundaries:

• Optical access — In measuring a confined flow, the laser beams require anoptical passage through the boundary. Light travels at a slightly differ-ent speed through different media (e.g. air, water, glass, plexiglass). Thespeed is also a function of the temperature of the medium. As a result,the laser beam undergoes refraction at interfaces between different me-dia (and across important temperature gradients). The optical passageshould ensure that the refraction of the beams is such that the beamsintersect in a common measuring volume. In practice, this can only beachieved using a plane, smooth sheet of transparent material. Further-more, the quality of the material should be high enough: (i) smooth planesurfaces, (ii) no gas bubble or other inclusions, (iii) no changes in the re-fractive index within the material. Using anything other than opticalgrade glass results in a drastically reduced data rate or an entire loss ofsignal.

Inserting a flat surface for optical access into a curved boundary resultsin a local distortion of the flow. As such, the optical passage should be assmall as possible. On the other hand, the laser beam intersecting angle 2 θshould be as large as possible to minimize the measuring volume, whichresults in a good spatial resolution.

• Seeding — Seeding particles are required for LDA measurements. Theamount of acquired velocity measurements per time is called the datarate. The data rate is roughly proportional to the concentration of seedingparticles crossing the measurement volume.

To obtain a good velocity distribution across several points in a measure-ment region, the seeding concentration should be as uniform as possiblein all points. The seeding is therefore introduced into the flow sufficientlyfar upstream of the measurement region, to obtain a uniform distribu-tion. However, certain flow phenomena inhibit the seeding distribution.In particular, compact exhaust manifold flows are characterized by phe-nomena like flow separation, recirculation and vortex break-down, whichare all prone to cause seeding problems.

Phase-locked measurements are used to resolve periodic flows (seeSect. 2.5). For HWA, the continuous output signal makes phase-lockingvery straightforward. Since the velocity samples for LDA are not equidis-tant in time, the phase-locked samples are binned in B phase intervals


of equal duration. The N (b) samples acquired in each bin b are av-eraged, producing B bin-averaged velocity values

−→U (b) per cycle (e.g.

using B = 36 equally-sized bins from 0 to 360 ca corresponds to onebin-averaged velocity value every 10 ca).

Experience learns that the number of samples per bin N (b) can varysignificantly through the cycle. It is often difficult to obtain enough sam-ples in each bin to produce a bin-averaged velocity

−→U (b) with sufficient

accuracy. This requires either a longer measuring time, or reducing thenumber of bins per cycle B, which results in a loss of temporal resolution.

The phase-locked HWA approach is not hampered by this, and the tem-poral resolution is only limited by the anemometer bandwidth. For amoderate bandwidth of 10 kHz, a temporal resolution of 1.8 ca is ob-tained at an engine speed of 3000 rpm.

These disadvantages make it very difficult for LDA to measure the time-resolvedvelocity distribution throughout the entire catalyst cross-section.

Kim et al. [59] and Park et al. [81] discuss phase-locked LDA measurementresults obtained in fired engine conditions inside the diffuser, upstream of a CCcatalyst. Measurements are taken along a single line. The authors dissolve liq-uid titanium(iv) isopropoxide (Ti[OCH(CH3)2]4) into the fuel, at a volumetricconcentration between 3 to 7 %. The titanium isopropoxide burns along withthe fuel in the combustion chamber and forms titanium dioxide (TiO2). Thissolid substance is often used as seeding medium in optical anemometry. It isparticularly used in combustion flow research, since TiO2 features a high melt-ing point of 1850 C, with excellent light scattering properties. Solid seedinghas the tendency to accumulate and clog small openings, such as the catalystchannels. However, Kim et al. [59] claim no clogging occurs at the appliedseeding concentrations. This technique has been initially introduced by Zhaoet al. [114].

Liu et al. [70] discuss phase-locked LDA measurement results obtained30 mm downstream of a close-coupled catalyst in fired engine conditions. Mea-surements are shown in a few points along a single line. The authors comparethese measurements to CFD results. The correspondence is not very good,yet the obtained spatial resolution does not allow for a good validation. Nomention is made of the applied seeding.

Benjamin et al. [14] present LDA measurements downstream of a close-coupled catalyst, in a fired engine. The setup is basically identical to the oneused by Liu et al. [70]. The authors use a fiber-optic single component LDAwith Ar+ laser and a 10 MHz frequency shift. The focal length in 120 mm,with a 16 mm beam spacing. The measuring volume is about 2.2 mm long.The authors [14] use the same titanium isopropoxide mixed with the fuel, asdescribed earlier [59, 81, 114].

Benjamin et al. [14] report no clogging of the catalyst substrate, even afterextended experiments. However, deposits quickly accumulate on the sparkplugs and in the injector nozzles. The authors report extensive difficulties in


measuring close to the optical windows. Also, in some crankshaft positionwindows, the seeding density is considerably smaller than in other windows. Ingeneral, an uneven spatial and temporal distribution of seeding concentration,along with the loss of signal due to wall reflections make this experimentaltechnique very difficult to use in exhaust systems.

Hwang et al. [53] provide some qualitative results using phase-locked LDAon an isothermal flow rig. The authors employ liquid aerosol seeding usingdioctyl phthalate (DOP).

Each of these studies [59, 81, 70, 53, 14] shows the difficulties in obtaininghigh resolution results using LDA in exhaust systems.

During the calibration of the oscillating hot-wire anemometer (see Sect. 3)in a custom-built miniature wind tunnel, a two-component LDA system is usedwith frequency shifting on both components. Diethylhexylsebacat (DEHS) oilmist is used as seeding. The LDA system and calibration wind tunnel aredescribed in Sect. 3.6.

Particle image velocimetry (PIV) is an optical measurement technique thatuses a high-speed camera to record pairs of successive images of a particle seededflow field. Each image pair is separated by a very short time interval, as smallas 2 µs. The two images are cross-correlated. This yields a two-dimensionalparticle displacement field, which is equivalent to the velocity field. This typeof PIV which enables quantitative velocity measurements is sometimes referredto as digital particle image velocimetry (DPIV), as opposed to the older methodused only for high speed flow visualization. Adrian [5] and Westerweel [111]provide excellent reviews on PIV theory and applications.

Applying PIV in exhaust systems will be plagued by similar problems asLDA: (i) obtaining an adequate seeding density throughout the cross-sectionand the engine cycle, and (ii) providing optical access. The quality of theoptical access is less restrictive for PIV when compared to LDA, due to thedifferent operating principle. No sources are available in the literature on us-ing PIV in exhaust systems, although the technique has been frequently andsuccessfully applied for measuring in-cylinder flows. Brucker [24] discusses athree-dimensional fast scanning approach using PIV with application in com-bustion chamber flows.

Appendix D

Modeling one-dimensionalgas dynamics

D.1 Model descriptionThe Euler equations describe the motion of a compressible, inviscid fluid,whereas the motion of viscous fluids is described by the more general Navier-Stokes equations [48, 49].

In this thesis, only one-dimensional variations of the primitive variablespressure p, velocity U and density ρ are considered. In particular, the numericalmodel of the exhaust system used in Sect. 5.2.3 and Sect. 5.3.4 assumes thatthe primitive variables vary only along the lengthwise axis of large length-to-diameter ratio components (e.g. exhaust runners, exhaust pipe), and thatcomponents with negligible momentum can be described by a single point model(e.g. cylinders, diffuser, catalyst substrate).

The one-dimensional Euler equations express the conservation of mass, mo-mentum and energy in the lengthwise z-direction. For unsteady, one-dimensionalflow in a duct with variable cross-section, including wall friction and heat trans-fer, the Euler equations in conservative form are:

∂ (ρA)∂t

+∂ (ρUA)∂z

= 0

∂ (ρUA)∂t

+∂(ρU2A

)∂z

= −∂ (pA)∂z

+ p∂A

∂z− f

4Ad

U

|U |ρU2

2∂ (ρEA)

∂t+∂ (ρUEA)

∂z= −∂ (pUA)

∂z+ ρqA (D.1)

where the quantities ρ [kg/m3], U [m/s], E [J/kg], p [Pa] denote average valuesacross the duct cross-section such that the conservation laws are fulfilled. The

267

268 Appendix D Modeling one-dimensional gas dynamics

factor U/|U | ensures that the friction acts counter to the local flow direction.In the perimeter 4A/d [m], d is the hydraulic diameter [m]. Furthermore, forgas flows, the ideal gas equation p = ρrT is assumed valid, where r is thespecific gas constant [J/(kgK)]. The total internal energy per unit mass E isdefined as E = e + U2/2 . For an ideal gas, e = cvT , where cv is the specificheat capacity [J/(kgK)] at constant volume.

The Euler equations (D.1) can be written in conservative vector notationas:

∂ξ

∂t+∂F∂z

= Q (D.2)

where the boldface symbols represent vectors. The conservative variable vec-tor ξ, the flux vector F and the source term Q are defined as:

ξ =

ρAρUAρEA

, F =

ρUAρU2A+ pAρUHA

, Q =

0−f 4A

dU|U |

ρU2

2

ρqA

(D.3)

where the total enthalpy per unit mass H [J/kg] is defined as H = h+ U2/2 .For an ideal gas, h = cpT , where cp is the specific heat capacity [J/(kg K)] atconstant pressure.

D.1.1 Decoupling the Euler equationsIn order to solve the Euler equations numerically, the set of coupled partialdifferential equations is to be transformed into an uncoupled set of scalar dif-ferential equations. In the following derivation, a constant cross-section is as-sumed for the sake of simplicity; thus the cross-section A vanishes in Eqs. (D.2)and (D.3).

With the Jacobian matrix J defined as J = ∂F/∂ξ , and since F is homo-geneous in ξ [49], Eq. (D.2) becomes:

∂ξ

∂t+ J

∂ξ

∂z= Q (D.4)

where for the one-dimensional case, J is given by the Eq. (E16.2.3) inHirsch [49]. In order to obtain the eigenvalues of the Euler equations, thesystem is written as a function of the primitive variables ρ, U and p instead ofthe conservative variables (ρ, ρU and ρE). Similar to ξ, a primitive variablevector ζ is defined as ζ = [ρ, U, p]T . Rewriting the Euler equations yields:

∂ζ

∂t+ J

∂ζ

∂z= Q (D.5)

The transformation matrix to convert between conservative and primi-tive variables is M = ∂ξ/∂ζ . M and its inverse M−1 are given by theEqs. (E16.2.7) and (E16.2.8) in [49]. The primitive Jacobian J is given byEq. (E16.2.9) in [49]:

D.1 Model description 269

J =

U ρ 00 U 1/ρ0 ρc2 U

(D.6)

which is a much simpler structure compared to the conservative JacobianJ (Eq. (E16.2.3) in [49]). Introducing the relation ξ = M ζ, Eq. (D.4) be-comes:

M∂ζ

∂t+ JM

∂ζ

∂z= Q (D.7)

or after left multiplication with M−1:

∂ζ

∂t+(M−1JM

) ∂ζ∂z

= M−1Q (D.8)

Comparing Eqs. (D.8) and (D.4) yields J = M−1JM and Q = M−1Q . Now,J can be diagonalized as:

J = RΛR−1 (D.9)

where Λ is a diagonal matrix with diagonal elements λi, i = 1 . . . 3. Denotingthe columns of R as ri, Eq. (D.9) can be rewritten as:

J ri = λiri (D.10)

where ri represent the right eigenvectors of J . Solving the eigenvalue prob-lem (D.9) or (D.10) yields the following three eigenvalues:

λ1 = U, λ2 = U + c, λ3 = U − c (D.11)

The right and left eigenvector matrices R and R−1 are derived in Sect. 16.4.1in Hirsch [49]. Inserting Eq. (D.9) into Eq. (D.5) yields, after left multiplicationwith R−1:

R−1 ∂ζ

∂t+ ΛR−1 ∂ζ

∂z= R−1Q (D.12)

or by defining the characteristic variable vector ψ as ψ = R−1ζ:

∂ψ

∂t+ Λ

∂ψ

∂z= R−1Q (D.13)

Equation (D.14) represents the characteristic form of the Euler equations,which corresponds to a set of three decoupled scalar partial differential equa-tions:

∂ψi

∂t+ λi

∂ψi

∂z= q′i (D.14)

where ψi are the components of ψ and λi are the characteristic propagation orconvection speeds in Eq. (D.11).


