svenska mekanikdagar 2019 stockholm 11-12 juni/smd...f orord svenska mekanikdagar arrangerades f or...

Svenska mekanikdagar 2019

Stockholm 11-12 juni

Omslagsbild: copyright c© Michael Tompsett

Forord

Svenska mekanikdagar arrangerades for forsta gangen 1974, och 2019 blir det 26:e arrange-

manget. Konferensen organiseras av Nationalkommitten for Mekanik som ar en under-

avdelning till Kungliga Vetenskapsakademien. Motesserien har sedan starten utgjort en

viktig plattform for utbyte av ideer mellan forskare inom mekanikomradet.

2019 ars upplaga innehaller ca 90 presentationer och forelasningar i fyra parallella sessioner

under tva dagar. Vard for konferensen ar KTH och Odqvistlaboratoriet for experimentell

mekanik och vi hoppas det blir tva intressanta och angenama dagar som foder nya insikter,

moten och utbyten av tankar och ideer.

Valkomna till Kungliga Tekniska hogskolan!

Organisationskommitten:

Stefan Hallstrom, Lattkonstruktioner

Michael Liverts, Mekanik

Erik Olsson, Hallfasthetslara

Romain Rumpler, Marcus Wallenberg-laboratoriet for ljud och vibrationer

Soren Ostlund, Hallfasthetslara

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Sponsorer

http://www.comsol.com/

http://www.studentlitteratur.se/

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http://www.comsol.com/

http://www.studentlitteratur.se/

Tidigare mekanikdagar

Tidigare mekanikdagar Odqvistforelasare2017, UU, Uppsala Solveig Melin2015, LiU, Linkoping Larsgunnar Nilsson2013, LTH, Lund Anders Klarbring2011, Chalmers, Goteborg Kenneth Runesson2009, KTH/Scania, Sodertalje Sture Hogmark2007, LTU, Lulea Henrik Alfredsson2005, LTH, Lund Fred Nilsson2003, Chalmers, Goteborg Bo Jacobson2001, LiTH, Linkoping Niels Saabye Ottosen1999, KTH, Stockholm Peter Gudmundson1997, LTU, Lulea Martin Lesser1995, LTH, Lund Bertil Storakers1993, SP, Boras Arne Johansson1992, KTH, Stockholm Viggo Tvergaard1990, Chalmers, Goteborg Inge Ryhming1988, FFA/KTH, Stockholm Frithiof Niordson1987, SAAB/LiTH, Linkoping Sune Berndt1985, LTH, Lund Marten Landahl1983, ASEA, Vasteras Georg Drougge1982, UU, Uppsala Hans-Christian Fischer1980, LuTH, Lulea Janne Carlsson1979, Chalmers, Goteborg Bertram Broberg1977, LiTH, Linkoping Lars Jarfall1976, KTH, Stockholm Jan Hult1974, KVA, Stockholm Bengt Joel Andersson

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Konferenslokaler och karta(Conference venue and directions)

Guest Wi-Fi available in the conference rooms:SSID: KTH-ConferencePassword: nugeguzy

Eduroam also available on campus

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Konferensmiddag(Conference dinner)

Middagen halls i Bryggarsalen, Norrtullsgatan 12N. For att ta sig fran KTH till

konferensmiddagen finns alternativen:

• Ta buss 4, 6 eller 72 fran Ostra station till Odenplan. Restid ca 10 minuter, buss gar

ca var 5:e minut. (Med SL-appen kan man kopa enkelbiljetter relativt enkelt och fa

kvitto.) Promenera sedan till Bryggarsalen enligt kartan nedan (ca 5 minuter).

• Promenera hela vagen till Bryggarsalen enligt kartan nedan (ca 30 minuter).

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Programoversikt

Programoversikt – SMD2019

Tisdag 11/609:00-09:30 Registrering

09:30-09:40 Oppnande09:40-10:20 Odqvistforelasning: Dan Henningson, KTH

Large scale numerical experiments of pitching wingsand the role of laminar-turbulent transition

10:20-10:30 Studentlitteratur10:30-10:55 Kaffe10:55-12:05 Parallella sessioner 112:05-13:20 Lunch13:20-13:50 Gemensam forelasning: Leif Asp, Chalmers

Structural Battery Composites – on their characterisationand modelling

13:55-15:05 Parallella sessioner 215:05-15:30 Kaffe15:30-16:40 Parallella sessioner 316:50-17:30 Labbrunda19:00-22:00 Konferensmiddag - Bryggarsalen

Onsdag 12/608:30-09:00 Gemensam forelasning: Delphine Bard-Hagberg, LTH

Acoustic issues in wooden multi storey buildings09:05-09:50 Parallella sessioner 409:50-10:15 Kaffe10:15-11:50 Parallella sessioner 511:50-13:10 Lunch13:10-13:40 Gemensam forelasning: Nazanin Emami, LTU

Thermomechanical characterisation of newly developed multiscalethermoplastic composites for tribological applications

13:45-14:30 Parallella sessioner 614:30-15:00 Kaffe15:00-16:35 Parallella sessioner 716:40-16:50 Avslutning

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Forelasningar

Forelasningar – SMD2019

Tisdag 11/6, Rum F2

09:40-10:20 OdqvistforelasningDan Henningson, KTHLarge scale numerical experiments of pitching wingsand the role of laminar-turbulent transition

13:20-13:50 ForelasningLeif Asp, ChalmersStructural Battery Composites – on their characterisationand modelling

Onsdag 12/6, Rum F2

08:30-09:00 ForelasningDelphine Bard-Hagberg, LTHAcoustic issues in wooden multi storey buildings

13:10-13:40 ForelasningNazanin Emami, LTUThermomechanical characterisation of newly developed multiscalethermoplastic composites for tribological applications

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Sessionsprogram

Tisdag 11/6

09:40 Odqvistforelasning D. Henningson, KTHRum F2 Large scale numerical experiments of pitching wings and the role of

laminar-turbulent transition10:20 Sponsorpresentation J. Fredholm, Studentlitteratur

Parallella sessioner 1

Materialmekanik I Jets Stromningsmekanik I Kompositmekanik IRum F2 Rum K2 Rum K51 Rum K53

Hakan Hallberg Johan Revstedt Mattias Liefvendahl Malin Akermo

10:55Fractional strain-gradient plasticity

Large eddy simulationand aeroacoustics ofheated rectangularsupersonic jets

Large-eddy simulationof an internal ship aircavity

Simulation of failureat different scalesin fiber-reinforcedcomposite materialsusing a phase-fieldapproach to fracture

C F O Dahlberg, MOrtiz

S Chen, R Gojon, MMihaescu

T Mukha, R E Ben-sow

J J Espadas Es-calante, P Isaksson

11:20Modelling the cyclicbehaviour of an addi-tively manufacturedductile nickel-basedsuperalloy

Reacting Spray A andscaled jet analysis

Computation of thestable atmosphericboundary layer usingthe explicit algebraicReynolds-stress model

Design and processanalysis of compositereinforcement forautomotive Body-in-White

T Lindstrom, DEwest, K Simons-son, R Eriksson, J-ELundgren, D Leider-mark

M Gholamisheeri, DNorling, T Hallqvist

V Zeli, G Brethouwer,S Wallin, A Johansson

S Kumaraswamy, Zvan der Putten, RGutkin, M Akermo

11:45Innovative weldingof rails – Resultingmicrostructure andresidual stresses

High-fidelity numer-ical simulations of aliquid jet in air cross-flow: A case study ofinterface-capturingmethods for turbulenttwo-phase flows

Wall modelling orwall resolving inlarge-eddy simula-tion – What are thetrade-offs in cost andaccuracy?

Virtual material test-ing of composite mate-rials

B L Josefson, JBrouzoulis, R Biss-chop, T Andersson, MMaglio

Z Ge, S S Jain, SMirjalili, M E Rosti,M S Dodd, L Brandt

M Liefvendahl, TMukha, S Reza-eiravesh

R Gutkin, K Stahl, AAndersson, L E Asp

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13:20 Forelasning Leif Asp, ChalmersRum F2 Structural Battery Composites – on their characterisation and modelling

Parallella sessioner 2 (Tisdag 11/6)

Turbulens I Materialmekanik II Kompressibel Optimering Istromning

Rum F2 Rum K2 Rum K51 Rum K53Jens Fransson Stefan Lindstrom Michael Liverts Marten Olsson

13:55Towards efficient wall-bounded turbulencesimulations

Regimes of fibre depo-sition on flow obstruc-tions with applica-tions to nuclear powerplants

Influence of systemdynamics on exhaustvalve flows

Optimal cooling by2D topology optimiza-tion of 3D-modelledconvection-diffusionand stokes flow multi-physics problem

R Pozuelo, S Hoyas, PSchlatter, R Vinuesa

J D Redlinger-Pohn,M Liverts, F Lundell

P M Winroth, P HAlfredsson

J Lundgren, A Klar-bring, J-E Lundgren,C-J Thore

14:20Microwave stimulationof turbulent flames

Numerical model re-duction for compu-tational homogeniza-tion of heterogeneousporous media

Richtmyer-Meshkov vsKelvin-Helmholtz in-stability in an ellipticinhomogeneity

Topology optimizationbased on finite strainviscoplasticity

C Fureby, T Hur-tig, N Zettervall, HSundberg, A Ehn, ENilsson, J Larfeldt, JEngdahl

F Ekre, R Janicke, FLarsson, K Runesson

S Sembian, M Liverts,N Apazidis

N Ivarsson, M Wallin,D Tortorelli

14:45Recent progress onfree-stream turbulenceinduced transition

An a posteriori errorestimator for numeri-cal model reduction incomputational homog-enization of porousmedia

A qualitative studyof the interaction ofa blast wave with amulti-faceted obstacle

A topology optimiza-tion method for as-built metal additivemanufacturing

J H M Fransson F Ekre, F Larsson, KRunesson, R Janicke

R Mariani, S Sembian,N Apazidis

S Suresh, C-J Thore,A Klarbring

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Parallella sessioner 3 (Tisdag 11/6)

Stromningsmekanik II Turbulens II Vibrationer BiomekanikRum F2 Rum K2 Rum K51 Rum K53

Lisa Prahl Wittberg Jens Fransson Romain Rumpler Fredrik Larsson

15:30Blood flow dynamicsand mixing: a studyof the return cannula

Interscale transport inwall-bounded turbulentflows

Centrifugal pendulumvibration absorbers(CPVA)

Biomechanical model-ing of aortic surfacedynamics - Impor-tance and applications

J Lemetayer, L Fuchs,L M Broman, L PrahlWittberg

G Ferrante, A Morfin,T Kawata, R Orlu,P Schlatter, P H Al-fredsson

E R Gomez, I LopezArteaga, L Kari

J Bondesson, T Lundh

15:55A plea for use of hy-drogel spheres forinvestigating densemultiphase flows

Isolated roughness-induced boundarylayer transition

Friction induced drivetrain vibrations

Proposing an evo-lution law for thecontractile elementin musculoskeletalmodeling

S Zade, F Lundell, LBrandt

S B Mamidala, SHara, J H M Frans-son

J Sjostrand, I LopezArteaga, L Kari

L J Holmberg, ARoser, P R Roca, JStalhand

16:20Topology of colloidaldispersions in ex-tensional flow usingoptical coherence to-mography

Transition in a swept-boundary layer subjectto surface roughnessand free-stream turbu-lence

Prediction of shockand vibration causedby a bird strike to anaircraft structure

A FEM for two fibrefamily reinforced finitehyperelasticity

C Rydefalk, K Gowda,F Lundell

L De Vincentiis, DHenningson, A Hanifi

A Rehnberg, A Josefs-son, N Osterstrom

A Zdunek, W Rachow-icz

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Onsdag 12/6

08:30 Forelasning Delphine Bard-Hagberg, LTHRum F2 Acoustic issues in wooden multi storey buildings

Parallella sessioner 4

Stromningsmekanik III Turbulens III Kompositmekanik II DynamikRum F2 Rum K2 Rum K51 Rum K53

Ugis Lacis Ramis Orlu Stefan Hallstrom Mikael Enelund

09:05Nanofibril behaviourduring assembly ofstrong filaments isrevealed by decay ofbirefringence

Cross-flow instabilityand transition on arotating cone

Predicting non-linearshear deformation andfailure in 3D fibre-reinforced composites

An inverse estimationfor acoustic materialproperties characteri-sation

F Lundell, C Brouzet,N Mittal, T Rosen, LD Soderberg

K Kato, T Kawata, ASegalini, P H Alfreds-son, R J Lingwood

C Oddy, M Ekh, MFagerstrom

H Mao, L Manzari, PGoransson

09:30Particle wall interac-tion

Turbulent dropbreakup mechanismsin high-pressure ho-mogenizers

Impact of climaticloadings on the effi-ciency of bonding ofconcrete structureswith CFRP

Component modesynthesis interfacereduction and modaltruncation augmen-tation using coarsemeshes

A Rinehart, U Lacis, SBagheri

P Olad, A Hakansson,L Brandt, F Innings

P Godonou M Gibanica, T J SAbrahamsson, D JRixen

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Parallella sessioner 5 (Onsdag 12/6)

Materialmekanik III Stromningsmekanik IV Optimering II AkustikRum F2 Rum K2 Rum K51 Rum K53

Peter Gudmundson Fredrik Lundell Anders Klabring Susann Boij

10:15A continuum-basedmodel for precipitationstrengthening appliedto experiments on amaraging stainlesssteel Fe–15Cr–5Ni

Cubes or spheres -does it matter? Tran-sition in particulatepipe flow

Metamodeling usingspline kriging forefficient global designoptimization

Determination ofnon-linear scatteringmatrices of perforatedplates

P Crone, J Faleskog M Leskovec, F Lun-dell, F Innings

P N Lind, M Olsson N Khodashenas, HBoden, S Boij

10:40Singularity-free defectmechanics for polarmedia

CFD study of the flowin a return cannula

Topology optimizationusing an evolution-based anisotropichigh-cycle fatigueconstraint

Investigation of thesound transmissionthrough a locally res-onant metamaterialcylindrical shell in thering frequency region

S M Mousavi F Fiusco, L M Bro-man, L Prahl Wit-tberg

S Suresh, S B Lind-strom, C-J Thore, BTorstenfelt, A Klar-bring

Z Liu, R Rumpler, LFeng

11:05Respecting fullgrain boundary en-ergy anisotropy inmesoscale simulationsof polycrystals

Flow dynamics ofcolloidal fibre disper-sion in geometricallyvarying flow-focusingchannels

A discussion on sec-ond order reliabilitymethods

A simplified model forthin acoustic screens

H Hallberg, V V Bula-tov

K Gowda, C Rydefalk,L D Soderberg, FLundell

M Olsson, R Mansour M Gaborit, PGoransson, O Dazel

11:30On evolvinganisotropy in pearliticrail steel - modelingand experiments

Computational studyof the flow in a devicefor neonatal contin-uous positive airwaypressure

Stochastic multiscalemodelling of fibernetworks

Numerical predictionof thermoacousticinstabilities using lin-earized navier-stokesequations methodologyin frequency domain

K A Meyer, M Ekh, JAhlstrom

N Berg, T Drevham-mar, L Prahl Wittberg

R Mansour, A Ku-lachenko, M Olsson

W Na, S Boij, GEfraimsson

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13:10 Forelasning Nazanin Emami, LTURum F2 Thermomechanical characterisation of newly developed multiscale thermo-

plastic composites for tribological applications


Aerodynamik Mekanik, allmant Geomekanik I Tra & PapperRum F2 Rum K2 Rum K51 Rum K53

Henrik Alfredsson Johan Tryding Par Jonsen Kristofer Gamstedt

13:45Stratofly The new SI and it’s

impact on metrol-ogy in industry andresearch

Inelastic mechanicalbehaviour of graniteunder spherical inden-tation test

In-plane elastic be-haviour of transparentwood composite mea-sured with digitalimage correlation

C Fureby F Arrhen H Shariati, M Saadati,P-L Larsson

E Jungstedt, LBerglund, S Ostlund

14:10Plasma drag reductionmethodology for ef-fective energy usage -Prometheus

Fracture processes inpackaging material –A review of researchcollaboration betweenBTH and a packagecompany

Multiscale analysisof quartz sand un-der load by neutrondiffraction and digitalimage correlation

The significance of thelongitudinal swellingof fibers on paper in-plane hygroexpansion

P Sujar-Garrido, ROrlu, P Elofsson, P HAlfredsson

S Kao-Walter, E An-dreasson, M S Islam,E Mfoumou

S D Athanasopoulos,S A Hall

A Brandberg, A Ku-lachenko

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Brottmekanik & Materialmekanik IV Geomekanik II Stromningsmekanik Vutmattning

Rum F2 Rum K2 Rum K51 Rum K53

Magnus Ekh Carl Dahlberg Per-Lennart Larsson Ramis Orlu

15:00When, where, how;predicting crystallo-graphic cracking

A generalization of acohesive mixed modemodel

Towards the discreteelement modeling ofrock drilling

Dynamics of tip-vortices of two in-linewind turbines

D Leidermark, CBusse

J Tryding, M Ristin-maa, E Borgqvist

A Wessling, P Jonsen,J Kajberg

V G Kleine, E Kleus-berg, A Hanifi, D SHenningson

15:25A continuous-time,high-cycle fatiguemodel and rotarystress states

A study of the fracturebehaviour of ultrathincoatings on a polymersubstrate

Full scale modelingand validation of wearin a power shovelbucket

Validating an exper-imental setup of awing model inside awind tunnel

S B Lindstrom, SSuresh, C-J Thore, AKlarbring

M V Tavares daCosta, J Bolinsson,P Fayet, E K Gamst-edt

A Svanberg, P Jonsen A Parikh, E Dogan,F Mallor, M Atzori,R Vinuesa, R Orlu, PSchlatter

15:50A probabilistic modelfor multiple mecha-nism brittle fracturein ferritic steels

Mechanical propertiesof lithium-ion batteryelectrodes

Modelling and vali-dation of the inter-actions between pulp,charge and mill struc-ture in a full- bodymodel tumbling mill

Design considerationsfor the flow conditionsaround a wing modelinside a wind tunnel

M Boasen, C F ODahlberg, J Faleskog,P Efsing

P Gupta, I B Ucel, PGudmundson

P Jonsen, B Palsson F Mallor, E Dogan,M Atzori, A Parikh,R Vinuesa, R Orlu, PSchlatter

16:15Experimental fracturemechanics to studyenvironmentally as-sisted degradation inhigh strength steel

The obscure truth be-hind colorful plots:why my measurementsmake no sense – per-haps yours neither

DEM simulation ofasphalt under flowand compaction usinga new viscoelasticcontact law

A E Halilovic, P Efs-ing, J Faleskog

L Manzari, PGoransson, J Cuenca,I Lopez Arteaga

E Olsson, D Jelagin,M N Partl

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Forelasningar

(Kronologisk ordning)

13

Svenska Mekanikdagar, KTH, 11-12 juni 2019

Large scale numerical experiments of pitching wings and the role of laminar-turbulent transition

D.S. Henningson

Department of Mechanics, KTH, Stockholm, Sweden Recent unsteady aerodynamic experiments in the subsonic [1] range have revealed a non-linear aerodynamic response of natural laminar flow (NLF) airfoils undergoing harmonic pitch oscillations. The experimental results have indicated that these aerodynamic non-linearities are associated with the free movement of transition over the airfoil and that the boundary layer dynamics including transition and separation play an important role in the unsteady aerodynamic characteristics of the airfoil. Understanding of the unsteady boundary layer response is crucial for developing new models that can predict such nonlinear behavior. In order to study these effects large scale numerical experiments of a natural laminar airfoil undergoing small-amplitude pitch-oscillations are performed at chord-based Reynolds numbers of Rec = 100.000 and 750.000. The simulations are performed with a high-order spectral-element method (SEM) with the domain discretized by up to 1.6 billion grid points. The time-dependent transition and separation characteristics are calculated over the course of the oscillation cycles. The transition point is observed to undergo large changes over the course of the cycles varying by up to 30-60% of the chord length.

Figure 1: Instantaneous vortical structures at two

closely spaced angles of attack for Re=100.000 [2]. Colors indicate streamwise velocity.

Figure 1 and 2 shows the instantaneous vortex structures and the large changes occurring in the boundary layer characteristics. In many cases the varying boundary layer characteristics lead to emergence of non-linear aerodynamic forces acting on the airfoil, often with the unsteady characteristics related to those observed for stationary airfoils. Analysis of the mechanisms of laminar-turbulent transition responsible for the unsteady behavior will be described. References

[1] Mikaela Lokatt. On Aerodynamic and Aeroelastic Modeling for Aircraft Design. Doctoral thesis, KTH Royal Institute of Technology, September 2017.

[2] Prabal Negi, Ricardo Vinuesa, Ardeshir Hanifi, Philipp Schlatter and Dan Henningson. Unsteady aerodynamic effects in small-amplitude pitch oscillations of an airfoil. Int. J.of Heat and Fluid Flow 71 (2018) 378–391

I would like to acknowledge my co-workers P. Negi, S.M. Hosseini, A. Hanifi, R. Vinuesa and P. Schlatter.

Figure 2: Instantaneous vortical structures at two

closely spaced angles of attack for Re=750.000 modeling an experiment by Lokatt [1].

Corresponding author email: [email protected]

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Structural Battery Composites – on their characterisation and modelling

L.E. Asp1

1Department of Industrial and Materials Science, Chalmers University of Technology, Gothenburg, Sweden

Since weight reduction is vital in transportation, lightweight materials have been identified as key for successful electrification of road transport and to meet the reduced emission demands for aircraft. Reduced weight is required for increased range and energy efficiency of electric cars [1] and the aircraft industry has expressed a desire for mass-less energy storage for their transition to all-electric aircraft. Although the introduction of composites in electric vehicles is already underway, additional lightweight solutions for the vehicle systems are required, e.g. efficient energy storage solutions. Current battery systems add significant weight (typically 350 to 500 kg) to an electric car. Furthermore, such systems do not contribute to the structural performance; i.e. they are structurally parasitic. Regarding aircraft, just 1 kg reduction in the weight of each aircraft in the Lufthansa fleet would result in fuel savings of 30 tonnes of kerosene per year1. Thus, there are compelling arguments for materials with combined structural and added performance-linked capabilities, e.g. electric energy storage [2].

Figure 1: Research areas for realisation of structural battery composites

Since year 2007 an interdisciplinary team of scientists across Sweden has performed research to realise multifunctional composite materials that simultaneously and intrinsically can carry mechanical loads and store electrical energy – i.e. structural battery composite materials. Researchers at

1http://www.lufthansagroup.com/fileadmin/downloads/en/LH-fuel-efficiency-0612.pdf, 2012.

Chalmers, KTH, Swerea SICOMP and Luleå University of Technology have investigated different constituent materials, i.e. carbon fibres and polymer matrix systems, as well as different material architectures to realise high performance structural battery composites. In this plenary presentation, the author aims to provide an overview of the most recent results from this research work. Figure 1 provides an illustration on issues addressed.

This plenary presentation will focus on issues related to modelling of the multifunctional performance of structural battery composites, the underlying multi-physics model and related material properties [3]. The presentation will also concern the reinforcement/electrode materials and in particular some recent results linking the carbonaceous microstructure of different types of carbon fibres to their multifunctional performance capacities will be discussed. Finally, different polymer electrolytes as bulk matrix material or thin coatings will be discussed in the context of different material architectures. Acknowledgements

Contributions from Mr David Carlstedt, Mr Shanghong Duan, Assoc. Prof. Fang Liu and Profs Dan Zenkert and Göran Lindbergh are gratefully acknowledged, as is funding from the European Union, Clean sky Joint Undertaking 2, Horizon 2020 under Grant Agreement Number 738085 and USAF, contract FA9550-17-1-0338.

References

[1] Wismans, J. et. al. Proceedings of the 22nd International Technical Conference on the Enhanced Safety of Vehicles, 2011, Washington DC, USA, paper 11-0128.

[2] Asp L.E. and Greenhalgh E.S., Structural Power Composites, Composites Science and Technology, 101, 2014, pp. 41-61.First, A., Second B.C., Third, D., Title of a book (2nd ed.). Publication City: Publisher Press (2015).

[3] Carlstedt D., Asp LE., Thermal and diffusion induced stresses in a structural battery under galvanostatic cycling. Accepted: Composites Science and Technology, 2019.

__________________________________________ Corresponding author email: [email protected]

15


Acoustic issues in wooden multi storey buildings

D. Bard-Hagberg1

1Department of Construction Science, division of engineering acoustics, LTH, Lund, Sweden

Wood, is increasing as structural material in buildings, improving the conditions for circular economy within the construction sector. However, structural wood is still creating doubts amongst many developers and one issue is the difficulty to easily fulfil similar sound insulation requirements as we are used to from the history with concrete. The design of wood buildings requires specific knowledge and depending on the system they are sensitive to failure during the building phase. But still, it is possible to erect wood buildings with high acoustic performance, it is just a matter of knowledge and awareness of where to put priority. There are a number of building systems on the market today fulfilling high acoustic requirements, all having their advantages. For high rise buildings Cross Laminated Timber is clearly dominating the market and it is increasing very fast.

Figure 1: CLT plate with 5 layers However, the acoustic challenges increase when

the buildings become high. For example, to secure the Swedish sound insulation class B (according to SS 25267 [1]), either the walls have to be very thick or elastomers have to be installed between the different storeys. Additionally, high design margins are needed since the real efficiency of acoustic measures are unknown, for example the wall elements are tightly connected due to static reasons (point connectors). Therefore, it is the duty of acousticians to ensure that the requirements we are stating in the design process really correspond to the annoyance of the habitants for different building categories. We should not lower the overall quality but instead refine the requirements to be more “spot on” in each single situation. Therefore, increased knowledge is necessary, in particular regarding annoyance in different housing categories. In wood building design, current building requirements have to be questioned and adapted in order to • avoiding low frequencies causing high noise levels

in specific cases

• minimize risk for annoying vibrations • optimize the buildings to allow flanking

transmission to some extent, still without creating annoyance

• adapt to new building categories and sizes of future apartments.

Figure 2: Cederhusen, thirteen storey wood buildings under construction in Stockholm.

Involving severe acoustic challenges. Current requirements globally, and in Sweden as

well, are adapted to concrete buildings. Following these national rules create solutions that is complex and sometimes wood is deleted as structural material in favour of concrete due to historical requirements rather than knowledge [2, 3].

To simplify for new material to enter the market it is important to always update requirements and follow the demographic situation in any country. We have to develop solutions that is environmentally friendly but still good enough to provide high quality dwellings.

References

[1] Swedish Standards Institute, Sound classification of building – dwellings. Stockholm, SIS (2012)

[2] Negreira, J, Vibroacoustic performance of Wooden Buildings, Doctoral Thesis, ISBN 978-91-7623-643-7 (pdf), Lund 2016

[3] Hagberg, K, Management of acoustics in lightweight buildings, Doctoral Thesis, ISBN 978-91-7753-601-7 (pdf)


16


Thermomechanical characterisation of newly developed multiscale thermoplastic composites for tribological applications

Nazanin Emami

Department of Engineering Sciences and Mathematics, Luleå University of Technology, Sweden Over the past two decades, there has been a growing demand to use environmental friendly tribological systems. Naturally, increased environmental awareness and demand for sustainable solutions has led to a transition from oil-filled bearings to oil-free bearings and use of tribological contact materials that generate minimal contamination and wear. A prime example is the use of Environmentally Adapted Lubricants(EALs). However, EALs have a definite half-life and are not completely oil or additive free. These concerns have resulted in the industry turning towards water based lubricants to satisfy their needs. Tribological systems where water can be readily used as lubricant are prevalent in the marine, hydro power and pump industries. The most important attributes of materials for water lubricated bearings are that they should have low friction and wear under the boundary conditions which will inevitably be met during running, start up and shut down of a tribological contact/operation. Conventional materials like metals and ceramics have been found lacking in performance when used as tribological surfaces in water lubricated systems. From a performance, maintenance and economical point of view, it is advantageous to replace metal based tribological parts in various industries and applications with Polymer Based Materials (PBMs). Polymers have excellent properties that includes lightweight, low maintenance, and lower cost and at the same time, very good mechanical properties, resistance to corrosion and chemical solutions, low friction, etc. Also, polymers can be easily modified both on surface and in bulk. Therefore, they are often and easily used as a matrix material to produce composites with easily varied physicochemical properties. This makes polymers very promising materials with ability to control their frictional and wear behaviour in tribological contacts. Application of polymers and polymer composites in water lubricated bearings introduces many advantages which cannot be achieved with conventional metallic bearing materials, coatings or ceramics [8]. Many PBMs are self-lubricating and form transfer layers at the tribological contact leading to improvement in tribological performance. Formation of a lubricating layer prevents or reduces the contacts of the surfaces. At present, studies dealing with PBMs in water lubricated contacts are few and scarce. Existing commercial PBMs have shown disadvantages in longtime tribological performance. In view of the above mentioned issues, and taking into account, long-term performance, recyclability and sustainability of water lubricated bearing in the future, it is necessary that effort is taken to develop new multiscale and multifunctional polymer based composites in order to improve the mechanical and

thermal properties of PBMs along with their tribological behaviour. Since 2009, at polymer tribology group at the LTU, we have developed different carbon based multiscale thermoplastic composites for dry and water lubricated tribological condition. The studied thermoplastics are single matrix or polymer blend of PEEK, PTFE, PPS and UHMWPE. Reinforcement such as; short carbon fiber (SCF), different carbon based nanoparticles (nano-diamond and MWCNTs) as well as 2D materials i.e. graphene and graphene oxide derivatives and MoS2 have been studied. Exfoliation of the surface functionlaised nanoparticles carried out using wet chemistry and optimised ball-milling were used to physically blend the SCF with polymer matrix. The combined addition of nanoparticles and micro and macro reinforcement material in new polymer based multiscale composites has shown great promise in improving mechanical, thermal and tribological properties of the polymeric bearings. In spite of numerous advances, there still exist many challenges and research gaps that need to be addressed in the manufacturing of multiscale composites and using them in water lubricated application. The purpose of this plenary presentation is to briefly describe the manufacturing process in developing new multiscale thermoplastic composites, as well as discuss the relation between thermomechanical properties of these composites to the theribologcal performance for dry or/and water based lubricated contact within hydropower bearing.

