internal combustion engines - princeton university1-d codes (e.g., gt-power, avl- boost, ricardo...

1 PCI-1-2, 2018

Internal Combustion Engines I: Fundamentals and Performance Metrics

Prof. Rolf D. Reitz,

Engine Research Center, University of Wisconsin-Madison

2018 Princeton-Combustion Institute Summer School on Combustion

Course Length: 9 hrs (Mon.- Wed., June 25-27)

Copyright ©2018 by Rolf D. Reitz. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Rolf D. Reitz.

Hour 2: 1-D modeling, Charge Preparation

2 PCI-1-2, 2018


Short course outline:

Internal Combustion (IC) engine fundamentals and performance metrics, computer modeling supported by in-depth understanding of fundamental engine processes and detailed experiments in engine design optimization.

Day 1 (Engine fundamentals)

Hour 1: IC Engine Review, Thermodynamics and 0-D modeling Hour 2: 1-D modeling, Charge Preparation Hour 3: Engine Performance Metrics, 3-D flow modeling

Day 2 (Computer modeling/engine processes)

Hour 4: Engine combustion physics and chemistry Hour 5: Premixed Charge Spark-ignited engines Hour 6: Spray modeling

Day 3 (Engine Applications and Optimization) Hour 7: Heat transfer and Spray Combustion Research Hour 8: Diesel Combustion modeling Hour 9: Optimization and Low Temperature Combustion

Mass conservation:

( )( )0cv

A A dxt

ρ ρ∂ = + ∇ ⋅ ∂ ∫ V

1g = / ) 0SystemdMg dt =

( ) ( ) 0A AVt x

ρ ρ∂ ∂+ =

∂ ∂

21 2 / 0V V PV fV Dt x xρ

∂ ∂ ∂+ + + =

∂ ∂ ∂

Momentum conservation:

Energy conservation:

Divergence theorem

1.

2.

3.

cv fixed

2/ / 2wf Vτ ρ=

P=ρRT

Supplementary:

e=cvT

5 unknowns U: ρ, V, e, P, and T 5 equations for variation of flow variables in space and time

4.

5. State

1-D compressible flow

)system relcv cssystem

dMg d dgd gd g dAdt dt dt

ρ ρ ρ= ∀ = ∀ + ⋅∫ ∫ ∫ V n

d Adx∀ =

dx

Reynolds Transport Equation

Anderson, 1990

3 PCI-1-2, 2018


In 1-D models friction factors are used to account for losses at area change or bends by applying a friction factor to an “equivalent” length of straight pipe

R Flow losses

Apply experimentally or numerically determined Loss Coefficient to equivalent straight pipe

2 / 2PP C Vρ∆ =

4 PCI-1-2, 2018


L

τ=L/c=1 m/330 m/s = 3 ms

1-D Modeling Codes

1-D codes (e.g., GT-Power, AVL-Boost, Ricardo WAVE) predict wave action in manifolds At high engine speed valve overlap can improve engine breathing inertia of flowing gases can cause inflow even during compression stroke.

Variable Valve Actuation (VVA) technologies, control valve timing to change effective compression ratio (early or late intake valve closure), or exhaust gas re-induction (re-breathing) to control in-cylinder temperatures.

Residual gas left from the previous cycle affects engine combustion processes through its influence on charge mass, temperature and dilution.

AVL Boost, Ricardo WAVE, GT-Power 1 ca deg = 0.1 ms @ 1800 rev/min 5 PCI-1-2, 2018


6 PCI-1-2, 2018

∆xi

i = 1, 2, 3, 4, …….. , M-1, M

To integrate the partial differential equations: Discretize domain with step size, ∆x Time marches in increments of ∆t from initial state 0 and: , , , ,n n n n n

i i i i i iU V e P Tρ

1( , )( , ) n ni i i

i i

U x n dt U UU x tx x x

+∆ ⋅ −∂= =

∂ ∆ ∆

1( , )( , ) n ni i iU x n dt U UU x t

t t t

+∆ ⋅ −∂= =

∂ ∆ ∆

Considerations of stability require the Courant-Friedrichs-Levy (CFL) condition

min( /(| | )n ni i it x V c∆ ≤ ∆ +

t=n∆t n=0, 1, 2, 3, ....

niU

Numerical solution


t - ti

me

x – distance along duct

P: particle-path

Wave diagram

dx Vdt

=slope

V

V

dx V cdt

= −slope

slope dx V cdt

= +

L: left-running wave

R: right-running wave

All points continuously receive information about both upstream and downstream flow conditions from both left and right-running waves. These waves originate from all points in the flow.