D.1.2 Discretization schemesSince the Euler equations can be transformed into a set of decoupled partialdifferential equations (D.14), the equations are hyperbolic. This means thateach characteristic variable ψi represents a wave traveling in positive or negativelengthwise z-direction, depending on the sign of the corresponding eigenvalueλi. For a positive eigenvalue λi > 0, the solution ψi in point zj can onlybe influenced by values in upwind points zj−1, zj−2, . . . and not by downwindpoints zj+1, zj+2, . . ..

For a cell-centered discretization, the following computation scheme results(neglecting the source term):

∂ξj

∂t= − 1

∆z(F j+1/2 − F j−1/2

)(D.15)

where the time evolution of the conservative variable ξj results from integratingthis expression in each node j. For a simple central differencing scheme, thenumerical fluxes F j±1/2 in Eq. (D.15) are defined as:

F j+1/2 =12

(F j + F j+1) (D.16)

and analogous for F j−1/2 . This scheme is not stable, unless some artificialdissipation is introduced [49]. The reason is the hyperbolic nature of the Eulerequations as noted above.

First order upwind schemes

First-order upwind schemes that do take these physics into account are dis-cussed in Chap. 20 of Hirsch [49]. The expression for the numerical flux con-tains an additional flux difference term ∆F j,j+1 that ensures the physical flowof information along the characteristics:

F j+1/2 =12

(F j + F j+1 − |∆F j,j+1|) (D.17)

The flux difference term is defined as:

∆F j,j+1 = J j,j+1

(ξj+1 − ξj

)=

(J+

j,j+1 + J−j,j+1

) (ξj+1 − ξj

)(D.18)

and the absolute value of the flux difference term is defined as:

|∆F j,j+1| = |J j,j+1|(ξj+1 − ξj

)=

(J+

j,j+1 − J−j,j+1

) (ξj+1 − ξj

)(D.19)

In Eqs. (D.18) and. (D.19), the superscripts + and − indicate the positiveand negative parts of the Jacobian, respectively. These matrices are defined

D.1 Model description 271

based on the positive and negative eigenvalues λi. Using the notation as inSect. D.1.1, and combining Eqs. (D.9) and J = M−1JM yields:

J = MRΛR−1M−1 (D.20)

Based on the above eigenproblem expansion, the positive and negative parts ofJ are defined as:

J± = MRΛ±R−1M−1 (D.21)

where Λ+ and Λ− contain only positive and negative eigenvalues, respectively.Symbolically, Λ± = diag

[λ±i], where λ+

i = max (λi, 0) and λ−i = min (λi, 0).

Second order TVD schemes

In the above described upwind scheme, the numerical fluxes (D.17) are definedbased on the values in two points j and j + 1. The upwind scheme is only firstorder accurate, i.e. the error is proportional to the mesh size ∆z. To improvethe accuracy of the upwind scheme, the fluxes should be calculated based onthe values in more than two points.

A scheme preserves monotonicity if, as a function of time, (i) no new localextrema can be created and (ii) the magnitude of the value of a local extremumis non-increasing. According to Godunov’s theorem, a linear scheme for con-vection equations can only be monotone if it is first order accurate (Chap. 21in [49]).

However, by introducing the proper non-linearity into a second orderscheme, monotonicity may be maintained. This is done by non-linear lim-iter functions. In case the scheme tends to create or amplify a local extremum,the limiter locally reduces the scheme to first order accuracy, thereby ensur-ing monotonicity. The similar total variation diminishing (TVD) property isintroduced by Harten.

Two such limiter functions that are used in second order TVD schemes arethe minmod and superbee limiter. The minmod limiter takes two arguments,and returns the argument with smallest absolute value (if both have the samesign) and zero otherwise. The superbee limiter is used by Vandevoorde [101]in a second order TVD scheme, with very good results. The same approach isused for the gas dynamic model in this thesis. The superbee limiter functionis defined as:

Lim (x, y) =x

|x|max

[0,max

[min

(2 |x| , xy

|x|

),min

(|x| , 2xy

|x|

)]](D.22)

Most finite difference schemes are cell-centered, i.e. the nodes form thecenter of the control volumes. All variables are computed at the nodes, yetthe flux balances are fulfilled at the volume edges or vertices, in between thenodes. Vandevoorde [101] examined a number of cell-centered upwind andTVD schemes, and found that the these do not guarantee the conservation


1 2 j j +1 n

∆zL

A

Figure D.1 – Cell-vertex discretization

of mass near section changes. Vandevoorde [101, 103] introduced a new cell-vertex second order TVD scheme, where the nodes coincide with the edges ofthe control volumes. Thus, the flux balances are fulfilled in the nodes and theconservation laws are satisfied in case of section changes. Figure D.1 shows thecell-vertex discretization nomenclature for the model used in this thesis.

For first order time stepping, the cell-vertex TVD algorithm is as follows:

ξm+1j = ξm

j − ∆t∆z

[D+

j−1/2∆F j,j−1

+ 12 Lim

(D+

j+1/2∆F j+1,j ,D+j+1/2∆F j,j−1

)− 1

2 Lim(D+

j−1/2∆F j,j−1,D+j−1/2∆F j−1,j−2

)+D−

j+1/2∆F j+1,j

− 12 Lim

(D−

j+1/2∆F j+1,j ,D−j+1/2∆F j+2,j+1

)+ 1

2 Lim(D−

j−1/2∆F j,j−1,D−j−1/2∆F j+1,j

)]where j and m are the node and time step index, respectively. In analogy toEq. (D.21), the positive and negative decision matrices D± are defined as:

D± = MRH±R−1M−1 (D.23)

where H + and H− are diagonal matrices defined as H + =diag[max(sgn(λi), 0)] and H− = diag[−min(sgn(λi), 0)].

D.1.3 Zero-dimensional volumes

Components in the model that feature a small length-to-diameter aspect ratioare not discretized, and rather simply modeled as zero-dimensional volumes,where all state variables are assumed constant throughout the volume andstored in a single point. For instance, the cylinders, diffuser and exit cone aremodeled as zero-dimensional compressible volumes with conservation of massand energy. The working fluid (air) is assumed an ideal gas. As such, thefollowing equations are solved in these volumes:

D.2 Model validation 273

∂m

∂t=

∑min −

∑mout

∂ (mcvT )∂t

=∑

(mH)in −∑

(mH)out −mrT1V

∂V

∂t(D.24)

where the volume V can be time-dependent, as is the case for the cylinders.No heat transfer is modeled.

D.1.4 Implementation

The model used in this thesis is the second order TVD cell-vertex scheme usingthe superbee limiter, as described in Sect. 2.8 of Vandevoorde [101] and inVandevoorde et al. [103]. The boundary conditions (e.g. open end, restrictedflow through exhaust valves) are implemented according to [101], with valvedischarge coefficients according to Heywood [47].

The model is implemented as a Simulink11 library block, making it easy toconstruct a model for the exhaust system comprising several one-dimensionalpipes, junctions and zero-dimensional compressible volumes. Time integrationis performed using Simulink’s built-in fourth order Runge-Kutta scheme.

Figure D.2 shows a diagram of the Simulink model for one-dimensional flowin a variable cross-section pipe. In the diagram, ‘U’ represents the conserva-tive state variable ξ, ‘S’ is the cross-sectional area A. Inside the block ‘Truthmatrices i±1/2’, the local eigenvalues and eigenvectors are determined. For il-lustration, Fig. D.2c shows the calculation of the right eigenvector product MR(see Eq. (D.20)). The ‘Lim’ blocks implement the superbee limiter function.

In Sect. D.2, this model is validated using some benchmark problems, sim-ilar to the approach in Vandevoorde [101]. Section D.3 examines the spatialand temporal resolution of the model in terms of the node spacing.

D.2 Model validation

D.2.1 Sod’s shock tube

Description

The Sod [93] shock tube or Riemann problem is a generally accepted benchmarkfor one-dimensional gas dynamic schemes. The shock tube consists of a straight,frictionless, constant cross-section pipe with a different initial conditions ateither side of a central diaphragm. At time t = 0, the imaginary diaphragmis removed, thus creating a compression shock wave, an expansion wave and acontact discontinuity. The solution can be analytically determined.

The problem is discussed in Sect. 16.6.3 in Hirsch [49]. Here, the valuesfor the initial pressures and temperatures are taken according to Vandevo-orde [101], instead of [49]. The right boundary is atmospheric (patm and Tatm)and the left boundary is an infinite reservoir at 1.5 patm and 1.2Tatm. The


StateDerivatives

1U

U

x

d

dU/dt

U

qQ

Source

U U(E)

U U(E)

U U(E)

1sxo

IntegrateState

type

U_BCU_IC

Initial Conditions

0Heat flux

to gas (W/m²)

xd

type

par

U_BC

U

U'

BoundaryConditions

1BC

(a)

col row

returns eigenvectors R

9R33

8R32

7R31

6R23

5R22

4R21

3R13

2R12

1R11

kappa

c

u2

u2

u2

u2

2

2

2

3

2

1

2

2T

1v

v

v

v+c

v-c

v²/2

(c)

State derivative

1dU/dt

A

X AX

A

X AX

A

X AX

A

X AX

A

X AX

AX AX

A

X AX

A

X AX

U(k+1)

U(k)

D+

D-

Truth matricesi-1/2

U(k+1)

U(k)

D+

D-

Truth matricesi+1/2

x(i-2)

x(i+2)

x(i+2)

x(i+2)

x(i-1)

x(i-1)

x(i-1)

x(i+1)

x(i+2)

x(i-2)

x(i-1)

x(i+1)

x(i-2)

x(i-2)

x(i+1)

x(i+1)

ro

v

T

U

ro

v

T

U

ro

v

T

U

ro

v

T

U

u2

Lim

Lim

Lim

Lim

pi/4

-1

1

1

1

1

dx

emU

ro

v

T

U(k+1)

S(k+1)U(k)

S(k)

DF(k+1/2)

U(k+1)

S(k+1)U(k)

S(k)

DF(k+1/2)

U(k+1)

S(k+1)

U(k)S(k)

DF(k+1/2)

U(k+1)

S(k+1)

U(k)S(k)

DF(k+1/2)

2

2

3d 2

x

1U

D+(i+1/2)

D+(i+1/2)

D-(i-1/2)

D-(i-1/2)

dF(i-3/2)

dF(i+3/2)

D+(i-1/2)

D+(i-1/2)

dF(i-1/2)

dF(i-1/2)

dF(i-1/2)

D-(i+1/2)

D-(i+1/2)

dF(i+1/2)

dF(i+1/2)

dF(i+1/2)

S

(b)

Figure D.2 – One-dimensional gas dynamic pipe model: (a) overview, (b) the statederivatives according to the second order TVD scheme [101], (c) the right eigenvectormatrix MR (see Eqs. (D.20) and (D.20))


thermodynamic properties are assumed constant (i.e. γ = 1.4). The analyticaltime-dependent solution is given in Sect. 16.6.3 in [49] and Sect. 2.2.1 in [101].

Validation

Figure D.3 gives the results for the shock tube, for two discretization schemes.Case (a) is the scheme used in this thesis. Both cases use the same numberof nodes, fourth order Runge-Kutta integration and a CFL number ' 0.6 (seethe note on the Courant-Friedrichs-Lewy number on p. 191).