References [1] H. Vadivel, A. Golchin and N. Emami “Tribological behaviour of carbon filled hybrid UHMWPE composites in water”. Tribology International Vol.124, 2018, p 169-177. 2018 [2] L. Melk and N. Emami, “Mechanical and thermal performances of UHMWPE blended vitamin E reinforced carbon nanoparticle composites”. Compos. Part B Eng., vol. 2146, pp. 20–27. 2018. ________________________________________ Corresponding author email: [email protected]

17

Presentationer

(Alfabetisk ordning efter 1:e forfattare)

19


The new SI and it’s impact on metrology in industry and research

F. Arrhén1

1Department of Metrology, RISE Research Institutes of Sweden

In 20th of May 1875, the treaty of the Metre was signed by 18 countries including Sweden. This event was a giant step forward for the globalization of both trade and research. From this date with the definition of the metre and the kilogram, we all had a common reference for measures for trade and science in the areas of length and mass.

Over the years several changes have been made to the practical system of units with the additions of units for time, electrical current, temperature, luminosity and in 1971 amount of substance.

Unfortunately, there are some problems built into the system as it has been designed. First, it still relies on one artefact, the kilogram prototype, the IPK which have been quite stable over its first 130 years.

Still, there is a deviation between the mass of the IPK and the average values of the official copies, showing a drift of about 50 μg over 100 years and so far, there have not been any possible method to determine whether this have been caused by change in mass of the IPK or the copies.

Another problem is the dependency of several other units on the IPK. The assumed instability of the IPK is forwarded to several other units including three base units.

Figure 1: Dependencies of base units To bring the SI up to today’s high requirements on

measurements and to ensure its stability and trying to foresee future changes, new definitions was decided in 2018 and realized May 20th, 2019. The new SI is not defined in terms of units but as the numerical values of several fundamental constants. From these constants the different units can be realized. The new definitions are as follows: • the unperturbed ground state hyperfine transition

frequency of the caesium 133 atom ΔνCs is 9 192 631 770 Hz,

• the speed of light in vacuum c is 299 792 458 m/s, • the Planck constant h is 6.626 070 15 × 10–34 J s,

• the elementary charge e is 1.602 176 634 × 10–19 C,

• the Boltzmann constant k is 1.380 649 × 10–23 J/K, • the Avogadro constant NA is 6.022 140 76 × 1023

mol–1, • the luminous efficacy of monochromatic radiation

of frequency 540 × 1012 Hz, Kcd, is 683 lm/W

Figure 2: The New SI Together with these new definitions, there are so

called “mise en pratique” on how to realize the units from the defined constants.

There are several benefits with this new principle of defining the system. • Since there will be several laboratories realizing

each base unit, the system will be more robust. • As the technology continues to develop, the

uncertainties of the realizations will improve. • New realizations of units based on the constants

and even realizations of other units than base units will be possible

• The numerical values of the chosen fundamental constants will no longer change.

• There will be possible for well-established laboratories to realize the units directly, removing the need for traceable calibrations of reference standards.

References [1] Stock et al, The revision of the SI—the result of

three decades of progress in metrology, Metrologia, 56, 1-14, (2019)

[2] Newell et al, The CODATA 2017 values of h, e, k, and NA for the revision of the SI. Metrologia, 55, L13 – L16, (2018)


20


MULTISCALE ANALYSIS OF QUARTZ SAND UNDER LOAD BY NEUTRON DIFFRACTION AND DIGITAL IMAGE CORRELATION

S.D. Athanasopoulos1, S.A. Hall1,2

1Divisiont of Solid Mechanics, Lund University, Lund, Sweden

2Lund Institute of Advanced Neutron and X-ray Science, Lund, Sweden

Since the first photoelasticity-based experimental

works on force transmission through glass particles in the 1950s (e.g., [1]), there have been several studies, using various methods, in the effort of characterising the distribution and development of forces/stresses throughout granular (geo-)materials (e.g., [2]). In recent years, Neutron Strain Scanning (NSS) has been successfully used as a new experimental tool to infer the force/stress distribution in granular media under load (e.g., [3]), by measuring the variations in interplanar distances of crystals (i.e., the crystallographic – or grain – strains).

The presented work considers a novel plane-strain experiment performed on a quartz sand specimen with the time-of-flight neutron strain scanner ENGIN-X, at the ISIS spallation source in the UK, see Figure 1. NSS provided the opportunity to measure over a two-dimensional grid of gauge volumes in the specimen, the averaged crystallographic strains of the constituent grains of each gauge volume, during mechanical loading and as a function of an applied boundary load. In parallel, photographs of the specimen in the plane-strain direction were being acquired continuously through a sapphire window, to derive the strain field of the specimen by Digital Image Correlation (DIC).

Figure 1: The experimental setup in ENGIN-X.

A: High resolution camera. B: Lighting system.

C: Stress rig. D: Beam defining optics system.

E: Detector. F: Connection of the apparatus to the

pressure controller.

From the NSS data, full-field mappings of the

microscale stress distribution were derived, see Figure 2–top, as well as single “micro-stress” average values for each of the produced mappings, see Figure 2–bottom. By associating traditional macroscale boundary measurements with the mesoscale DIC-derived strain field and the NSS-

inferred microscale stress distribution, a completely novel multiscale analysis for granular (geo-) materials has been enabled.

Figure 1: (Bottom) The applied axial stress and the

mean axial component of the micro-stress as

functions of the macroscopic axial strain.

(Top) The DIC-derived axial component of the total

strain field (left) and the NSS-derived mappings of

the axial component of the total micro-stress (right)

for load step 9.

References

[1] Wakabayashi, T., Photo-elastic method for determination of stress in powdered mass. Journal of the Physical Society of Japan, 5(5), 383-385 (1950)

[2] Hurley, R., Marteau, E., Ravichandran, G., Andrade, J.E., Extracting inter-particle forces in opaque granular materials: Beyond photoelasticity. Journal of the Mechanics and

Physics of Solids, 63(3), 251-254 (2014) [3] Hall, S.A., Wright, J., Pirling, T., Andò, E., Can

intergranular force transmission be identified in sand?. Granular Matter, 13(3), 251-254 (2011)

__________________________________________ Cor. author email: [email protected]

21


COMPUTATIONAL STUDY OF THE FLOW IN A DEVICE FOR NEONATALCONTINUOUS POSITIVE AIRWAY PRESSURE

N. Berg1, T. Drevhammar2, L. Prahl Wittberg1

1Linne Flow Centre & BioMEx, Department of Mechanics, KTH, Stockholm, Sweden2Department of Women’s and Children’s Health, Karolinska institutet, Stockholm, Sweden

Neonatal continuous positive airway pressure (CPAP) isa non-invasive method to support breathing in newbornswith lung disease. The lung pressure is maintained aboveatmospheric throughout the breathing cycle, which in turnmay increase the functional residual capacity and reducework of breathing [1]. CPAP treatment has been used ex-tensively for more than 40 years to treat preterm and terminfants with respiratory distress.

The CPAP can be generated with a variety of meth-ods, and the choice of method affects the required workof breathing. Here, the Infant Flow driver is considered,which has previously been shown able to generate a steadypressure throughout the whole breathing cycle [2]. Infantflow belongs to a class of devices relying on injection of ahigh-speed drive flow which, when decelerated, leads to arise in static pressure. The geometry is displayed in Figure1, and includes, apart from the drive flow inlet, an outletopen to the surrounding air and an interface to the new-borns nasal airway. Whilst this device has been success-fully applied to neonates, there are still complications re-sulting in patient stress and trauma, as well as an increasein the work required for exhalation. Moreover, the currentunderstanding of the physical processes in this class of de-vices is limited. The aim of this study is to bridge this gapusing computational fluid mechanics (CFD) to simulate theflow in the device during spontaneous breathing.

The flow in the NCPAP unit is assumed to be incom-pressible and the governing equations for an unsteadythree-dimensional flow are solved. Drive flow rates rang-ing from 20 m/s to 60 m/s were considered. A time-dependent flow rate was imposed at the nasal interfacesimulate spontaneous breathing. The Large eddy simula-tion (LES) methodology was applied, resolving the larger,energy-containing scales of the flow, whereas the smallerscales were modeled with the WALE subgrid scale model.The governing equations were discretized with a finite vol-ume scheme with second order accuracy in space and time.The required temporal and spatial resolution was deter-mined through a mesh convergence study.

The velocity field during inhalation and exhalation at adrive flow rate of 60 m/s is displayed in Figure 1. The re-sults confirm the previously suggested mechanism of ”flu-idic flip”, where the jet is deflected toward the outlet to theambient air during exhalation. This effect is further en-hanced at lower drive flow rates. Lower flow rates also leadto an increased jet length during inspiration. Moreover, theflow is highly turbulent and features periodic vortex shed-ding in the shear layers at the jet edge with a frequency of10-20 kHz (depending on flow rate), similar to the Kelvin-

Figure 1: Simulation domain (top), and average velocity magni-tude at selected cutplanes during peak expiration (mid-dle) and inspiration (bottom).

Helmholtz instability.The performance of CPAP devices depends strongly on

the details of the flow. The knowledge gained from the de-tailed simulations contribute to the understanding of CPAPfunction.

References

[1] Gupta, S., and Donn, S. M. Continuous positive air-way pressure: physiology and comparison of devices.In Seminars in Fetal and Neonatal Medicine, 21(3),204–211. WB Saunders (2016)

[2] Moa, G., Nilsson, K., Zetterstrom, H. and Jonsson,L.O. A new device for administration of nasal con-tinuous positive airway pressure in the newborn: anexperimental study. Critical care medicine, 16(12),1238–1242 (1988)

Corresponding author: [email protected]

22


BIOMECHANICAL MODELING OF AORTIC SURFACE DYNAMICS -IMPORTANCE AND APPLICATIONS

J. Bondesson1 and T. Lundh2

1Division of Dynamics, Chalmers University of Technology, Gothenburg, Sweden2Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden

According to the World Health Organization, 31% ofall deaths globally are caused by cardiovascular diseaseevery year, which made it the single largest cause ofdeath in 2016. Some vascular diseases are treated us-ing grafts, stents and stent grafts, implanted either throughopen surgery or by endovascular repair.

Accurate description of anatomies and dynamics ofvessels is crucial for understanding how morphology ischanged when diseased, and how native anatomy is af-fected by interventions and implants. In addition, this workaims to support improvement of surgical techniques andstent graft design.

A tool for automatic segmentation of arbitrary surfaceshas been developed by generalizing input capabilities (toinclude stereo lithographic format) and refining the tech-niques proposed by Lundh et al, schematically seen in fig-ure 1 [1]. Utilizing this improved Lagrangian cylindricalcoordinate system description a study on the importanceof surface curvature is presented. Along with this, so far,two additional studies utilizing these methods have investi-gated vessel compliance and endograft mal-apposition re-spectively.

Initial results from these three studies have been pre-sented at the Leipzig interventional course (LINC) in 2018[2-4], and also, a glimpse of an application with quantifi-cation of longitudinal surface curvature for an aortic endo-graft shown in figure 2 for systolic and diastolic states. Themethods show good coherence with analytical models, andforms a natural foundation for further development and ex-traction of clinically relevant measures for tubular anatomicstructures.

Figure 1: Schematic description of Lagrangian coordinate sys-tem definition for tubular anatomic structures. Left;longitudinal view with δ as a fiducial marker (origin), aset of centroids, C, corresponding contours, S, and cir-cumferential zero-points, γ. Right; Description of eachcoordinate along S in relation to C and γ using polarcoordinates, θ and r. Figure from [1].

Figure 2: Example of absolute longitudinal curvature quantifiedon the surface of a thoracic aortic endograft using in-vivo images for systolic (a,b,e) and diastolic (c,d,f)pressure states. g shows the point-wise curvature dif-ference between the two states. Figure from [1].

Starting off in the established framework and algorithms,future work will focus on additional method develop-ment for analysis of dissection morphology and also time-resolved studies with the use of several frames from in-vivopatient data. The overall aim is to further develop robustand intuitive models for extraction of more realistic bound-ary conditions for stent testing and to gain better under-standing of diseased anatomies. This will enable devicesand interventions to improve and ultimately give better out-comes for treated patients.

References

[1] Lundh T, Suh G-Y, Digiacomo P, Cheng CP. A La-grangian cylindrical coordinate system for character-izing dynamic surface geometry of tubular anatomicstructures, Med Biol Eng and Comput. https://

doi.org/10.1007/s11517-018-1801-8, 2018.[2] Bondesson J, Suh G-Y, Lundh T, Lee JT, Dake MD,

Cheng CP. A https://linc2018.cncptdlx.com/

media/125.pdf, 2018[3] Suh G-Y, Cabreros S, Kim J, Bondesson J, Lee

JT, Dake MD, Cheng CP. A https://linc2018.

cncptdlx.com/media/137.pdf, 2018[4] Frolich M, Suh G-Y, Bondesson J, Lee JT, Dake MD,

Cheng CP. A https://linc2018.cncptdlx.com/

media/124.pdf, 2018


23


A probabilistic model for multiple mechanism brittle fracture in ferritic steels

Magnus Boåsen, Carl F.O. Dahlberg, Jonas Faleskog, Pål Efsing

Department of Solid Mechanics, KTH, Stockholm, Sweden

The fracture toughness of low alloy steels depends

on several factors. Firstly, there is the strong temperature dependence which at low temperatures results in fracture associated with low fracture toughness and a significant scatter. At higher temperatures the fracture becomes progressively more ductile until no more brittle fracture is observed. Secondly, the geometrical size will affect the toughness, where a cracked small geometry will be tougher than a large. Thirdly there is the effect of the crack tip constraint which influences the otherwise self-similar stress field, thus resulting in higher fracture toughness.

Fracture testing of thermally aged weld metal from the decommissioned pressurizer of Ringhals unit 4 reveals two simultaneous failure mechanisms that are active at temperatures relevant for brittle fracture. Operating at 345 ˚C for a period of 28 years resulted in an increase of the yield strength as well as an increased ductile-to-brittle transition temperature, as compared to the as welded condition. Fracture testing has been carried out using specimens with different crack depths, in order to reveal constraint/large scale yielding effects related to the fracture toughness of the aged weld metal. The fracture surfaces of the tested specimens revealed that the lowest toughness specimens relate to intergranular initiation, while the higher toughness specimens relate to a mixture of intergranular and transgranular initiation of the brittle fracture. The resulting toughness distribution can be seen in Figure 1.

A weakest link model that incorporates the effects of multiple failure mechanisms has been created to model the experiments, such that further insight into the fracture toughness distribution can be established. It is assumed that both the intergranular and transgranular mechanisms are mutually exclusive and follow the weakest link assumption for failure, i.e. failure of one material point/sub-volume results in total failure of the entire structure. For the case of two failure mechanisms the weakest link expression assumes the form

A BA B

0 0

1 exp d ,fV

h hP V

V V

where the micromechanical relation to the initiation and propagation of the triggering mechanism comes in through the functions hA and hB. The model is viewed as an extension of the non-local weakest link model by Kroon and Faleskog [1]. The model correlates well with the experimental rank probabilities shown in Figure 1, it is able to capture both the wide distribution of fracture toughness as well as the strong constraint effect.

References

[1] M. Kroon and J. Faleskog, “A probabilistic model for cleavage fracture with a length scale - influence of material parameters and constraint,” International Journal of Fracture, vol. 118, pp. 99-118, 2002.

__________________________________ Corresponding author email: [email protected]

Figure 1 Rank probabilities of the thermally aged weld metal fracture tests. Specimens with crack depth to specimen width ratio a/W = 0.5, 0.1.

24


THE SIGNIFICANCE OF THE LONGITUDINAL SWELLING OF FIBERSON PAPER IN-PLANE HYGROEXPANSION

A. Brandberg1,2 and A. Kulachenko1,2

1Department of Solid Mechanics, KTH, Stockholm, Sweden2CD Laboratory for Fiber Swelling and Paper Performance, Graz University of Technology, Graz, Austria

Cellulose products are sensitive to moisture. The bondsbetween fibers in, for example, a sheet of copy paper dis-solve when exposed to water and the fibers contain hy-groscopic regions which readily absorb moisture causingswelling already at moderate changes to moisture content.The swelling of fibers begin at a smaller moisture changethan the opening of bonds and is anisotropic. Therefore,changes to the moisture content of the sheet induce me-chanical strains in the network which lead to in-plane (ex-pansion or shrinkage) and out-of-plane (curl and cockle)dimensional changes. Finding ways to control and managemoisture sensitivity is important in many applications suchas digital printing where exposure to moisture is unavoid-able during the deposition of ink.

A multi-scale model is implemented which allows thestudy of both in- and out-of-plane hygroexpansion prop-erties of the sheet at sizes large enough to be industriallyrelevant. The model consists of two scales: One smallscale where a finite element representation of each bondis created and solved, evaluating the effect that transverseswelling of one fiber has on the longitudinal strain of an-other, and a second where the entire sheet is modeled [1].

At the sheet scale fibers are modeled with beam ele-ments. The bonds between fibers are modeled as point-to-point penalty contacts. Additional strains caused by theincompatibility of the transverse and longitudinal hygroex-pansion of the crossing fibers is resolved at the bond scaleand then transfered to the fibers where they are added to theinelastic axial strains of the beam elements via superposi-tion. The magnitude of the transfered strains is found byenforcing strain energy parity between the two scales,

∫ w/2

−w/2

(∫

A

σ0εhdA

)dxe =

∫ Le

0

(∫

A

σ0εh

)dxe. (1)

Here, xe is the coordinate along the length of the ele-ment, w is the fiber width, σ0 is the current stress in the el-ement, εh is the strain at the bond due to transverse shrink-age of the other fiber,A is the cross-section area of the fiber,Le is the length of the element and εh is the resulting straindistribution along the length of the beam element.

When describing the bond as a plane structure, the trans-verse shrinkage of fibers contributes the majority of thehygroexpansion seen on the sheet level. However, whendescribing the bond as a three dimensional structure onlya fraction of the transverse strains are transferred and infact the transverse shrinkage accounts for only about halfof the total hygroexpansion of the sheet, as shown in Fig-ure 1. This confirms the analytical predictions of Uesaka

that the longitudinal fiber shrinkage contributes materiallyto the hygroexpansion coefficient of the entire sheet [2].

Figure 1: The influence of the longitudinal hygroexpansion offibers on the hygroexpansion coefficient of the entiresheet for varying degrees of structural anisotropy ascompared to the case when both longitudinal and trans-verse hygroexpansion are included. About half of βstems from the longitudinal hygroexpansion, and thisratio is not a function of the structural anisotropy of thesheet.

References

[1] Motamedian, H.R., Kulachenko, A., Simulating thehygroexpansion of paper using a 3D beam networkmodel and concurrent multiscale approach. Interna-tional Journal of Solids and Structures, 161, 23-41,(2019)

[2] Uesaka, T., General formula for hygroexpansion ofpaper. Journal of Materials Science, 29(9), 2373-2377, (1994)


25


LARGE EDDY SIMULATION AND AEROACOUSTICS OF HEATEDRECTANGULAR SUPERSONIC JETS

Song Chen1, Romain Gojon2, Mihai Mihaescu1

1Linne FLOW Centre, Department of Mechanics, KTH, Stockholm, Sweden2ISAE-SUPAERO, Universite de Toulouse, Toulouse, France

Recent years have seen a revival interest in civil super-sonic flights with a stringent standard on noise. Jet noise,as the main contributor to the ground-level noise duringtaking-off and landing, needs to be studied and understoodfor the purpose of noise reduction [1]. The jet from thehigh-performance engines of future civil supersonic aircraftis high-speed and high-temperature. Current scaled labo-ratory experiments are facing difficulties in long-durationtesting at high-temperature regimes. High-fidelity compu-tational aeroacoustics, without the constraint of tempera-tures, thus becomes a promising tool for this topic. Inthis work, implicit Large Eddy Simulations (LES) are per-formed to investigate the flow fields and acoustic character-istics of a rectangular supersonic jet.

The rectangular nozzle has an aspect ratio of 2.0, whichhas been tested at the University of Cincinnati. The jetsin this study are over-expanded with a Mach number ofaround 1.36. Four jet temperature ratios (TR) of 1.0,2.0, 4.0, and 7.0 are investigated, in which the maxi-mum jet total temperature is about 2100 K. In the im-plicit LES method, an artificial dissipation mechanism isused to damp the numerical oscillation and to representthe effect of small-scale turbulence [2]. Pre-calculatedtemperature-dependent thermal properties of air from thechemical equilibrium assumption are also implanted intothe flow solver to include the air disassociation effects inthe high-temperature regime. The direct computation of thenear-field acoustics by LES is complemented by far-fieldacoustics calculations via the Ffowcs Williams-Hawkingsacoustic analogy. The grid used for the CFD computationhas around 160 million number of cells, and the numericalcomputations are performed on PDC Beskow.

Numerical results show that the length of the jet coreregion of the highly-heated jet (TR = 7.0) is reduced byaround 30% as compared to the cold one. There are twosets of shock trains in this jet: one from the sharp nozzlethroat and the other from the nozzle lip. As shown by thenormalized mean pressure fields for different TRs in Figure1, the shock strength and structures are affected by the vari-ation of jet temperatures. Meanwhile, the convection ve-locity of the jet shear layer is significantly increased in hotjets, which yields a strong Mach wave radiation noise com-ponent propagating downstream in a cone shape. This canbe seen in Figure 2. In the far fields, the overall sound pres-sure levels are amplified in all directions by the high tem-peratures. Furthermore, in the downstream directions, thedirectivity of the Mach wave radiation component becomesdistinct from the large turbulence structure noise compo-nent in high-temperature jets.

Figure 1: Normalized mean pressure to show the shock structuresnear the nozzle lip: (a) TR 1.0; (b) TR 2.0; (c) TR 3.0;and (d) TR 7.0.

Figure 2: Snapshot of the instantaneous jet plume and radiatingacoustic fields for TR 7.0. [3]

References

[1] Romain Gojon, Christophe Bogey, and Mihai Mi-haescu, Oscillation Modes in Screeching Jets, AIAAJournal, 56, 2918-2924, (2018).

[2] Romain Gojon, Florian Baier, Ephraim Gutmark, andMihai Mihaescu, Temperature Effects on the Aerody-namic and Acoustic Fields of a Rectangular Super-sonic Jet, AIAA 2017-0002, (2017).

[3] Song Chen, Romain Gojon, and Mihai Mihaescu,High-Temperature Effects on Aerodynamic andAcoustic Characteristics of a Rectangular SupersonicJet, AIAA 2018-3303, (2018).

Corresponding authors:[email protected], [email protected]

26


A continuum-based model for precipitation strengthening applied to experiments on a maraging stainless steel Fe–15Cr–5Ni

P. Croné, J. FaleskogDepartment of Solid Mechanics, KTH, Stockholm, Sweden

The current work, which builds on the work presented in [1], focuses on predicting the macroscopic mechanical properties of particle reinforced steels by the development and use of a suitable continuum model. More precisely, a small strain, isotropic, strain gradient plasticity theory is employed to predict strengthening and hardening in the material.

The underlying physical idea is that the material microstructure is dominated by precipitated particles, either impenetrable or not, depending on their size, which act as obstacles to bulk dislocation movement and hence will cause additional dislocation pile-ups. For the crystal lattice to accommodate the resulting gradients in plastic strain, additional, so called, geometrically necessary dislocations (GNDs) are nucleated, the density of which, has been shown to be proportional to the gradient of plastic strain. The nucleation of GNDs increases the total dislocation density and causes additional strengthening in the material. At this point, it becomes obvious that the problem is dependent upon some microstructural length scale, such as the average distance between precipitated particles. The general trend is clear, i.e. that smaller is stronger, which is supported by experiments.

Without having to resort to simulations using crystal plasticity or dislocation dynamics theories, the isotropic continuum strain gradient theory offers a versatile and relatively straight forward manner to study these problems of size dependent plasticity.

To study the relative roles of penetrable- and impenetrable particles on the macroscopic hardening, an imposed distribution of particle size, based on measurements on the current steel is employed. Depending on ageing time of the specimens, different distributions, ranging from those dominated by large(impenetrable) particles to those characterized by small(penetrable) particles, may be used. Using a new model for the interfacial energies at the particle-matrix interface, which has a saturating behavior with respect to the density of present dislocations, along with experimental flow curves for the matrix material at hand, it is the goal of the current work to obtain quantitative predictions on both strengthening and hardening through FEM simulations on a suitable RVE.

References [1] Asgharzadeh,Mohammadali. Strain Gradient

Plasticity Modelling of Precipitation Strengthening. Diss. KTH Royal Institute of Technology, 2018.


27


FRACTIONAL STRAIN-GRADIENT PLASTICITY

C.F.O. Dahlberg1 and M. Ortiz2

1Department of Solid Mechanics, KTH, Stockholm, Sweden2Division of Engineering and Applied Science, California Institute of Technology, Pasadena, USA

Prompted by the mounting experimental evidence point-ing to a gaping discrepancy between the size-dependentyield strength of metals and predictions from conventionalstrain-gradient plasticity (SGP), e. g. [1, 2, 3], we havedeveloped [4] a newfractional strain-gradient theory ofplasticity (FSGP) that uses fractional derivatives of plas-tic strain as a means of quantifying the inhomogeneity ofplastic deformation.

A common form of the size dependent yield stress canbe written

σy = σ0

[1 +

(ℓ

h

)α], (1)

whereσ0 is the large scale yield stress in uniaxial tension,ℓis a material length scale,h is an appropriate size measureof the plastically deforming region andα is a scaling expo-nent. Conventional SGP almost invariably predicts a sizescaling exponentα = 1 that, in many cases, grossly over-estimates the experimentally-observed values, e.g. figure 1where the scaling isα ∼ 0.2.

Figure 1: Shear flow stress as a function of thickness for Cu lay-ers. A discrepancy between power law fits and SGPmodel output are indicated by solid and dashed lines,respectively. Insert shows SEM image of experimen-tal setup. From Muet al. [2], figure 4(a), courtesy ofCambridge University Press.

We take this discrepancy to suggest that the differentialstructure of conventional strain-gradient plasticity is overlystiff and proceed to relax the excessive rigidity by recourseto fractional plastic-strain gradients. Specifically, by allow-ing the free energy to depend on a fractional derivatives ofstrain, we show that the size-scaling discrepancy betweenconventional SGP and the experimental data in [2, 3] isresolved. When applied in the shear layer configuration,

the theory predicts a size scaling relation with exponentαequal to the fractional order of plastic strain-gradient differ-entiation. Through this identification, the observed exper-imental scaling can be exactly matched by an appropriatechoice of fractional differential order.

The form of the non-local fractional plastic strain-gradient contribution to the free energy is explicitly givenby a double-integral representation and its fractional differ-ential character is set simply by an appropriate choice ofexponents in the interaction kernel.

When applied in the shear layer configuration the stressat yielding is

τy = τ0

[1 +

(ℓ

h

)s], (2)

where the parameter0 ≤ s ≤ 1 is the fractional orderof plastic strain-gradient differentiation. The relaxed scal-ing law (2) can be made to match the observed scaling law(figure 1) simply by takings = α i. e., by identifying theorder of differentiation with the observed scaling exponent.As already noted,α ∼ 0.2 for polycrystalline Cu which,according to the identification suggests that polycrystallineCu is strongly ‘fractional’, i. e., the order of differentia-tion in the nonlinear energy is much smaller than1. Oversuch range of parameters, fractional strain-gradient plastic-ity represents a large quantitative and qualitative correctionwith respect to conventional strain-gradient plasticity.

References

[1] Evans, A.G. and Hutchinson, J.W., A critical assess-ment of theories of strain gradient plasticity.Acta Ma-terialia, 57, 1675–88, (2009)

[2] Mu, Y., Zhang, X., Hutchinson, J.W. and Meng,W.J. Dependence of confined plastic flow of polycrys-talline Cu thin films on microstructure.MRS Commu-nications Research Letters, 20, 1–6, (2016)

[3] Mu, Y., Zhang, X., Hutchinson, J.W. and Meng, W.J.Measuring critical stress for shear failure of inter-facial regions in coating/interlayer/substrate systemsthrough a micro-pillar testing protocol.Journal ofMaterials Research, 32, 1421–31, (2017)

[4] Dahlberg, C.F.O. and Ortiz, M., Fractional strain-gradient plasticity.European Journal of Mechanics -A/Solids, accepted, avaliable online, (2019)


28


TRANSITION IN A SWEPT-BOUNDARY LAYER SUBJECT TO SURFACEROUGHNESS AND FREE-STREAM TURBULENCE

L. De Vincentiis1, D. Henningson1, A. Hanifi2

1Department of Mechanics, KTH, Stockholm, Sweden

Surface imperfections such as gaps, steps or roughnesscan cause premature transition from laminar to turbulentflow in boundary layers. Studying this problem for a sweptwing has a great relevance since modern aircrafts are usu-ally equipped with such.In the present work, the combined effects of an isolatedroughness element together with the presence of free-stream turbulence on a swept-wing boundary layer are in-vestigated numerically. This problem has been addressedthrough an experimental campaign (Orlu et al., 2015)within the European project RECEPT. In these experi-ments, a cylindrical roughness element was placed on theupper surface of a 35-degree swept wing at a negative angleof attack. For different heights, diameters, free stream tur-bulence levels and incoming velocities triggering of transi-tion behind the roughness was monitored by means of anIR camera.Here, the problem is addressed by means of direct numer-ical simulations using the spectral element code Nek5000.In a preliminary step, Reynolds-Averaged Navier-Stokes(RANS) simulations are performed following the setup ofthe experiment. These simulations are used to define theboundary conditions for the direct numerical simulation,where a smaller computational domain is used.In absence of free-stream turbulence, depending on theheight of the cylinder, it is possible to observe either thepresence of stationary crossflow vortices behind the rough-ness element which does not trigger the transition or an un-steady solution where transition is clearly visible. Thesecases were further studied using an impulse-response anal-ysis. Those cases in which transition takes place behindthe roughness were found to be globally unstable. In thosecases which exhibit a steady laminar solution, the distur-bances grow behind the roughness but are then damped andconvected downstream.In agreement with the observations in the experiments, thescenario is strongly modified once the free-stream turbu-lence is included in the simulations. In order to do soFourier modes with random phase shift are superimposed atthe inlet. Even for a very low free-stream turbulence level(0.03%), it is possible to observe growing disturbances be-hind small roughness elements that form turbulent spotswhile traveling downstream. These are then advected outfrom the computational domain. If the level of free-streamturbulence is increased one order of magnitude, a clearlaminar-turbulent transition takes place behind the rough-ness.