7 PCI-1-2, 2018

Analytical solutions – Method of Characteristics

Hour 2: 1-D modeling, Charge Preparation Anderson, 1990

t - ti

me

x – distance along duct

P: particle-path

Wave diagram

dx Vdt

=slope

V

V

dx V cdt

= −slope

slope dx V cdt

= +

L: left-running wave

R: right-running wave

min( /(| | )n ni i it x V c∆ ≤ ∆ +

t∆

x∆

R:, L:, P:, are called Characteristic Lines in the flow

8 PCI-1-2, 2018

Analytical solutions – Method of Characteristics


P: Slope nP

dx Vdt

=

∆t

∆x

1 2 3

4

R P L Time level n

Time level n+1

t

x

Slope n nR R

dx V cdt

= +

Slope n nL L

dx V cdt

= −

V

dP cdV Fdtρ+ = dP cdV Gdtρ− = 2/d dp c Hdtρ − =Along R: Along L: Along P:

( ), , , , ln /F G H Functionsof q f A dx=

2( )P Pc dP cdS d Hdtc

ρρ ρ

= − =

Note: from Gibbs’ equation

The discrete versions are:

4 4( ) ( ) ( )R R R RP P c V V F tρ− + − = ∆

4 4( ) ( ) ( )L L L LP P c V V G tρ− − − = ∆

4 42

1( ) ( )P P PP

P P H tc

ρ ρ − − − = ∆

3 equations to solve for

4 4 4and, V Pρ(Solution variables known)

9 PCI-1-2, 2018

Hour 2: 1-D modeling, Charge Preparation Moody, 1989

Flow velocities in IC engine cylinders are usually << than the speed of sound. Lagrange ballistics shows that cylinder pressure and density is the same at all points within the combustion chamber.

X

x

Vpiston

head

For dV<<c relative density change is small– density and pressure changes only in time

4 ( ) ( )R R piston RP P c V Vρ= − −R: 2

4 4( ) / )P P PP P cρ ρ= + −P:

4 ( ) (0 )L L LP P c Vρ= + −L:

~dP cdVρ

Pressure increases by dP each wave reflection (dV<0) in order to alternately ensure that the flow meets the boundary conditions: V=0 at head, and V=Vpiston at piston. Order of magnitude analysis of L:, R:, and P: gives

~d dVc

ρρ

pistondxSlope Vdt

=

and

t

x

Lagrange ballistics

10 PCI-1-2, 2018

Hour 2: 1-D modeling, Charge Preparation Thompson, 1972

Steady Compressible flow – A review

/Tds dh dp ρ= −

dh VdV= −

Gibbs

Energy

Euler dP VdVρ= −

2

2

(1 )dA M dPA Vρ

−=

0d dA dVA V

ρρ

+ + =AV Constρ =

2( 1)dA dVMA V

= −

for M<1 for M>1 Subsonic nozzle Subsonic diffuser Supersonic diffuser Supersonic nozzle dA<0 dA >0 dA <0 dA >0 from ρAV dV>0 dV <0 dV <0 dV >0 from Euler dP<0 dP >0 dP >0 dP <0 kinetic energy pressure recovery kinetic energy

Traffic flow behaves like a supersonic flow!

11 PCI-1-2, 2018


Area-velocity relations

201

1

112

T MT

γ −= + 2 10

11

1(1 )2

P MP

γγγ −−

= +

P0 P=Pb

P/P0 Pb

0

1

x

0.528

reservoir ambient

M=1 Manifold pressure, P1 cmHg

m

Choked

WOT

ψ

Ex. Flow past throttle plate

Choked flow for P2 < 53.5 kPa = 40.1cmHg

40.1 76

1

Isentropic nozzle flows

ψ

0

12 PCI-1-2, 2018


P1 P0

Model passages as compressible flow in converging-diverging nozzles

A*/A

0 P/P0 0 1

1

0.528

Subsonic Supersonic

0 ∞ M 1

reservoir throat exit

2 solutions for same area

P0 A*

1*2( 1)

1 00

2( )1Mm P A

RT

γγ γ

γ

+−

= =+

With M=1: Fliegner’s formula

1/ 20 0 0

0

( / ) /( / )