Each series of four plots show the following dimensionless quantities as afunction of the dimensionless lengthwise coordinate z/L (from left to right andtop to bottom): the pressure p/patm , the velocity U/catm , the speed of soundc/catm and the density ρ/ρatm . The solid line (

) is the analytical solution

and the markers ( ) are the numerical solution.

The deviation between the numerical and analytical solution for the shocktube problem is used in Sect. D.3.1 to estimate the spatial resolution of fourdifferent schemes.

The cell-vertex TVD scheme features an excellent shock capturing perfor-mance, which may be noted in Fig. D.3a. Furthermore, Vandevoorde et al.[102] prove this scheme to be the best solution for modeling the compressiblegas dynamics in intake and exhaust pipes of internal combustion engines.

In this thesis, the gas dynamic model is also used to predict the frequencyresponse of the exhaust manifold. This is relevant with regard to the Helmholtzresonances discussed in Sect. 5.3. Therefore, the performance of the modelin terms of its temporal or frequency characteristics is determined using thefollowing two benchmark problems. Sections D.2.2 and D.2.3 compare thenumerical and analytical frequency response of a straight pipe of constant cross-section and a single expansion chamber muffler.

D.2.2 Frequency response of a pipe

Description

The considered test pipe is frictionless, of constant cross-section, L = 1 m long,with open end boundary conditions on either side. The right side boundary isatmospheric (patm = 1 atm, Tatm = 273.15 K). At the left side, a fluctuatingpressure patm +p is applied, where p represents the acoustic pressure, with zeromean.

The transfer function of the pipe is defined here as the dimensionless ad-mittance Y /Y0 at the inlet side. The admittance Y is the inverse of theimpedance Z, defined36 as Z = p/U [Pa/(m/s)]. The characteristic impedanceZ0 [Pa/(m/s)] is defined as the ratio of sound pressure p to the particle veloc-ity U for a plane wave traveling in open field. This corresponds to Z0 = ρc. The

36The acoustic impedance defined here as Z = p/U [Pa/(m/s)] is actually the specificacoustic impedance. The impedance as such is defined in the acoustic literature as ZA =Z/A [Pa/(m3/s)], where A [m2] is the considered cross-sectional area. [20]


0 0.5 11

1.2

1.4

p / p

0 (−

)


0 0.5 10

0.05

0.1

0.15

U /

c 0 (−

)

2nd order cell−vertex TVD (superbee), 64 nodes, CFL = 0.59

0 0.5 11

1.05

1.1

c / c

0 (−

)

z / L (−)0 0.5 1

1

1.1

1.2ρ

/ ρ0 (

−)

z / L (−)

(a)

0 0.5 11

1.2

1.4

p / p

0 (−

)


0 0.5 10

0.05

0.1

0.15

U /

c 0 (−

)

1st order cell−centered upwind, 64 nodes, CFL = 0.59

0 0.5 11

1.05

1.1

c / c

0 (−

)

z / L (−)0 0.5 1

1

1.1

1.2

ρ / ρ

0 (−

)

z / L (−)

(b)

Figure D.3 – Sod’s shock tube benchmark problem, using (a) the second order TVDcell-vertex scheme [101] and (b) a first order upwind cell-centered scheme


dimensionless admittance is therefore Y /Y0 = ρcUi/pi , where the subscript idenotes the inlet conditions [20].

Analytical

For plane waves37 traveling in a straight pipe of constant cross-section (seeChap. 2 in Beranek [20]), the solution for the particle displacement ξ of theone-dimensional wave equation can be written in the following form:

ξ (z, t) = ejωt (A cos kz + jB sin kz) (D.25)where j =

√−1, k = ω/c is the wave number [m−1] and A and B are unknown

coefficients. The velocity U and sound pressure p are related to ξ as U = ∂ξ/∂tand p = −ρc2∂ξ/∂z . Consequently:

U (z, t) = jωejωt (A cos kz + jB sin kz) (D.26)p (z, t) = −ρc2ejωtk (−A sin kz + jB cos kz) (D.27)

The transfer function Y /Y0 can be obtained as ρcUz=0/pz=0 . Filling inthe above expressions for U and p and evaluating at z = 0 yields Y /Y0 =−A/B . The coefficients A and B are determined by introducing the boundaryconditions (i.e. p = 0 at z = 0 and z = L), yielding A/B = j cos kL/sin kL , or:

Y

Y0=ρcUi

pi= − j

tan kL= − j

tan (2πfL/c )(D.28)

From this theoretical admittance (D.28), the standing wave resonance fre-quencies are tan kL = 0, or f = n · c/(2L) , where n ∈ Z. At low frequencyf c/(2L) , Y ∼ −j/f . Thus, the admittance is unbounded and the velocitylags the pressure by 90 .

Validation

The open end boundary conditions are applied to a numerical model of the pipe.The inlet pressure pi is perturbed using a multisine signal (see Sect. D.4.3). Thetransfer function is determined using the approach described in Sect. D.4.

Figure D.4 presents two Bode diagrams of the admittance Y /Y0 = ρcUi/pi ,for a different number of nodes, yet both using the second order TVD cell-vertex scheme. The solid line (

) corresponds to the analytical solution in

Eq. (D.28). The markers ( ) result from the numerical solution, using the

transfer function estimation method described in Sect. D.4.As expected, Fig. D.4 shows that the spectral resolution increases as the

number of nodes increases. Based on this benchmark problem, Sect. D.3.2discusses the frequency (or temporal) resolution.

37The assumption of planar acoustic waves poses some limitations to the pipe diameterd. (i) d should be small enough to avoid transverse resonances, or d < λ/1.2 [33], whereλ = c/(2πf) is the wavelength [m]. (ii) d should be large enough to avoid viscous distortionof the wavefronts, or d > 0.1/

√f [20]. These conditions are fulfilled in exhaust systems for

the frequency range of interest (10 < f < 1000 Hz), except inside the catalyst substrate.


102

103

−20

0

20

40

Am

plitu

de (

dB)

of ρ

cU/p

FRF, L = 1 m, c = 343.1 m/s, 16 nodes, CFL = 0.466From: Inlet pressure p, To: Inlet velocity ρcU


102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

1/2 1 3/2 2 3 4 6 8 102f L/c (−)

(a)

102

103

−20

0

20

40

Am

plitu

de (

dB)

of ρ

cU/p

FRF, L = 1 m, c = 343.1 m/s, 64 nodes, CFL = 0.490From: Inlet pressure p, To: Inlet velocity ρcU


102

103

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

1/2 1 3/2 2 3 4 6 8 102f L/c (−)

(b)

Figure D.4 – Frequency response function of a pipe, between inlet pressure andinlet velocity, using the second order TVD cell-vertex scheme [101], with (a) 16 nodesand (b) 64 nodes

D.2.3 Frequency response of a mufflerDescription

The 1954 NACA Technical Report by Davis et al. [33] provides a theoretical andexperimental approach to determine the attenuation of exhaust mufflers. Theauthors provide detailed instructions for an appropriate experimental setup,which may be used to determine the acoustical characteristics of mufflers with-out net flow. The appendices in [33] give the theoretical derivation of theattenuation for various muffler geometries.

The single expansion chamber with infinite connecting pipes is the simplesttype of muffler. Davis et al. [33] define Muffler 2 as a single expansion chamberwith an area ratio m = 16, a chamber length L = 24 inch (' 610 mm) andconnecting pipe diameter of d = 3 inch (' 76 mm). This reference muffler(see Fig. D.5) is chosen to validate the frequency characteristics of the one-dimensional gas dynamics code for a case of varying cross-sectional area.

The attenuation of an acoustic element placed in a pipe is defined in deci-bel [dB] as:

Attenuation = 10 log10

(Average incident sound power

Average transmitted sound power

)(D.29)

If the attenuation is considered between two points of equal cross-section, the


Figure D.5 – Reference single ex-pansion chamber muffler (Muffler 2with m = 16 and L = 24 inch)(Source: [33])

0 200 400 600 0 0

10

20

30

40

50

Am

plitu

de (

dB)

of p

i2 /po2

Attenuation of expansion chamber mufflerRef: Davis e.a. (1954) NACA Report 1192, Muffler 2

Frequency f (Hz)


Figure D.6 – Attenuation of thereference muffler in Fig. D.5, us-ing the second order TVD cell-vertexscheme [101]

attenuation can be determined as 10 log10 |pi/po |2, where pi and po are theacoustic pressures at the inlet and outlet. The attenuation of an acousticelement is also referred to as the transmission loss (Boonen [21] Chap. 3)

Analytical

Appendix A in [33] describes the analytical derivation of the attenuation forthe single expansion chamber muffler, with an infinite tailpipe. The resultingexpression is given by Eq. (A10):

Attenuation = 10 log10

[1 +

14

(m− 1

m

)2

sin2 kL

](D.30)

where m is the area expansion ratio, k is the wave number and L is the chamberlength. Eq. (D.30) indicates that the attenuation is zero for incident frequenciesequal to the standing wave resonance frequencies kL = nπ or f = n · c/(2L) ,where n ∈ Z.

Validation

Figure D.6 shows the satisfactory agreement between the numerical result usingthe gas dynamic model (

) and the theoretical attenuation (

) according to

Eq. (D.30). The deviation that exists between numerical and analytical solutionis likely due to the insufficiency of the non-reflecting boundary conditions usedin determining the numerical result. Further improvements are possible yet notwithin the scope of this thesis.


101

102

103

10−3

10−2

10−1

Spat

ial r

esol

utio

n δ

z (−

)

Number of nodes (−)

Sod’s shock tube (CFL = 0.5)Spatial resolution

2nd order cell−vertex TVD (superbee)2nd order cell−vertex TVD (minmod)2nd order cell−centered TVD (superbee)1st order cell−centered upwind

Figure D.7 – Spatial resolution based on Sod’s shock tube problem, for differentdiscretization schemes

D.3 Resolution

D.3.1 Spatial resolution

The spatial resolution of the discretization scheme is defined here based on thedifference between the numerical and analytical solution to Sod’s shock tubeproblem introduced in Sect. D.2.1.

More specifically, a spatial difference measure ∆z [m] is defined as the rootmean square lengthwise deviation between the numerical and analytical curvesfor the speed of sound c/catm , as shown in Fig. D.3. The dimensionless spatialdifference δz = ∆z/L is plotted in Fig. D.7.

Figure D.7 shows that the cell-vertex TVD scheme with superbee limiteroutperforms all other schemes. For this scheme, the spatial resolution δz isroughly inversely proportional to the number of nodes.

D.3.2 Temporal resolution

The temporal or frequency resolution of the discretization scheme is definedhere based on the difference between the numerical and analytical solution tothe admittance of a pipe with two open ends, which is the benchmark problemused in Sect. D.2.2.

The maximum resolved frequency is defined rather arbitrarily as the max-imum frequency where the magnitude of the admittance 20 log10 (|Y /Y0 |) ex-ceeds 16 dB. The maximum frequency is plotted in Fig. D.8a versus the numberof nodes. The magnitude resolution δampl [dB] is defined as the root-mean-square deviation between the magnitude of the theoretical and numerical ad-mittance. A similar definition is used for the phase resolution δphase ( ) (seeFig. D.8b).

D.4 Identification 281

101

102

103

0.5

1

2

3

4

6

810

15

Max

imum

fre

quen

cy 2

fL/c

(−

)


FRF (CFL = 0.5), bandwidth2nd order cell−vertex TVD (superbee)

max(2fL/c) (−)

(a)

0 50 100

100

101

102

Freq

uenc

y re

solu

tion


FRF (CFL = 0.5), frequency resolution2nd order cell−vertex TVD (superbee)

δampl (dB)

δphase (°)

(b)

Figure D.8 – Frequency resolution based on the admittance of a pipe with two openends, for the second order TVD cell-vertex scheme

Based on Fig. D.8a, the minimum number of nodes can be determined toresolve a given frequency. The maximum frequency fmax2L/c roughly equals1/8 of the number of nodes. As such, fmax ' (c/∆z )/16 . Typically, theresolution is expressed in terms of the number of nodes per required wavelengthnλ [-]. Introducing ∆z = λmin/nλ in the above expression yields:

fmax =c

nλ∆z

⇔ n = nλL

λmin(D.31)

where the number of nodes per wavelength nλ ' 16. For instance, if c =340 m/s and ∆z = 10 mm, fmax ' 2000 Hz.