(a)

(b)

(c)

Figure 1: Isosurfaces of spanwise velocity coloured by stream-wise velocity for the steady solution (a), the globallyunstable solution (b) and the solution for high level offree-stream turbulence (c)

References

[1] R. Orlu, N. Tillmark, P. H. Alfredsson, Measuredcritical size of roughness element, RECEPT projectTechnical Report TR D1.14, (2015)


29


AN A POSTERIORI ERROR ESTIMATOR FOR NUMERICAL MODELREDUCTION IN COMPUTATIONAL HOMOGENIZATION OF POROUS

MEDIA

Fredrik Ekre 1, Fredrik Larsson1, Kenneth Runesson1, Ralf Janicke1

1Department of Industrial and Materials Science, Chalmers, Gothenburg, Sweden

Multiscale methods are of high interest in the engineer-ing community due to their ability to predict the overallresponse at a suitable macroscale, while accounting for thestructure on the underlying scales. One standard approachis the so-called “finite element squared” (FE2) procedure,where a new boundary value problem is defined on a Repre-sentative Volume Element (RVE) in each quadrature pointof the (macroscale) mesh. The RVE problem is solved inorder to obtain the effective response of the material andis thus replacing the otherwise needed macroscale consti-tutive relation of empiric character. It is known that theFE2 strategy can be computationally intractable, in particu-lar for fine macroscale meshes in three dimensions. There-fore it is of interest to reduce the cost of solving the indi-vidual RVE problems by introducing a reduced basis, heredenoted Numerical Model Reduction (NMR). It is obviousthat the richness of the reduced basis will determine theaccuracy of the solution, which calls for error control. Sev-eral methods for estimating the error for a reduced basisapproximation have been developed. One example of anerror estimator for two-scale transient linear heat flow isEkre et al. [1].

In this presentation we consider application of NMR tohomogenization of quasi-static poroelasticity, see Janickeet al. [2], where the displacement field of the solid skeleton,and the pressure field of the liquid are the unknowns. Thereduced fields are defined as the sum of NR modes, i.e. thepressure field p(x, t) is decomposed as

p(x, t) ≈ pR(x, t) =

NR∑

a=1

pa(x)ξa(t), (1)

where pa(x) are the pre-computed spatial modes and ξa(t)are the unknown time dependent coefficients. The reduceddisplacement field is defined in a similar fashion. Usingthe reduced fields for the solution results in a system ofsize NR, which typically is much smaller than the original,fully resolved, problem.

The spatial modes pa(x) are constructed by employ-ing Proper Orthogonal Decomposition (POD) on the RVEproblem. Thus, we compute the modes based on “snap-shots” from training computations on the fully resolvedproblem. Examples of two such pressure modes are shownin Figure 1 for the situation of a water-saturated patch in-side a air-saturated porous rock. Considering linear elas-tic response for the solid skeleton, the displacement fieldspertinent to each pressure mode can be precomputed in anoff-line stage, guaranteeing equilibrium for the reduced ap-proximation.

Figure 1: Two pressure modes computed with POD for an RVE.

It is obvious that the use of the reduced basis introducesan error which is of interest to control. We present a strat-egy for estimating the error due to NMR, thus extendingthe work by Janicke et al. [2]. In this work we ignore thethe error from time- and space-discretizations, by consid-ering the fully resolved problem to be exact, and introducean estimator purely for the “NMR”-error. In particular weaim for guaranteed explicit bounds on the error both in (i)a global norm and (ii) “quantities of interest”, within therealm of goal oriented error estimation. The basis of theerror estimation is the construction of a symmetric formof the space-time variational format, from which we definea norm. Considering a linear model problem, the NMR-induced error in this norm can be bounded explicitly. Fur-thermore, based on this norm, explicit bounds can be com-puted for linear functionals of the output, representing user-defined quantities of interest.

Finally, we present numerical results for a single RVEproblem in three spatial dimensions. In particular, weinvestigate the efficiency of the NMR procedure and thesharpness of the error bounds.

References

[1] Ekre, F., Larsson, F., Runesson, K. On error con-trolled numerical model reduction in FE2-analysisof transient heat flow. Int J Numer Methods Eng.2019;136. https://doi.org/10.1002/nme.6041

[2] Janicke, R., Larsson, F., Runesson, K. and Steeb,H. Numerical identification of a viscoelastic substi-tute model for heterogeneous poroelastic media bya reduced order homogenization approach. Comput.Methods Appl. Mech. Engrg., Vol. 298, pp. 108-120,(2016). http://dx.doi.org/10.1016/j.cma.2015.09.024


30


NUMERICAL MODEL REDUCTION FOR COMPUTATIONALHOMOGENIZATION OF HETEROGENEOUS POROUS MEDIA

F. Ekre, R. Janicke, F. Larsson, K. RunessonDepartment of Industrial and Materials Science, Chalmers University of Technology, Goteborg, Sweden

We consider the model problem of heterogeneous porousmedia. To this end we seek to solve for the displacementsof the solid skeleton and pressure in the pore-fluid from thefollowing system of partial differential equations:

− σ ·∇ = b (1)Φ +w ·∇ = 0 (2)

Eq. (1) pertains to quasi-static equilibrium, where σ and bare the total Cauchy stress an imposed body force, respec-tively. Mass conservation of the fluid phase is ensured inEq. (2), where Φ is the stored fluid and w is the (Darcy-type) seepage. We shall assume that the constitutive rela-tions have highly heterogeneous parameters in space.

Using the framework of Variationally Consistent Ho-mogenization (VCH), cf. [1], a two-scale finite ele-ment formulation can be derived for the problem, wherebyan ”effective” homogeneous problem is obtained on themacroscale and the underlying scale is resolved on Repre-sentative Volume Elements (RVEs). The VCH frameworkallows for choosing different scale transitions of the un-known fields. In the case of formulating a macroscopic dis-placement field, the effective problem reads as follows:

− σ ·∇ = b (3)

Eq. (3) represents macroscopic equilibrium, where thestress response σ is evaluated from finite element analy-sis of the system given by Eqs. (1) and (2) inside an RVE.As a result from the underlying fluid seepage, the effectiveresponse can be shown to be that of apparent viscoelastic-ity.

Introducing, in addition to a macroscopic displacementfield, a macroscopic pore pressure gives rise to a macro-scopic (homogeneous) counterpart of Eqs. (1) and (2). Inthat case, the macroscale properties Φ and w also becomethe result of a suitably formulated RVE-problem.

The two-scale formulations described above give riseto a so-called finite element squared (FE2) formulations,where each quadrature point on the macroscale is coupledto an individual FE-problem on an RVE. For a transientproblem, this relation cannot be upscaled a priori, even ifthe equations are linear.

Although more efficient than solving the original - fullyresolved - problem, the computational effort for solving anFE2 problem is extremely high. It is however possible toobtain a vast speed-up by considering Numerical ModelReduction (NMR). Following previous work [2], we usea reduced basis on the RVE obtained from Proper Orthogo-nal Decomposition (POD). Considering a linear problem, itsuffices to construct a basis for the pressure fields. In Figure

1, two such pressure modes are illustrated for an RVE of aporous media with impermeable inclusions (excluded fromthe figure). The pertinent displacement fields can be solvedfor in the off-line stage. In solving the two-scale problem,during the on-line stage, the relations for the macroscopicfluxes can be expressed in terms of pre-computed parame-ters. In this, the coefficients of the reduced pressure basistake the roll of internal variable on the macroscale.

Finally, although numerical model reduction as de-scribed above is highly efficient, it is imperative to retaina required accuracy relative to the unreduced FE2 problem.To this end, an a posteriori error estimator for the NMRerror is developed for the present case. The estimator is afurther development from previous results for the heat-flowproblem [3].

Numerical examples with application to geomechanicsresolved in three spatial dimensions investigate the behav-ior of the proposed procedure in terms of accuracy, robust-ness and computational efficiency.

Figure 1: Example pore-pressure modes in a porous media withimpermeable inclusions (excluded from the figure).

References

[1] Su, F., Larsson, F., Runesson, K., Computationalhomogenization of coupled consolidation problemsin microheterogeneous porous media, Int. J. Numer.Meth. Eng., 88, 1198-1218 (2011)

[2] Janicke, R., Larsson, F., Steeb, H., Runesson, K.,Numerical identification of a viscoelastic substitutemodel for heterogeneous poroelastic media by a re-duced order homogenization approach, Comp. Meth.Appl. Mech. Eng., 298, 108-120 (2016)

[3] Ekre, F., Larsson, F., Runesson, K., On error con-trolled numerical model reduction in FE2-analysis oftransient heat flow, Int. J. Numer. Meth. Eng., In press(2019)


31


SIMULATION OF FAILURE AT DIFFERENT SCALES INFIBER-REINFORCED COMPOSITE MATERIALS USING A PHASE-FIELD

APPROACH TO FRACTURE

Juan Jose Espadas Escalante§ and Per IsakssonDivision of Applied Mechanics, Uppsala University, Uppsala, Sweden

Fiber-reinforced composite materials have been used fordecades in structural applications where a lightweight isof concern. Industrial prototyping demand reliable modelscapturing their mechanical behavior. Modeling the behav-ior of composite materials is a challenging task due to thedifferent scales and complex mechanisms involved duringthe failure process [1].

Progressive failure in composite laminates is typicallymodeled with the use of local continuum damage mod-els. Although they provide an overall idea of structuralintegrity, they can struggle to represent cracks accurately[2]. Thus, more sophisticated techniques are often neededrepresenting cracks either in a discrete manner by consider-ing strong discontinuities [3] or in a continuum manner byconsidering cracks as diffuse topologies. Phase-field (PF)approaches to fracture belong to the latter category but canbe conceived also as a type of enhanced gradient damagemodel [4]. They are based on the variational format of theGriffith’s criterion using a critical energy release rate Gc.The total potential energy,

Π =

∫

Ω

ΨdΩ

︸︷︷︸strain energy

+

∫

Γ

GcdΓ

︸︷︷︸fracture energy

, (1)

represents the contribution of the elastic and fracture ener-gies on a body with domain Ω and evolving internal discon-tinuities Γ. Crack growth is automatically determined bythe minimization of (1), which is an advantage over otherpopular techniques since tracking of cracks or the use of ad-hoc criteria is avoided. PF approaches are capable of cap-turing complex crack growth scenarios [5], and have beenrecently adopted in the simulation of failure in compositesusing the finite element method [6, 7].

Some results of using a PF fracture theory to model fail-ure in composite laminates at the micro-, meso- and macro-scales (coupon level) will be presented, Fig. 1. At themicro-scale, cracks developed in a unidirectional ply sub-ject to transverse tension and transverse compression areaddressed. At the meso-scale, transverse cracking kineticsdeveloped in woven composite laminates are explored. Fi-nally, at the coupon level, the strength of quasi-isotropicnotched laminates are studied with special focus on pre-dicting hole size effects.

PF approaches to fracture are to date among state-of-art techniques to model fracture development and conse-quently, they are not well established yet as an industrialstandard. Results support the fact that PF fracture theoriesare feasible to model complex failure mechanisms observedexperimentally in composite laminates at different scales.

meso-scale (mm-cm)

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micro-scale (µm-mm)

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Cracks developed under transverse tension and compression in unidirectional plies

macro-scale (cm-m)

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Transverse cracking kinetics in woven composite laminates

Strength of notched laminates

Figure 1: Failure of composites at different scales.

References[1] Camanho P.P., Hallet S.R. Numerical modelling of

failure in advanced composite materials. Ed. ElsevierScience, 2015.

[2] Gorbatikh L., Ivanov D., Lomov S., Verpoest I. Onmodelling of damage evolution in textile compos-ites on meso-level via property degradation approach.Composites part A 2007; 38: 2433-2442.

[3] Moes N, Dolbow J, Belytschko T. A finite elementmethod for crack growth without remeshing. Int. J.Num. Meth. Eng. 1999; 46: 131-150.

[4] de Borst R., Verhoosel C. Gradient damage vs phase-field approaches for fracture: similarities and differ-ences. Comp. Meth. Appl. Mech. Eng. 2016; 312: 78-94.

[5] Pham K.H., Ravi-Chandar K., Landis C.M. Experi-mental validation of a phase-field model for fracture.Int. J. Fract. 2017; 205:83-101.

[6] Quintanas-Corominas A., Reinoso J., Casoni E.,Turon A., Mayugo J.A. A phase field approach to sim-ulate intralaminar and translaminar fracture in longfiber composite materials. Compos. Struct. 2019. Inpress.

[7] Espadas-Escalante J.J., van Dijk N.P., Isaksson P. Aphase-field model for strength and fracture analysesof fiber-reinforced composites. Compos. Sci. Tech-nol. 2019; 174:58-67.

§ Corresponding author: [email protected]

32


INTERSCALE TRANSPORT IN WALL-BOUNDED TURBULENT FLOWS

G. Ferrante1,3, A. Morfin1,3, T. Kawata1, 2, R. Orlu1, P. Schlatter1, P. H. Alfredsson1

1Linne FLOW Centre, KTH Mechanics, Royal Institute of Technology, Stockholm, SE-100 44, Sweden2Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510, Japan

3Department of Industrial Engineering, Alma Mater Studiorum,Universita di Bologna, 47100 Forlı, Italy

Couette, pipe, channel, and zero-pressure gradient(ZPG) turbulent boundary layer (TBL) flows have clas-sically been considered as canonical wall-bounded turbu-lent flows since their near-wall behavior in viscous unitsis generally considered to be universal, i.e., invariant ofthe flow case and the Reynolds number. Nevertheless, theidea that large-scale motions, being dominant in regionsfurther away from the wall, might interact with and in-fluence small-scale fluctuations close to the wall has notbeen disregarded. This view was mainly motivated dueto the observed failure of collapse of the Reynolds normalstresses in viscous scaling. While this top-down influencehas been studied extensively over the last decade, the ideaof a bottom-up influence (backward energy transfer [1]) isless examined. An exception is the recent experimentalwork by Kawata and Alfredsson [2] in a Couette flow at lowReynolds numbers. They investigated the interscale inter-actions by filtering the fluctuating part of the velocity fieldat different wave numbers and computing some of the termsin the scale-by-scale transport equation for the Reynoldsstress component -〈uv〉. Then, they analyzed the gain andloss of the Reynolds-stress intensity at each length-scale asa result of different physical effects: production (transferfrom the mean flow), redistribution driven by the fluctuat-ing pressure field, viscous dissipation, spatial viscous andturbulent transport as well as interscale transport.

The results from [2] are shown in Fig.1 (a-b). Theyshow the interscale and spatial transport terms (tr−uv anddt−uv respectively) of the transport equation of the -〈uv〉co-spectrum E−uv at Re = 2000 (Reτ = 108). In a) theblue regions show a loss of -〈uv〉 content at small valuesof the spanwise wavelength and a gain at larger scales isidentified by the red/yellow areas. This trend is observedthroughout the whole channel height, but an intense peak islocated close to the wall. A redistribution of the Reynoldsshear stress from the near-wall region to the channel centreis observed for both large and small scales in b), showingthe scale-by-scale turbulent spatial transport of −〈uv〉.

In the present work, the terms of the E−uv transportequation are obtained from Direct Numerical Simulation(DNS) data of a Couette flow atRe = 2000. The spectra oftr−uv and dt−uv are reported in fig. 1 c) and d), respectively.These two terms are in qualitative agreement with the ex-perimental results (a-b). Still, discrepancies are apparent inthe amplitudes, which are higher in the DNS compared toexperiments, possibly due to measuring difficulties in thenear-wall region. Note that the high peaks close to the walland out of the measurement domain (white band) cause thecontour colors in (c-d) to saturate since the same scale as in(a-b) is used. Based on the qualitative agreement between

the experimental and numerical results conveyed here, theaim of the present work is to extend the analysis by Kawataand Alfredsson to canonical wall-bounded flows and assessits Reynolds-number dependence. Data from a TBL [3]covering an order of magnitude in Reynolds number willbe utilized thereby helping us to address two open ques-tions: Is the inverse interscale transport of the Reynoldsshear stress a common feature of near-wall turbulence andif so, what is its Reynolds-number dependence?

References

[1] A. Cimarelli and E. de Angelis, The physics of energytransfer toward improved subgrid-scale models. Phys.Fluids. 26, 055103 (2014).

[2] T. Kawata and P. H. Alfredsson, Inverse interscaletransport of the Reynolds shear stress in plane Cou-ette turbulence. Phys. Rev. Lett. 120, 244501 (2018).

[3] G. Eitel-Amor, R. Orlu and P. Schlatter, Simulationand validation of a spatially evolving turbulent bound-ary layers up to Reθ = 8300. Int. J. Heat Fluid Flow.47, 57–69 (2014).


Figure 1: Space-wavelength diagrams of a) and c) scale by scaleinterscale transport kztr−uv and b) and d) turbulentspatial transport kzdt−uv of the premultiplied Reynoldsshear stress co-spectra kzE−uv . The values are scaledby u3

τ/h. DNS and experimental results are reportedin the upper and lower panel, respectively. The blackdashed line indicates the channel centre y/h = 0.

33


CFD STUDY OF THE FLOW IN A RETURN CANNULA

Francesco Fiusco1, L. Mikael Broman2,3, Lisa Prahl Wittberg1

1Linne FLOW center & BioMEx, KTH Mechanics, Stockholm2ECMO Centre Karolinska, Solna

3Department of Physiology and Pharmacology, Karolinska Institutet, Stockholm

Cannulation is common in several medical methods, for example when blood needs to be removed from or returned to the circulation. In this work, the focus is on return can-nula flow associated with Extracorporeal Membrane Oxy-genation (ECMO). ECMO is a life-saving therapy for the critically ill where the function of the heart and/or the lungs needs to be either supported or replaced. The ECMO cir-cuit is composed of a drainage and a return cannula, as well as an oxygenator and tubing with a blood pump driving the flow. D ue t he exposure t o n on-physiological fl ow condi-tions, there is an increased risk for thrombosis in which shear stresses acting on the blood are of importance as they can induce platelet activation or red blood cells damage. Thus, understanding the properties of cannulated flows is important to assess and mitigate the thrombogenicity of the ECMO circuit [1].

Regarding the cannulae, geometrical parameters such as the shape of the tip, insertion angle and presence of lateral orifices alter the flow structures and mixing properties. This works aims at characterizing the flow properties of the can-nula represented in Figure 1, which due to manufacturing processes has a sharp restriction near the tip. The cannula is placed in a vessel of larger diameter (18.3 mm) charac-terized by a co-flow w ith a r ate o f 1.3 L /min. T he can-nula has a diameter of 3.44 mm and has a flow rate equal to 2.6 L/min. The total length of the vessel is 1 m, while the cannula is 50 cm long; the walls of both the cannula and the vessel are rigid. These conditions come from an ex-perimental setup used for the validation of the simulation and correspond to a Reynolds number of the jet equal to Re ≈ 7000. The baseline case simulation is carried out using water to enable comparison with experimental data. Moreover, using a Newtonian blood analog fluid a s well as a non-Newtonian blood viscosity model will be investi-gated and compared with the simulations using water.

Figure 1: Detail of the mesh

Large Eddy Simulations (LES) with WALE subgridmodel were carried out using the Star-CCM+ R© solver. The

flow was simulated for 5 s of physical time. The resultsshow the development of a Kelvin-Helmoltz instability inthe shear layer due to the mixing of the flow exiting thecannula and the co-flow; this results in recirculation re-gions being created between the cannula jet and the wallsdownstream of the cannula tip, as shown in Figure 2. Thesezones influence the mixing properties of the flow (e.g. par-ticles suspended in the flow would have a higher residencetime in those regions).

Figure 2: Recirculation bubbles

References

[1] Fuchs G., Berg N., Broman L.M., Prahl Wittberg L.,Flow-induced platelet activation in components of theextracorporeal membrane oxygenation unit. Scientificreports, 8, 13985, (2018)


34


RECENT PROGRESS ON FREE-STREAM TURBULENCE INDUCEDTRANSITION

Jens H. M. FranssonDepartment of Mechanics, KTH, Stockholm, Sweden

Today, we cannot honestly say that we are capable to ac-curately predict the transition location in a boundary layer subject to free-stream turbulence (FST). Not even in the simplest boundary layer flow, namely the one developing over a flat plate under zero-pressure gradient condition, we are successful. There are numerous empirical relations for predicting the transition location in the presence of FST, mostly only based on the turbulence intensity (T u) as in-put, but none with an accuracy better than typically 65% for all T u. Thus, in a sense we have failed in delivering a sim-ple and reliable transition prediction model for engineering predictions, which takes both T u and the FST characteris-tic length scale into account in a physically correct way.

Free-stream turbulence and its effect on boundary-layer transition is an intricate problem. Elongated streamwise streaks of low and high speed are created inside the bound-ary layer and their amplitude and spanwise wavelength are believed to be important for the onset of transition. The streaks are unsteady and their amplitude grows with the square root of the downstream distance until the appear-ance of the first turbulent spots. The spanwise wavelength is often said to adopt to the boundary-layer thickness, giv-ing streaky structures of aspect ratio one after some adap-tation length [1]. Furthermore, the transitional Reynolds number is often simply correlated with T u and the char-acteristic length scales of the FST are often considered to have a small influence on the transition location.

Here, I present new analysis of the results from a large experimental measurement campaign [2], where both the T u and the characteristic length scales of the FST are varied. The flat plate boundary-layer experiments were performed in the Minimum-Turbulence-Level wind tun-nel, known as the MTL facility, which is located in the Odqvist Laboratory at KTH. A five metre long flat plate was mounted inside the test section and to minimize the leading edge pressure gradient effect, a trailing edge flap with a 6 angel along with an asymmetric leading edge was used. The wind-tunnel ceiling contains 6 adjustable spanwise sections allowing a zero pressure gradient bound-ary layer to develop over the plate. The generation of FST was accomplished by means of turbulence generating grids of different mesh widths and bar diameters. Most of the grids were active in the sense that they could be pressurised with the feature of regulating the strength of small upstream directed jets allowing to adjust the T u level in a quick and easy way for a given geometrical grid. Totally eight dif-ferent grids were used giving, in total, 42 unique FST con-ditions, which have been studied and their effect on bound-ary layer transition analyzed. A dual-sensor hot-wire probe (X-type) was used to measure two velocity components simultaneously in order to characterize the

FST in terms of its intensity, all characteristic length scales and turbulence anisotropy. Inside the boundary layer a hot-wire probe of single type was used. The transition location was determined with a user independent intermittency program [3].

The results show that the integral length scale (Λx) of the FST affects the transition location differently depending on T u in a given boundary layer. On the one hand, for small T u an increase in Λx advances transition, in agreement with established results. On the other hand for large T u an increase in length scale postpones transition. In the present experimental setup both trends have been observed and an hypothesis for the trend change is formulated. In addition, we believe that one has overlooked the significance of Λx in the transition process. For low T u levels a 12% increase of Λx can advance the transition point by as much as 35%, and for high T u levels an 18% increase of Λx can delay transition by 22%. These results contradict previous results that the streaks adopt to the boundary layer thickness independent of the FST characteristics, i.e. if the streamwise streaks are important for the transition onset, they are also likely to be affected by the FST. Our measure-ments show that the aspect ratio of the streaky structures correlates with a FST Reynolds number and that the aspect ratio can change by a factor of two at the location of transi-tion.

References

[1] Matsubara, M. and Alfredsson, P. H., (2001) Dis-turbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech., vol. 430, pp. 149-168.

[2] Shahinfar, S., (2011) Transitional boundary layerscaused by free-stream turbulence. Licentiate thesis,KTH, Stockholm, TRITA-MEK Tech. Rep. 2011:02.

[3] Fransson, J. H. M., Matsubara, M. and Alfredsson,P. H., (2005) Transition induced by free stream turbu-lence. J. Fluid Mech., vol. 527, pp. 1-25.


35


STRATOFLY

C. Fureby1

1The Swedish Defence Research Agency, Stockholm, Sweden

STRATOFLY, Stratospheric Flying Opportunities for High-Speed Propulsion Concepts, is a H2020 project investigating different aspects of the feasi-bility of high-speed civilian air traffic. Due to the expected growth in the air-traffic during the next decades, the need to better connect the continents with reduced emissions requires novel approaches for long-range flights. Previously, [1], it has been identified that the stratosphere provides an unex-ploited air space suitable for high-speed (hyperson-ic) flight trajectories. This, however, puts new and challenging requirements on not only the flight ve-hicle and its propulsion system but also on many other aspects ranging from the passenger experience to flight routing, and how the climate in the strato-sphere may be affected.

The STRATOFLY project, [2], is coordinated by the Politecnico di Torino, POLITO, and involves an additional nine research organisations CIRA, ON-ERA, VKI, DLR, Fundacion de la Ingenieria Civil De Galicia, ONERA, CNRS, NLR, FOI and TUHH, from seven countries. The project runs from mid-2018 until mid-2021. The research objectives are to: (i) decrease the flight time of long-range civil flights by using a new flight vehicle concept, (ii) identify hypersonic flight trajectories in the stratosphere, (iii) decrease emissions and noise and minimize the cli-mate impact from flying the stratosphere, (iv) inves-tigate the passenger experience, (v) evaluate the sus-tainability of operability of hypersonic vehicles and (vi) increase the maturity level of enabling technol-ogies for future reusable launchers.

The project is multi-disciplinary and combines technological and operative issues. Crucial techno-logical issues for the success of the hypersonic vehi-cle include an innovative propulsion system based on a turbine based combined cycle duel mode ram-jet, new structural multi-bubble configuration, and novel systems for the thermal, heat and energy man-agement. Fundamental operative issues are the re-duction of emissions, noise and the sustainability of unexplored trajectories, guaranteeing the safety lev-els necessary for passenger transport.

The project builds on the LAPCAT-II MR2.4 flight vehicle, [3], an artist’s impression of which is presented in figure 1. The vehicle layout is based on an aerodynamically efficient wave rider design sup-porting an air-intake that feeds an elliptically shaped constant cross section dual mode ramjet combustor foreseen to operate from Ma=4.5 up to Ma=8. Be-low Ma=4.5 an air-turbo-ramjet accelerator engine is used for the initial acceleration, whose flow path is integrated into the air-intake and accessible by means of sliding doors. Both the dual mode ramjet

and the air-turbo-ramjet accelerator discharge in a nozzle with two sections, the first acting as the combustion chamber for ramjet mode operation. The engine is mounted as a dorsal unit leaving the aerodynamically better performing windward side free for optimization.

Figure 1: Artist impression of the STRATOFLY

MR2.4 flight vehicle flight vehicle.

In the paper to be presented a brief overview of the whole project will be provided. Specific focus will be devoted to the unique waverider flight con-figuration, the structural multi-bubble air-frame con-figuration, and the novel turbine based combined cycle dual mode ramjet propulsion system.

The combined use of experiments and high-fide-lity Large Eddy Simulation (LES) with comprehen-sive combustion chemistry provides the most con-venient method for analysing the propulsion system. Figure 2 shows experimental images and simulation results at two different operating conditions, corre-sponding to ramjet and scramjet operation, of a model-scale version of the MR2.4 flight vehicle combustor, [4], in the ONERA LAERTE facility.

Figure 2: Experiments and simulations of ramjet

(top) and scramjet (bottom) combustion

References

[1] Steeland J.; 2008, AIAA 2008-2578. [2] https://www.h2020-stratofly.eu [3] Langener T., Steelant J. Karl S. & Hannemann

K.; 2012, “Design and Optimization of a Small Scale M=8 Scramjet Propulsion System”,

[4] Vincent-Randonnier A., Ristori A., Sabelnikov V., Zettervall N. & Fureby C.; 2018, Proc. Comb. Inst. 37, p 3703.

_________________________________________ Corresponding author email: [email protected]

36


MICROWAVE STIMULATION OF TURBULENT FLAMES

C. Fureby1, T. Hurtig1, N. Zettervall1, H.Sundberg1, A. Ehn2, E Nilsson2, J. Larfeldt3, J Engdahl4

1Defence Security Systems Technology, The Swedish Defence Research Agency, FOI, Stockholm, Sweden 2Division of Combustion Physics, LTH, Lund, Sweden

3Siemens Industrial Turbomachinery AB, Finspång, Sweden 4SSAB, Borlänge, Sweden

Combustion processes are used to generate elec-

trical and mechanical energy in a variety of applica-tions. As requirements regarding efficiency, emis-sions, extended operational envelopes, and fuel flex-ibility change, new technologies are necessary. A innovative technology may be to use Plasma Assist-ed Combustion (PAC), [1].

The central idea of PAC is to add a small amount of electric energy to a flame to achieve a flame en-hancing effect in terms of increased laminar flame speed, su, reduced ignition delay time, τign, and im-proved flame stability. PAC has been used for fuel-reforming, [2], and flue-gas treatment, [3], but can also be used to influence the flame, [4]. Different techniques may be used to supply the electric energy such as Dielectric Barrier Discharges (DBD), [5], Gliding Arc Discharges, [6], and microwaves, [4]. For example, [5], demonstrated that the lift-off of a non-premixed methane-air jet flame decreases with increasing electrical field strength of a DBD.