P Vm AV A RTRT c

P AM P P T TRT

ρ γ

γ −

= =

=

Choked flow, M=1

Minimum area point

1/ 211 11

*0 0

2 1( ) 1 ( )1 2

A P PA P P

γγγγ γ γ

γ

+−−

+ = − −

12( 1)

2*

1 2 ( 1)(1 )1 2

A MA M

γγγ

γ

+− −

= + +

Area Mach number relations

13 PCI-1-2, 2018


M=1 M=1

Application to turbomachinery

Reduced flow passage area

P0 /P Total/static pressure ratio

1/0.528=1.89 1.0

Choked flow

Increased speed

0

0

//ref

ref

m T TP P

Variable Geometry Compressor/ turbine performance map

“Corrected mass flow rate”

A measure of effective flow area

1*2( 1)

1 00

2( )1Mm P A

RT

γγ γ

γ

+−

= =+

Fliegner’s Formula:

14 PCI-1-2, 2018


M=1

15 PCI-1-2, 2018

Turbocharging

Improved


Pulse-driven turbine was invented and patented in 1925 by Büchi to increase the amount of air inducted into the engine. - Increased engine power more than offsets losses due to increased back pressure - Need to deal with turbocharger lag

Turbocharging Purpose of turbocharging or supercharging is to increase inlet air density, - increase amount of air in the cylinder.

Mechanical supercharging - driven directly by power from engine.

Turbocharger - connected compressor/turbine - energy in exhaust used to drive turbine.

Supercharging necessary in two-strokes for effective scavenging: - intake P > exhaust P - crankcase used as a pump

Some engines combine engine-driven and mechanical (e.g., in two-stage configuration).

Intercooler after compressor - controls combustion air temperature.

16 PCI-1-2, 2018


Turbocharging Energy in exhaust is used to drive turbine which drives compressor Wastegate used to by-pass turbine

Charge air cooling after compressor further increases air density - more air for combustion

17 PCI-1-2, 2018


Regulated two-stage turbocharger Duplicated Configuration per Cylinder Bank

EGR Cooler

EGR Cooler

EGR Valve

EGR Valve

LP stage Turbo-Charger with Bypass

LP stage Turbo-Charger with Bypass

HP stage Turbo charger

HP stage Turbo charger

Regulating valve

Regulating valve Charge Air Cooler

Charge Air Cooler

Compressor Bypass

Compressor Bypass

LP TURBINE

Regulating Valve

LP Stage Bypass

HP TURBINE Compressor Bypass

GT-Power R2S Turbo Circuit

18 PCI-1-2, 2018


Centrifugal compressor typically used in automotive applications Provides high mass flow rate at relatively low pressure ratio ~ 3.5 Rotates at high angular speeds - direct coupled with exhaust-driven turbine - less suited for mechanical supercharging Consists of: stationary inlet casing, rotating bladed impeller, stationary diffuser (w or w/o vanes) collector - connects to intake system

Automotive compressor

19 PCI-1-2, 2018


P 0

P 3 T

S

P 1

P 2

P 0 3

= P 0,in

= P out

V 1 2 / 2 c P

Air at stagnation state 0,in accelerates to inlet pressure, P1, and velocity V1.

Compression in impeller passages increases pressure to P2, and velocity V2.

Diffuser between states 2 and out, recovers air kinetic energy at exit of impeller producing pressure rise to, Pout and low velocity Vout

Compressor

( )1

0,

1

a

aa

c a out in

a P in out

c in

W m h h

m c T pWp

γγ

η

−

= −

⋅ ⋅ = −

c

)()(

inout

inisenoutc TT

TT−

−= −η

Heywood, Fig. 6-43

Heywood, 1988

20 PCI-1-2, 2018


Note: use exit static pressure and inlet total pressure, because kinetic energy of gas leaving compressor is usually not recovered

Compressor maps Work transfer to gas occurs in impeller via change in gas angular momentum in rotating blade passage

Surge limit line – reduced mass flow due to periodic flow reversal/reattachment in passage boundary layers. Unstable flow can lead to damage

At high air flow rate, operation is limited by choking at the minimum area point within compressor Pressure ratio evaluated

using total-to-static pressures since exit flow kinetic energy is not recovered

Non-dimensionalize blade tip speed (~ND) by speed of sound

Speed/pressure limit line

Supersonic flow

Shock wave

Heywood, Fig. 6-46 21 PCI-1-2, 2018

Hour 2: 1-D modeling, Charge Preparation Heywood, 1988

Compressor selection

To select compressor, first determine engine breathing lines. The mass flow rate of air through engine for a given pressure ratio is:

= IMP = PR * atmospheric pressure (no losses)

= IMT = Roughly constant for given Speed

η

22 PCI-1-2, 2018


Engine breathing lines

Engine Breathing Lines1.4L Diesel, Air-to-Air AfterCooled, Turbocharged

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000

Intake Mass Flow Rate (lb/min)

Com

pres

sor P

ress

ure

Rat

io

Torque Peak (1700rpm)

Trq Peak Operating Pnt

Rated (2300rpm)

Rated Operating Pnt

Parameter Torque Peak Rated UnitsHorsepower 48 69 hp

BSFC 0.377 0.401 lb/hp-hrA/F 23.8 24.5 none

23 PCI-1-2, 2018


Compressor maps

0.5

0.6

0.7

0.8

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Corrected Air Flow (kg/s)

Efficiency (T/T)

35000 40000 50000 70000

90000 110000 130000 150000

170000 180000 190000

35000 4000050000 70000

90000110000

130000

150000

170000

180000

190000

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Corrected Air Flow (kg/s)

Pressure Ratio (t/t)

GM 1.9L diesel engine

Serrano, 2008

24 PCI-1-2, 2018


P

V

TDC BDC

Pexhst Pintake

Compression

Expansion

Available work (area 5-6-7)

Blowdown

Automotive turbines

P-V diagram showing available exhaust energy - turbocharging, turbocompounding, bottoming cycles and

thermoelectric generators further utilize this available energy

1

2

3 4

5

6 7 8

9

Pamb 6’

Naturally aspirated: Pintake=Pexhst=Patm (5-7-8-9-1) Boosted operation: Negative pumping work: P7<P1 – but hurts scavenging

6’’

Compressor Turbine

0,( )t g in outW m h h= −

1

0,1

g

goutt g P in t

in

PW m c T

P

γγ

η

− = −

Reitz, 2007

25 PCI-1-2, 2018


c

Turbochargers

out

Radial flow – automotive; axial flow – locomotive, marine

0

3

0

3

0

3

TTNN

pp

TT

mm

corrected

gcorrected

=

=••

T

S

P 1

P 2

P 0 3

P 0 = P 0,in

P 3 = P out

V 1 2 / 2 c P

)()(

inisenout

inoutt TT

TT−

−=

−

η

26 PCI-1-2, 2018


( )

11

3

4

1

3

1

2 111

−

−⋅⋅

+

⋅⋅

+=

−

•

•aa

g

g

pp

m

mTCpTCp

pp

mechct

air

fuel

a

g

γγ

γγ

ηηη

Wt = Wc

Heywood, 1988

27 PCI-1-2, 2018


. .

Summary

1-D models/codes based on thermodynamic models are available, and they are very useful for understanding charge preparation and engine breathing. But, 1-D models require calibration against engine or theoretical data. Turbocharging increases overall engine efficiency by using available energy in exhaust and by reducing pumping work.

28 PCI-1-2, 2018


29 PCI-1-2, 2018


1-2:3,7-9,11-14 J. D. Anderson, Modern Compressible Flow (With Historical Perspective), McGraw-Hill (2nd or 3rd Edition), 1990.

1-2:5 1-1:34-36 http://www.ricardo.com/en-GB/What-we-do/Software/Products/WAVE

1-2:9 F.J. Moody, Introduction to Unsteady Thermofluid Mechanics, John Wiley & Sons, 1989.

1-2:10 P.A. Thompson, Compressible Fluid Dynamics, McGraw-Hill, 1972.

1-2:20-21,27 J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw Hill, 1988.

1-2:24 Serrano J.R., Arnau F.J., Dolz V. , Tiseira A., and Cervello C., “A model of turbocharger radial turbines appropriate to be used in zero- and one-dimensional gas dynamics codes for internal combustion engines modeling”, Energy Conversion and Management,49 (2008) 3729–3745, 2008.

1-2:25 Reitz, R.D., and Hoag, K.H., "Reciprocating Engines (Diesel and Gasoline)," Encyclopedia of Energy Engineering and Technology (EEE), B. Capehart, Editor, Marcel Dekker Publishing, New York, 2007.

References

internal combustion engines - princeton university1-d codes (e.g., gt-power, avl- boost, ricardo...

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