D.4 Identification

D.4.1 PurposeThe purpose of identification is to retrieve the frequency response function ortransfer function of a particular dynamic system. The transfer function F (f)refers to the ratio F = Y /U of an output Y (f) to an input signal U (f), bothtransformed into the Fourier domain.

Identification is usually applied to ‘black box’ systems or complex multi-dimensional systems, where no analytical derivation can be used to determinethe transfer function.

In the framework of this thesis, identification is used to determine thefrequency response function of the close-coupled catalyst exhaust manifold


in Sect. 5.3.4. In this appendix, identification is used in the same way inSects. D.2.2) and D.2.3).

D.4.2 ApproachThe system under investigation is excited using an input signal u (t). The inputand resulting output y (t) signals are transformed to the frequency domain,resulting in U (f) and Y (f). Dividing these yields the transfer function F (f) =Y /U . The transfer function is usually represented as a Bode diagram, plottingthe magnitude and phase of F as 10 log10 (|F |) [dB] and ∠ (F ) []. The Bodediagram provides only a linearized view of the true system. Gas dynamics inparticular is a non-linear phenomenon, especially for high Mach number flows,yet also at low Ma for restricted flows.

The frequency response function F (f) is estimated using the MATLAB11

function TFE, which is part of the System Identification Toolbox. The fre-quency response function is estimated as the quotient of the cross spectrum ofinput and output signals Puy (f) and the power spectrum of the input signalPuu (f).

D.4.3 Multisine signalsA multisine is a commonly used input signal for the identification of dynamicsystems. The multisine u is a sum of a i = 1 . . . n sine functions with frequenciesfi and phases φi:

u (t) =n∑

i=1

sin (2πfi t− φi) (D.32)

The frequencies fi are chosen between a minimum and maximum frequencyfmin and fmax. The phase angles can be set to zero, or randomized. Bothapproaches result in a multisine signal with (i) an unconfined amplitude in thetime domain and (ii) a spiky frequency spectrum.

A better approach is to chose the phase angles so that the amplitude remainsbounded and the frequency spectrum is as smooth as possible between fmin

and fmax. This type of signal enables a better identification, since the inputsignal spectrum U (f) is constant in the frequency range of interest, i.e. eachfrequency is excited with the same amplitude.

Guillaume et al. [41] introduced the crest factor-minimization algorithmwhich determines the optimal phase angles φi to obtain a smooth spectrum.This algorithm is applied for generating the multisines used in this thesis.

Figure D.9 provides an example of (a) a multisine signal and (b) its Fourierspectrum. This particular signal is generated at a sample frequency of 1 kHz,containing frequencies between fmin = 10 Hz and fmax = 100 Hz.

D.4 Identification 283

0 0.2 0.4 0.6 0.8 1−2

−1

0

1

2

Multisine signalUsing crest−factor minimization by Guillaume e.a. (1991)

0 0.05 0.1 0.15 0.2−2

−1

0

1

2

Time t (s)

(a)

100

101

102

−200

−150

−100

−50

0

Am

plitu

de (

dB)

Multisine signal, Fourier spectrumfs = 1 kHz, ∆t = 1 s, f

min = 10 Hz, f

max = 0.1 kHz

100

101

102

−180

−90

0

90

180

Phas

e (°

)

Frequency f (Hz)

(b)

Figure D.9 – Example multisine signal (a) and its Fourier spectrum (b), generatedusing the crest factor-minimization algorithm by Guillaume et al. [41]

Nederlandse samenvatting

Experimentele stromingsdynamicain uitlaatsystemen van voertuigen

met voorkatalysator

285

Experimentele stromingsdynamicain uitlaatsystemen van voertuigenmet voorkatalysator

1 Inleiding: Uitlaatsystemen

1.1 Achtergrond

Sinds de jaren 1970 gelden er wettelijke bepalingen die de uitstoot van scha-delijke stoffen bij voertuigen met inwendige verbrandingsmotoren beperken(Tabel 1.1). De voornaamste schadelijke componenten zijn koolstofmonoxide(CO), stikstofoxiden (NOx) en koolwaterstoffen (CxHy) voor benzinemotorenen NOxen roetdeeltjes (PM) voor dieselmotoren. De steeds strengere emissie-wetgeving resulteren in talloze technologische verbeteringen aan de constructieen het management van de verbrandingsmotor. De katalysator werd geïn-troduceerd in het uitlaatsysteem om de gevormde polluenten om te zetten inonschadelijke stoffen zoals CO2 en water. De traditionele katalysator is gemon-teerd in de uitlaatleiding, zodat een uniforme stromingsverdeling eenvoudig terealiseren is.

De Euro III norm zorgde voor een kentering, door de introductie van eenkoude start fase in de homologatiecyclus. Aangezien de katalytische reactie-snelheid slechts significant is boven een temperatuur van 250 tot 400 C, isde opwarmtijd sindsdien een cruciale ontwerpparameter. Een snelle opwar-ming wordt bekomen door de katalysator vlakbij de motor te plaatsen, alsgeïntegreerd deel van de uitlaatcollector. Dit type wordt close-coupled38 ofvoorkatalysator genoemd.

De thesis onderzoekt de stroming in uitlaatcollectoren met voorkatalysator,en draagt bij tot de state-of-the-art in dit gebied van toegepaste stromingsme-

38Cursief gedrukte woorden zijn eigen aan het Engelstalige vakjargon. Om ondubbelzin-nigheden te vermijden worden ze vaak in plaats van hun Nederlandse vertaling gebruikt.

287

288 Nederlandse samenvatting

underbody catalyst

driving direction

muffler tailpipe

diffuser

exit cone

close-coupled catalyst

runners(headers)

manifold(collector)

hot end cold end

downpipe

Figuur 1.1 – Benamingen in het uitlaatsysteem

chanica. Het onderzoek is relevant voor katalysatoren bij benzine- en diesel-motoren, alsook roetfilters en NOx-filters.

1.2 Ontwerpaspecten

Een modern uitlaatsysteem ontwerpen is een hoogtechnologische opdracht, diegeavanceerde kennis vergt van transiënte stroming en warmteoverdracht in eencomplexe geometrie. Het uitlaatsysteem bestaat uit het hot end en cold end.Het hot end omvat de uitlaatcollector en voorkatalysator. Het cold end omvatde geluiddemper(s) en eventuele hoofdkatalysator. De collector bestaat uitcollectorbuizen of runners die samenkomen in de diffusor voor de katalysator(zie Fig. 1.1).

Pas wanneer de katalysatortemperatuur 250 tot 400 C overschrijdt gaande reacties op. Door de katalysator dicht bij de motor te plaatsen, warmt dezesneller op (ca. 10 s) dan de traditionele katalysator in het cold end (ca. 2 min).Dat veroorzaakt een sterke emissiereductie bij koude start. De motornabijeplaatsing, samen met de beperkte ruimte in het motorcompartiment, resulteertin korte runners en complexe scherpe bochten.

De levensduur hangt af van (i) de thermische belasting en (ii) katalysator-degradatie. De stroming veroorzaakt een verdeling van warmteoverdrachtsco-ëfficiënt op de binnenwand. Hot spots zijn zones met hoge wandtemperatuur,ten gevolge een hoge warmteoverdracht. Differentiële thermische uitzetting enopeenvolgende thermische cycli induceren spanningen in de wanden, die de kansop faling (vb. van lasnaden) vergroten.

Door deactivatie of degradatie van een katalysator vermindert de reactie-snelheid. Deactivatie is onvermijdelijk maar kan beperkt worden door eendegelijk collectorontwerp. Een katalysator voor verbrandingsmotoren bevatactieve Pt, Pd en Rh partikels, fijn verdeeld in de poreuze washcoat. De was-hcoat wordt aangebracht op een draagstructuur. Dit is meestal een cordieriet(2MgO · 2Al2O3 · 5SiO2) matrix [56], bestaande uit parallelle kanaaltjes metdiameter d = 0.8 tot 1.1 mm en wanddikte t = 0.06 tot 0.17 mm (Tabel 1.2).

1 Inleiding: Uitlaatsystemen 289

Bartholomew [11] en Forzatti en Lietti [38] bespreken deactivatie ten gevolgevan chemische, thermische, fysische en mechanische processen. Het overzichtvan Neyestanaki et al. [80] is toegepast op katalysatoren voor verbrandingsmo-toren.

Chemische deactivatie is het gevolg van chemisorptie van ‘giffen’ op ka-talytische oppervlakken. Bij katalysatoren voor verbrandingsmotoren zijn ditcontaminanten in motorolie en brandstof (vb. P, Pb, Zn, S). Chemische deacti-vatie is proportioneel met de hoeveelheid verwerkt uitlaatgas. Katalysatorzonesmet een hogere snelheid zijn meer onderhevig aan chemische degradatie.

Thermische deactivatie is het gevolg van verschillende processen [11, 38],voornamelijk het verminderen van contactoppervlak door sintering. De sin-tersnelheid verloopt exponentieel met de temperatuur (Vgl. (1.1)). Gezien dekatalysatortemperatuur kan oplopen tot meer dan 1000 C, betekent een be-perkte daling van de temperatuur een aanzienlijke verbetering van de levens-duur. Omdat de katalytische reacties exotherm zijn, is het verwerkte uitlaatgaswarmer dan het onverwerkte. Bovendien blijkt lokale periodieke terugstromingop te treden in katalysatoren [70, 81, 59, 84, 85], ten gevolge van resonantie-effecten (Hoofdstuk 5), loshechting en recirculatie in de collector. Periodieketerugstroming van heet uitlaatgas vormt een extra thermische belasting voorde katalysator.

Een uniforme stromingsverdeling in de katalysator is vereist om lokale che-mische en thermische deactivatie te voorkomen. Enerzijds verwerken hoge snel-heidszones meer gifstoffen en zijn dus meer onderhevig aan chemische deacti-vatie. Anderzijds is de temperatuur hoger door de reactiewarmte. Bovendiengarandeert een uniforme stromingsverdeling een minimale drukval en optimaalconversierendement van de katalysator (Fig. 1.5).

De ontwerpeisen zijn tegenstrijdig: een langere katalysator betekent eenhogere drukval maar verbetert de stromingsuniformiteit (door de hogere tegen-druk) en het conversierendement (door de uniforme reactorverblijftijd). An-derzijds stijgt de kostprijs van de katalysator met het volume. Tabel 1.3 geefteen overzicht van ontwerpaspecten (kostprijs, drukval, conversie-efficiëntie enstromingsuniformiteit) en de relatieve invloed van de belangrijkste parameters.Volgens Tabel 1.3 is het ontwerp optimaal voor een maximale porositeit ε enminimale kanaaldiameter d. Deze vaststelling komt volgens Wiehl en Vogt [112]overeen met de waargenomen evolutie.

1.3 Literatuuroverzicht

Historische studies [51, 64, 109, 110, 60] (1970 tot 2000) onderzochten de druk-val en snelheidsverdeling in uitlaatsystemen in stationaire condities. Dit is eenaanvaardbare vereenvoudiging voor een traditionele katalysator, typisch 1 tot2 m van de motor verwijderd. Met de introductie van de motornabije kataly-sator is de focus van het onderzoek verschoven naar pulserende stroming (1995tot heden).