Here, we will review relevant experimental and computational studies of microwave enhanced com-bustion performed in the projects EFFECT I and II, funded by the Swedish Energy Agency. Both exper-imental and computational studies of laboratory flames will be discussed to establish the current state-of-art, and to provide a general framework for applying these technologies to practical applications mainly in power-generation gas turbines, aero-en-gines and in ram-scramjet combustors.

As described in [4], figure 1, a turbulent low-swirl methane-air flame has been subjected to microwave irradiation, with a power corresponding to 1% of the thermal power of the flame. Here, a magnetron pro-vides a microwave field that is contained by an en-closure, corresponding to a combustor casing, al-lowing the microwaves to interact with the flame. A significant increase in flame size was observed as a consequence of enhanced reaction rates and new re-action pathways resulting from the creation of new species, excited species and ions.

Figure 1: Experimental set-up for microwave en-hanced low-swirl burner combustion experiment.

Microwave assisted combustion involves the fuel-air chemistry together with chemistry associated with singlet oxygen, O2

*, ozone, O3, chemionization, electron impact dissociation and ionization, and electron attachment and dissociation. A skeletal re-action mechanism has been extended to include mi-crowave associated reactions, and Large Eddy Sim-ulation (LES) computations have been perform to mimic the experiments, figure 2.

Figure 2: Experimental images without (a) and with (b) microwave-stimulation together with LES pre-dictions at different electrical field strengths, E/N.

Experiments and simulations predict an increasing reactivity with microwave stimulation both for lam-inar and turbulent flames, resulting in a wider flame that anchors closer to the burner. Detailed compari-sons between the experiments and simulations pre-dict qualitatively and quantitatively similar flame speed increases as well as OH and CH2O distribu-tion modifications, in turn revealing that the LES model captures the key processes.

This model can then be used to study how other combustor applications will be influenced by mi-crowave irradiation, and how this technology can be used to improve combustion efficiency.

References

[1] Starikovskiy A. & Aleksandrov N.; 2013, Prog. Energy Comb. Sci., 39, p 61.

[2] Kim Y., Abbate S., Ziock H., Anderson G.K. & Rosocha L.A.; 2007, IEEE Transactions on Plasma Science, 35, p. 1677.

[3] Lin H., Huang Z., Shuangguan W. & Peng X.; 2007, Proc. Comb. Inst., 31, p 3335.

[4] Ehn A., Petersson P., Li Z., Aldén M., Fureby C., Hurtig T., Zettervall N. & Larfeldt J., 2014, Proc. Comb. Inst. 35, p 3487.

[5] Vincent-Randonnier A. & Teixeira D.; 2008, Int. J. Plasma Env. Sci. Tech., 2, p 119.

[6] Matveev I, Matveeva S, Gutsol A, Fridman A.; 2005, AIAA-2005-1191.

________________________________________ Corresponding author email: [email protected]

37


A SIMPLIFIED MODEL FOR THIN ACOUSTIC SCREENSM. Gaborit1,2, P. Göransson1, O. Dazel2

1Department of Aeronautical & Vehicle Engineering, KTH, Stockholm, Sweden 2LAUM UMR CNRS 6613, Le Mans Université, Le Mans, France

Noise mitigation structures are widely used nowa-days and under constant development both from a re-search and engineering point of view. Thin layers areused in order to protect the said structures and/ortune their behaviour. In the case of porous layers suchas the ones used for sound proofing in a room acous-tics context, these layers have a prominent impact andmust be accounted for.

The present contribution [1] presents a simplifiedmodel for the films used in acoustic panels. Indeed, thecurrent way to model such films is based on Biot the-ory [2] which predicts three kinds of waves interactingin the layer. The films being very thin (sub-millimetrerange) and this kind of complex interactions buildingup with the propagation distance, it is shown that asimpler model can be used to accurately compute theresponse.

The work is based on manipulating the transfer ma-trix through the layer. To compute the matrix thepropagation equations in the film are rewritten underthe form [3, 4]:

∂s(z)

∂z= αs(z), s(0) = exp(−dα)︸︷︷︸

T (d)

s(d) (1)

where s is the so-called state vector, α the associatedstate matrix, T (d) the transfer matrix through a layerof thickness d in the z direction.

The transfer matrix is then linearised via a Taylorexpansion at the first order supported by the thinnessof the film with respect to the considered wavelength(kd ≪ 1, with k the wave number). This linearisationtransforms the propagation through the layer into ajump in value between both its sides.

Several other assumptions are then proposed basedon the order of magnitude of the said jumps for eachof the fields in the state vector. Particularly, it isshown that jumps for the solid displacements can beneglected, such as the coupling between tangential andnormal fields. The final model resemble an equivalentfluid model (whose components remain intact) and in-cludes coupling between the pressure and total dis-placement as well as between the shear stresses andtangential displacements [1, 3].

Tests are provided on several cases and include a sys-tematic assessment of the quality of the approximatedmodel from 10 to 4000 Hz and incidence angles in the[0, 89] ° range. Figure 1 shows a test configurationsand the associated results for two different films.

z

x

θ

500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

0

25

50

75

Inci

denc

eA

ngleθ

0.000

1.142

2.285

3.427

4.569×10−3

500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

0

25

50

75

Inci

denc

eA

ngleθ

0.000

0.515

1.031

1.546

2.062×10−2

Figure 1: Top: one of the configurations used to validatethe model. The film is laid on a PEM over a rigidbacking. Middle & Bottom: absolute error mapsfor two different films (note the scaling factors).

In the tested configurations, the method exhibit verylow error levels for all angles and frequencies. Theerror slightly increases at grazing incidence where thekd ≪ 1 assumption becomes invalid because of thelong propagation path. As expected, the resonanceswhich trigger different couplings because of the higheramplitudes are sources of error as well.

References[1] Mathieu Gaborit, Olivier Dazel, and Peter Görans-

son. “A Simplified Model for Thin Acoustic Screens”.In: The Journal of the Acoustical Society of America144.1 (July 2018), EL76–EL81.

[2] J.-F. Allard and Noureddine Atalla. Propagation ofSound in Porous Media: Modelling Sound AbsorbingMaterials. 2nd. Hoboken, N.J: Wiley, 2009. 358 pp.

[3] Olivier Dazel et al. “An Alternative Biot’s Displace-ment Formulation for Porous Materials”. In: The Jour-nal of the Acoustical Society of America 121.6 (2007),p. 3509.

[4] O. Dazel et al. “A Stable Method to Model the Acous-tic Response of Multilayered Structures”. In: Journalof Applied Physics 113.8 (2013), p. 083506.


38


HIGH-FIDELITY NUMERICAL SIMULATIONS OF A LIQUID JET IN AIRCROSSFLOW: A CASE STUDY OF INTERFACE-CAPTURING METHODS

FOR TURBULENT TWO-PHASE FLOWS

Zhouyang Ge1, Suhas S. Jain2, Shahab Mirjalili2, Marco E. Rosti1, Michael S. Dodd2, Luca Brandt1

1Linne FLOW Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, Stockholm, Sweden2Center for Turbulence Research, Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

Two-phase flows are ubiquitous in natural and industrialprocesses, such as raining, ocean wave breaking, transportof biological fluids, emulsification of food products, andatomization of fuel sprays. Detailed knowledge of theseprocesses are not only important for improving our under-standing of the nature, but may also guide further tech-nological development to address the rising environmentalconcern nowadays. However, the numerical study of two-phase flows has been a long standing challenge, particularlyin the context of turbulent environments. These challengesinclude, but are not limited to (1) enforcing mass, momen-tum and kinetic energy conservation, (2) modeling discon-tinuous properties, especially large jumps in density, acrossthe interface (3) handling complex topology and separationof scales, (4) achieving robustness for simulation of realis-tic flows, and (5) accurately implementing surface tensionforces.

The objective of this study is to perform a systematiccomparison of the interface capturing methods for two-phase turbulent flows, using a liquid jet in air crossflow(LJAC) as the test case (see Fig. 1 for an illustration). LJAChas the complexity of involving all the challenges identi-fied above, while mimicking typical airbreathing propul-sion systems in a simple way. Specifically, we simulatea water jet in uniform air crossflow at ambient condi-tions using an interface-correction level set method (ICLS)[1], a geometric volume-of-fluid method (Basilisk) [2], analgebraic volume-of-fluid method (MTHINC) [3], and adiffuse-interface method [4] with uniform Cartesian grids,in such a way that the comparison is consistent. The phys-ical properties are chosen such that the liquid Reynoldsnumber, Rel, is 15800, the gas Weber number, Weg , is40, and the momentum flux ratio, Q, is 88.2, matching theexperimental study of Sallam et al. [5].

Finally, we evaluate the numerical methods on their ca-pability to accurately capture the multiscale physics forhigh density and viscosity ratios (845 and 48, respectively,for the water-air system) in realistic turbulent environ-ments. The obtained ensemble of high-fidelity simulationsmay also form a basis for uncertainty analyses, potentiallyleading to a more reliable description of not only the LJACcase, but perhaps also other scenarios in general. With thecombined effort, we plan to explore these possibilities andeventually summarize the outstanding challenges and ad-vantages of the different methods, along with the best mod-eling practices.

Figure 1: A low-resolution test run of the LJAC case at liquidReynolds number Rel = 15800, gas Weber numberWeg = 40, and momentum flux ratioQ = 88.2, usingthe ICLS method. The magnitude of the velocity fieldin the air phase is indicated by the background color(lighter colors depict higher velocities).

References

[1] Z. Ge, J.-C. Loiseau, O. Tammisola, L. Brandt. J.Comput. Phys. 353, pp.435-459, 2018.

[2] S. Popinet, J. Comput. Phys. 228(16), pp.5838-5866,2009.

[3] Ii, S., Sugiyama, K., Takeuchi, S., Takagi, S., Mat-sumoto, Y., Xiao, F. J. Comput. Phys. 231, pp.2328-2358, 2012.

[4] S. Mirjalili, C.B. Ivey, A. Mani, ArXiv: 1803.01262,2018.

[5] Sallam, K., Aalburg, C., Faeth, G., AIAA journal, 42(12), 2529–2540, 2004.

Corresponding author: [email protected] (Zhouyang Ge)

39


Reacting Spray A and Scaled Jet Analysis

M. Gholamisheeri1, D. Norling1,2, T. Hällqvist2

1Engine Predevelopment, Scania AB, Södertälje, Sweden 2 Engine Predevelopment, Scania AB, Södertälje, Sweden 3 Engine Predevelopment, Scania AB, Södertälje, Sweden

This work investigates the performance of a series of different size jets (scaled) in a constant pressure and volume chamber and, under steady state condition. Initially, a single free jet is modelled which is similar in characteristics and configuration to the Spray A injector, from Engine Combustion Network (ECN) [1] and the liquid penetration length and pressure rise are compared to the experimental measurements of [1]. The ECN is an international collaboration among both experimental and computational researchers in engine combustion that provides a library of experiments for model validation. For initial spray A simulation, grid resolution effect, number of injected parcels, the choice of spray cone angle and break up time constant [KH-RT] are studied. It was concluded that the number of injected parcels are dependent on the grid cell size and injector nozzle diameter. In addition, the spray cone angle was found to be an important parameter that influences spray evaporation, parcel interaction and pressure rise. The validation of the pressure and penetration length data with experimental measurements suggests the a cone angle of 25 and a breakup time constant of 16. A comparison between RANS results, LES [2] results and Experimental pressure data is shown in Figure 1.

Figure 1: Pressure data for Spray A simulations, a

comparison with Experimental measurements. Thereafter, a simulation campaign is performed with scaled injectors (cross sectional area of the injector orifice (Ai), and injected mass (mi) are scaled) while the injection duration is kept constant. The purpose is to find the optimal spray size for high thermal efficiency and least emissions of an engine through analysis of the burn rate (heat release rate (HRR) and emission data). For brevity, only HRR for the different size jets is provided here. Initial and boundary conditions can be found []. Figure 2a shows the actual HRR illustrating that with the larger orifice and increased injected mass, the rate of heat release is higher and the reaction time is longer. With a smaller orifice and less fuel mass, an increased rate of combustion is achieved. In Figure 2b on the other

hand, the scaled HRRs, (i.e. the rate that can be obtained if two of the half size jets, four of the quarter size ones and so on) are in place. Here we can clearly see that several smaller jets burn faster than a single original size jet (as long as there is no interaction between the individual flames). If the HRR results is scaled back (in a way to be able to compare them with the original jet), see Figure 2b, a good agreement is achieved for various scaled jets and the original spray A configuration. This result indicates that with the scaled jets (two half jets or four quarter size ones), it is possible to achieve similar burn rates and, hence, combustion efficiency, as the original jet. However, the interaction of the plume of these scaled jets must be taken into consideration.

Figure 2: Original (right) and Scaled (left) HRRs. To find the similarity between the re-scaled results

of scaled jets and original spray A configuration, emission species such as HC, CO, CO2, NOx and soot are compared. Results showed that with a larger orifice, although initial burn rate is slower, the net heat release is higher and net remaining hydro carbons (HCs) are less. In addition, it was found that a linear correlation between the mass flow rate and bun rate exist that leads us to the foreseeable choice of two/four simultaneous injectors with half/quarter orifice area (Ai) and injected mass (mi), respectively. The plume to plume interaction and injection strategy with higher number of injectors, is remained to be studied in the future. References

[1] ECN. (2018). Retrieved from ECN: https://ecn.sandia.gov/

[2] Gong, G., Jangi, M., Bai, X., Large Eddy Simulation of n-Dodecane Spray Combustion in a High Pressure Combustion Vessel. Applied Energy V.136 P.373-381 (2014)

_________________________________________ Corresponding author email: [email protected]

40


COMPONENT MODE SYNTHESIS INTERFACE REDUCTION AND MODALTRUNCATION AUGMENTATION USING COARSE MESHES

Mladen Gibanica1,2, Thomas J. S. Abrahamsson1, Daniel J. Rixen3

1Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Goteborg, Sweden2Volvo Car Corporation, Goteborg, Sweden

3Technical University of Munich, Garching, Germany

High fidelity finite element (FE) models are common inmany industries today. For dynamic analysis reduced ordermodels are often computed and used in subsequent anal-yses, e.g. in simulations where the models are evaluatedmany times. It is therefore important that the reduced ordermodels can be computed efficiently and are as small as pos-sible. One of the most commonly used reduction methodsis the Craig-Bampton (CB) method [1], built from staticconstraint (or Guyan) modes [2] and fixed interface vibra-tion modes. As a consequence, all interface degrees-of-freedom (DOFs) are keep in the CB model. However, forhigh fidelity models with many DOFs it can be expensiveto compute CB models, mainly due to the computationalcost associated with computing the Guyan modes. Also,because the interface DOFs are kept intact the CB modelscan have unnecessarily many DOFs, e.g. it is not uncom-mon that many more Guyan modes than fixed interface vi-bration modes are present in the reduction basis. This canseverely limit the reduced order models practical use.

A method is presented that can reduce the computationaltime of generating CB models, and also reduces the numberof interface DOFs. Interface reduction has previously beenproposed where the Guyan modes are linearly combined toform characteristic constraint (CC) modes [3]. However, tocompute the interface reduction basis Guyan modes mustbe computed for each substructure, which is expensive forhigh fidelity models, with many interface DOFs. Here, amultifidelity method is presented, first introduced in [4],that can compute the interface reduction basis cheaply. Theoriginal fine mesh is coarsened, keeping interface DOFs in-tact, see Figure 1 for a simple plate example. The coars-ened model is used to compute the interface reduction ba-sis. Mesh coarsening is in general cheap, and computingthe interface reduction basis from a coarse mesh is alsocheap. This basis is used on the fine mesh to reduce thenumber of interface DOFs, also reducing the cost of com-puting the CC modes. Using the coarse interface reductionmethod results in a negligible accuracy loss and significantspeed up in generating CB models.

Modal truncation augmentation vectors (MTAs) [5, 6]have been proposed to improve the accuracy of CB reducedorder models. The MTAs can be seen as a generalisation ofthe Guyan modes, also providing dynamic corrections forthe reduced order models. Therefore, for a fixed model or-der, including some MTA vectors instead of only fixed in-terface vibration modes in the reduction basis can improvethe accuracy of the reduced order models. However, thenumber of MTA vectors depend on the number of interface

Figure 1: Fine (top) and coarsened mesh (bottom) of a plate con-sisting of two substructures, one substructure in lightgrey (left) and the other in dark grey (right)

DOFs. Therefore, for high fidelity models with many in-terface DOFs, interface reduction is necessary to keep thecomputational time of the MTAs reasonable. The possi-bility of computing accurate MTA vectors with the coarseinterface reduction method is studied here.

Acknowledgements

Volvo Car Corporation is gratefully acknowledged for pro-viding the funding for this research.

References

[1] Bampton, M.C.C., Craig, Jr.R.R., Coupling of sub-structures for dynamic analyses, AIAA Journal, 6(7),1313-1319, (1968)

[2] Guyan, R.J., Reduction of stiffness and mass matri-ces, AIAA Journal, 3(2), 380-380, (1965)

[3] Castanier, M.P., Tan, Y.-C., Pierre, C., Characteris-tic Constraint Modes for Component Mode Synthesis,AIAA Journal, 39(6), 1182-1187, (2001)

[4] Gibanica, M, Abrahamsson, T.J.S., Rixen, D.J., A re-duced interface component mode synthesis methodusing coarse meshes, Procedia Engineering, 199, 348-353, (2017)

[5] Dickens, J., Stroeve, A., Modal truncation vectorsfor reduced dynamic substructure models, 41st Struc-tures, Structural Dynamics, and Materials Conferenceand Exhibit, Atlanta, GA, USA, (2000)

[6] Rixen, D.J., High order static correction modes forcomponent mode synthesis, WCCM V, Vienna, Aus-tralia, (2002)


41


IMPACT OF CLIMATIC LOADINGS ON THE EFFICIENCY OFBONDING OF CONCRETE STRUCTURES WITH CFRP

P. Godonou1,1Department of Engineering Sciences, UU, Uppsala, Sweden

IntroductionTo extend the service life of Reinforced Concrete

(RC) structures, a current practice is to strengthenthem using Carbon Fiber Reinforced Polymers(CFRP). The structural behaviour of the bonding depends on stress states at the concrete surface, in the bonding agent (usually epoxy) and in the CFRP as shown in Figure 1. For successful strengthening, ideal temperature (T) and Relative Humidity (RH) are suggested as in [1]. The actual conditions during curing are often different, which can compromise the structural reliability of the repaired structure. To quantify the effects of varying T and RH, concrete samples are strengthened in a climate chamber. A third variable was the pre-treatment of concrete surface, which was either ground or blasted.

Figure 1: Stresses in bonding zone and test setup

The following typical materials are used in theexperiments:· Concrete samples of class K30.· Primer of type “BP50 Super/Hardener 50”.· Epoxy “BPE Composite 417/NM 417B”.· Carbon fiber of type BPE Composite 200S.

Tensile and delamination tests were performed on the CFRP system, and the degree of cure measured. Results from so-called Pull-off tests as shown in Figure 1, are used to assess the bonding quality.

ResultsTable 1 shows some test results, with Ni as the number of samples used in the investigation.

Table 1. Results in case of ground concrete surface

Specimen 5oC/

RH 85%

15oC/

RH 85%

20oC/

RH 85%

5oC/

RH 35%

15oC/

RH 35%

20oC/

RH 35%

su,mean

(MPa)1,86 1,74 2,25 1,68 1,66 2,10

su,

deviation

0,29 0,25 0,12 0,21 0,24 0,22

Fracturelocation

Concrete Concrete Concrete Concrete Concrete Concrete

Ni 8 5 8 8 8 5

· The highest bonding strength regardless of theclimatic conditions is achieved for groundconcrete surface.

· Ground concrete surface ensures desiredfailure in concrete as shown in Figure 2.

· High RH seems to favor good curing in thecase of ground concrete surface while it hasthe opposite effect in the case of blastedconcrete surface.

· Low temperature and high RH do not worsenthe delamination fracture mode

· A dramatic increase in strength occurs afterfurther curing for the samples with blastedconcrete surface.

Figure 2: Failure modes for ground (left) resp.blasted (right) concrete surfaces

ConclusionsTo mitigate the risks, the following approaches

during strengthening work are suggested:· Use a ground concrete surface· Decrease high RH and low temperature during

cure by means of infrared heating for example· Extend the curing period with at least an

additional 10 days before loading the structure· Use a strengthening system with an acrylic resin

as MMA resin, which has proven to be excellentfor temperature varying from –10oC to +30oC [2].

References[1] Technical Report TR55 Design Guidance for

strengthening concrete structures using fibrecomposite materials, Concrete Society (2012)

[2] Sano T., Hayashi S. And Furukawa T., Studies

on Applicability of CF Sheets/MMA Resinsystem for Strengthening Concrete Structures,43rd International SAMPE Symposium, pp. pp.1780-1789, (1998)

__________________________________________Corresponding author email: [email protected]

42


CENTRIFUGAL PENDULUM VIBRATION ABSORBERS (CPVA)

Erik R. Gomez1,2, Ines Lopez Arteaga2,3, Leif Kari2

1Transmission Development, Scania CV AB, Sodertalje, Sweden2The Marcus Wallenberg Laboratory for Sound and Vibration Research (MWL), KTH, Stockholm, Sweden

3Department of Mechanical Engineering, Section Dynamics and Control, TUE, Eindhoven, The Netherlands

The CPVA has been used since the 1930s in aircraftengines but has recently gained interest by heavy vehiclemanufacturers. Environmental legislation has forced thedevelopment of the combustion engine to find more inno-vative ways to reduce emissions. Increased cylinder pres-sure, down-sizing and down-speeding are a few ways toreduce fuel consumption and emissions. However, all ofthese measure increase the torsional vibration in the power-train and therefore increase the emitted noise such as gearrattle from the transmission. The CPVA has potential tocomplement the traditional vibration isolation techniquesin a cost efficient manner without significantly increasingthe weight of the powertrain.

A CPVA is a passive mechanical vibration absorber usedto abate torsional vibrations with distinct order character-istics such as in the case of a reciprocating engine. Unliketraditional vibration isolation methods with fixed frequencytuning, the fundamental nature of the CPVA allows for ab-sorption of a specific order over the complete operating ro-tational velocity range of an engine. The eigenfrequency ofthe CPVA is proportional to the mean rotational velocity Ωof the rotor and the linear tuning order nt is merely a geo-metrical relation between the distancesR and L depicted inFigure 1. The linear tuning order is given by Eq. (1) whenthe pendulum body is assumed to be a point-mass, [1],

nt = Ω

√R

L. (1)

Figure 2 shows the linear angular acceleration responseof a rotor equipped with a CPVA for a sweeping sinusoidalexcitation of order n. The minimum occurs when the tun-ing order matches the excitation order i.e. n/nt = 1.

CPVAs are non-linear systems possessing a set of richdynamics. An example of the dynamics is the multipleorder response due to a pure sinusoidal excitation wherehigher harmonics of the excitation orders are amplified inthe rotor response, [2]. The circular path pendulum has anon-linear amplitude-dependent eigenfrequency which canhowever be addressed by prescribing the pendulum mass tofollow a tautochronic trajectory path and thus maintain itstuning at large amplitudes.

The challenges and fundamental properties of the CPVAare presented with focus on future implementation in aheavy truck application.

References

[1] R W Zdanowich and T S Wilson. The elements of pen-dulum dampers. ARCHIVE: Proceedings of the Institu-

Figure 1: Rotor equipped with a single pendulum absorber.

Figure 2: Linear rotor angular acceleration response.

tion of Mechanical Engineers 1847-1982 (vols 1-196),143(1940):182–210, jan 1940.

[2] Erik R Gomez, Ines Lopez Arteaga, and Leif Kari.Multiple-order excitation and response of centrifugalpendulum vibration absorbers. Proceedings of ISMA2018 - International Conference on Noise and Vibra-tion Engineering and USD 2018 - International Con-ference on Uncertainty in Structural Dynamics, pages4305–4319, 2018.


43


FLOW DYNAMICS OF COLLOIDAL FIBRE DISPERSION INGEOMETRICALLY VARYING FLOW-FOCUSING CHANNELS

K. Gowda1, C. Rydefalk1, L. D. Soderberg1,2, F. Lundell1,2

1Department of Mechanics, KTH, Stockholm, Sweden2Wallenberg Wood Science Center, KTH, Stockholm, Sweden

Making strong filaments from cellulose nanofibrils(CNF) can potentially lead to new high performance bio-based composites competing with conventional glass fibercomposites. Such very strong cellulose filaments havebeen demonstrated and obtained through the hydrodynamicalignment of colloidal fibre dispersion (CNF dispersion)by using the concept of flow-focusing [1, 2]. After thealignment of nanofibrils, ions were diffused into the col-loidal fibre dispersion, resulting in a dispersion-gel transi-tion, which locked the aligned structure in a gel. In orderfor further development and upscaling of this technology,an improved understanding of the alignment process is nec-essary.

In this work, 3D numerical simulations supportedwith experimental measurements, similar to our previousstudy [3] is carried out to investigate the fundamentals ofthe alignment process. Here, the emphasis is on under-standing the topological behaviour of colloidal fibre disper-sion subjected to extensional flow in a geometrically vary-ing hydrodynamic flow-focusing channels.

Q2/2

Q2/2

Q1

1 2 40 5 63

Downstream positionsx/h

600

Q1

Q2/2

Q2/2

300

Q2/2

Q2/2

Q1

(a)

(b) (c)

Figure 1: Schematic of geometrically varying flow-focusingchannels. Q1 and Q2 indicate the flowrate of core andsheath flows respectively.

As depicted schematically in Fig. 1, flow-focusing isachieved in a geomterically varying microfluidic channelsystem, where a core flow of colloidal fibre dispersion (Q1)is focused by the injection of two sheath fluids (Q2) therebycreating an extensional flow at the intersection. As the corefluid is accelerated, the fibrils align in the flow direction.The prime focus here is on the investigation of the flowdynamics such as topology of colloidal dispersion detach-ment from the channels walls, and on the evolution of col-loidal disperison thread shape. Figure 2 shows the cross-

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0.5

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Figure 2: Numerical cross-sectional contours of collidal disper-sion thread for various geometries at different down-stream positions. Black colour represents the core fluidwhile white colour indicates the sheath fluid.

sectional shape of the colloidal dispersion thread for the ge-ometires shown in Fig. 1 at various downstream positionshighlighted by white dashed line. 3D numerical simula-tions are performed using OpenFOAM and experimentalmeasurements with optical coherence tomography (OCT).

References

[1] Hakansson, K. et al., Hydrodynamic alignment andassembly of nanofibrils resulting in strong cellulosefilaments. Nature Communications, 5, 4018, (2014)

[2] Mittal, N. et al., Multiscale Control of NanocelluloseAssembly: Transferring Remarkable Nanoscale FibrilMechanics to Macroscale Fibers. ACS nano, 12(7),6378-6388, (2018)

[3] Gowda, K. et al., Effective interfacial tension in flow-focusing of colloidal dispersions: 3D numerical sim-ulations and experiments. arXiv:1901.08939, (2019)


44


Mechanical properties of lithium-ion battery electrodes

P. Gupta1, I. B. Ucel1, P. Gudmundson1

1Department of Solid Mechanics, KTH, Stockholm, Sweden

With a rapid increase in the share of electrically powered vehicles, a significant effort for the development of batteries with higher capacity, longer life time and a competitive cost are required. There is insufficient knowledge about methods and tools for prediction of battery lifetime and how it depends on materials, design and operating conditions. Battery cells swell and shrink during electro-chemical cycling. This causes mechanical degradation at microscopic and macroscopic length scales. The crack initiation and propagation in the electrode particles and binders result in macroscopic damages like local buckling, void initiation and delamination, see Figure 1. The mechanisms that control the damages are a combination of electro-chemical and mechanical degradation.

Figure 1: Structural composition of electrode [1] To characterize the degradation mechanisms, it is

essential to first obtain the mechanical properties of active layer in a dry electrode*. For this purpose, tensile tests on electrodes are conducted and the properties of the active layer are obtained using rule of mixture [2]. The porous active layer, see Figure 1, has however a much smaller stiffness in comparison to the aluminium current collector which leads to inaccurate measurements. Consequently, a method to estimate the mechanical properties using U-shaped bending test [3] is presented, see Figure 2. This test accurately represents the swelling mechanism in the electrodes during electro-chemical cycling.

The key idea here is to capture the variation in mechanical properties (typically stress-strain relation) when the electrode is subjected to electro-chemical cycling. This requires a simultaneous measurement of mechanical properties during electrochemical cycling. However, the proposed bending method is cumbersome, since an apparatus

needs to be designed which can be specifically used inside a glove box**.

Figure 2: U-shaped bending test

For this reason, it is convenient to use a 3-point flexural test equipment to measure the mechanical properties of electrode. This method has an advantage that the apparatus can be placed inside the glove box, and the related measurements can be done simultaneously. Elastic and plastic properties are obtained from the bending tests. The experimental results indicate significant differences between tensile and compressive loading. A constitutive model will be developed which takes into account the effect of electrochemical cycling.

References

[1] M. T. McDowell, S. Xia, and T. Zhu, “The mechanics of large-volume-change transformations in high-capacity battery materials,” Extrem. Mech. Lett., vol. 9, pp. 480–494, 2016.

[2] E. Sahraei, E. Bosco, B. Dixon, and B. Lai, “Microscale failure mechanisms leading to internal short circuit in Li-ion batteries under complex loading scenarios,” J. Power Sources, vol. 319, pp. 56-65,2016.

[3] M. J. Matthewson, C. R. Kurkjian, and S. T. Gulati, “Strength Measurement of Optical Fibers by Bending,” J. Am. Ceram. Soc., vol. 69, no. 11, pp. 815–821, 1986.

__________________________________________ Corresponding author email: [email protected] *Electrode subjected to no electrochemical-cycling **Vacuum chamber for electrochemical cycling

45


VIRTUAL MATERIAL TESTING OF COMPOSITE MATERIALS

R. Gutkin1,2, K. Ståhl2, A. Andersson2, L.E. Asp2

1Volvo Cars, Durability & Craftmanship, Göteborg, Sweden 2Division of Material and Computational Mechanics

Department of Industrial and Materials Science

Chalmers University of Technology, SE-412 96 Göteborg, Sweden

Composite materials offer significant

leightweigthing possibilities for automotive structures. However, to assess the strength and endurance of the structures, a large number of material properties are needed. The properties are dependent on the stacking sequence used and since polymeric matrices are used, they need to be measured for different environments. A testing program aimed at determining all these values would be very costly and time consuming. Virtual material testing is therefore investigated as a cost effective way to estimate some of the properties.

Virtual material testing relies on replacing physical coupon testing by virtual ones. Two key features are a detailed finite element model of the coupons and an advanced material model able to capture the different failure mechanisms. In the present contribution, detailed 3D finite element models are used to model the geometries of the coupons and an advanced material model for a unidirectional (UD), transversely isotropic, material system is first investigated [1]. The accuracy of the method is studied on a set of notched and notched laminates with different stacking sequences [2].

Figures 1 and 2 show that the model is able to predict accurately the notched strength in tension and compression for different laminate thicknesses and stacking sequences.

Figure 1: KTH Royal Institute of Technology

Based on those findings, developments to the material model are proposed so that textile material systems can be studied. A twill and an non crimp fabric (NCF) architectures are investigated. As shown in Figure 3, the meso-structures of both architectures are different which implies that the sequence of event leading to failure, and therefore driving the response, will differ between UD, NCF or twill materials, even though the basic failure mechanisms remain the same.

Figure 1: KTH Royal Institute of Technology

In this contribution, the developments made to the

material model will be detailed and a validation of the predictions in terms of notched and unnotched strength will be discussed. Finally, a process to implement virtual material testing in an industrial environment will be presented.

References

[1] Pinho, ST., Physically based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking. Part II: FE implementation. Composites Part A: Applied Science and Manufacturing, 37, pp. 766-777 (2006). [2] Green, A., Wisnom, M.R., Hallett, S.R. An experimental investigation into the tensile strength scaling of notched composites. Compos Part A – Appl S, 38, pp. 867–78 (2007). [3] Lee, J. and Soutis, C. Thickness Effect on the Compressive Strength of T800/924C Carbon Fibre-Epoxy Laminates, Composites Part A, 36, pp. 213 – 227 (2005). __________________________________________ Corresponding author email: [email protected]

46


EXPERIMENTAL FRACTURE MECHANICS TO STUDY ENVIRONMENTALLY ASSISTED DEGRADATION IN HIGH

STRENGTH STEEL

Armin E. Halilović, Pål Efsing, Jonas Faleskog

Department of Solid Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden

High strength steel can be susceptible to environmentally assisted degradation and like any other susceptible material may suffer premature failure due to loss of ductility and load bearing capacity. Environmentally assisted degradation is principally determined by a combination of a reactive environment, mechanical loading and the inherent susceptibility of the material. Since the combination of these three factors is very common; the understanding and avoidance of environmentally assisted degradation is crucial in all applications of high strength steels. This becomes even more important in view of the industrial drive towards higher strength steels, which have an improved strength/weight ratio and thus a lower environmental footprint.

In this work, a fracture mechanics method was developed by using single edge notch bend specimen. Testing in a hydrogen environment was chosen to study the influence of environmental assisted degradation. The material used was a martensitic high strength steel with a yield stress σY = 1650 MPa that exhibits near ideal plastic hardening. The environment was achieved through a sodium chloride solution with cathodic polarization.

The experiments were carried out according to ASTM E-1820 [1]. A parameter study was performed by varying hydrogen charging (H.C), Current density (C.D.) and load rate ().

It was observed that reducing the load rate from = 0.01 mm/s to = 0.0001 mm/s for specimens immersed in a 3.5 % NaCl solution and subjected to a current density of 0.1 mA/cm2 resulted in a 50 % decrease in fracture toughness seen Figure 1.

A method for evaluating the resistance curve was proposed as an alternative to the evaluation in ASTM E-1820 [1]. Finite element simulations of a single edge notch bend specimen with a stationary crack were plotted together with experimental data as seen in Figure 2. The value of J was determined using linear interpolation of the intersections between simulations and experiments.

Figure 1: Comparison between resistance curves performed in a) air with load rate 0.01 mm/s and in b) 3.5 % NaCl with cathodic polarization and load rate 0.0001 mm/s.

Figure 2: Outline for evaluation method of the resistance curve.

References

[1] Standard Test Method for Measurement of Fracture Toughness. American Society for Testing and Materials, Philadelphia, ASTM E-1820, 2019.


47


RESPECTING FULL GRAIN BOUNDARY ENERGY ANISOTROPY IN

MESOSCALE SIMULATIONS OF POLYCRYSTALS

H. Hallberg1, V.V. Bulatov2

1 Division of Solid Mechanics, Lund University, Lund, Sweden 2 Lawrence Livermore National Laboratory, Livermore, USA

Local variations in grain boundary energy have a profound impact on the kinetics of grain boundary migration in polycrystals. The anisotropy of the grain boundary energy is mainly a consequence of the structure of the adjoining crystals and of the local grain boundary character. From these dependencies, a complete representation of the local grain boundary character requires a total of five parameters: three parameters to describe the misorientation between the two adjacent crystals and two additional parameters to define the local orientation of the grain boundary plane with respect to some frame of reference. Accordingly, the grain boundary energy will tend to vary with the full set of five parameters. However, the energy anisotropy is disregarded in the vast majority of numerical simulation models and properties such as the grain boundary energy are assumed to be isotropic and constant. If energy variations are indeed considered, it is almost exclusively done under severely limiting simplifications and assumptions. A range of different numerical methods, such as level sets, phase fields, vertex models and cellular automata, can be used for mesoscale modeling of the evolution of a grain boundary network [1]. Regardless of which approach is adopted, grain boundary energy is usually assumed either to be a constant parameter or it is taken as a quantity that varies according to a Read-Shockley type of energy model, based on a single misorientation parameter. Few numerical models consider the influence of a full five-parameter characterization of grain boundaries in evaluating anisotropic grain boundary energies. The present work, recently published in [2], shows how numerical simulations of grain boundary migration can be performed at the mesoscale, in both 2D and 3D, based on a level set representation of the grain boundary network, while respecting the full extent of grain boundary energy anisotropy. The level set method is based on the introduction of a scalar field 𝜙(𝒙, 𝑡), i.e. the level set function, defined throughout the computational domain Ω, with 𝒙 and 𝑡 denoting the spatial coordinates and the time, respectively. The zero contour 𝜙 = 0 represents the spatial discontinuity Γ, being a grain boundary in the present case. The function 𝜙 is taken to be a distance function, meaning that its value at a certain point 𝒙 corresponds to the closest distance 𝑑(𝒙, 𝑡, Γ) between the point and the interface at time 𝑡. A sign convention is adopted whereby 𝜙 is defined to be positive inside the domain delimited by Γ, zero at the interface and negative elsewhere. The case of

two adjacent crystals (level sets) with orientations 𝒈𝑖 and 𝒈𝑗 is illustrated in Figure 1.

Figure 1: Level set representation of two adjacent crystals, with orientations 𝒈𝑖 and 𝒈𝑗, separated by the zero level set contour 𝛤𝑖𝑗 which is common to

the two level set functions 𝜙𝑖 and 𝜙𝑗. In the present work, a level set implementation is proposed that can accurately trace the evolution of a grain boundary network in a polycrystalline aggregate while respecting grain boundary energy anisotropy. Key components in the formulation are, for example, an efficient and simple scheme for unequivocal identification of crystal neighbors at junctions where an arbitrary number of crystals intersect. The implementation works without modifications in 2D as well as in 3D. The proposed level set formulation is also shown to provide grain boundary junction configurations that comply with classical equilibrium conditions. Full grain boundary energy anisotropy is considered by adopting a parametrization of the five-parameter grain boundary energy space, as proposed in [3]. References

[1] Hallberg, H., Approaches to modeling of recrystallization, Metals, 1, 16-48, (2011)

[2] Hallberg, H. and Bulatov, V.V., Modeling of grain growth under fully anisotropic grain boundary energy, Modelling and Simulation in

Materials Science and Engineering, in press [3] Bulatov, V.V., Reed, B.W., Kumar, M., Grain

boundary energy function for fcc metals, Acta

Materialia, 65, 161-175, (2014) __________________________________________ Corresponding author email: [email protected]

48


PROPOSING AN EVOLUTION LAW FOR THE CONTRACTILE ELEMENTIN MUSCULOSKELETAL MODELING

L.J. Holmberg1, A. Roser1, P.R. Roca1,2, J. Stalhand1

1Solid Mechanics, Department of Management and Engineering, Institute of Technology, Linkoping University, Sweden2Technical University of Madrid, Spain

The first useful mechanical model for a muscle contrac-tion was proposed by Hill [1] in 1938. By measuring thetemperature change in frog sartorius muscles during con-traction, Hill concluded that a muscle can be modelledby a contractile element in series with a spring (the ten-don). Despite its simplicity, the Hill model includes manysalient muscle features such as the length and contractionspeed dependence of the generated force. Combined with amathematically simple structure, this makes the Hill modelthe natural choice in musculoskeletal simulation tools, e.g.,OpenSim [2] and AnyBody [3].

Speed dependent characteristics of muscles togetherwith the serial arrangement requires an additive split of thetotal muscle-tendon length and speed into separate partsfor the muscle and tendon. The measurable quantities areusually the total muscle-tendon length and speed togetherwith the tendon force. Hence, the split between the mus-cle and tendon becomes arbitrary. Since the force-length-speed characteristics of a muscle refer to the contractileelement length rather than the total muscle-tendon length,the problem lacks a unique solution and becomes ill-posed.One solution is to reformulate the problem to a differential-algebraic equation and solve for a set of initial conditions.However, it is generally assumed that the tendon speed isnegligible and the contractile element speed is substitutedby the total muscle-tendon speed [4], e.g. in AnyBody. Theeffect of this substitution has not been thoroughly tested.

We propose a modified skeletal muscle model where thecontractile element behaves similar to a friction clutch [5].This is based on the cycling of the myosin heads as they at-tach to thin actin filaments and pull them towards the centerof the sacromere. Within this overall inwards movementthe actin filaments also have a short and rapid outward slip.In parallell with the contractile element we have a passiveelement, modeled as a spring, that represents any stiffnessin the muscle. Also in parallell we have a viscous damperthat represents any fluid in the muscle that would resist con-traction. These 3 elements are then in series with a springrepresenting the tendon. A force equilibrium thus yields

F T = FCE + F PE + FD (1)

where F T , FCE , F PE and FD is the force in the tendon,muscle, passive element and damper respectively.

The internal mechanical power of the model is

Pint = F T LT + FCE

(LCE + rω

)+ F PELCE + FDLCE

(2)

where LT and LCE are the time derivatives of tendon andmuscle length, rω is the unknown tangential speed of thefriction clutch and we interpret the maximum contractionspeed of the muscle as −rω = −vCE

max.We now assume that the internal energy of the system is

given by the strain-energy Ψ of which the total is

Ψ (LCE, LT ) = ΨPE (LCE) + ΨT (LT ) . (3)

The dissipation inequality states that the change in en-ergy cannot exceed internal power. Eqs. (1)–(3) thus give

(∂Ψ

∂LT− FCE − ∂Ψ

∂LCE

)LCE+FCE

(LCE + vCE

max

)≥ 0.

(4)To satisfy Eq. (4), both addends have to be ≥ 0.

No contractile force is generated below maximum con-traction speed −vCE

max, thus we assume

FCE = κ(LCE + vCE

max

), for LCE ≥ −vCE

max (5)

where κ is a positive function that accounts for filamentoverlap, i.e. the length dependence of muscle force.

To ensure that the first addend also is positive we assmue

∂Ψ

∂LT− FCE − ∂Ψ

∂LCE= γLCE (6)

where γ > 0. Combining Eqs. (5) and (6) leads to anevolution law of LCE

LCE =1

γ + κ

(∂Ψ

∂LT− ∂Ψ

∂LCE− κvCE

max

). (7)

References

[1] Hill A.V. Proc R Soc London B Biol Sci, 126, 136–195 (1938)

[2] Delp S.L. et al. IEEE Trans Biomed Eng, 54(11),1940–1950 (2007)

[3] Damsgaard M. et al. Simul Model Pract Theory,14(8), 1100–1111 (2006)

[4] Holmberg L.J. PhD thesis, Linkoping University,Linkoping: LiU-Tryck (2012)

[5] Sharifimajd B., Stalhand J. Biomech ModelMechanobiol. 12(5), 965–973 (2013)


49


TOPOLOGY OPTIMIZATION BASED ON FINITE STRAINVISCOPLASTICITY

Niklas Ivarsson1, Mathias Wallin1, Daniel Tortorelli2

1Division of Solid Mechanics, LTH, Lund, Sweden2Center for Design and Optimization, Lawrence Livermore National Laboratory, Livermore, CA, USA

In this talk, we present a framework that incorporate vis-coplastic material response and large deformation theoryinto topology optimization. The objective of the optimiza-tion is to maximize the viscoplastic energy absorption ofstructures subjected to impact loads. And because energyabsorption generally is affected by load magnitude and loadrate, dynamic, finite strain and rate effects are accounted forin the design process.

The motion equation is formulated and solved in a to-tal Lagrangian finite element setting in which the implicitNewmark scheme is used for the temporal discretization.The constitutive model that we employ was proposed by [1]and is based on finite strain isotropic hardening viscoplas-ticity. To solve the resulting coupled nonlinear residualequations, a nested Newton method is used together withan adaptive time-stepping procedure. The design is up-dated by the method of moving asymptotes (MMA), whichrequires sensitivities of the objective and constraint func-tions. For transient and path-dependent problems, thesesensitivities are path-dependent; we obtain them using theadjoint sensitivity scheme presented in [2].

The optimization algorithm is also extended to inversehomogenization material design, i.e. we present an opti-mization procedure for designing architected periodic vis-coplastic microstructures. Instead of a formal homogeniza-tion approach, we perform numerical tests on a single unitcell subjected to periodic boundary conditions to evaluateits macroscopic mechanical properties. The microstruc-tures are designed so as to maximize their macroscopicviscoplastic energy absorption, and exhibit near zero trans-verse contraction when subjected to large uniaxial tensileloads.

We formulate well-posed topology optimization prob-lems by restriction via the Helmholtz partial differentialequation filter, a periodic version is used for the inversehomogenization studies. Sharp boundaries between solidand void regions are obtained through RAMP penalizationand Heaviside thresholding. The design domain is dis-cretized with 8-node linear brick elements, which enablesthree-dimensional optimization problems to be solved butfor simplicity, we use plane conditions to solve two-dimensional problems. The examples of optimized macro-scopic structures, presented in [3], and of optimized peri-odic microstructures clearly demonstrate the importance ofthe load magnitude and the loading rate.

This work was partially performed under the auspicesof the U.S. Department of Energy by Lawrence LivermoreLaboratory under contract DE-AC52-07NA27344, cf. refnumber LLNL-CONF-717640. The financial support from

the Swedish research council (grant ngb. 2015-05134) isgratefully acknowledged. The authors would also like tothank Professor Krister Svanberg for providing the MMAcode.

References

[1] Simo JC, Miehe C. Associative coupled thermoplas-ticity at finite strains: Formulation, numerical anal-ysis and implementation. Computer Methods in Ap-plied Mechanics and Engineering 1992; 98:41104.

[2] Michaleris P, Tortorelli DA, Vidal CA. Tangentoperators and design sensitivity formulations fortransient nonlinear coupled problems with applica-tions to elastoplasticity. Int J Numer Methods Eng.1994;37(14):24712499.

[3] Ivarsson N, Wallin M, Tortorelli D. Topol-ogy optimization of finite strain viscoplas-tic systems under transient loads. Int J Nu-mer Methods Eng. 2018;114:13511367.https://doi.org/10.1002/nme.5789


50


MODELLING AND VALIDATION OF THE INTERACTIONS BETWEEN PULP, CHARGE AND MILL STRUCTURE IN A FULL-

BODY MODEL TUMBLING MILL

P. Jonsén1, B. Pålsson2

1Division of Mechanics of Solid Materials, LTU, Luleå, Sweden 2MiMeR – Minerals and Metallurgical Engineering, LTU, Luleå, Sweden

Grinding in tumbling mills is a process to reduce

the particle size of extracted ore and is regularly used in concentrating plants. It is a multi-physics process with many factors affecting the result. Major challenges for today’s wet tumbling mill operations

are to both increase the efficiency and obtain the right product properties. For tumbling mills, therefore, understanding of the charge motion within the mill is of importance. Tumbling mill systems consist of the mill lining, grinding balls, grinding media, and pulp that each need suitable numerical models to simulate correctly their physical behaviour. However, to efficiently model wet grinding in tumbling mills is a difficult task because of the complex behaviour of the pulp with free surfaces and large deformations. The difficulty is usually that the method to represent and reproduce its movements is computationally demanding and time consuming. A novel way to model wet grinding in tumbling mills via coupling of different numerical methods have been presented by Jonsén et al. [1]. In this work, the method in [1] is used to explore the possibility to efficiently model and simulate the whole mill body, including the pulp and the charge movement. This is done with a solver based on the particle finite element method (PFEM) [2] implemented in LS-Dyna. PFEM is a Lagrange based method that gives the opportunity to efficiently model the pulp free surface flow, and its interaction with grinding balls and mill structure. It uses an arbitrary Lagrangian Eulerian (ALE) approach in combination with an automatic volume mesher and finite element shape functions for solving incompressible flow. To handle free surface flows, there is also a bi-phasic flow capability that involves modelling using a conservative level-set interface tracking technique. In this case, the ICFD and DEM solvers are coupled via a two-way coupling.

The charge movement will induce loading on the

grinding media in a tumbling mill. Some important properties that will affect the grinding efficiency are the filling rate, rotational speed, density and viscosity. By the usage of a fluid PFEM-solver, the pressure can be predicted in the pulp during charge motion. A snapshot of the pressure distribution in front of the lifter as it travels through the graded charge with a magnetite pulp is obtained at the five o’clock position in Figure 1. The figure illustrates the pressure distribution along the lifter, mill shell and the mill end at the same time. From the pressure

distribution it is observed that pressure increase in front and close to the mill shell follows the lifters during the passage through the charge. One interesting feature that simulation can be used to study is the cyclic loading of the charge due to the lifter movements. As the lifter hits the charge, the pressure increases, but it decline as the lifter is about to leave the charge.

Figure 1: A snapshot of the pulp pressure distribution during grinding

Validation is done against experimentally measured driving torque signatures from an instrumented small-scale batch ball mill equipped with an accurate torque meter, and charge movements captured from high-speed video. Numerical results are in good agreement with experimental torque measurements.

References

[1] Jonsén, P. et al., Preliminary validation of a new way to model physical interactions between pulp, charge and mill structure in tumbling mills. Minerals Engineering, 130, 76-84 (2019)

[2] Pin, F.D. et al., The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid–

object interactions, Computers & Fluids, 36, 27–

38. (2007) __________________________________________ Corresponding author email: [email protected]

51


Innovative welding of rails – resulting microstructure and residual stresses

B. L. Josefson1, J. Brouzoulis2, R Bisschop3, T Andersson4, M Maglio2

1Department of Industrial and Materials Science, Chalmers, Göteborg, Sweden

2Department of Mechanics and Maritime Sciences, Chalmers, Göteborg, Sweden 3RISE, Borås, Sweden

4ÅF, Göteborg, Sweden

Rail welds constitute a problem in that there will be a degradation of the weld upper surface (the rail head) giving an irregular geometry and higher dynamic forces when trains pass. This is due to different microstructures in the weld and in the rail, and will result in higher cost for track maintenance. In the EU-project WRIST (a Horizon 2020 project) this problem has been addressed by developing and demonstrating two innovative methods for joining rails; automatic forged aluminothermic welding (ATW) and orbital friction welding (OFW). The aim is to reduce the width of the Heat Affected Zone (HAZ) and thereby minimize the loss of mechanical properties in the weld zone. At Chalmers, models for thermo-mechanical finite element analysis of the two welding methods have been developed. For the OFW method, a heat generation model has been validated against the pilot case of friction welding (FW) of a thin-walled pipe. Using this model, temperatures and deformations during OFW of rails have been simulated for the current design of the machine (Figure 1). The model gives the temperature history in the rail and intermediate disc, whereby cooling rates can be determined and the final microstructure and the size of the HAZ estimated for different choices of process parameters. Figure 2 shows the temperature field and deformations after the heating phase of OFW of a bar. For the ATW method, a thermo-mechanical model of the full process has been developed. The process includes preheating, tapping, pouring of molten material, applying a compressive force (forging) and shearing of excess material. Figure 3 shows the method used in track. The frame (in yellow) used to enforce the forging is visible. Also here, the final microstructure and the size of the HAZ is estimated. Figure 4 shows the resulting residual vertical stress field in the weld with high tensile values in the web.

Figure 1: Orbital friction welding machine (Gent)

Figure 2: Simulated OFW of bar

Figure 3: Thermite welding with extra forging

Figure 4: Residual vertical stress field _________________________________________ Corresponding author email: [email protected]

52


IN-PLANE ELASTIC BEHAVIOUR OF TRANSPARENT WOOD COMPOSITE MEASURED WITH DIGITAL IMAGE CORRELATION

Erik Jungstedt1,2, Lars Berglund2, Sören Östlund1

1Department of Solid Mechanics, KTH, Stockholm, Sweden

2Department of Fiber and Polymer Technology, KTH, Stockholm, Sweden

Wood has been used as a load-bearing material in

applications such as buildings and constructions for years, due to its renewable nature, easy manufacturing ability and excellent mechanical performance. The advancement of nanotechnology enables modifications within the wood hierarchical structure such as lumen and cell wall, providing new possible functionalities when impregnated in a poly methyl methacrylate (PMMA) matrix. Particularly, the concept of transparent wood composite stands out since it has interesting optical properties while preserving the load bearing capacity and microstructure that wood naturally has [1].

The reinforcement effects from a delignified, nanoporous wood template are unknown, and are compared with native wood veneer as the reinforcement. It has earlier been shown that transparent wood composites are possible to laminate for desired mechanical performance, which expands the usability for the material as it can be customized for applications [2]. However, characterization of the in-plane elastic parameters from a single ply is then a necessity as they form the basis of lamination theory of orthotropic materials. Within this work the interest is to determine the four elastic parameters. The in-plane strain field is also investigated in detail during deformation, and reinforcement effects are analysed. To resolve the matters a set of tensile experiments were done and a non-contact deformation measurement technique (digital image correlation, DIC) was used to capture the strain fields during quasi-static loading. The focus has been on small strip samples from veneers with material axes along the woods tangential (T) and longitudinal (L) axes.

It is found from experiments that native wood specimens has more strain concentration regions, at the same average strain level, than a transparent wood composites, see Figure 1.

Figure 1: Tensile loading across the fiber direction (T-axis) with strain field plots at average strain 0.0037 along the loading axis, vertical direction of the image. a) Native Wood and b) transparent wood composite.

References

[1] Y. Li, Q. Fu, S. Yu, L. Berglund, Optically Transparent Wood from a Nanoporous Cellulosic Template: Combining Functional and Structural Performance, Biomacromolecules.

[2] Q. Fu, M. Yan, E. Jungstedt, X. Yang, Y. Li, L.A. Berglund, Transparent plywood as a load-bearing and luminescent biocomposite, Compos. Sci. Technol. 164 (2018) 296-303. ______________________________________ Corresponding author email: [email protected]

53


FRACTURE PROCESSES IN PACKAGING MATERIAL A REVIEW OF RESEARCH COLLABORATION BETWEEN BTH AND A PACKAGE COMPANY

S. Kao-Walter1,4, E. Andreasson1,2, M.S. Islam1, E. Mfoumou3

1Department of Mechanical Engineering, Blekinge Tekniska Högskola, Karlskrona, Sweden

2Tetra Pak Packaging Solutions AB, Lund, Sweden 3Applied Research & Innovation, Nova Scotia Community College, Dartmouth NS, Canada

4Faculty of Engineering, Shanghai Polytechnic Univ., Shanghai, China

The research group in the department of mechanical engineering at Blekinge Institute of Technology has worked for several years with different projects together with Tetra Pak® - a packaging company. The work has been focused on fundamental mechanical and fracture mechanical understanding of the material behaviour in individual material layer and the corresponding laminate. A typical material structure used in most of the packages that the company produces is shown in Figure 1.

Figure 1: The material structure with an example of an aseptic package with a screw cap opening

One of the important conclusions from [1] is that if a thin sheet composed of metal and polymer are laminated together with a crack through the centre of the sheet, the peak load is almost the same as the sum of the peak loads for each layer during tensile testing. This suggests that both materials reach the peak stress simultaneously and are probably enforced by the large straining in a small region in the vicinity of the crack tip. It has also been observed that the energy required before onset of fracture is unexpectedly larger than for the sum of the single layers.

This has been further developed in [3]. With a micro-mechanical approach using SEM together with a slip-line theory, it was found that the fracture or failure process of the laminate is a continuous plastic deformation. However, the thickness of the polymer layer does not continuously reduce to zero in the laminate. A significant strain hardening occurs in a localised region where the metal layer has already broken.

Later, the mechanism of delamination and strength of bond of above-mentioned phenomenon has also been further studied both by experiment and Finite Element simulation method in [3, 4]. Particularly, contribution on the laminate interface

characterization and FEM simulation in shear was published in [4]. The essential work for shear fracture in polymer sheets had also been studied with a modified shear test specimen in [4].

In [2], an acoustic and laser sensing of vibration method has been introduced in order to remotely characterize the mechanical properties of the thin sheet based on a series of equations. One of them that has been used to predict the Young’s modulus of the laminate is:

𝑓𝑓0𝑛𝑛2 =𝐸𝐸𝑛𝑛2

4𝜌𝜌𝑏𝑏2𝜖𝜖

Where 𝑓𝑓0𝑛𝑛2 is the frequency, 𝐸𝐸 is the Young’s

modulus, 𝑛𝑛 is the mode number, 𝜌𝜌 is the density, 𝑏𝑏 and 𝜖𝜖 are the constant dimensional properties of the material and the strain for a given specimen.

Acknowledgement

The authors would like to thank for the financial support from Tetra Pak® and KKs foundation for several of us. We are also grateful for all supervisors and co-supervisors during our thesis works.

References

[1] Kao-Walter, S., “On the Fracture of Thin Laminates” Doctoral Dissertation Series No. 2004:07, Blekinge Institute of Technology (2004).

[2] Mfoumou, E., “Low Frequency Acoustic Excitation and Laser Sensing of Vibration as a Tool for Remote Characterization of Thin Sheets”, Doctoral Dissertation Series No. 2008:16, Blekinge Institute of Technology (2008).

[3] Andreasson, E., “Realistic Package Opening Simulation- An experimental Mechanics and Physics Based Approach”, Licentiate Dissertation Series Nu. 2015:02, Blekinge Institute of Technology (2015).

[4] Islam, S. “Shear Fracture and Delamination in Packaging Material- A study of Experimental Methods and Simulation Techniques”, Licentiate Dissertation Series Nu. 2016:05, Blekinge Institute of Technology, (2016).


54


CROSS-FLOW INSTABILITY AND TRANSITION ON A ROTATING CONE

K. Kato1, T. Kawata2, A. Segalini1, P. H. Alfredsson1, R. J. Lingwood1,3

1Department of Mechanics, KTH, Stockholm, Sweden2Department of Mechanical Engineering, Tokyo University of Science, Japan

3Department of Mechanical and Aerospace Engineering, Brunel University London, UK.

In three-dimensional boundary layers, such as those onswept wings, the existence of a cross-flow (spanwise) ve-locity component gives an inflectional velocity profile thatresults in a cross-flow instability. That instability devel-ops into stationary, chordwise-aligned co-rotating vorticesthat finally break down through a secondary instability, aprocess completely different compared to the amplifica-tion and breakdown of Tollmien-Schlichting waves in two-dimensional boundary layers.

The flow induced by a rotating disk or cone in a stillfluid can be regarded as a general model for such a bound-ary layer. In contrast to the swept-wing flow, the boundary-layer velocity field of the rotating-disk/cone flow can be de-scribed by a unique similarity solution. Also here the flowhas a cross-flow velocity component, directed toward theouter radial direction, giving rise to the same type of flowinstability that also here develops into co-rotating vortices.

The flow geometry is defined by the cone-apex angle (Fig. 1), and earlier research has shown that on a broad cone(including the disk case with = 90) cross-flow instabil-ities control the flow, whereas on sharper cones ( . 40)centrifugal instability becomes important. Our long-termaim is to shed light on these different instabilities and howthey influence laminar-turbulent transition. In our labora-tory we have earlier studied rotating disks, both throughexperiments and numerical simulations [1,2]; in the presentwork, however, we mainly report experimental results fora cone with = 60 and a base diameter of 474 mm, thatrotates at a rate of = 900 rpm.

An orthogonal coordinate system (x, , z) is defined inFig. 1, where x, and z are the coordinates along the gener-ating line of the cone, azimuthal and wall-normal directionswith the origin located at the apex of the cone. Lengths arenormalized by =

p/( sin ), where is the kine-

matic viscosity of the surrounding fluid. Artificial rough-ness elements with a height of a few micrometers were uni-formly mounted on the surface to trigger the cross-flow vor-tices deterministically. Hot-wire anemometry using a smallsingle wire probe was used to measure the azimuthal veloc-ity in the thin cone boundary layer (boundary layer thick-ness approx. 1.2 mm in the laminar region).