Verschillende auteurs (e.g. Benjamin et al. [13], Voeltz et al. [104], Breu-er et al. [23], Nagel en Diringer [79]) bespreken snelheidsmetingen en CFD


berekeningen in uitlaatcollectoren met voorkatalysator in stationaire stroming.Deze studies beogen vooral een maximalisatie van de uniformiteit met minimaledrukval.

De meest interessante studies zijn uitgevoerd in pulserende stroming, met(i) een isotherme pulserende stromingsopstelling [53, 22, 17, 69, 16, 15, 43, 18,58], of (ii) een isochore motoropstelling, die ofwel aangedreven is (i.e. zonderverbranding) [7, 86, 84, 85] ofwel werkend (i.e. met verbranding) [81, 59, 4, 70].

Met behulp van een isotherme opstelling is in Persoons et al. [88] de geldig-heid van het additieprincipe onderzocht (Hoofdstuk 4):

Additieprincipe De tijdsgemiddelde katalysatorsnelheidsverde-ling in pulserende stroming komt overeen met een lineaire combina-tie van snelheidsverdelingen bekomen in stationaire stroming doorelk van de uitlaatrunners, bij gelijk volumetrisch debiet (Vgl. (4.1)).

De geldigheid van deze aanname impliceert dat tijdsintensieve transiënte CFDberekeningen overbodig zijn om een collector te ontwerpen naar stromingsuni-formiteit en dat stationaire CFD berekeningen volstaan. De bevindingen vanPersoons et al. [88] worden deels bevestigd door Benjamin et al. [17] en Bressleret al. [22] (Hoofdstuk 4).

Omwille van de inherente variabiliteit in de geometrie van uitlaatsystemen,is de relevantie van een aantal studies beperkt [60, 104, 23, 79, 8] tot parti-culiere systemen. Dit staat in contrast met stromingsonderzoek in verbran-dingskamers, met min of meer identieke vorm. Ondanks de geometrische va-riabiliteit en de complexiteit van de stroming, kunnen verschillende aspectengerelateerd worden aan gepaste dimensieloze getallen, zoals het scavenging ge-tal S (Vgl. (1.4)) [88, 86] of vergelijkbare getallen [22, 17, 99]. Zo wordt deinvloed nagegaan van stromingsrandvoorwaarden en geometrie op bijvoorbeeldde geldigheid van het additieprincipe (Vgl. (4.1)) [88, 86], het conversierende-ment [99] en de drukval [109, 110].

Uit deze thesis resulteerden vier publicaties in internationale tijdschriftenmet review [88, 86, 83, 84] en twee bijdragen op internationale conferenties metreview [87, 85].

1.4 Doelstellingen van de thesisDe doelstelling is de experimentele studie van pulserende stroming in moder-ne compacte uitlaatsystemen met voorkatalysator. Aangezien heet corrosiefuitlaatgas snelheidsmetingen sterk bemoeilijkt, maakt de thesis gebruik vanopstellingen die koude pulserende stroming genereren, waarbij de stromings-gelijkvormigheid met werkelijke motorcondities onderzocht wordt. De koudepulserende stroming maakt het gebruik van snelheidsmeettechnieken mogelijkmet hoge resolutie in ruimte en tijd. De nauwkeurigheid en resolutie van de be-komen data moeten validatie van computational fluid dynamics berekeningenmogelijk maken.

De thesis richt zich op het meest relevante stromingsgerelateerde aspect inhet ontwerp van moderne uitlaatcollectoren, namelijk de snelheidsverdeling in

2 Experimentele aanpak 291

de katalysator. Een uniforme snelheidsverdeling is cruciaal voor een optimaalcollectorontwerp qua minimale drukval, maximaal conversierendement en hetvermijden van lokale katalysatordegradatie. Meerbepaald onderzoekt de thesisde invloed van (i) transiënte stromingsrandvoorwaarden en (ii) geometrischeaspecten (vb. diffusor volume, aantal en lengte van de runners, uitlaatklepti-ming) op de tijdsafhankelijke snelheidsverdeling in de katalysator.

Wanneer de experimentele technieken ontoereikend zijn om de waargenomenfysische verschijnselen te verklaren, wordt een ééndimensionaal gas dynamischnumeriek model van het uitlaatsysteem gebruikt. Het numeriek model wordttevens gebruikt om de stromingsdynamica te voorspellen buiten de mogelijk-heden van de experimentele aanpak.

Volgende aspecten vallen buiten de reikwijdte van de thesis:

• Computational fluid dynamics — De bekomen snelheidsgegevens zijndeels gebruikt voor de validatie van CFD simulaties, in het kader vanonderzoek in samenwerking met een industriële partner [2]. De CFD be-rekeningen zijn uitgevoerd door de industriële partner. De thesis richtzicht op de experimentele methodologie.

• Katalytische reactiekinetica — De reactiekinetica in de katalysator inwerkende motorcondities wordt verwaarloosd. De kwalitatieve invloedvan stromingscondities op het conversierendement kan geschat wordenaan de hand van een vereenvoudigd homogeen of heterogeen model vande kinetica, zoals beschreven in App. A.3.

• Andere aspecten, zoals warmteoverdracht, akoestiek en mechanische tril-lingen.

2 Experimentele aanpak

2.1 Experimentele opstellingenTijdens de thesis is gebruik gemaakt van twee types opstellingen, die beideeen pulserende luchtstroming genereren in het uitlaatsysteem bij omgevings-temperatuur: een (i) isotherme opstelling en een (ii) isochore of opgeladenaangedreven motor (CME) opstelling.

Bij de isotherme opstelling (Sect. 2.2.1) is de uitlaatcollector via een pul-sator gemonteerd op een buffervat (Fig. 2.2). Een roterende klep (Fign. 2.3en 2.4) en de originele cilinderkop (Fign. 2.5 en 2.6) zijn gebruikt als pulsator.Het debiet wordt gemeten met een ISO-genormeerde meetflens (Sect. 2.4.1).Debiet en pulsatiefrequentie worden ingesteld overeenkomstig motorbelastingen toerental. De stroming is onderzocht in twee types uitlaatcollectoren: meten zonder uitlaatklepoverlap (Tabel 2.1 en Fig. 2.1).

Omwille van de eenvoud wordt de isotherme opstelling gebruikt in verschil-lende studies [88, 58, 18, 69, 17, 16, 15, 43, 22]. De stroming verschilt echtersterk van een werkende motor (Fig. 2.9). De complexe geometrie van uit-laatcollector en cilinderkop maakt enkel een opstelling met schaalfactor 1 : 1


mogelijk. Om de snelheidsmetingen te vergemakkelijken is gekozen voor eenopstelling met koude stroming. Omwille van het temperatuurverschil is hetslechts mogelijk het tijdsgemiddelde Reynolds- en Machgetal bij benadering inovereenstemming te brengen met de werkelijke motorcondities.

De isotherme opstelling genereert een ééntrapse ‘uitlaatslag’. Figuur 2.10toont het verschil met werkelijke motorcondities, met tweetrapse uitlaatslag:(i) blowdown en (ii) uitdrijvingsfase. Het runnerdebiet vertoont een hogerefrequentie-inhoud bij de werkende motor. Bijgevolg verschilt de schijnbare pul-satieperiode (Vgl. (4.46)), waardoor de bevindingen op basis van de isothermeopstelling [88] niet kunnen geëxtrapoleerd worden naar werkelijke motorcondi-ties.

De isochore CME opstelling genereert koude pulserende stroming gelijkaar-dig aan werkelijke motorcondities. CME staat voor charged motored engine,of opgeladen aangedreven motor (Fig. 2.7). De verbrandingsmotor wordt aan-gedreven met een elektromotor. Op een verstevigde inlaatcollector wordt pers-lucht met instelbare druk aangelegd. Een laminaire stromingsmeter dient alsreferentie debietmeting. Er is geen brandstofinjectie of ontsteking. De inlaat-druk komt overeen met een bepaalde residuele cilinderdruk, vlak voordat deuitlaatklep opent. Bij normale motorwerking varieert deze druk tussen 2 en5 atm. De CME opstelling bekomt een gelijkaardige stroming met een inlaat-druk tussen 1 en 2.5 atm. De uitlaatslag bij de CME opstelling is gekenmerktdoor een blowdown en uitdrijvingsfase (Fig. 2.10).

2.2 Stromingsgelijkvormigheid

Sectie 2.3 bespreekt de stromingsgelijkvormigheid tussen CME en werkendemotor aan de hand van o.a. een analytische afleiding van het massadebiettijdens blowdown en uitdrijvingsfase. In Vgln. (2.1) en (2.2) stellen bevat term ide invloed van de inlaatdruk en term ii de invloed van de warmtevrijstellingtijdens de verbranding. Bij afwezigheid van verbranding (i.e. CME) is term ii= 1. Ter compensatie moet de inlaatdruk (term i) aangepast worden.

Figuur 2.11 toont deze debieten voor werkende motor met verbranding(links) en CME (rechts) in functie van de motorbelasting (i.e. motorkoppel),direct gerelateerd aan de inlaatdruk. Bij werkende motor is het maximum vanm1/m2 ' 6, en slechts 2.5 bij de CME opstelling. Ondanks de onvolledigegelijkvormigheid, genereert de CME opstelling een tweetrapse uitlaatslag zoalseen werkende motor.

2.3 Datareductie

Het identificeren van periodieke fenomenen vereist een conditionele (of phase-locked) meettechniek. De fase (of tijdsbasis) van phase-locked signalen komtovereen met een vaste referentie, vb. een referentiepuls die eens per perio-de optreedt. Een werkelijk signaal opgemeten in een periodieke stroming be-staat uit een cyclusafhankelijke (cycle-resolved) en onafhankelijke component

3 Oscillerende hittedraad anemometer (OHW) 293

(Vgl. (2.19)) ten gevolge van turbulentie, ruis of onstabiele stromingsverschijn-selen. Bruun [25] bespreekt de literatuur omtrent phase-locked meettechnieken.

Het bepalen van het ensemble gemiddelde (Vgl. (2.20)) verbetert de nauw-keurigheid op de cyclusafhankelijke component. De stroming in een volumetri-sche machine varieert van de ene cyclus tot de andere. Omwille van cyclischevariatie zijn er een groot aantal ensembles nodig om de fout op het cyclusaf-hankelijke gemiddelde klein genoeg te maken (Vgl. (2.25)).

De meting van turbulentiegrootheden bij cyclische variaties vereist een cy-clusafhankelijke (of cycle-resolved) analyse. Deze aanpak splitst de onafhanke-lijke component op in een bijdrage ten gevolge van cyclische variatie en turbu-lentie (Sect. 2.5.2).

3 Oscillerende hittedraad anemometer (OHW)

3.1 Inleiding

Het meten van bidirectionele fluïdumsnelheid is geen eenvoudige opdracht.Nochtans treedt periodieke terugstroming op in de voorkatalysator [70, 81, 59].Appendix C.2 toont aan dat optische technieken nauwkeurige snelheidsmetin-gen kunnen opleveren, zelfs in werkende motorcondities. Helaas gaat deze tech-niek gepaard met aanzienlijke problemen van optische toegang en verdeling vanseeding.

Hittedraad anemometrie (HWA) levert een hoge resolutie in ruimte en tijd,maar de ongevoeligheid aan stromingsrichting is een inherent nadeel. Sectie 3.1bespreekt enkele technieken om toch bidirectionele snelheden te meten metHWA. Elk heeft voor- en nadelen (vb. bandbreedte, verstoring van de stroming,afmetingen, omslachtigheid).

Een nieuwe laagfrequente oscillerende hittedraad anemometer (OHW) werdontwikkeld tijdens deze thesis, in analogie met recente hoogfrequente OHW sys-temen [78, 66]. De OHW is gebaseerd op een mechanische oscillator (Fig. 3.5).In tegenstelling tot hoogfrequente OHW systemen is de ogenblikkelijke probe-snelheid gekend (Vgl. (3.8)). Anderzijds is de oscillatiefrequentie een order-grootte kleiner (i.e. 50 Hz, tegenover 500 Hz of meer).

3.2 Methodologie

De richting van de stromingssnelheid U ten opzichte van de probe is aangeduidin Fign. 3.5 en 3.4. De probe beweegt met een snelheid Up (Vgl. (3.8)). Vooreen niet-ambigue meting moet de relatieve snelheid ten opzichte van de probeUrel = U − Up positief blijven. Wanneer de snelheid U ogenblikkelijk negatiefwordt, blijft de relatieve snelheid Urel positief wanneer de probe voldoende sneltegen de normale richting van de stroming beweegt, of Urel > 0 ⇔ Up < U < 0.

Tijdens elke beweging van de probe is er een ogenblik waar de probesnel-heid Up maximaal in grootte is en negatief. De tolerantie α op de maximaleprobesnelheid bepaalt het interval waarbinnen metingen genomen worden. De


probe probe holder oscillating probe holder base

rigid support tube

50 mm

dual balance shafts

U > 0U > 0U > 0

p

rel

opticalencoder

motor

Figuur 3.5 – Hittedraad oscillator

-4 -3 -2 -1 0-1

-0.5

0

0.5

1

1.5

2

2.5

3

a = 0.736, b = 0.5 (R2 = 0.949)

OH

W v

eloc

ity U

/(ω

ox o) (-

)


ox

o) (-)

55P11L, xo = 5.5 mm


Figuur 3.12c – Kalibratiecur-ve voor 55P11L probe met xo =5.5 mm

absolute snelheid volgt uit U ′ = Up+Urel (Vgl. (3.6)), waarbij Urel overeenkomtmet het anemometersignaal.

3.3 Kalibratie

De OHW is gekalibreerd bij gekende negatieve snelheid met behulp van eenspecifiek ontwikkelde windtunnel (Fig. 3.9). De kalibratie is uitgevoerd voorverschillende oscillatiefrequenties, twee amplitudes (xo = 5.5 en 2.85 mm) envoor drie probe types (Fig. 3.7 en Tabel 3.2). Een tweedimensionale laser Dop-pler anemometer (LDA) met Bragg cel frequentieverschuiving dient als referen-tie snelheidsmeting. De LDA meting is phase-locked met de oscillatorbeweging,zodat de evolutie van de stroming rond de probe kan onderzocht worden.

Figuur 3.12 toont de kalibratiecurves voor elk van de onderzochte probes enamplitudes. Figuur 3.13 toont de tijdsafhankelijke resultaten in functie van deprobepositie, telkens voor dezelfde referentiesnelheid. Op basis van Fig. 3.12cgeeft probe 55P11L met rechte verlengde uiteinden de beste resultaten, in com-binatie met de grootste amplitude (xo = 5.5 mm). De maximaal meetbarenegatieve snelheid bedraagt ongeveer −1 m/s. Deze waarde is vergelijkbaarmet andere systemen (Tabel 3.1).

Een schaalanalyse werd toegepast om de optimale ontwerpparameters (fre-quentie, amplitude en probe type) te bepalen. Als performantiemaat dient∆U , de afwijking tussen gemeten en verwachte snelheid (Vgl. (3.10)). De af-wijking wordt voor elke probe uitgezet versus een dimensieloze grootheid. UitFig. 3.14 volgt dat voor kleine snelheden ∆U/U vrij goed correleert met tweedimensieloze groepen: (i) enerzijds (ωoxoD/ν ) (D/xo ) voor de rechte probesen (ii) anderzijds (ωoxoD/ν ) (xo/D ) voor de 90 probe.

Bij gelijke probesnelheid ωoxo en voor een rechte probe, neemt de afwijking∆U af bij toenemende amplitude xo of afnemende frequentie ωo. Het omge-keerde is waar voor de 90 probe. Het verschillend gedrag is toe te schrijven

4 Additieprincipe 295

aan de lokale stroming rond de sensordraad.Beide gevallen zijn onderhevig aan praktische beperkingen. Voor een rechte

probe kan de amplitude niet willekeurig groot worden. Anderzijds treden er bijeen 90 probe bij stijgende frequentie mechanische vibraties op, die het anemo-metersignaal verstoren ten gevolge van strain gauging. De verdere optimalisatieis een mogelijk onderwerp van toekomstig onderzoek.

3.4 Toepassing en validatie

Sectie 3.8 bespreekt de gepaste defasering tussen oscillatorfrequentie en motor-toerental, waardoor geldige metingen worden genomen in alle krukasposities(Fig. 3.15). De verhouding tussen beide frequenties wordt aangeduid door Rf

(Vgl. (3.13) en (3.16)).Sectie 5.2.1 bespreekt de validatie van de OHW op de CME opstelling.

Het debiet bepaald door integratie van de snelheidsverdeling wordt vergele-ken met het referentiedebiet, gemeten met een laminaire stromingsmeter in hetinlaatsysteem. Figuur 5.20 toont aan dat de OHW met voldoende hoge pro-besnelheid (Rf 1) de fout op het debiet reduceert. De afwijking is het gevolgvan rectification of gelijkrichtfouten, omdat standaard HWA enkel gevoelig isaan de absolute waarde van de snelheid. Bij gebruik van standaard HWA isRf = 0; volgens Fig. 5.2.1 bedraagt de overschatting van de snelheid dan tot50%, afhankelijk van de grootte van de terugstroming.

4 Additieprincipe

4.1 Datareductie

De geldigheid van het additieprincipe (Vgl. (4.1)) is gekwantificeerd met behulpvan twee dimensieloze scalars rS en rM , die de gelijkenis aanduiden tussenpulserende en stationaire snelheidsverdeling, op basis van vorm (rS , Vgl (4.12))en magnitude (rM , Vgl. (4.28)).

De geldigheid van het additieprincipe is afhankelijk van een enkele dimensie-loze grootheid S die de stroming karakteriseert. Het uitdrijving of scavenginggetal S is de verhouding van twee belangrijke tijdschalen: S = Tp/Ts , met Tp

de schijnbare pulsatieperiode [s] (Vgln. (4.44) en (4.46)) en Ts de verblijftijd [s](Vgl. (4.43)) in het diffusorvolume voor de katalysator. De gelijkenisgroothe-den rS en rM vertonen exponentiële correlaties in functie van S. S stijgt metafnemend toerental, toenemende belasting, en afnemend diffusorvolume.

4.2 Resultaten

Secties 4.4.1 en 4.4.2 tonen aan dat het scavenging getal S gecorreleerd is metde overeenkomst tussen de stationaire en pulserende stromingsverdeling, enaldus met de geldigheid van het additieprincipe. In Fign. 4.13 tot 4.27 wijsteen vergelijking van de stationaire en pulserende verdelingen erop dat rM > 1.


0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

rS’’ = 1 - exp(- S / 0.723)

(R2 = 0.91)


Shap

e si

mila

rity

mea

sure

rS (

-)

ISOT, A, RVISOT, A, CHISOT, B, CHCME, B, CHrS’’

(a)

0 1 2 3 4 51

1.1

1.2

1.3

1.4

1.5

1.6

rM

’’ = 1.118 + 0.337 exp(- S / 0.723)

(R2 = 0.30)


Mag

nitu

de s

imila

rity

mea

sure

rM

(-)


’’

(b)

Figuur 4.29 – Correlaties voor gelijkenisgrootheden (a) rS en (b) rM versus scaven-ging getal S

Gegeven de definitie van rM (Vgl. (4.28)), is de stromingsuniformiteit steedshoger in pulserende dan in stationaire stroming.

Uit de gecombineerde resultaten voor de CME en isotherme opstelling volgteen verbeterde definitie van de pulsatieperiode Tp (Vgl. (4.46)), die rekeninghoudt met de hogere frequentie-inhoud van het collectordebiet bij de CMEopstelling. Op basis van de verbeterde definitie komen de resultaten op beideopstellingen goed overeen (Fig. 4.29), terwijl dat niet zo is voor de origineledefinitie van Tp (Fig. 4.28).

Het verband tussen de gelijkenisgrootheden rS en rM en het scavenginggetal S (Fig. 4.29) en de exponentiële correlaties voor rS en rM in Vgl. (4.47)vormen een belangrijk resultaat. De grafieken bevatten resultaten bekomen opisotherme en CME opstelling, voor uitlaatcollectoren met en zonder uitlaat-klepoverlap, en voor een roterende klep en cilinderkop als pulsator. Gezien deverschillende opstellingen is de overeenkomst opmerkelijk.

Tabellen 4.3 en 4.4 geven de statistische significantie van rS en rM voor deisotherme en CME opstelling. De P-waarden voor de statistische hypothesetes-ten leiden niet tot een duidelijke geldigheidslimiet voor het additieprincipe. Opbasis van de exponentiële correlaties voor rS en rM komt de grenswaarde logi-scherwijs overeen met de kritische waarde voor het scavenging getal Scrit, dievolgt uit de gefitte correlaties. Het additieprincipe is geldig wanneer S > Scrit.De statistische onzekerheid op Scrit is onderzocht met een Monte-Carlo analyse.Voor de gecombineerde resultaten van collector A en B is het kritische scaven-ging getal Scrit = 0.723 ± 0.052. Wanneer enkel de resultaten van collector Bbeschouwd worden, is Scrit = 0.722± 0.056.

De bekomen resultaten worden deels bevestigd door andere bronnen. Ben-jamin [17] toont het verband tussen stromingsuniformiteit en een getal over-eenkomstig aan het scavenging getal S. De resultaten zijn bekomen met eenisotherme opstelling. Net zoals rM stijgt de stromingsuniformiteit bij afnemendscavenging getal S. Bressler et al. [22] stelt dat de snelheidsverdeling in een

5 Stromingsdynamica 297

katalysator enkel afhankelijk is van een verhouding die overeenkomt met S. Deafwijking tussen pulserende en stationaire stromingsverdeling blijkt minimaalvoor hoge waarde van S, wat overeenkomt met het verband tussen rS en S.

4.3 Fysische interpretatie

De opmerkelijke correlatie tussen rS en S (Fig. 4.29) wijst op een analogietussen deze stroming en de nuldimensionale spoelproces van een mengvolumemet een scalaire grootheid, vb. een stofconcentratie. Sectie 4.6 werkt dezeanalogie uit, waaruit volgt dat het kritisch scavenging getal Scrit zich gedraagtals de verhouding van effectief gebruikt tot geometrisch diffusorvolume. Bijdeels stilstaande of circulerende stroming in de diffusor, neemt het effectievediffusorvolume dat deelneemt aan het spoelproces af. Dit leidt tot de hypothesedat het kritisch scavenging getal Scrit een maat is voor de efficiëntie ηD waarmeede collector (i.e. combinatie van runners en diffusor) de stroming verdeelt overde katalysator.

Gezien voor collector B Scrit = 0.722±0.056, stelt de hypothese dat slechts72% van de diffusor effectief gebruikt wordt voor de verdeling van de stroming.Dit wordt intuïtief bevestigd door de niet-optimale stromingsuniformiteit. Eenverdere optimalisatie van de collector zou de collectorefficiëntie ηD (= Scrit,het kritisch scavenging getal) verhogen en de stromingsverdeling verbeteren.

Verder onderzoek moet uitwijzen of het kritisch scavenging getal inder-daad overeenkomt met een collectorefficiëntie, wat een objectieve, kwantitatievemaat zou vormen voor de performantie van de uitlaatcollector qua stromings-uniformiteit.

5 Stromingsdynamica

5.1 Experimentele resultaten

De hoge bandbreedte van HWA maakt gedetailleerde tijdsafhankelijke metingenmogelijk. Bij vergelijking van de katalysatorsnelheid op de isotherme (Fig. 5.9a)en CME opstelling (Fig. 5.11a), blijkt een aanzienlijk verschil in de frequentie-inhoud. De stromingsdynamica in de CME opstelling komt beter overeen metwerkelijke motorcondities.