The obtained azimuthal velocity fluctuation v (normal-ized by the local wall velocity) captures the developmentof the instability. An example is shown in Fig. 1; inclined(with respect to ) and stationary (with respect to the disk)disturbances, grow to become spiral vortices, which are ob-served as pairs of high- and low-speed regions of phase-averaged velocity fluctuation v. For small x, the vorticesdevelops in accordance with local linear stability analysis.For larger x where nonlinearity becomes significant, the

roughness

abc

linear region

Figure 1: The coordinate system (x, , z) on the cone; the colorcontour shows the phase-average velocity v at z = 1.2.

(c)

012345

0 2 4 66 8 10 12 14 16

(b)

012345

0 2 4 66 8 10 12 14 16 18

(a)

0 2 4 66 8 10 12 14 16 180123

20

Figure 2: Cross sections of the spiral vortex at three different lo-cations: (a) x = 461, (b) x = 479 and (c) x = 498.The isolines shows a conditional-averaged azimuthalvelocity hvi with a spacing of hvi = 0.1. Negativecontours are dashed. x0 is the coordinate normal to thevortex axis as shown in Fig. 1.

high- and low-speed regions begin to be distorted; as xincreases these regions become more asymmetric and ex-tend toward the outer layer resulting in a thickening of theboundary layer as shown in Fig. 2. Finally, the vorticesbreak down, leading to transition to turbulence.

[1] Imayama, S., Alfredsson, P. H. & Lingwood, R. J. 2016Experimental study of rotating-disk boundary-layer flowwith surface roughness. J. Fluid. Mech. 786, 5–28.[2] Appelquist, E., Schlatter, P., Alfredsson, P. H. & Ling-wood, R. J. 2018 Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices. J. Fluid.Mech. 836, 43–71.


55


Determination of non-linear scattering matrices of perforated plates

N. Khodashenas 1, H. Bodén1, S. Boij1

1Department of Aeronautical and Vehicle Engineering, MWL, KTH, Stockholm, Sweden

Perforate plates and Micro-perforated plates (MPP) are devices used to absorb sound and reducing its intensity. They consist of a thin plate, with small punched or drilled holes. Perforates appears in many technical applications, e.g., automotive mufflers, aircraft engine liners, combustion chambers, ventilation systems and room acoustic. It is well-known from the literature that perforated plate noise reduction can be influenced by the mean flow field, temperature, and acoustic excitation level. They can become non-linear at fairly low acoustic excitation levels. The purpose of the present work is to study the non-linearity at the perforated plate, which is associated with large particle velocities, and directly extract the non-linear acoustic properties including harmonic interaction from a limited set of experiments using either random or periodic excitations. To increase the physical understanding and develop a model including these effects is the main goal of this project. To collect the required data experimental investigation has been performed on a sample with 2.4% open area which can be seen in figure 1 using tonal and broadband excitation.

Figure 1: Schematic of the setup

To model the non-linearity, techniques has been developed to study perforated plates in the non-linear regime [1-3]. Non-linear losses are associated with the acoustic particle velocity in the holes and vortex shedding at the outlet side of the perforated opening due to high-pressure levels. For pure tone excitation, the impedance will be associated with the acoustic particle velocity at that frequency. If the acoustic excitation is random or periodic with multiple harmonics the impedance at a specific frequency will depend on the particle velocity at other frequencies. A non-linear scattering matrix describing the relation between the high-level excitation at frequency f and response at f and 3f can be described by the following matrix equation [1].

" 𝑃$(𝑓)

𝑃$(3𝑓)) = +

𝑆-,- 0𝑆0-,- 𝑆0-,0-

1 " 𝑃2(𝑓)

𝑃2(3𝑓))

Experimental results for the scattering coefficient from the different incident frequencies with different levels of excitation to the third harmonic of that frequency can be seen in figure 2. The absolute value of scattering matrix element S3f,f is plotted against an inverse Strouhal_number based on the acoustic particle velocity in the holes and the hole diameter.

Figure 2: Scattering matrix element S3f,1f

These preliminary results show that it is promising to describe the physics of nonlinear harmonic interaction effects for perforates with the nonlinear scattering matrix model coefficient.

References [1] Bodén, H. “One-sided multi-port techniques for

characterisation of in-duct samples with nonlinear acoustic properties,” Journal of Sound and Vibration, 331, 3050-3067, (2012).

[2] Bodén, H. “Two-sided multi-port techniques forcharacterisation of in- duct samples with non-linear acoustic properties.” Acustica united with Acta Acustica, 99, 359-378, (2013).

[3] Boden, H. "Non-linear System IdentificationTechniques for Determination of the Acoustic Properties of Perforates." In 21st AIAA/CEAS Aeroacoustics Conference, 3266, (2015).

[4] Khodashenas. N, Bodén. H, Boij. S."Determination of nonlinear acoustic properties of perforates using band-limited random excitation." 11th European Congress and Exposition on Noise Control Engineering, Euronoise, (2018).

Corresponding author email: [email protected]

Abs

(S3f

,f )

Invers Strouhal-number

56


DYNAMICS OF TIP-VORTICES OF TWO IN-LINE WIND TURBINES

V. G. Kleine1,2, E. Kleusberg1, A. Hanifi1, D. S. Henningson1

1KTH Royal Institute of Technology, Linne FLOW Centre, Dept. of Mechanics, Stockholm, Sweden2Instituto Tecnologico de Aeronautica, Divisao de Eng. Aeronautica e Aeroespacial, Sao Jose dos Campos - SP, Brazil

The dynamics and hydrodynamic stability of a vor-tex system behind two in-line wind turbines operatingat low tip-speed ratios is investigated using the actuator-line method in conjunction with the spectral-element flowsolver Nek5000. To this end, a simplified setup with twoidentical wind turbine geometries, based on the setup ofBlind Test 2 [1], rotating at the same tip-speed ratio issimulated and compared with a single turbine wake. Thisnumerical setup was validated against experimental cam-paigns undertaken at the Norwegian University of Scienceand Technology (NTNU Blind Tests) [2].

Using the rotating frame of reference, a steady solution isobtained, which serves as a base state to study the growthmechanisms of induced perturbations to the system. It isshown that, already in the steady state, the tip vortices ofthe two turbines interact with each other, exhibiting the so-called overtaking phenomenon. Hereby, the tip vortices ofthe upstream turbine overtake those of the downstream tur-bine repeatedly (Fig. 1).

Figure 1: Streamwise velocity along the wake for the steady solu-tion for a single turbine (top) and in-line turbines (bot-tom). Iso-surfaces of vorticity magnitude are shown ingrey.

In order to study the stability of the system, the tip vor-tices are perturbed harmonically, following the methodol-ogy applied in previous studies [3, 4]. By applying tar-geted harmonic excitations at the upstream turbine’s bladetips a variety of modes are excited and grow with down-stream distance. Dynamic mode decomposition (DMD) ofthis perturbed flow field showed that the unstable out-of-phase mode (azimuthal wavenumber k = 3/2) is domi-nant, both with and without the presence of the second tur-bine. Further, short-wave instabilities were shown to growin the numerical simulations, similar to existing experimen-tal studies [5].

The perturbations of the upstream turbine’s helical vor-tex system led to the destabilization of the tip vorticesshed by the downstream turbine. Two distinct mechanismswere observed: for the frequency associated to wavenum-ber k = 3/2 the downstream turbine’s vortices oscillate in

Figure 2: Selected dynamic modes depicted using positive andnegative iso-contours of the real part of streamwisecomponent of the mode downstream of the second tur-bine (6.5 ≤ z ≤ 9). Iso-surfaces of vorticity are shownin grey. Left: k = 3/2. Right: k = 3.

phase with the vortex system of the upstream turbine whilefor k = 3 a clear out-of-phase behaviour is observed, ascan be seen in Fig. 2. By calculating the velocity inducedby helical vortex filaments [6], a simplified model is devel-oped and applied in attempt to understand the dynamics ofthe vortices.

References

[1] Pierella, F., Krogstad, P., and Sætran, L., Blind Test2 calculations for two in-line model wind turbineswhere the downstream turbine operates at various ro-tational speeds, Renewable Energy, 70, 62–77 (2014)

[2] Kleusberg, E., Mikkelsen, R.F., Schlatter, P., Ivanell,S., and Henningson, D.S., High-order numerical sim-ulations of wind turbine wakes. Journal of Physics:Conference Series, 854 012025 (2017)

[3] Ivanell, S., Mikkelsen, R., and Sørensen, J.N. andHenningson, D.S., Stability analysis of the tip vorticesof a wind turbine. Wind Energy, 13:705715 (2010)

[4] Sarmast, S. and Dadfar, R. and Mikkelsen, R.F. andSchlatter, P. and Ivanell, S. and Sørensen, J.N. andHenningson, D.S, Mutual inductance instability of thetip vortices behind a wind turbine. Journal of FluidMechanics, 755, 705–731 (2014)

[5] Leweke, T. and Quaranta, H.U. and Bolnot, H. andBlanco-Rodrıguez, F.J. and Le Dizes, S., Long-andshort-wave instabilities in helical vortices. Journal ofPhysics: Conference Series, 524 012154(2014)

[6] Fukumoto, Y. and Okulov, V.L., The velocity field in-duced by a helical vortex tube. Physics of Fluids, 17107101 (2005)


57


Design and process analysis of composite reinforcement for automotive Body-in-White

S.Kumaraswamy1, Z. van der Putten1, R.Gutkin , M.Åkermo2 1Volvo Car Corporation, Gothenburg, Sweden

2Department of aeronautical engineering, KTH, Stockholm, Sweden

Automotive body structures have traditionally been dominated by sheet metal parts. The low cost and existing knowledge of product development makes steel and aluminium sheet metal a preferred choice for body structures. However, the weight penalty of the usage of steel has an effect on the efficiency and emissions of the automotive[1][2]. One of the main hurdles to implementing fiber-composites is the lack of existing processes and workflow to efficiently develop the components. The paper focusses on development of a composite part while demonstrating the key steps in the process. A closed loop between design development based on structural and process simulations is demonstrated. The automotive Body-in-white generally consists of 200 individual components. These structures are developed to meet the crash safety, solidity and durability requirements of the automotive. A conventional C-ring is a set of steel parts which are welded together to improve the torsional stiffness of the body. This makes it a promising yet challenging area to implement structural composites into. In the presented work, composite C-ring is consequently designed, an optimised laminate stack-up is chosen and the design is refined using process analysis.

Figure 1. Conventional C-ring in a Volvo S90

Design and Process analysis In order to meet the high-volumes required by the automotive industry, prepreg compression moulding(PCM) has been chosen as the preferred manufacturing method for the composite C-ring. The artefacts i.e. forming induced defects of PCM have a pronounced impact on the properties of the final part. Hence, process modelling and analysis is key to ensure the quality and fulfilment of the intended function. The initial design of the C-ring is based on a topology analysis done to highlight the load paths critical for the torsional stiffness of the body. An initial design is made based on the topology optimisation. This initial design is then analysed by a simple draping tool for the basic formability of the 2D textile into a 3D shape. The feedback from the draping analysis is used to refine the design to suit

composite manufacturing. Free size composite optimisation is then used to define the stacking sequence of the composite laminate. Process modelling is thereafter used to detect forming defects during manufacturing of the component. The fiber directions and presence of other defects are simulated. Process modelling helps manipulate the occurrence of defects by changing the lay-up of the plies in the component or refining the process setup to suit the geometry i.e. blank holder configurations and positions. Commercially available tools such as LS-Dyna and AniForm are used to perform the process analysis. The results from the process simulation is then fed back into the structural analysis to verify that the forming induced defects and shear deformations of the fibers have not had a considerable impact on the performance of the component. A comparison of the initial investment for the existing steel C-ring assembly and the proposed composite C-ring is given. A comparison of the part price of the composite C-ring is made. Results and Discussion A Composite C-ring reinforcement is developed which meets performance requirements and offers a substantial weight saving on the existing steel assembly. The usage of process modelling has helped refining the design of the part and optimising material usage and reducing the risks of manuafacturing errors and thereby lowering the cost. Along with the weight saving, usage of fiber composites also helped integrating multiple components which reduces the cost of joining and initial investments. The key steps in development of composite body-in-white part are highlighted. The closed-loop simulation-centric workflow is proposed and demonstrated. Constitutive modelling of prepreg compression moulding aids to refine the design of a composite structure. Potential areas of improvement for the process modelling of composites are highlighted. References

[1] S.Kumaraswamy, Literature review, Integrated design and process analysis of composite body.

[2] H Molker,Renaud Gutkin, Leif Asp, Effeicient sizing method for composites n automotive applications, 16 th European conference on composite materials, 2014

[3] LSTC, LS Dyna User manual, 2016 [4] Altair Engineering, Optistruct User tutorials, 2014 [5] A. C. Long and M. J. Clifford, “Composite forming

mechanisms and materials characterisation,” Compos.

Form. Technol., pp. 1–21, 2007. __________________________________________ Corresponding author email: [email protected]

58


WHEN, WHERE, HOW; PREDICTING CRYSTALLOGRAPHIC CRACKING

D. Leidermark1 and C. Busse1

1Division of Solid Mechanics, Linkoping University, 58183 Linkoping, Sweden

Today, gas turbines are operating under more cyclic load-ing conditions due to power grid balancing of intermittentrenewable energy sources. This increases the risk for fa-tigue, and primarily thermomechanical fatigue at the highoperating temperatures. One of the critical regions is thefirst turbine stage, where the turbine blades are often cast insingle-crystal form of nickel-base superalloys due to theirexcellent properties at high temperatures.

The anisotropic behaviour of these materials bringsmany difficulties in terms of testing, modelling and fatiguelife prediction. The ability to predict the total life of sucha critical gas turbine component is of high value to the in-dustry, where traditionally attention has been on predictingthe crack initiation life. Hence, little has been done in thearea of crack growth predictions in single-crystal nickel-base superalloys over the recent years.

Basically, the crack growth behaviour in single-crystalnickel-base superalloys can be summarised into:When,whereandhow?

It has been observed that macroscopic Mode-I crackstransitions to crystallographic slip planes for continuedgrowth in these materials, and the momentwhenthe cracktransitions is of interest and plays an important role in thecrystallographic cracking framework. Work with a transi-tion criterion is currently ongoing.

The correct choice of crack driving force parameter isvital for a meaningful prediction ofwhere the crystallo-graphic cracking will occur,i.e. which crystallographic slipplane will the crack transition to. An equivalent resolvedstress intensity factor was developed based on anisotropicstress intensity factors to identify the crystallographic planein comparison to observed behaviour, according to

kEQ =√ψk2

I + k2II + k2

III (1)

wherekI = lim

r→0

√2πr n · σ · n

kII = limr→0

√2πr s · σ · n

kIII = limr→0

√2πr t · σ · n

(2)

are the anisotropic stress intensity factors resolved on thecrystallographic planes, wheren is the slip plane normal,sis the slip direction andt is orthogonal to these. The modelcan be applied for arbitrary crack front shapes and crystal-lographic orientations in a 3D context, which was validatedby isothermal crack growth tests at500C for two differentspecimen geometries, accounting for crystallographic mis-alignments. Good correlation to experiments was obtainedwhen predicting the active global crystallographic crackingplanes after the transition from the Mode-I crack [1].

After the transition, the crystallographic crack frontshape is more hyperbolic and advances at a higher rate

Crystallographic

Mode-I

Figure 1: Fracture surface of a Kb-specimen, showing the twocracking modes and heat tints. The dashed lines displaythe heat tints on the crystallographic planes.

compared to the Mode-I crack front, see Figure 1 for a typ-ical fracture surface. Hence, an evaluation ofhowthe crackfront and growth rate on the crystallographic slip planesdevelop was done to be able to quantify a crack growthmodel for single-crystal nickel-base superalloys [2]. Basedon the above equivalent resolved stress intensity factor, tak-ing ψ = 0, and evaluating heat tints from the experiments,the following model was obtained

(dL

dN

)

c

= Cc (∆kEQ)nc (3)

whereCc andnc are material parameters, and(dL/dN)c

is the crystallographic crack growth rate based on the crys-tallographic crack length,L. The crack growth model en-ables to correlate all the crystallographic cracks in a nar-row band, and also showing that the crystallographic crackgrowth rate is higher compared to Mode-I.

Hence, a methodology able to predict crystallographiccracking in single-crystal nickel-base superalloys has beendefined and developed. Good correlation to performed ex-periments was obtained, regardingwherethe crack transi-tions to andhowfast it propagates.

References

[1] Busse, C., Palmert, F., Sjodin, B., Almroth, P.,Gustafsson, D., Simonsson, K., Leidermark, D., Pre-diction of crystallographic cracking planes in single-crystal nickel-base superalloys, Engineering FractureMechanics, 196, 206-223, (2018)

[2] Busse, C., Palmert, F., Wawrzynek, P., Sjodin, B.,Gustafsson, D., Leidermark, D., Crystallographiccrack propagation rate in single-crystal nickelbase su-peralloys, MATEC Web Conferences, 12th Interna-tional Fatigue Congress, 165, 13012, (2018)


59


BLOOD FLOW DYNAMICS AND MIXING: A STUDY OF THE

RETURN CANNULA

J. Lemétayer1, L. Fuchs1, L. M. Broman2,3, L. Prahl Wittberg1

1Linné FLOW Center & BioMEx, Department of Mechanics, KTH, Stockholm, Sweden 2ECMO Centre Karolinska, Karolinska University Hospital, Stockholm, Sweden

3Department of Physiology and Pharmacology, Karolinska Institutet, Stockholm, Sweden

Cannula flow is of interest in several medical

situations where the blood needs to be drained from or returned to the circulatory system. One such application is Extracorporeal Membrane Oxygenation (ECMO), a life-saving therapy used for temporary support of lung and heart function in the critical ill. However, ECMO treatment is not complication free. Complications associated with ECMO circuitry are thromboembolic and hemorrhagic events due to the non-physiological exposure of blood flow to artificial surfaces.

In this study, the focus is on the return cannula, a particularly sensitive component due to the interaction between the cannula blood flow and the blood flow in the punctured vessel [1]. The geometry of the cannula, its position in the vessel and the flow rate are parameters whose effects have to be established to reduce ECMO related complications.

The investigated geometry is a cannula placed in an outer cylinder, maintaining the dimensions as found in ECMO (Figure 1). The experimental set-up is designed such that the lateral position of the cannula can change (rotation system on Figure 1). To assess the level of mixing between cannula and vessel flows as well as the stresses in the flow, experiments using Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) are carried out for different cannula to vessel flow rate ratios.

Figure 1: Representation of the experimental set-up

The overall aim with this study is to understand the flow and the mixing associated with a cannula placed in a vessel. The experimental data describes the development of the cannula jet showing the shear

layer between the cannula jet and the vessel flow. In the shear layer, the shear stress intensity is comparable to the threshold for platelet activation previously reported in literature [2]. The cannula jet induces a mixing through three mixing processes. Kelvin-Helmholtz vortices and lateral entrainment of the vessel flow contribute to the mixing like for a free jet. Moreover, due to the confinement by the vessel, a backflow along the vessel wall forms (represented by white arrows on Figure 2). This flow structure is the most efficient mixing process and also the most sensitive to the geometry and flow conditions. Using Proper Orthogonal Decomposition (POD), the complexity of the backflow has been elucidated, highlighting the main structures composing the flow.

Figure 2: Instantaneous flow fields of the mixture

fraction for a flow rate of 1.3 L/min in both the cannula and the vessel with a 1 s interval

References

[1] Fuchs, G., Berg, N., Broman, L.M., Prahl Wittberg, L., Flow-induced platelet activation in components of the extracorporeal membrane oxygenation circuit, Scientific Reports, 8(1), 13985 (2018)

[2] Sallam, A.M., Hwang, N.H.C, Human red blood cell hemolysis in a turbulent shear flow: contribution of Reynolds shear stresses, Biorheology, 21(6), 783-797 (1984)


Tank

Outer tube

Cannula

Rotation system

t

t+1s

60


CUBES OR SPHERES - DOES IT MATTER?TRANSITION IN PARTICULATE PIPE FLOW

M. Leskovec1,2, F. Lundell1,2,3, F. Innings4,5

1Department of Mechanics, KTH, Stockholm, Sweden2Linne Flow Centre, Stockholm, Sweden

3Wallenberg Wood Science Center, Stockholm, Sweden4Tetra Pak Processing Systems, Lund, Sweden

5Department of Food Technology, Lund University, Lund, Sweden

Studies of transitional pipe flow have been performedsince the 1880s and the work of Reynolds [1]. However,some aspects of this flow phenomena is still not fully un-derstood. Pipe flow slightly above a certain Reynolds num-ber (Re = UbD/ν, where Ub is bulk flow velocity, D pipediameter and ν is kinematic viscosity) is seen to be unsta-ble and turbulent spots appear that grow in size and ampli-tude. The flow is in a state known as the intermittent regimewhere the flow is transitioning from laminar to turbulence.This threshold Re is called the critical Reynolds number(Rec) and for a Newtonian fluid it ranges from 1700−2300.It is possible to trigger the transition earlier or delay it tohigher Re by introducing or reducing perturbations fromthe flow. One way of introducing perturbations is the addi-tion of solid particles to form a suspension flow. Matas etal. [2] showed that Rec for suspensions not only dependson particle size (dp) and volume fraction of particles (φ =volume of particles/volume of fluid), but also that Rec isa non-monotonic function of φ for a range of particle sizes(1/65 < dp/D < 1/10).

Velocity fields of the suspension flows could provide in-formation needed for further insights to this flow phenom-ena. At high φ issues can arise for traditional experimentalmethods, such as Particle Image Velocimetry (PIV). Par-ticles disturb the measurements and lead to noisy data, ormaybe no data at all. MacKenzie et al. [3] performed ve-locity and turbulence stress measurements in fibre suspen-sion flows using Phase-Contrast Magnetic Resonance Ve-locimetry (PC-MRI). With this method, it is possible to ob-tain experimental data from non-transparent suspensions.

This work aims at investigating the dependency on Recfor larger particles (dp/D > 1/5) and whether the particleshape could change the transitional behaviour in suspen-sion pipe flow. Experiments are performed in a continuousflow loop driven by a centrifugal pump (Flygt 3085.183)with a modified casing and impeller to handle the parti-cles. The flow rate is measured using an electromagneticflow meter (Krohne Optiflux 1000) and the pressure dropbetween two taps in the pipe wall is measured using adifferential pressure transducer (0-6 kPa, model: FKC11,Fuji Electric, S.A.S.). The inner diameter D of the pipeis 34 mm and the first pressure tap is located 90 L/Ddownstream the entrance of the pipe. The experimentalrig can been used to measure the Fanning friction factor(f = τw/

12ρU

2b . τw is wall shear stress which is obtained

from the pressure drop and ρ is fluid density). For spheri-

cal particles of size dp/D = 1/6 with varying φ the fric-tion factor is seen to increase for a given Re, see Figure1. The investigated flow cases show a different transitionalbehaviour for this range of Re, the flow seems to go fromlaminar to turbulent by-passing the traditional transitionclearly seen for single-phase flow. Future investigationswill be done by changing the geometrical shape of the par-ticles (to cubical) and also by spanning a larger range ofReynolds numbers. The friction factor will be measuredalong with velocity and turbulence statistics for a numberof flow cases. It is possible that the transition is occurringat even lower Re and further investigations can give vitalinformation on how the introduction of disturbances fromparticles triggers this transition.

103

104

Re

10-2

10-1

f

16/Re

C-W

0%

5%

10%

20%

30%

Figure 1: Increasing the particle volume fraction increases thepressure drop in the system. It also changes the crit-ical Reynolds number where transition occurs.

References

[1] Reynolds, O., Philos. Trans. R. Soc. London 174, 935(1883)

[2] Matas, J.-P., Morris, J.F., and Guazzelli, E., Phys.Rev. Lett. 90, 014501 (2003)

[3] MacKenzie, J., et al., Physics of Fluids 30, 025104(2018)


61


WALL MODELLING OR WALL RESOLVING IN LARGE-EDDYSIMULATION – WHAT ARE THE TRADE-OFFS IN COST AND

ACCURACY?

M. Liefvendahl1,2, T. Mukha2, S. Rezaeiravesh3

1Swedish Defence Research Agency (FOI), Stockholm, Sweden2Department of Mechanics and Maritime Sciences, Chalmers, Goteborg, Sweden


Wall-bounded flows are a challenge for large-eddy sim-ulation (LES). A key difficulty is that in the very near-wallflow, the energetic eddies are not “large”, instead they scalewith the viscous length scale, δν = ν

√ρ/τw (see e.g. [2]),

determined by the wall-shear stress. Thus two approachesnaturally arises. Either these eddies are resolved, which isreferred to as wall-resolved (WR-)LES, or a specific modelis developed for the near-wall flow, which is the concept ofwall-modelled (WM-)LES.

The choice between the two approaches has fundamen-tal implications for the resulting computational cost of thesimulation, as was pointed out already in [1], as well as forthe predicitive accuracy and what information can be ex-tracted from the simulation concerning the near-wall flow.This important trade-off (cost/accuracy) will be discussedbased on recent very extensive simulation campaigns of tur-bulent channel flow with WRLES [4], and WMLES [5], re-spectively. The simulations were done using the softwareOpenFOAM, for which the WMLES-capabilities were sig-nificantly extended by the development of an open sourcelibrary for wall-modelling [3].

For a turbulent boundary layer, the ideal for WMLES isthat a fixed grid resolution relative to the boundary layerthickness, δ, suffices. For channel flow, δ corresponds tothe channel half-width, and thus a Re-number independentgrid. For WRLES on the other hand, eddies on the scaleof δν must be resolved which leads to the number of gridpoints growing as, N ∼ Re2τ .

Figure 1: Error (in %) for the friction velocity as function of gridresolution for WRLES.

The predictive accuracy for the friction velocity (WR-LES, Reτ = 300), as a function of the grid resolution inthe stream- and spanwise directions, is illustrated in fig-ure 1. The meta-model for the error is calculated based on25 channel flow WRLES-computations.

The error in the friction velocity (WMLES, Reτ =

5200), depending on choice of subgrid model, convectivescheme (red vs blue), wall-model parameter and grid reso-lution, is shown in figure 2.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

h/δ

-10

-8

-6

-4

-2

0

2

4

ε[〈u

τ〉]

%

WALE, n/δ = 15

WALE, n/δ = 25

Smagorinsky, n/δ = 15

Smagorinsky, n/δ = 25

Figure 2: Error in the friction velocity as a function of a wall-model parameter (sampling height, h) for WMLES.

The investigation will present the corresponding resultsalso for other quantities of interest, such as profiles of themean velocity and Re-stress components. Recommenda-tions will be given concerning choice of approach, appro-priate grid resolution and choice of wall model.

References

[1] Chapman, D.R., Compuational aerodynamics devel-opment and outlook, AIAA Journal, 17, 1293–1313,1979.

[2] Pope, S. B., Ten questions concerning the large-eddysimulation of turbulent flows, New Journal of Physics,6, 1–22, 2004.

[3] Mukha, T., Rezaeiravesh, S., Liefvendahl, M., A li-brary for wall-modelled large-eddy simulation basedon OpenFOAM technology, Accepted for publicationin Computer Physics Communications, 2019.

[4] Rezaeiravesh, S., Liefvendahl, M., Effect of grid reso-lution on large-eddy simulation of wall-bounded flow,Physics of Fluids, 30, 1–22, 2018.

[5] Rezaeiravesh, S., Mukha, T., Liefvendahl, M., Sys-tematic study of accuracy of wall-modeled large-eddy simulation using uncertainty quantification tech-niques, Submitted to Computers & FLuids, 2018.


62


METAMODELING USING SPLINE KRIGING FOR EFFICIENT GLOBALDESIGN OPTIMIZATION

Petter N. Lind and Marten OlssonDepartment of Solid Mechanics, KTH, Stockholm, Sweden

Metamodeling is a prominent tool for reducing the num-ber of function evaluations needed when performing designoptimization of computationally expensive models. TheKriging models have, among all models, gained interest fortheir exact interpolation properties and good accuracy, inparticular when used with sparse data sets [1]. The Krigingmodel facilitates an additive split into a trend and Gaussianpart which provide useful estimates of the pointwise varia-tions and errors performed when fitting the surrogate modelto the data set [2]

YYY (xxx) = FFF (xxx)βββ + eee(xxx). (1)

The first part of the right hand side of Eq. (1), FFF (xxx)βββ constitutes the trend response of the Kriging model where FFF (xxx) is a matrix of user selected trend functions and βββ its linear coefficients. The second part of Eq. (1) is the mean value of a Gaussian process that estimates the, assumed, systematic error made when fitting the trend functions.

The most efficient Kriging models of t oday implement low order polynomials as trend functions [3] and are com-monly referred to as the ordinary Kriging models. The cur-rent work present an innovative augmentation, Spline Krig-ing (SKG), that facilitates the use of natural cubic splines (NCS) in the construction of the trend functions. The us-age of NCS in the Kriging formulation has a pair of bene-fits: First, it allows for a more organic shape compared to the polynomial trend function definition without a signifi-cant increase of degree of freedoms. Secondly, it permits a global surrogate model definition which allows for imple-mentation with any global design optimization algorithm.

Preliminary experiments using the Branin test function show promising results. A statistical experiment was per-formed where 50 randomly optimal LHS for sets spanning from 16 to 38 points were generated and used for fitting OKG and SKG models. The SKG model obtained, on av-erage, a coefficient of determination value of above 99%with 18 data points in the LHS set, Figure 1. The SKG model also outperformed OKG in root mean square error (RMSE) using the same statistical approach, Figure 2.

References

[1] Jones, D. R. (2001). A taxonomy of global optimiza-tion methods based on response surfaces. Journal ofglobal optimization, 21(4), 345-383.

[2] Sasena, M. J. (2002). Flexibility and efficiency en-hancements for constrained global design optimiza-tion with kriging approximations (Doctoral disserta-tion, University of Michigan)

Figure 1: Coefficient of determination against number of samplesin the optimal LHS setup for OKG and SKG.

Figure 2: RMSE against number of samples in the optimal LHSsetup for OKG and SKG.

[3] Zhao, L., Choi, K. K., Lee, I. (2011). Metamodelingmethod using dynamic kriging for design optimiza-tion. AIAA journal, 49(9), 2034-2046.


63


A CONTINUOUS-TIME, HIGH-CYCLE FATIGUE MODEL AND ROTARYSTRESS STATES

S. B. Lindstrom1, S. Suresh1, C.-J. Thore1, A. Klarbring1

1Division of Solid Mechanics, Linkoping University, Sweden

We investigate the properties of a previously publishedcontinuous-time model for high-cycle fatigue [1, 2] in thecase of given nonproportional stress fluctuations ¯σ. Themodel is attractive owing to its potential to capture fatiguefor arbitrary stress histories, and this has motivated its usein recent developments in topology optimization with fa-tigue constraints [3].

For this continuous-time fatigue model, a back-stress ¯αis introduced to represent the stress history, and an en-durance function

β =1

Se

[√32‖¯s− ¯α‖ +Atr(¯σ) − Se

], (1)

is defined, where ‖ · ‖ denotes the Frobenius norm, ¯s isthe deviatoric stress, Se [Pa] is the endurance limit, andA > 0 is the absolute value of the slope of the linear partof the Haigh diagram. Two differential Eqs. (DEs) controlthe development of the back-stress and damage:

˙α = Θ(β)Θ(β)C(¯s− ¯α)β, (2a)

D = Θ(β)Θ(β)KeLβ β, (2b)

where Θ denotes the Heaviside step function, and C > 0,K > 0 and L > 0 are model parameters. The Heavisidestep functions appearing in these DEs ensure that damageonly develops during onloading. For the pristine material,the initial conditions are D = 0, ¯α = ¯0, and failure oc-curs when D = 1. This model has been demonstrated toreproduce the Wohler curve and Haigh diagram for steel,for stress fluctuations within the linear elastic regime andcyclic, proportional load. It also reproduces the depen-dence of the fatigue limit on the phase difference betweentwo independently controlled normal stresses [1].

We investigate the behavior of the continuous-timemodel for a superposition of uniaxial tension and simpleshear, with a phase difference ψ that is varied from ψ = 0for a proportional stress fluctuation to ψ = π

2 for a rotarystress state (Fig. 1). From experiments for a range of differ-ent steel alloys, it is known that rotary stress states, ψ = π

2 ,are much more harmful to the material than proportionalstress states, ψ = 0 [4].

We successfully fit the continuous-time model to theWohler and Haigh diagrams of AISI 4340 steel alloy, andwe show that it is also possible to adjust the model param-eters so that the rotary stress gives a shorter life than thecorresponding proportional stress state. However, we alsoobserve several problems with the model behavior for ro-tary stress states: The endurance limit is not affected bythe phase difference ψ, which is irreconcilable with exper-imental data, and leads to dangerous overestimation of fa-tigue life in the lower stress range. Moreover, we observethat the damage development for the rotary—and close to

-500

0

500

-500 0 500

√3σ

12

[

M

P

a

σ11 [MPa

Figure 1: Investigated stress paths, with phase difference ψ = 0(solid), ψ = π/3 (dashed) and ψ = π/2 (dotted).

rotary—stress states becomes erratic, in the sense that thedamage per cycle does not converge to a constant value. Webelieve that this is due to the stress path being tangential tothe endurance surface defined by β = 0, where the modelbehavior is numerically unstable due to the step functionsappearing in the DEs.

We conclude that the validity range of the existing for-mulations of the continuous-time model does not includestress fluctuations that differ significantly from propor-tional. A reformulation of the governing Eqs. is required tocontrol the model behavior for rotational stress states, andto produce a conservative fatigue life prediction in such sit-uations.

References

[1] Ottosen, N.S., Stenstrom, R., Ristinmaa, M., Con-tinuum approach to high-cycle fatigue modeling. Int.J. Fatigue, 30(6), 996-1006 (2008)

[2] Brighenti, R., Carpinteri, A., Vantadori, S., Fatiguelife assessment under a complex multiaxial load his-tory: An approach based on damage mechanics. Fa-tigue Fract. Eng. M., 35(2), 141-153 (2012)

[3] Suresh, S., Lindstrom, S.B., Thore, C.-J., Torsten-felt, B., Klarbring, A., An evolution-based high-cycle fatigue constraint in topology optimization. InH. C. Rodrigues et al. (Ed.), EngOpt2018 Conf. Proc.(pp. 844-854), Lisbon, Portugal (2018)

[4] Anes, V., Reis, L., Lin, B, de Freitas, M., New ap-proach to evaluate non-proportionality in multiaxialloading conditions. Fatigue Fract. Eng. M., 37, 1338-1354 (2014)


64


MODELLING THE CYCLIC BEHAVIOUR OF AN ADDITIVELYMANUFACTURED DUCTILE NICKEL-BASED SUPERALLOY

T. Lindstrom1, D. Ewest2, K. Simonsson1, R. Eriksson1, J-E. Lundgren2, D. Leidermark1

1Division of Solid Mechanics, Linkoping University, SE-58183 Linkoping, Sweden2Siemens Industrial Turbomachinery AB, SE-61283 Finspang, Sweden

With the introduction of additive manufacturing (AM)as a manufacturing process, the design freedom of compo-nents has increased which enables new possibilities to op-timize components. One application for AM is gas turbinecomponents, where it can be used to optimize componentswith respect to efficiency, fuel flexibility and performance.Today, AM is already adopted to repair and decrease costsof combustor components in gas turbines [1]. Such com-ponents are exposed to high temperatures and large me-chanical loads, and are therefore advantageously manufac-tured by ductile nickel-based superalloys due to their ex-cellent high temperature performance. However, due to theAM technique, the material will receive elongated grains inthe building direction, which leads to transversely isotropicmaterial behaviour. To be able to predict the cyclic life ofsuch components, a constitutive model that is able to de-scribe the material behaviour up to steady-state conditionsof a component, which also takes the material anisotropyinto account, is of great importance.

In order to characterize the behaviour of the material,uniaxial strain controlled low-cycle fatigue tests with spec-imens manufactured from a material similar to Hastelloy Xhave been conducted, with specimens manufactured in dif-ferent orientations relative the building platform of the AMmachine; 0, 45and 90(as illustrated in Fig. 1).

Figure 1: Illustration of the building orientations of the test spec-imens.

To avoid influence from the surface during testing, theas-built specimens where machined to its final diameter.

To set up the constitutive relations for the material, astructural tensor approach has been used since this directlyincorporates the material direction, i.e. the building direc-tion, into the constitutive model. From the building direc-tion v, the structural tensor is defined as

M = v ⊗ v (1)

For a transversely isotropic material, the elastic be-haviour is described with five independent constants, where

two of these describes the isotropic behaviour while thethree others describes the anisotropic behaviour based onthe above defined structural tensor. The yield behaviouris modelled using a Hill criterion, where a fourth-orderanisotropic tensor enters the yield function to take care ofthe directional dependent yield behaviour. The Hill crite-rion is defined as

f =√

σ2Y (S− ααα) : P : (S− ααα)− σY = 0 (2)

where P is the anisotropic tensor dependent on the struc-tural tensor, S is the deviatoric stress, ααα is the backstressand σY is a constant stress value.

For the backstress evolution, a multilinear kinematichardening model is used where no uniaxial ratcheting ef-fects are present and therefore a stable hysteresis loop is ob-tained. To take care of the anisotropic hardening behaviour,the structural tensor is also present in the hardening rela-tions in the constitutive model.

The steady-state behaviour of the material is simulatedwith use of a simple cycle jumping procedure, where thematerial properties are changed from virgin properties tomid-life properties. To validate the results, common fatigueidentification parameters used for lifing predictions, such asplastic strain range, hysteresis area and, as previously usedfor crack initiation prediction of this specific alloy [2], themaximum stress, have been compared with those obtainedfrom experiments with good agreement.

References

[1] Andersson, O., Graichen, A., Brodin, H., Navrotsky,V., Developing Additive Manufacturing Technologyfor Burner Repair, Journal of Engineering for GasTurbines and Power, 139, 031506 (2016)

[2] Lindstrom, T., Eriksson, R., Ewest, D., Simonsson,K., Lundgren, J-E., Leidermark, D., Crack initiationprediction of additive manufactured ductile nickel-based superalloys, MATEC Web of Conferences, 165,04013 (2018)


65


INVESTIGATION OF THE SOUND TRANSMISSION THROUGH ALOCALLY RESONANT METAMATERIAL CYLINDRICAL SHELL IN THE

RING FREQUENCY REGION

Z. Liu 1, R. Rumpler1,2, L. Feng1

1The Marcus Wallenberg Laboratory for Sound and Vibration Research (MWL), Department of Aeronautical and VehicleEngineering, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden

2Centre for ECO2 Vehicle Design, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

Locally resonant metamaterial flat panels have provedto potentially exhibit extraordinary sound transmission lossproperties when the resonance frequency of the resonatorsis tuned to the coincidence frequency region. Whether thistechnique is also effective to address the ring frequency ef-fect for curved panels is investigated. For this purpose, acylindrical shell, as a representation of curved panels, isstudied from a theoretical and numerical point of view, witha specific focus on the transmission loss behaviour aroundthe ring frequency region when the shell is mounted withlocal resonators. The influence from the resonators is pre-sented, and compared with that for a flat panel. An inverseeffect of the resonators is observed on the sound transmis-sion loss between the metamaterial cylindrical shell and themetamaterial flat panel when the resonance frequency ofthe resonators is tuned to be below or above the ring orcoincidence frequency, respectively. Rather than the ex-traordinary improvement observed for the metamaterial flatpanel, tuning such conventional resonators to the ring fre-quency of curved panels generates two side dips despite asharp improvement at the ring frequency itself. This phe-nomenon is explained from an effective impedance point ofview.

Figure 1: Metamaterial flat panel.

The influence of the resonators is systematically stud-ied by tuning the resonance frequency of the resonatorsto be below, at, or above the specific frequencies of inter-est. These inverse effects of the resonators observed withthe sound transmission loss are found between the mass-controlled region and stiffness-controlled region. Theseopposite behaviours may be explained in terms of placing

Figure 2: Metamaterial cylindrical shell.

the resonance of the resonators in the mass- or stiffness-controlled regions.

As to tuning the resonance of the resonators to the spe-cific frequencies of interest, the sound insulation behaviourof the shell, unlike for the flat panel at the coincidence fre-quency, results in the appearance of side dips, here denotedas ‘side effects’, associated with the resonance of the res-onators. Physically:• For a flat panel at the coincidence frequency, the

impedance is transferred from the mass-controlled re-gion to the stiffness-controlled region,

• For a cylindrical shell at the ring frequency, theimpedance is transferred from the stiffness-controlled re-gion to the mass-controlled region.

This provides the underlying physical explanation for theineffectiveness of tuning resonators to the ring frequency, apoint which may be further explained from an impedancepoint of view, as detailed in reference[1].

References

[1] Liu, Zibo, Romain Rumpler, and Leping Feng. Inves-tigation of the sound transmission through a locallyresonant metamaterial cylindrical shell in the ring fre-quency region. Journal of Applied Physics 125, no. 11(2019): 115105.


66


NANOFIBRIL BEHAVIOUR DURING ASSEMBLY OF STRONGFILAMENTS IS REVEALED BY DECAY OF BIREFRINGENCE

F. Lundell1, C. Brouzet1, N. Mittal1, T. Rosen2, L. D. Soderberg1

1Linne FLOW Centre & Wallenberg Wood Science Center, Department of Mechanics, KTH, Stockholm, Sweden2Department of Chemistry, Stony Brook University, NY, USA

Utilising biological resources for high-performance ma-terials is necessary if a sustainable society is to be devel-oped. We have demonstrated[1] that hydrodynamic assem-bly in flow-focusing (see figure 1) can be used to makestrong filaments from cellulose nanofibrils, which are near-crystalline bundles of cellulose with a width around 4-20 nm, a typical length of 1 µm and can be obtained bydisintegrating cellulose fibers in paper pulp.

The key to achieve extraordinary mechanical propertiesof the final material is the alignment of the nanofibrils: thematerial gets stiffer and stronger if the fibrils are alignedwith the filament. To understand the rotational behaviour ofthe nanofibrils during the process is therefore of uttermostimportance.

This talk will summarise recent progress obtained witha flow-stop technique (figure 1)[2]. The fibrils are firstaligned by an acceleration, giving rise to a birefringencethat can be detected with crossed polarizers. The flowis stopped intermittently, and as the fibrils return to anisotropic orientation distribution the birefringence decays.

The nanofibrils in the dispersions typically have a lengthdistribution. Short fibrils react to flow and also return toisotropy faster than longer fibrils. Thus, if predominantlyshorter fibrils are aligned when the flow is stopped, fasttimescales will dominate in the decay of the birefringence.Vice versa, if only the long fibrils are aligned longer timescales with dominate. Thus, a Laplace transform of thebirefringence decay contains information of the length dis-tribution of the fibrils that are aligned before stop[3].

This technique has enabled us to gain new understandingof the fibril alignment in our system such as this depicted infigure 2: upstream (early on in the acceleration) short fibrils

Figure 1: Setup for dynamic measurements alignment decay[2].Particles are aligned in a flow-focusing setup andstopped with fast valves. The decay of the birefrin-gence after stop is measured and analyzed

Figure 2: Decay curves at different positions in the channel.Upstream (magenta), short timescales dominate sinceshort fibrils are aligned to a larger extent than long fib-rils. Downstream (black), longer timescales dominate,revealing that at this position, it is the longer fibrils thatare aligned.

are aligned while ong fibrils are not. Further downstream,the situation is the opposite. The relation between thesefindings and material assembly[4] will be elaborated in thetalk

References

[1] Hakansson, K.M.O., Fall, A.B., Lundell, F., Yu, S.,Krywka, C., Roth, S.V., Santoro, G., kvick, M., Prahl-Wittberg, L., Wagberg, L. & Soderberg, L.D., Hy-drodynamic alignment and assembly of nanofibrils re-sulting in strong cellulose filaments. Nature Commu-nications 5, 4018 (2014)

[2] Rosen, T., Mittal, N., Roth, S.V., Zhang, P., Soder-berg, L.D. & Lundell, F., Dynamic characteriza-tion of cellulose nanofibrils in sheared and extendedsemi-dilute dispersions, Arxiv:1801.07558, RetrievedJanuary 23, 2018, https://arxiv.org/abs/1801.07558(2018)

[3] Brouzet, C., Mittal, N., Soderberg, L.D. & Lundell,F., Size-Dependent Orientational Dynamics of Brow-nian Nanorods. ACS Macro Letters 7 (8), 1022-1027,(2018)

[4] Brouzet, C., Mittal, N., Lundell, F. & Soder-berg, L.D., Characterizing the Orientational andNetwork Dynamics of Polydisperse Nanofibers onthe Nanoscale. Macromolecules 52 (6), 2286?2295(2019)


67


OPTIMAL COOLING BY 2D TOPOLOGY OPTIMIZATION OF3D-MODELLED CONVECTION-DIFFUSION AND STOKES FLOW

MULTI-PHYSICS PROBLEM

J. Lundgren1, A. Klarbring1, J-E. Lundgren2, C-J. Thore1

1Department of Management and Engineering, Linkoping University, Linkoping, Sweden2Siemens Industrial Turbomachinery AB, Finspang, Sweden

In high temperature applications, where cooling is nec-essary to maintain an acceptable operating temperature, ac-curate and straightforward design modelling tools are re-quired. We propose a 2D topology optimization approachfor coupled thermal-fluid problems in 3D, with high physi-cal relevance, but still at a low computational cost. Optimalcooling of the structure is achieved by minimizing the p-norm approximated maximum temperature T

(ρ(x)

)in the

solid domain Ωs:

maxx∈Ωs

T(ρ(x)

)≈[∫

Ωs

∣∣T(ρ(x)

)∣∣p dV

]1/p

,

where ρ(x) is the design variable at the position x. The2D design approach, in which the 3D geometry is obtainedby extrusion of a 2D design, see Figure 1, implies straightcooling channels, but reduces the number of design vari-ables and simplifies manufacturing.

TO of 3D HT problems with 2D design 5

x

z

y

Fig. 2: The optimization variables ρ ∈ Rmxy are found in one layer (blue) of the3D design domain. This makes all elements in one z-column (red) to have thesame density after the full 3D design has been extruded

Assuming a structured mesh similar to the one used in [5], the discrete versionof the 2D-to-3D filter, which makes ρ ∈ Rmxy 7→ ρ ∈ Rm, reads

ρ = H2Dρ, where H2D =[I . . . I

]T,

in which I is an identity matrix of appropriate size. Combining both filters givesρ = H2DHBρ. Discretization of (1) eventually leads to the following matrixproblem for the unknown nodal temperatures t:

K(ρ)t = f(ρ)− K(ρ)t0, (8)

where t0 collects the known nodal temperatures, K(ρ) ∈ Rn×n, K(ρ) ∈ Rn×n0 ,and where n0 and n are the number of nodes with known and unknown tem-peratures, respectively. If the nodal temperatures on the periodic boundaries Γ1

and Γ2 are collected in t1 and t2, respectively, the periodicity condition t1 = t2

gives

t =

t1

t2

tR

= D

[t1

tR

]= Dtp, D =

I 0I 00 I

(9)

where tR contains the remaining nodal temperatures and I denotes identitymatrices of appropriate sizes. Now, using (9) in (8) and multiplying with DT

from the left yields

DTK(ρ)Dtp = DT(f(ρ)− K(ρ)t0) ⇔ Kp(ρ)tp = fp(ρ)−DTK(ρ)t0.

This system has a unique solution tp = tp(ρ), which satisfies the periodic bound-ary conditions on Γ1 and Γ2 for every admissible design and adequate choices ofparameters ks, kf , α and β.

The stiffness contribution in (3) from the design-dependent convection is eval-uated over the design-dependent boundary Γhfs(ρ), which is an approximationof the fluid-solid interface layer Γfs(ρ) on the FE mesh:

Γfs(ρ) ≈ Γhfs(ρ) = x ∈ ∪me=1Γe \ ∂Ω :∣∣(Dne,k ρ)(x)

∣∣ > 0,

Figure 1: A plane with the design variables (blue), and a block ofelements with the same design density (red).

The fluid state problem is that of Stokes flow, extendedwith a Brinkman term for design parametrization, with in-flow boundary conditions:

∇ ·(2µD(u)

)− α(ρ)u = ∇p in Ω,

∇ · u = 0 in Ω,

u = u0 on Γu,

where µ is the viscosity of the fluid, D is the rate-of-deformation tensor, p is the pressure and α is the inversepermeability, which acts like a resistance to the flow in the

solid domain. This Stokes-Brinkman flow model has pre-viously been shown to successfully counteract the appear-ance of minimal fluid members [1] and yields physicallymeaningful velocity solutions.

The thermal state problem is a steady-state convection-diffusion heat transfer problem, with temperature and con-vection boundary conditions:

−∇ ·(k(ρ)∇T − c(ρ)Tu

)= Q in Ω,

T = T0 on ΓT,

k(ρ)∇T · n = h(ρ)(T∞ − T ) on Γh,

where k is the conductivity, c is the convection parameter,Q is the given heat generation in the domain, n is the nor-mal to the domain boundary, h is the external heat transfercoefficient and T∞ is the ambient temperature.

The convection velocities in the Stokes flow problem areobtained by a penalty finite element method, which is im-plemented as a less computationally expensive alternativeto mixed formulations, which are common practice. In thepenalty method, the incompressibility condition is relaxedin the following way:

∇ · u = − pλ,

where λ 1, such that a nearly incompressible state isobtained. Consequently, the pressure can be eliminated al-ready in the continuous formulation.

The topology optimization problem is solved bygradient-based methods, in which sensitivities obtainedfrom the adjoint method are used. The significance of themodel is demonstrated by examples of relevance for gasturbine applications, where the cost-effectiveness and phys-ical relevance are highlighted.

References

[1] Borrvall, T., Petersson, J., Topology optimization offluids in Stokes flow. Int. J. Numer. Meth. Fluids, 41,77-107, (2003)



DESIGN CONSIDERATIONS FOR THE FLOW CONDITIONS AROUND AWING MODEL INSIDE A WIND TUNNEL

F. Mallor1, E. Dogan1, M. Atzori1, A. Parikh1, R. Vinuesa1, R. Orlu1, P. Schlatter1

1Linne FLOW Centre, KTH Mechanics, Stockholm SE-100 44, Sweden

The development and behavior of turbulent boundarylayers (TBLs) under high pressure gradients as appearingon wing surfaces are still open research topics. Recent ad-vancements in high-performance computing have allowedfor the study of such TBLs through highly resolved numer-ical simulations. For the present study, we chose the NACA4412 profile that has been a benchmark airfoil in the studyof the development of boundary layers over wings, mainlydue to its pressure-gradient distribution being quite inde-pendent of Reynolds number (Re), as well as having be-nign stall properties. Recently, well-resolved large-eddysimulations (LES) [1] have been performed at moderatebut yet relevant Reynolds numbers over this profile, al-lowing to obtain accurate boundary layer data and high-order statistics. However, the experimental data is limitedto the pioneering work by Wadcock and Coles [2,3] fromthe 1970s and 80s. Thus, we aim at providing high qualityexperimental data with recent advanced measurement tech-niques, and in guidance of the numerical work performedwithin the Linne FLOW Centre, new – more detailed – ex-periments are planned in the Minimum Turbulence Level(MTL) wind tunnel at KTH Mechanics. Correspondingpreliminary experimental results are being described in acompanion abstract.

The test wing model is designed with a chord lengthof 0.5 m in order to achieve a similar Reynolds-numberrange as Wadcock [3]. This leads to a blockage ratio ofaround 8% and 14% for angles of attack of 5 and 12 de-grees, respectively, in the MTL wind tunnel (a test sectionof 1.2 × 0.8 m2). In order to mitigate the blockage effect,the use of wall liners on the side walls of the MTL was pur-sued. The present work summarises the design process andeffect on the flow inside the wind tunnel of such inserts.

The main goal of these liners is to reduce the interfer-ence from the wind-tunnel walls so that the flow aroundthe wing resembles that of a free flight case. To achievethis, 2D Reynolds-Averaged Navier–Stokes (RANS) simu-lations using the k − ω shear-stress transport (SST) modelwere performed for each angle of attack (α) and Reynoldsnumber (based on chord length and free-stream velocity)of interest (α = 5, 10, 12 degrees; Re = 400 × 103, 106

and 1.64× 106), both for the wing in free-flight conditionsand inside the wind tunnel. Due to the development of theboundary layer around the wind-tunnel wall liners, an itera-tive process was followed in order to obtain a proper insertgeometry. This iterative process was performed until theshape of the displacement thickness (δ1) profile around thetop and bottom inserts matched a streamline of the free-flight case within a 0.5 mm margin.

Especially, for the higher angle of attacks (10 and 12

Figure 1: Friction coefficient cf around the wing for (black cir-cles) free-flight conditions, (red lines) original windtunnel and (blue lines) wind tunnel with liners, at α =12 degrees and Re = 106.

degrees), larger differences between the wind-tunnel andfree-flight simulations are observed: the wake is deflectedup and the separation region near the trailing edge beginsearlier for the wind-tunnel case. The early separation iscertainly not desirable, since the focus of this experimen-tal campaign is to obtain accurate boundary-layer measure-ments. By introducing the wall liners, this effect is miti-gated substantially, as it can be seen in the skin-friction co-efficient distribution around the wing, reported in Figure 1.

cf =τwall12ρU

2∞(1)

The full presentation will detail different liner designsand preliminary measurements to cross-validate their effec-tiveness in the setup to achieve the desired flow conditions.

References

[1] Vinuesa, R., Negi, P.S., Atzori, M., Hanifi, A., Hen-ningson, D.S., Schlatter, P., Turbulent boundary lay-ers around wing sections up to Rec= 1,000,000. Int. J.Heat Fluid Flow, 72, 86-99, (2018)

[2] Coles, D., Wadcock, A.J., Flying-hot-wire study offlow past an NACA 4412 airfoil at maximum lift.AIAA J., 17, 321-329, (1979)

[3] Wadcock, A.J., Investigation of low-speed turbulentseparated flow around airfoils. NASA Technical Re-port, NASA CR 177450, (1987)


69


ISOLATED ROUGHNESS-INDUCED BOUNDARY LAYER TRANSITION

S. B. Mamidala 1, S. Hara1, J. H. M. Fransson1


Protruding surface roughness such as rivet heads, spotwelds are a long-lasting problem on laminar boundarylayer, particularly driven by their numerous applications inaerospace industry [1]. However, small-scale variations inthe height of these surface rugosities can cause laminar-turbulent transition, thus resulting in an increase of theskin-friction coefficient [2,3].

The transition scenario in a simplified, three-dimensional cylindrical roughness is often characterizedby its roughness Reynolds number, which is defined bythe roughness height and the corresponding local velocity.Depending on the roughness Reynolds number and theroughness height, it has been shown that transition caneither be promoted or delayed. [4] gives us an insightinto the well-known empirical transition criteria involvedin roughness-induced transition, but as agreed withprevious experimental work, there is a huge scatter inthe experimental data. To our knowledge, no systematicexperimental study has focused on a deeper understandingbetween the transitional Reynolds number, roughnessheight and the roughess Reynolds number.

The current experiments are performed on a flat-plateboundary layer under zero-pressure-gradient conditionsin a low-turbulence wind tunnel at KTH. The localisedroughness has a automated traverse to adjust the heightwith a precision upto 1µm. The measurements ofthe streamwise velocity are performed using a hot-wireprobe. Also, two-point spatial correlation measurementsusing two hot-wire probes were performed to characterisethe instability modes. Two-dimensional TS (Tollmien-Schlichting) waves were introduced upstream of theroughness location to perturb the laminar base-flow andstudy their interaction with the roughness element.

The results to be presented in this conference include aclear insight into the transition criteria and the influenceof TS waves on this type of transition process. Asystematic parametric study has been performed by varyingthe roughness diameter, height and the free-stream velocity.Moreover, the current results show significant hysteresisin the critical value of the roughness height that causestransition, which was not studied in previous literature[5,6]. As doubted in [6], co-existence of two instabilitymodes namely, the sinuous and varicose modes at lowerdiameters is proven experimentally for the first-time. Thereexists a critical height where mode-switching happensbetween these sinuous and varicose modes.

In the past, there were several attempts made to studythe influence of TS waves on a roughness element, but itwas not clearly understood. In the current results, it isshown that when this disturbance hits a roughness elementof sufficient height, it can be strongly amplified with athreat of subsequent laminar-turbulent transition.

References

[1] Hood, J., The effects of some common surfaceirregularities on wing drag, NACA Technical Notesno. 695 (1939)

[2] Tani, I., On the permissible roughness in the laminarboundary layer, NASA Tech. Reports, NASA-TM-89802 (1940)

[3] Fage, A., The smallest size of a spanwise surfacecorrugation which affects boundary layer transitionon an aerofoil, A. R. C. Tech. Report, Reports andMemoranda No. 2120 (1943)

[4] Doenhoff, A.E., Braslow, A.L., The effect ofdistributed surface roughness on laminar flow,Boundary Layer and Flow Control- Its Principles andApplication, pp. 657-681 (1961)

[5] Loiseau, J., Robinet, J., Cherubini, S., Leriche, E.,Investigation of the roughness-induced transition:global stability analyses and direct numericalsimulations, J. Fluid Mech., vol. 760, pp. 175-211(2014)

[6] Puckert, D.K., Rist, U., Experiments on criticalReynolds number and global instability in roughness-induced laminar-turbulent transition, J. Fluid Mech.,vol. 844, pp. 878-904 (2018)


70


STOCHASTIC MULTISCALE MODELLING OF FIBER NETWORKS

R. Mansour, A. Kulachenko, M. Olsson


Efficient design of new wood fiber-based materials requires detailed knowledge of the deformation and failure mechanisms at different length scales. The mechanisms that control the mechanical properties of paper materials originate from the structure at the microscale, where the following contributing factors play the crucial role: fiber mechanical properties, fiber morphology and orientation, number of interfiber contacts, bonding properties and disordered nature of the fiber network [1]. Therefore, it is natural to tackle the questions related to the mechanics of the fiber networks at the scale where all the essential components can be taken into consideration. Only such an holistic approach which can link the raw materials with the properties of the final products allows for optimization of the raw materials, with respect to their morphological properties e.g. fiber length, fiber wall thickness and the source of the fibers, which are often the main concern of the papermakers.

Figure 1. (a) Example of fiber-based product, (b) micro-tomography of fiber network, and (c) fiber network schematic reconstruction.

Experimental studies are in general limited by the difficulties of identifying the effects of individual components in such a complex system involving both the properties of the fibers and the network geometry. In addition, most of the studies are focused only on the mean properties of the products, while the reliability is often connected to the variability of the properties [2, 3].

The recent advances in numerical methods, high-performance computational infrastructure and fiber-scale experimental tools finally enable the possibility for a holistic approach, where the

networks [1] are studied on the scale of the individual constituents [4]. However, these tools cannot be directly employed for product development due to the overwhelming computational costs required to capture the relevant product sizes.

In this work, a stochastic multiscale approach is proposed to address the computational difficulties associated with generation and finite-element simulation of large random fiber networks. The model is based on stochastic volume elements [5] and random field generation of local material properties. The model is validated by 1) ensuring accurate prediction of mechanical failure, i.e., strength and strain to failure as well as strain localization pattern; 2) generation of continuum random realizations that are statistically equivalent to the ones generated using direct simulation of fiber networks; 3) verifying that the strength scaling follow the one observed in experimental studies. The proposed method paves the way for tailoring fiber properties and linking these to the performance of the end product.