Figuren 5.14 tot 5.18 tonen de hoge resolutie in ruimte en tijd bekomenmet de OHW. Figuren 5.16 tot 5.18 tonen de tijdsafhankelijke snelheidsver-deling in de katalysator tijdens de beginfase van de uitlaatslag van de eerstecilinder. De grijze zones wijzen op terugstroming. Terugstroming is maximaalvlak na de blowdown, maar treedt ook op tijdens de uitdrijvingsfase omwillevan de sterke resonantie-effecten. Deze experimenten zijn uitgevoerd op deisochore CME opstelling, aan 1200 rpm en voor drie motorbelastingen. Perio-dieke terugstroming is vastgesteld in een breed werkingsbereik. Bepaalde zones(Fig. 5.22) zijn meer onderhevig aan terugstroming, vooral aan de buitenrandvan de doorsnede, maar evengoed in het centrale deel, overeenkomstig de tijds-gemiddelde stromingsverdeling. Figuur 5.23 toont dat de lokale snelheid in elk


van de zones in Fig. 5.22 dezelfde fluctuaties vertonen; de stroming in de geheledoorsnede fluctueert in fase.

De frequentie van deze snelheidsfluctuaties is onafhankelijk van toerentalof debiet (Tabel 5.2), wat wijst op een gasdynamische Helmholtz resonantie.De Helmholtz-gerelateerde fluctuaties zijn het meest uitgesproken tijdens deuitdrijvingsfase. Op het eerste zicht beïnvloeden de resonanties de tijdsgemid-delde snelheidsverdelingen niet. Echter, de fluctuaties verhogen de schijnbarepulsatiefrequentie 1/Tp en verlagen bijgevolg de waarde van het scavenginggetal S. Gezien het verband tussen rS , rM en S, beïnvloeden de resonan-ties indirect de stromingsuniformiteit en de geldigheid van het additieprincipe.Andere auteurs [70, 81, 4] vinden gelijkaardige snelheidsfluctuaties tijdens deuitdrijvingsfase.

Figuur 5.38 toont een equivalent model van de laagfrequente gasdynamica inde uitlaatcollector, waarbij componenten met aanzienlijke impuls zich gedragenals onsamendrukbare massa’s, en de andere als samendrukbare veren. Het gas-dynamische systeem wordt beschouwd als mechanisch massa-veer-demper equi-valent, met demping veroorzaakt door vb. de uitlaatkleppen, wandwrijving, ende katalysatordrukval. De Helmholtz resonantiefrequentie wordt gegeven doorVgl. (5.5), overeenkomstig de nulde orde gasdynamische resonantiefrequentie.Hogere orde akoestische resonanties zijn afkomstig van staande golfpatronen inhet leidingensysteem.

Vergelijking (5.5) geeft een goede voorspelling van de geobserveerde fluctu-atiefrequenties, tussen 140 en 200 Hz voor collector B. Aangezien het uitlaat-systeem bestaat uit verschillende componenten is het niet duidelijk om welkeresonantie het gaat, temeer omdat de samendrukbaarheid van cilinder en dif-fusor gelijkaardig zijn. Aan de hand van een numeriek gasdynamisch modelwordt de oorsprong van de resonanties achterhaald.

5.2 Numerieke analyse

Secties 5.2.3 en 5.3.4 maken gebruik van een gasdynamisch ééndimensionaalmodel van het uitlaatsysteem. Zoals beschreven in App. D is het model geïm-plementeerd in Simulink11, en is het gebaseerd op een tweede orde cell-vertextotal variation diminishing (TVD) discretisatieschema [101] met vierde ordeRunge-Kutta tijdsintegratie. Het model is gevalideerd met relevante testgeval-len (vb. tijdsevolutie van schokgolven in een leiding (App. D.2.1), geluiddem-ping in een eenvoudige uitlaatdemper met enkele expansiekamer (App. D.2.3)),en houdt rekening met de gekende stromingsweerstand van uitlaatkleppen, lo-kale drukverliezen in gekromde uitlaatrunners en de drukval in de katalysator(App. A.2). Het inlaatsysteem en de verbranding worden niet beschouwd, maarde initiële toestand wordt in de cilinders opgelegd vààr elke uitlaatklep opent.De discretisatie van de uitlaatleidingen is gekozen overeenkomstig App. D.3, zo-dat het model een frequentieresolutie heeft van ca. 2000 Hz. Bijgevolg kan hetnumeriek model dienen om de Helmholtz resonanties (ca. 200 Hz) te verklaren.

De invloed is nagegaan van de aanwezigheid van een uitlaatleiding metdemper, stroomafwaarts van de katalysator. Aangezien alle metingen gebeurd

5 Stromingsdynamica 299

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 600 rpm, Q

ref = 26.5 m3/h, p

i = 1.00 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(a)

0 180 360 540 720−2

−1

0

1

2

3

4

5N = 1200 rpm, Q

ref = 97.3 m3/h, p

i = 2.20 atm


Mea

n ve

loci

ty (

−)

Time−resolved

Um,exp

Um,num

(d)

Figuur 5.28a,d – Tijdsafhankelijke numerieke en experimentele katalysatorsnelheidUm (ωt) [-], voor (a) N = 600 rpm (lage last), (d) N = 1200 rpm (hoge last)

zijn met vrije uitstroming, maakt het model het mogelijk de validiteit hiervanna te gaan.

Figuren 5.28 en 5.29 tonen aan dat de katalysatorsnelheid goed voorspeldwordt door het numeriek model, ondanks de driedimensionale stroming in dediffusor. Bij sterke terugstroming (Fig. 5.28b,d en Fig. 5.29b) blijkt de OHWmet de maximaal meetbare −1 m/s niet in staat de correcte snelheid weer tegeven. Op basis van de goede overeenkomst tussen experimentele en nume-rieke resultaten, is het model betrouwbaar genoeg om de stromingsdynamicate voorspellen buiten het bereik van de experimentele opstelling, vb. (i) inaanwezigheid van een uitlaatleiding, en (ii) in werkelijke motorcondities.

Figuur 5.32 toont het verschil tussen een werkende motor en de CME opstel-ling, voor vergelijkbare condities. De frequentie van de Helmholtz fluctuaties ishoger, evenredig met de vierkantswortel van de temperatuurverhouding. Verderis het maximum debiet tijdens de blowdown groter, zoals reeds aangeduid bijde bespreking van de stromingsgelijkvormigheid (Sect. 2.3). De terugstromingna de blowdown is sterker in werkende motorcondities.

Figuren 5.33 en 5.34 tonen dat de aanwezigheid van een uitlaatleiding nietveel invloed heeft op de katalysatorsnelheid, althans in CME condities. Bijwerkende motorcondities is er wel een verschil merkbaar met en zonder uitlaat-leiding (Fign. 5.35a en 5.32a).

Frequentie respons functies van de uitlaatcollector worden bepaald met hetnumeriek model, om het Helmholtz resonantieverschijnsel verder te verklaren.Voor de CME opstelling (en voor werkende motorcondities) blijkt het gas in deopen runner en katalysator te oscilleren op het samendrukbaar cilindervolume.Nochtans zijn voor de isotherme opstelling soortgelijke maar zwakkere fluctua-ties waargenomen, waarbij de diffusor zich samendrukbaar gedraagt, met quasidezelfde resonantiefrequentie tot gevolg.

In de CME opstelling is een faseverschuiving van π/2 rad merkbaar tussen


de snelheid in runner en katalysator, wat ook wijst op een samendrukbaardiffusorvolume. Dit wordt niet bevestigd door het numeriek model. Figuur 5.45toont dat de uitlaatleiding slechts een kleine invloed heeft op de transfer functievan de uitlaatcollector.

De transferfunctie in Fig. 5.42c komt overeen met de akoestische admittantievan de uitlaatcollector. Deze plot komt kwalitatief overeen met het omgekeerdevan de akoestische impedantie opgemeten door Boonen [21] met behulp van eendubbele microfoon techniek.

Andere auteurs bevestigen de waargenomen stromingsdynamische fenome-nen. Adam et al. [4], Park et al. [81], Liu et al. [70] en Benjamin et al. [14]tonen numerieke en experimentele resultaten in uitlaatcollectoren met voor-katalysator, in werkende motorcondities. Sterke snelheidsfluctuaties wordengeobserveerd tijdens de uitdrijvingsfase, met frequenties tussen 300 en 600 Hz.Afgezien van de verschillende geometrieën, zijn deze frequenties ongeveer twee-maal de waarde bij de CME opstelling, omwille van temperatuurafhankelijkheidvan de geluidssnelheid in Vgl. (5.5) en de temperatuurverhouding van ca. 4 : 1.

6 Ontwerpoverwegingen

Voor het industrieel ontwerp van uitlaatcollectoren vormt het additieprinci-pe besproken in Hoofdstuk 4 een interessante bevinding. Het additieprincipehoudt in dat het ontwerp kan volstaan met stationaire CFD berekeningen, endat tijdsintensieve transiënte CFD berekeningen overbodig zijn. Rekening hou-dend met de steeds kortere ontwikkelingstijden vormt dit een belangrijk besluit.Het huidige onderzoek stelt een objectieve grenswaarde vast (i.e. het kritischscavenging getal Scrit) voor de geldigheid van het additieprincipe.

Uitgaande van de correlatie voor rM (Vgl. (4.47)) blijkt de stromingsuni-formiteit steeds groter voor pulserende dan stationaire stroming. Voor groteS waarden evolueert rM naar een constante waarde, groter dan één. Bijgevolgvoldoet de stromingsuniformiteit van een collector ontworpen voor stationairestroming zeker voor pulserende stroming.

De stromingsuniformiteit in pulserende stroming wordt groter wanneer S <Scrit. Een grotere diffusor verkleint het scavenging getal S en vergroot aldusde stromingsuniformiteit. Dit triviale besluit is onderworpen aan geometrischeen thermische beperkingen van het motorcompartiment. Sectie 6.2 maakt eeninteressante opmerking bij bovenstaande vaststelling, gerelateerd aan de Helm-holtz resonanties in de collector, en verbindt op indirecte manier de bevindingenvan Hoofdstukken 4 en 5.

De Helmholtz-gerelateerde snelheidsfluctuaties verhogen de pulsatiefrequen-tie en verlagen het scavenging getal. Gezien het verband tussen S, rS en rM ,lijken de resonanties positief voor de stromingsuniformiteit; hoe hoger de reso-nantiefrequentie fH , hoe beter de stromingsuniformiteit.

Volgens Vgl. (5.5) is fH ∝ 1/√L en fH ∝ sqrtT , met L de runnerlengte

en T de temperatuur. Beide aspecten komen overeen met de evolutie van mo-derne uitlaatsystemen, waarin de katalysator zo dicht mogelijk bij de motor

7 Conclusie 301

wordt geplaatst (L %) en warmteverliezen beperkt worden (T 1). Kortom, degeobserveerde Helmholtz snelheidsfluctuaties zijn voordelig voor de stromings-uniformiteit.

7 ConclusieDe thesis betreft een experimentele studie van de pulserende stroming in mo-derne uitlaatcollectoren met voorkatalysator. Gezien de problemen met CFDvoorspelling van de stroming, en het belang van de stromingsuniformiteit in dekatalysator, richt de thesis zich op het ontwikkelen van een experimentele aan-pak die nauwkeurige bidirectionele snelheidsmetingen oplevert, met een hogeresolutie in ruimte en tijd.

• Met het oog op hoge resolutie snelheidsmeettechnieken, maakt de thesisgebruik van opstellingen die koude pulserende stroming genereren in hetuitlaatsysteem, waarbij de stromingsgelijkvormigheid met een werkendemotor onderzocht wordt [88, 87, 86, 84, 85].

• Een nieuwe oscillerende hittedraad anemometer (OHW) is ontwikkeldom bidirectionele snelheid te meten met dezelfde resolutie als standaardhittedraad anemometrie. De OHW is gekalibreerd in een specifieke wind-tunnel, met laser Doppler anemometrie als referentie snelheidsmeting.De maximaal meetbare negatieve snelheid bedraagt −1 m/s, vergelijk-baar met andere systemen. De kalibratie is uitgevoerd voor verschillendeprobe types. Uit een schaalanalyse volgt dat probes met rechte en 90řuiteinden zich verschillend gedragen, waaruit richtlijnen volgen ter opti-malisatie van het systeem. De OHW is succesvol toegepast bij metingvan de bidirectionele snelheidsverdeling in uitlaatsystemen met voorka-talysator [83, 84, 85].

• De experimentele validatie van het additie principe (Vgl. (4.1)) is ge-baseerd op de correlatie tussen het scavenging getal S (Vgl. (1.4)) entwee dimensieloze maten voor de gelijkenis tussen snelheidsverdelingenin pulserende en stationaire stroming. De validatie is ondersteund doorstatistische hypothesetesten [88, 86].

De kritische waarde van het scavenging getal Scrit dient als geldigheids-grens voor het additieprincipe. Het additieprincipe is geldig als S > Scrit.In dat geval is de correlatiecoëfficiënt tussen de snelheidsverdelingen inpulserende en stationaire stroming hoger dan 0.63.

Het additieprincipe houdt enkele belangrijke implicaties in voor het in-dustrieel ontwerp van uitlaatcollectoren met voorkatalysator:

(i) Gebaseerd op de correlatie voor rM (Vgl. (4.47)) is de stromingsuni-formiteit in pulserende stroming steeds hoger dan voor stationairestroming. Een collector ontworpen voor stationaire stroming zal dusvoldoen qua uniformiteit in pulserende stroming.


(ii) In het geldigheidsgebied van het additieprincipe (S > Scrit), kunnenstationaire CFD berekeningen de tijdsgemiddelde pulserende stro-ming accuraat voorspellen, wat resulteert in een kortere product-ontwikkelingstijd.

• Sterke fluctuaties in de katalysatorsnelheid zijn waargenomen in de CMEopstelling, alsook door andere auteurs in werkelijke motorcondities [81,59, 4, 70]. Deze fluctuaties worden in Hoofdstuk 5 toegeschreven aanHelmholtz resonanties. Deze aanname wordt bevestigd door middel vantransfer functies, bepaald met een ééndimensionaal gasdynamisch modelvan het uitlaatsysteem [84, 85].

• Het optreden van ogenblikkelijke lokale terugstroming in de katalysatoris onderzocht in de CME opstelling, en is reeds geobserveerd door andereauteurs [70, 81, 59]. Gezien de inherente ongevoeligheid van hittedraadanemometrie (HWA) voor de richting van de snelheidsvector, gebruikenandere onderzoekers optische snelheidsmeettechnieken. Problemen metoptische toegang en seeding beperken de ruimtelijke en tijdsresolutie. Metde OHW [83] is lokale periodieke terugstroming gemeten in de katalysa-tordoorsnede, op de CME opstelling [84, 85].

• Een numeriek ééndimensionaal gasdynamisch model van het uitlaatsys-teem werd ontwikkeld op basis van een tweede orde cell-vertex total va-riation diminishing discretisatieschema [101]. Het model is gevalideerdvoor relevante testgevallen. Omdat numerieke en experimentele resulta-ten voor de katalysatorsnelheid goed corresponderen, wordt het model ge-bruikt om de stromingsdynamica te voorspellen buiten de mogelijkhedenvan de experimentele aanpak, vb. de aanwezigheid van een uitlaatleidingmet demper, of de invloed van werkende motorcondities. Op basis vanhet gasdynamisch model worden transfer functies van de gasdynamica inde uitlaatcollector opgesteld, die beter inzicht geven in de geobserveerderesonantiefenomenen [84, 85].

Deze thesis draagt bij tot het begrip van stromingsdynamica in uitlaatcol-lectoren met voorkatalysator in het algemeen, en de snelheidsverdeling in dekatalysator in het bijzonder. De experimentele aanpak resulteert in hoge reso-lutie bidirectionele snelheidsmetingen die moeilijk te bekomen zouden zijn inwerkende motorcondities. De geldigheid van het additieprincipe is vastgesteld,met belangrijke implicaties voor het optimaal ontwerp van deze systemen. Totslot is de stromingsdynamica geanalyseerd met behulp van een ééndimensionaalgasdynamisch model van het uitlaatsysteem.

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Curriculum vitae

Tim Persoons was born in Leuven (Belgium) on 21 Nov. 1976. He graduatedas Burgerlijk Werktuigkundig-Elektrotechnisch Ingenieur, richting Mechanica(Mechanical Engineer), at the Katholieke Universiteit Leuven in 1999.

From Oct. 1999 till Sept. 2001, Tim was employed as research assistantat the dept. Mechanical Engineering (K.U.Leuven), working on model-basedcontrol of internal combustion engines, under supervision of Prof. dr. ir. EricVan den Bulck. During that time, he focused on the implementation of asimulated drive train with manual transmission and virtual driver on a dynamicengine test stand. The research dealt with the design and optimization of afeedforward/feedback controller for automated homologation test cycle drivingof a combustion engine in the virtual vehicle environment, created by a dynamicengine test stand. Currently, Tim is involved in comparing a backsteppingnon-linear controller and a proportional integral derivative feedback controllerfor combustion engine speed control, in cooperation with Prof. dr. ir. EricVan den Bulck and Prof. dr. ir. Jan Swevers (K.U.Leuven, dept. MechanicalEngineering).

In Oct. 2001, Tim began work on an experimental study of pulsating flowin automotive exhaust manifolds with close-coupled catalyst, under supervi-sion of Prof. dr. ir. Eric Van den Bulck. The study was part of a researchproject, partially funded by IWT-Vlaanderen [2], in cooperation with the re-search department of Bosal International, Lummen (B), a Belgian-Dutch basedTier 1 manufacturer of automotive exhaust systems. From Oct. 2001 to thepresent, Tim focuses on experimental fluid dynamics in modern compact au-tomotive exhaust systems with close-coupled catalysts. An oscillating hot-wireanemometer has been designed, calibrated and applied for bidirectional velocitymeasurements in exhaust systems, featuring sufficiently high spatial and tem-poral resolution for validation of the computational fluid dynamics techniquesat Bosal Research.

Based partly on the ongoing doctoral work, a new IWT project [3] started in2003. Tim was involved in the experimental study of flow, wall shear stress andpressure drop in pipes with interacting bends, typical of compact automotiveexhaust systems. At the same time, work began to investigate the relationshipbetween inclined, swirling flow and the inlet pressure loss, and its influence on

313

314 Curriculum vitae

the flow distribution in catalyst substrates.From 1999 to 2005, Tim taught the combustion engine lab sessions for

course H263 Voertuig- en Vliegtuigpropulsie. Since 1999, he has coached eightMaster’s theses of Mechanical Engineering students, in the fields of combustionengine control and experimental fluid dynamics.

List of publications

International journals with review(1) T. Persoons, A. Hoefnagels, and E. Van den Bulck. Calibration of an

oscillating hot-wire anemometer for bidirectional velocity measurements.Exp. Fluids, 40(4):555–567, 2006. http://dx.doi.org/10.1007/s00348-005-0095-4

(2) T. Persoons, A. Hoefnagels, and E. Van den Bulck. Experimental vali-dation of the addition principle for pulsating flow in close-coupled cat-alyst manifolds. J. Fluids Eng.-Trans. ASME, 128(4):656–670, 2006.http://dx.doi.org/10.1115/1.2201646

(3) T. Persoons, A. Hoefnagels, and E. Van den Bulck. Experimental studyof flow dynamics in close-coupled catalyst manifolds. Int. J. Engine Res.(in press).

(4) T. Persoons, E. Van den Bulck, and S. Fausto. Study of pulsating flow inclose-coupled catalyst manifolds using phase-locked hot-wire anemome-try. Exp. Fluids, 36(2):217–232, 2004. http://dx.doi.org/10.1007/s00348-003-0683-0

(5) K. Clement-Nyns, T. Persoons, and E. Van den Bulck. Pressure drop ofpipe sections with single and double 90 degree bends. J. Fluids Eng.-Trans. ASME (in review)

International conferences with review(1) T. Persoons, A. Hoefnagels, and E. Van den Bulck. Experimental study

of pulsating flow in a close-coupled catalyst manifold on a charged mo-tored engine using oscillating hot-wire anemometry. In SAE 2006 WorldCongress, 3-6 Apr. 2006, Detroit (MI), USA, 2006.

(2) T. Persoons, E. Van den Bulck, and S. Fausto. Study of pulsating flow in aclose-coupled catalyst manifold. In FISITA World Automotive Congress,23-27 May 2004, Barcelona, Spain, F2004-F436, 2004.

(3) K. Nevelsteen, T. Persoons, and M. Baelmans. Heat transfer coefficientsof forced convection cooled printed circuit boards. In Proc. 6th Int.Workshop on Thermal Investigations of IC’s and Systems, Therminic,Sep 2000, Budapest, Hungary, pp. 177–182, 2000.

http://dx.doi.org/10.1007/s00348-005-0095-4

http://dx.doi.org/10.1115/1.2201646

http://dx.doi.org/10.1007/s00348-003-0683-0

http://dx.doi.org/10.1007/s00348-003-0683-0

“I worry about ridiculous things, you know, how does a guy who drives asnowplough get to work in the morning. . . That can keep me awake fordays. . . ”

Billy Connolly (Scottish comedian, 1942)

Index

addition principle, 103definition, 104industrial implications, 17, 229literature on, 147mixing analogy, 149relation to Helmholtz resonance,

228validation

approach, 106correlations, 144–147interpretation, 144, 225

blow-by leakage, 49, 182, 210

catalyst, 241chemistry, 6, 203, 249deactivation, 4, 202design criteria, 8geometry, 3, 241pressure loss, 8, 11, 242

CFD, problems with, 17collector efficiency, 150, 229

exhaust manifold, 10frequency response, 213literature on flow in, 19–26measurement location, 35pressure loss, 10, 11specifications, 33thermal load, 16

flow dynamics, 155experimental results, 156–181

in one exhaust stroke, 162, 175modeling, 187, 267

benchmarking, 273

CFL number, 191discretization, 269equations, 267exhaust system, 188–192filling-and-emptying, 45

flow rate measurement, 54cylinder pressure based, 42, 59,

182laminar flow element, 42, 56, 182orifice, 37, 54

in pulsating flow, 55flow uniformity, 107

quantifying, 107–109related to diffuser flow, 161related to pressure drop, 10

Helmholtz resonance, 204, 213analytical model, 205frequency range, 210relation to addition principle, 228

hot-wire anemometry, 259directional ambiguity, 72–76principle, 76problems with, 45, 72, 210

laser Doppler anemometry, 260directional ambiguity, 261principle, 260problems with, 263reference for OHW, 89seeding, 260

oscillating hot-wire anemometer, 79calibration, 85–97flow disturbance, 93, 97limitations, 184, 193

316

Index 317

operation, 98oscillator, 80prong vibration, 75validation, 182

phase-locked measurement, 61cycle-resolved analysis, 64uncertainty, 64

pulsating flow rigs, 33, 36–44operation, 41, 170pulsator devices, 37, 159, 204

reverse flow, 182, 193

effect of cold end, 198, 201effect of fired conditions, 197, 201physical relevance, 202

scavenging number, 122critical value, 146, 150

similarityexhaust stroke, 41, 44, 53

thermodynamic analysis, 46,253

velocity distributions, 110–122

valve overlap, 35, 42, 49, 168

experimental flow dynamics in automotive exhaust systems with

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