References

[1] Kulachenko, A., Uesaka, T. Direct simulations of fiber network deformation and failure. Mech. Mater., 51, 1–14 (2012)

[2] Uesaka, T. Statistical aspects of failure of paper products in Niskanen, K. (Ed.), Mechanics of Paper Products (Chapt 8). De Gruyter, Berlin/Boston (2012)

[3] Mattsson, A., Uesaka, T., Characterisation of time-dependent, statistical failure of cellulose fibre network, Cellulose, 25, 2817–2828 (2018)

[4] Borodulina, S., Motamedian, H.R., Kulachenko, A., Effect of fiber and bond strength variations on the tensile stiffness and strength of fiber networks. Int. J. Solids Struct, 154, 19–32 (2018)

[5] Mansour, R., Kulachenko, A, Chen, W, Olsson, M, Stochastic Constitutive Model of Isotropic Thin Fiber Networks Based on Stochastic Volume Elements, Materials, 12, 1–28 (2019)


(a)

(b) (c)

71


THE OBSCURE TRUTH BEHIND COLORFUL PLOTS: WHY MYMEASUREMENTS MAKE NO SENSE—PERHAPS YOURS NEITHER

Luca Manzari1, Peter Göransson1, Jacques Cuenca1,2, Ines Lopez Arteaga1

1KTH Royal Institute of Technology, Stockholm2Siemens Industry Software, Leuven

We are living in the era of big data, machine learningand computer vision. Smartphones with at least twocameras, self-driving cars and algorithms that recog-nize people and things are at the heart of a revolutionthat has lead to cheaper-than-ever access to computa-tional power, memory and bandwidth.

The academic field has not been indifferent to suchtrends: full-field optical measurements are becom-ing more and more common, replacing strain gaugesand arrays of accelerometers with lasers and—mostimportantly—high-speed cameras. Given the highercomplexity of the procedures required to obtain a dis-placement from a sequence of pictures than from thechange in resistance of a thin wire, the devices areoften bundled with a piece of software that takescare of the data analysis. While there is in princi-ple nothing wrong with trusting devices to performtheir design task, the layer of abstraction introducedbetween the researcher and the measured quantity in-evitably implies a certain loss of control over the pro-cess. This may be acceptable to a certain degree (weare not metrologists, but engineers!), yet the eager-ness of getting results may understandably lead tonot questioning the quality of the measurement itself.It is in the end in the interest of the manufacturerto showcase a well-functioning measuring system, andthe overly smoothed colorful plots—coupled with thelack of warning signs when things go wrong under thehood—well reassure the unaware end-user.

The speaker himself uses a pair of high-speed cam-eras along with the bundled software for strain mea-surements to measure a sample of material undergoingforced sinusoidal oscillation at different frequencies.These displacement fields are meant to be the targetof an optimization procedure aimed at characterizingthe material under analysis, modeled as an anisotropiccontinuum whose behavior can be described by 21 elas-tic constants and additional parameters for modellingviscoelasticity. How to make sure that the measure-ments are valid? And what does “valid” really mean?How good is good enough? Are 50 GB s−1 of stereopictures really needed?

An attempt to answer these questions is made by go-ing back to the very essence of the material model usedfor the inverse estimation of the material parameters:an anisotropic, linear viscoelastic solid. Linearity inparticular is enforced throughout the whole measure-ment process, both as a data reduction tool and as ametric to assess the confidence of the measured data.

In a never-ending quest for the fit-for-purpose mea-surement, both correct and deceivingly correct resultsfrom stereo digital image correlation (DIC) are pre-sented along with some in-house developed tools, ad-vocating for critical use of the instrument and bringingus hopefully closer to the sought after true value.

A simplified representation of the experimental setup: twohigh-speed cameras, a white light source, a 20x20x20 mmcube of melamine foam (in blue) with a seismic mass onits top face and its bottom face glued to a rigid foundationmounted onto a uniaxial electrodynamic shaker.

Estimated frequency per all DIC tiles of both a sampleface and the foundation in the 3 directions of space. Yis the direction of shaking, and Z the direction normal tothe sample face. The excitation frequency is 355 Hz. Tileswhose estimated frequency is more than 2 Hz away fromthe excitation frequency are not plotted.


72


AN INVERSE ESTIMATION FOR ACOUSTIC MATERIAL PROPERTIESCHARACTERISATION

Huina Mao 1, Luca Manzari1, Peter Goransson1

1Department of Aeronautical and Vehicle Engineering, KTH, Stockholm, Sweden

1 Introduction

Noise daily effects a large number of people, e.g., traf-fic noise, which leads to cardiovascular disorders if peo-ple spend long periods in noisy environments. The ad-vent of manufacture technology has recently enabled tomanufacture materials tailored for specific applications,e.g., acoustic metamaterial in aeronautics [1], and vehi-cles [2]. In order to understand the material properties foranisotropic and viscoelastic acoustic materials, experimen-tal and numerical methods are proposed here. The latestusing 3D digital image correlation (DIC) dynamic displace-ment measurements, originally developed in KTH, techni-cally motivated to inverse estimate acoustic foam materials.

2 Purpose and Method

The purpose is to develop an inverse estimation methodfor dynamic material properties characterisation based onthe measurement data from dynamic deformation measure-ments. The proposed methodology is schematically sum-marized in Figure. 1.

Update Hooke’s tensor

(Optimization)

EquivalentSolid Model

Target deformation

Kelvin Cell Foam Model

Deformation

Updated Hooke’s matrix

Yes

NoCriteria

෩𝐇

𝐹tar 𝐹pre𝐇 = 𝐹tar

𝐹pre෩𝐇

Predicted deformation

Figure 1: Inverse estimation flowchart: minimization of the dis-placement difference on free faces (colorful contourplot) between target and predicted model.

3 Primary Results• An inverse estimation has been developed and success-

fully estimated the static, elastic, anisotropic cellular ma-terials. The predicted equivalent model has a same defor-mation as the target cellular model under static loads, seeFig. 2.

• Deformations of melamine foam under dynamic vibra-tions were successfully captured by our DIC system, seeFig. 3

• Our 3-D printed acoustic foam material, designed foraeronautic acoustic noise reduction, demonstrates astrong shear-compression coupling affects, see Fig. 2.

(a) (b)Figure 2: Anisotropic cellular material under static compression:

(a) Target model; (b) Equivalent model.

(a) (b)

Figure 3: Dynamic deformation component at frequency 335 Hzon a free face: (a) Real part; (b) Imaginary part.

4 ConclusionIn both experimental and numerical tests, a generalanisotropic material properties were observed, i.e., thegiven material has different types of anisotropy in the elas-tic and anelastic parts, which effects noise reduction func-tions. Recent 3-D printed foams opens a new door to designmaterials according acoustic requirements. Thus, under-standing material properties for anisotropic and viscoelas-tic acoustic materials is a urgent topic.

References

[1] Palma G, Mao H, Burghignoli L, Gransson P, IemmaU. Acoustic Metamaterials in Aeronautics. AppliedSciences. 2018; 8(6):971.

[2] Li, Junfei, et al. ”Acoustic metamaterials capable ofboth sound insulation and energy harvesting.” SmartMaterials and Structures 25.4 (2016): 045013.


73


A QUALITATIVE STUDY OF THE INTERACTION OF A BLAST WAVEWITH A MULTI-FACETED OBSTACLE

R. Mariani1, S. Sembian2, N. Apazidis2

1Department of Aeronautics and Vehicle Engineering, KTH, Stockholm, Sweden2Department of Mechanics, KTH, Stockholm, Sweden

The phenomenon of a classical two-dimensional singlediffraction of a planar shock wave has been extensivelystudied, with work focusing on the understanding of thedynamics of the diffraction process, as well as on the under-standing of the process leading to the formation of a vortex[1]. Law et al. [2] conducted work on the topic of mul-tiple diffraction of a planar shock wave along a complexconvex wall, but limited their study on the flow phenom-ena related to the shock waves, with no emphasis on thegeneration of vorticity due to the diffraction of the shockwave. More recently, Chaudhuri et al. [3] evaluated theinteraction of a planar shock wave with arrays of classi-cal geometric shapes in terms of shock wave attenuation,and Dey et al. [4] completed a numerical visualization ofthe diffraction of shock waves by classical geometry, pro-viding additional insight on the generation of vorticity asa function of the geometry of the obstacle. It is the objec-tive of the current study to further the knowledge in theunderstanding of the phenomena of shock wave diffrac-tion by multiple faceted geometries and evaluate the pro-cess of multiple vortex generation and the interaction of acomplex shock wave system. A preliminary experimen-tal study was conducted using the existing blast appara-tus at the Fluid Physics Laboratory [5], which focused onthe qualitative understanding of the phenomenon of shockwave interaction with a multi-faceted, axisymmetric, equi-lateral hexagon obstacle. Preliminary qualitative resultsshow that, upon impacting on the edge-point of the obsta-cle, part of the blast wave is reflected upstream, while theremaining part is reflected as over the hexagon surface. Asthe shock wave continues propagating downstream, it en-counters a first set of convex corners, where a first diffrac-tion occurs and a first set of vortices are generated thatpropagate downstream and outwardly from the obstacle.As the shock waves continues propagating downstream, itencounters a second set of convex corners of same anglebut opposite aperture, where a new diffraction and a newset of vortices is generated. These vortices are equal inmagnitude and opposite in rotation (with respect to the lon-gitudinal axis of the hexagon). Initally, these vortices areseparated by an axial slipstream generated by the interac-tion of the shock wave with the downstream edge point ofthe hexagon, allowing them to propagate independently. Asthe slipe stream becomes weaker and the vorteces movefarther downstream, they dissipate and the flow behind theobstacle transitions into a large turbulent wake bounded byvortex streams generated at the first set of convex corners.An example of the flow behind the obstacle is shown in Fig.1. In addition to the complex vortex flow generated by the

sequence of shock wave diffraction, equally interesting andcomplex flow phenomena occur in relation to the structureof the shock wave system downstream of the obstacle, asshown in Fig. 2, where a system of incident shocks, triplepoints, Mach stems, and slip lines is clearly visible.

Figure 1: Flow structure of an impinging and diffractig blastwave with a hexagon

Figure 2: Structure of the shock wave system

References

[1] Sun, M., Takayama, K, Vorticity production in shockdiffraction. J. Fluid Mech., 478, 237-256, (2003)

[2] Law, C., Skews, B.W., Ching, K.H., Shock wavediffraction over complex convex walls. Proceeding ofthe 27th International Symposium on Shock Waves,July 15-21, Goettingen, Germany, 1467-1472 (2007)

[3] Chaudhuri, A., Hadjaji, A., Sadot, O., Ben-Dor, G.,Numerical study of shock-wave mitigation throughmatrices of solid obstacles. Shock Waves, 23, 91-101,(2013)

[4] Dey, S., Murugan, T., Chatterjee, D., Numerical visu-alization of blast wave interacting with objects. J. ofApplied Fluid Mech., 11, 5, 1201-1206, (2018)

[5] Sembian, S., Liverts, M., Tillmark, N., Apazidis, N.,Plane shock wave interaction with a cylindrical watercolumn. Phisics of Fluids, 28, (2016)


74


ON EVOLVING ANISOTROPY IN PEARLITIC RAIL STEEL- MODELING AND EXPERIMENTS

K. A. Meyer1, M. Ekh1, J. Ahlstrom1

1Department of Industrial and Materials Science, Chalmers, Gothenburg, Sweden

Due to cold working during manufacturing, sheet met-als often exhibit a pronounced plastic anisotropy. This isoften modeled with an initial anisotropic yield surface (seee.g. Barlat et al. [2]). In railway rails however, large shearstrains accumulate in the surface layer during service (seee.g. Alwahdi et al. [1]). It is therefore necessary to modelthe evolution of the material behavior during the rollingcontact loading.

In [4] we developed a predeformation technique capa-ble of reproducing the large shear strains found in the sur-face layer of rails. It consists of twisting cylindrical testbars under high axial compressive loads. We have furtherquantified the evolution of the elastic and yielding behaviorduring the predeformation loading.

In this contribution we evaluate the ability of differentcrystal plasticity model formulations to describe the evo-lution of the yield surfaces found in the experiments. Themain goal of this study is to identify which mechanismsthat are necessary to model the key features observed fromthe experiments. Figure 1 shows the measured yield sur-faces (shown as markers) at different degrees of deforma-tion. The solid lines are fitted elliptic Hill[3] yield surfaces.

Initial Low shearMedium shear Large shear

−500 0 500

−400

−200

0

200

400

600

800

σ [MPa]

√3τ

[MPa]

Figure 1: Yield surfaces after different degrees of shear deforma-tions.

The crystal plasticity responses for multiple crystalorientations are homogenized using the Taylor assump-tion of homogeneous strains. The cylindrical test barsare modeled using a newly developed framework foraxial-torsional loading, accounting for the strain gradientin the radial direction (https://github.com/KnutAM/

matmodfit). This enables material parameter identifi-cation of the computationally expensive crystal plasticitymodels for solid test bars. In order to simulate the yieldsurface measurements, an element removal and remeshingprocedure is applied to obtained thin-walled, predeformed,test bars. These are then loaded in different directions tocompute the evolved yield surfaces.

References

[1] F. A. M Alwahdi, A. Kapoor, and F. J. Franklin. “Sub-surface microstructural analysis and mechanical prop-erties of pearlitic rail steels in service”. Wear 302.1-2(2013), pp. 1453–1460.

[2] F. Barlat, H. Aretz, J.W. Yoon, M.E. Karabin, J.C.Brem, and R.E. Dick. “Linear transfomation-basedanisotropic yield functions”. International Journal ofPlasticity 21.5 (May 2005), pp. 1009–1039.

[3] R. Hill. “A Theory of the Yielding and Plastic Flowof Anisotropic Metals”. Proceedings of the Royal So-ciety A: Mathematical, Physical and Engineering Sci-ences 193.1033 (1948), pp. 281–297.

[4] Knut Andreas Meyer, Magnus Ekh, and JohanAhlstrom. “Modeling of kinematic hardening at largebiaxial deformations in pearlitic rail steel”. Inter-national Journal of Solids and Structures 130-131(2018), pp. 122–132.


75


Singularity-free defect mechanics for polar media

S.M. Mousavi1

1Department of Engineering and Physics, Karlstad University, Karlstad, Sweden

Generalized continuum mechanics offers

frameworks which are suitable for the analysis of complex materials and nonclassical phenomena. In particular, micropolar elasticity, with three translational and three rotational degrees of freedom, suits for simulation and analysis of granular materials [1].

As a crucial aspect, a continuum theory such as micropolar elasticity should also include models of simple and complex defects to address material failure. Within micropolar elasticity, we observe singular fields for defects (e.g. at the dislocation and disclination core or at the crack tip). In this study, we analyse defects within the higher order continuum theory (i.e. micropolar elasticity), higher-order as well as higher-grade continuum theory (i.e. gradient micropolar elasticity), and nonlocal higher-order theory (i.e. nonlocal micropolar elasticity). We observe that gradient micropolar elasticity and nonlocal micropolar elasticity both provide regularized fields for the defects. This contribution provides realistic predictions in the analysis of the granular materials and systems with desired internal length scales.

In this study, a library of simple line defects (i.e. dislocation being displacement discontinuity and disclination being rotational discontinuity) is introduced. Then the well-established dislocation based fracture mechanics is systematically generalized to the dislocation and disclination based fracture mechanics of polar media undergoing plane strain [2].

We consider Polystyrene foam weakened by a straight crack of length 2a in the x-y plane, parametrically given by

, 0 1 1x as y s (1)

The plane is subjected to the far-field stress and couple stress fields

, , / 1lyy xy zy

(2)

This result of this study shows that, within the three

frameworks addressed here (i.e. micropolar, nonlocal micropolar, and gradient micropolar elasticity theories), the crack can be represented as a distribution of glide and climb edge dislocations together with wedge disclinations. The stress and couple stress fields of nonlocal micropolar elasticity are demonstrated in figure 1 where the fields are regularized at the crack tip.

Figure 1: Stress and couple stress contour around the straight crack within nonlocal micropolar

elasticity with the internal length scale ε = a/10.

It is concluded that, by extending the micropolar elasticity to its nonlocal and gradient versions, we can obtain regularized continuum theories which suits for the analysis of granular materials and systems. This continuum model can be used for materials for which particles can displace and rotate. To complete this study, these results shall be compared with discrete simulations of materials with such deformation mechanisms (e.g. granular materials and cellular materials). Acknowledgments SMM acknowledges financial support from the Starting Grant of the Swedish Research Council (2018-03636). References

[1] Eremeyev, V.A., Lebedev L.P., Altenbach, H., Foundations of micropolar mechanics. Springer (2013).

[2] Mousavi, S.M., Singularity-free defect mechanics for polar media, submitted.


76


LARGE-EDDY SIMULATION OF AN INTERNAL SHIP AIR CAVITY

T. Mukha1 and R. E. Bensow1

1Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden

Air lubrication is a technology promising to allow for a15-20% reduction in the drag of a ship hull through cov-ering a part of the wetted surface with an air layer [2, 1].Although prototypes of large displacement air-cavity shipshave been successfully tested, further proof of the concept’sfeasibility for oceanic operations is necessary in order forit to be adopted for commercial projects [2].

In this work, simulating an internal air cavity in modelscale is considered, see Figure 1 for a schematic overviewof the case geometry, and the applied boundary conditions.The focus is on accurately resolving the transient processesclose to the beach wall of the cavity, governing the dis-charge of air. To this end, the open-source CFD softwareOpenFOAM R© is used to conduct an implicit large-eddysimulation, with the volume of fluid method used for cap-turing the air-water interface.

−4 −2 0 2 4 6 8 10x

−0.2

−0.1

0.0

0.1

y Water inlet,U0 = 2 m/s

Air inlet,∆p = −100 Pa

Pressure outlet,p = 0 Pa

Beach wall

Figure 1: A side view of the simulation domain, also showingthe imposed boundary conditions. The bottom wall,not shown in the figure, is located at y = −1.5 m.The magenta line shows the averaged location of theair-water interface.

Previous study of external air cavities [4] proposed thatone of the main reasons for the discharge of air is a re-entrant jet, which continuously sheds off air packets in theclosure region. Results from the internal cavity simulationsconducted here indicate that air discharge occurs via a dif-ferent mechanism. A highly unsteady reverse flow is ob-served near the beach wall (see Figure 2), and the air isengulfed by overturning waves, which are formed acrossthe surface of the air-water interface. Similar entrainmentdynamics have been previously observed in a turbulent hy-draulic jump [3].

Analysis of the velocity field reveals that in the closureregion the water flow coming from upstream separates fromthe air-water interface and becomes highly turbulent. Theprofiles of mean velocity and the Reynolds stress compo-nents in this region resemble those of a detached shearlayer. A recirculation region is formed above, inside whichthe air-water interface is located.

To further analyse the air discharge dynamics, the totalamount of air present in a control volume downstream ofthe entrainment region has been computed at each time-step of the simulation. The autocorrelation function of this

signal reveals a peak at a frequency of ≈ 6.3 Hz, indicatingthat the air discharge process is periodic. Furthermore, theregistered frequency agrees well with that observed in thetemporal autocorrelation functions of components of ve-locity, computed at selected locations inside the separatedshear layer. This indicates a connection between the turbu-lent flow dynamics and the air entrainment process. A moredetailed investigation of this coupling is a work in progress.

Figure 2: A snapshot of the air-water interface close to the beachwall, colour shows the value of the streamwise com-ponent of velocity. Arrows show the direction of thevelocity field.

Aside from further characterisation of the air dischargeprocess and its interaction with the surrounding flow, fu-ture work will focus on development of lower-fidelity mod-elling approaches that can accurately capture these phe-nomena.

References

[1] S. Gokcay, M. Insel, and A. Y. Odabasi. Revisitingartificial air cavity concept for high speed craft. OceanEngineering, 31:253–267, 2004.

[2] K. I. Matveev. Three-dimensional wave patterns inlong air cavities on a horizontal plane. Ocean Engi-neering, 34(13):1882–1891, 2007.

[3] M. Mortazavi, V. Le Chenadec, P. Moin, and A. Mani.Direct numerical simulation of a turbulent hydraulicjump: Turbulence statistics and air entrainment. Jour-nal of Fluid Mechanics, 797:60–94, 2016.

[4] O. Zverkhovskyi. Ship drag reduction by air cavities.Phd thesis, Delft University of Technology, 2014.


77


NUMERICAL PREDICTION OF THERMOACOUSTIC INSTABILITIESUSING LINEARIZED NAVIER-STOKES EQUATIONS METHODOLOGY IN

FREQUENCY DOMAIN

W. Na 1,2, S. Boij1,2, G. Efraimsson1

1Department of Aeronautical and Vehicle Engineering, KTH, Stockholm, Sweden2The Marcus Wallenberg Laboratory for Sound and Vibration Research, KTH, Sweden

A big amount of research including numerical studiesand experimental work shows that the combustion drivenoscillations is one of the most important sources of noiseassociated with flames in the combustion process. Combus-tion driven oscillations arise when positive coupling occursbetween the flame, the acoustics, and the flow, e.g. whenthe flame acts as an amplifier of the disturbances (acousticor fluid) at some natural frequency of the combustion sys-tem. When it occurs, it can give rise to extremely high noiselevels within a relatively narrow frequency range, whichcould lead to a huge damage to the structure of combustors.Combustion oscillations normally occur if there is somesimilarity between a characteristic frequency of the flameand a natural Helmholtz resonator or organ pipe frequencyin the combustion chamber, or air and fuel supply systemsin combination. It is often the case that the noise from com-bustion oscillations is difficult to attenuate. Where such os-cillations arise, a solution must be found which breaks thelink between the combustion process and the system acous-tics.

The thermoacoustic instability of a Rijke tube withmeanflow effect is simulated by the proposed numericalmethodology- Linearized Navier-Stokes equations method-ology (LNSE) in frequency domain. The numerical modelunder investigation is presented in Figure 1.

Figure 1: Rijke Tube: a straight duct is separated by a flame lo-cated in the center. Cold duct with lower temperature isat the upstream of the flame, while hot duct with higher.

The full set of LNSE are solved, including the energyequation and the entropy expression, the numerical solveris capable to describe three modes of perturbations: acous-tic, vorticity and entropy. In the flame, acoustic and flowcoupling, the vorticity and entropy waves are convectedby the mean flow, whereas acoustic waves travel with thespeed of sound, altered by the local flow velocity. Mean-while, the acoustic wave reflected upstream and the entropywaves will lead to the fluctuations of the variables (heat re-lease rate) in the flame region, sometimes together with theshrinking of the flame front surface.

x(m)0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

1.2

|p(x)|

Ma=0.001

Ma=0.15

x(m)0 0.2 0.4 0.6 0.8 1

-4

-2

0

2

4

6

arg(p(x))

Ma=0.001

Ma=0.15

x(m)0 0.2 0.4 0.6 0.8 1

×10 -3

0

1

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|u(x)|

Ma=0.001

Ma=0.15

x(m)0 0.2 0.4 0.6 0.8 1

-4

-2

0

2

4

arg(u(x))

Ma=0.001

Ma=0.15

Figure 2: Structure of the third eigenmode at Mach number 0.001and Mach number 0.15 respectively, as obtained nu-merically by the LNSE solver for f = 0.05L.

Real frequency

0 100 200 300 400 500 600 700

Ima

gin

ary

fre

qu

en

cy

-60

-50

-40

-30

-20

-10

0

10

Ma=0.15

Semi-analytical

Numerical by LNSE

Ma=0.001Almost no-flow case

More stable

Figure 3: Meanflow effects on thermoacoustic instability, Machnumberer increases from 0.001 upto 0.15.

References[1] W. Na, Frequency Domain Linearized Navier-Stokes

Equations Methodology for Aero-Acoustic and Ther-moacoustic Simulations, Licentiate thesis, KTHRoyal Institute of Technology, 2015.

[2] W. Na, G. Efraimsson and S. Boij. Prediction ofThermoacousic Instabilities in Combustors UsingLinearized Navier-Stokes Equations in FrequencyDomain. In proceedings of the 22nd InternationalCongress on Sound and Vibration (ICSV22), 12-16July 2015, Florence, Italy.


78


PREDICTING NON-LINEAR SHEAR DEFORMATION AND FAILURE IN 3DFIBRE-REINFORCED COMPOSITES

C. Oddy 1, M. Ekh1, M. Fagerstrom1

1Department of Industrial and Materials Science, Chalmers University of Technology, Gothenburg, Sweden

A class of composite materials with fully 3D fibre-reinforcements have shown weight efficient strength and stiffness characteristics. They have also shown promising energy absorption capabilities. In fact, Khokar et al. [1] have demonstrated that, in bending, such a 3D carbon fibre reinforced polymer (CFRP) I-beam has two to three times the specific energy absorption capability of a steel I-beam with equivalent geometry. As the name suggests, yarns are interlaced in three principal directions. This is illustrated in Figure 1. During the weaving process, developed by Khokar [2], warp yarns (blue) are interlaced with horizon-tal weft (red) and vertical weft (green) yarns in a grid-like set. This fibre network suppresses delamination and allows for stable and progressive damage growth in a quasi-ductile manner.

Figure 1: Sketch of the 3D-woven reinforcement

While the considered 3D fibre-reinforced compositeshows promise, developing a computationally efficientmaterial model is crucial to supporting the material’swidespread adoption across multiple industries. With theultimate goal of developing a macroscale homogenisedmodel to predict how the material deforms and eventuallyfails under loading, this work proposes a candidate for aphenomenologically based orthotropic viscoelastic damagemodel.

Previous experimental results [3] indicate that this classof 3D fibre-reinforced composites exhibits linear materialbehaviour when loaded along one of the three nominal fibredirections. Shear loading however, produces a prominentnon-linear response. This is likely due to the viscoelasticbehaviour and damage of the polymer. Accounting for thisnon-linear shear behaviour and eventual material degrada-tion is essential to developing an accurate computationalmodel of the overall behaviour of this class of material. Inorder to capture both the aforementioned linear and non-linear behaviours, a model inspired by crystal plasticitywith viscoelastic slip planes is proposed. Specifically, a

Norton type viscoelasticity model driven by shear tractions in preferred material planes is adopted. These planes are determined by the three reinforcement directions and are illustrated in Figure 2. As such, viscoelastic strain strictly develops when there is pronounced shear loading in these planes.

Figure 2: Illustration of the considered slip planes and shear trac-tion vector

To enable the model to account for material degrada-tion and failure, the components of the stiffness tensor areassumed to degrade in accordance with pertinent damagemodes. For this purpose models for unidirectional lami-nated composites such as [4] (extended to 3 reinforcementdirections,) as well as those for 3D fibre-reinforced com-posites [5], have been explored. The applicability of theproposed model is assessed against results from mechani-cal experiments carried out under tensile, compressive andshear loading.

References

[1] Khokar, N., Winberg, F., Hallstrom, S., Novel 3DPreform Architecture for Performance and Reliabilityof Structural Beams. Proceeding of ICCM20, Copen-hagen, Denmark.

[2] Khokar, N., 3D-Weaving: Theory and Practice. Jour-nal of the Textile Institute, 92(2), 193-207, (2001).

[3] Ekermann, T., Hallstrom, S., Mechanical Characteri-sation of Composites with 3D-Woven Reinforcement.Proceeding of ICCM20, Copenhagen, Denmark.

[4] Maim, P., Mayugo, J., Camanho, P., A Three-Dimensional Damage Model for TransverselyIsotropic Composite Laminates. Journal of Compos-ite Materials, 42(25), 2717-2746, (2008).

[5] Marcin, L., Carrre, N., Maire, J., A MacroscopicVisco-Elastic Damage Model for Three-DimensionalWoven Fabric Composites. Proceeding of ECCM13,Stockholm, Sweden.


79


Turbulent drop breakup mechanisms in high-pressure homogenizers

P. Olad1, A. Håkansson1, L. Brandt2, F. Innings1,3

1Department of Food Technology, Engineering, and Nutrition, LTH, Lund, Sweden 2 Department of Mechanics, KTH, Sweden,

3Tetra Pak Processing Systems, Lund, Sweden

Understanding the different mechanisms of drop

breakup is beneficial in different applications including the food industry where more efficient breakup may reduce energy consumption in high-pressure homogenizers (HPH) and rotor-stator mixers (RSM). Drop breakup in these devices are due to interactions with the turbulent flow [3]. Previous investigations have provided detailed characterization of the turbulent velocity field in these machines [1, 2], however, a quantitative link between turbulent field and drop breakup is still missing, which is needed for modelling and prediction.

The overall aim of this research project is to improve our fundamental understanding of turbulent drop breakup in HPHs and RSMs by quantifying breakup rates and fragment size distributions. The project includes both an experimental part (breakup visualization in a scale-up model) and resolved DNS simulations.

As the first step, we constructed the scale-up model (see Fig. 1 and Fig. 2). Since it was not possible to achieve full dynamic similarity between the scale-up model and an industrially operational HPH, two high-pressure homogenizers including a production- and a pilot-scale homogenizer were taken as references. Different design parameters were varied to ensure that the most important dimensionless numbers e.g. Reynolds numbers (Re), Weber number (We), Capillary number (Ca), and different length ratios such as the initial drop size to the gap height ratio (D/h) and the gap height to the Kolmogorov scale (h/η) are within the range of values typical of these two reference working conditions. The variation of the governing non-dimensional numbers is achieved by adjusting different parameters such as the flow velocity and the fluid material properties. We considered a 45% Brix sugar-water solution and a gap velocity of 16 m/s. The obtained geometry and dimensionless numbers are presented in table 1.

Production-scale HPH

Pilot-scale HPH

Scaled-up model

h [µm] 150 15 750 Re 2.6×104 1.7×103 2.1×103 Ca 0.06 0.40 0.39 We 1600 700 810 h/η 690 90 100 D/h 0.03 0.33 0.33

Table 1: Dimensions and dimensionless numbers for the three cases

Figure 1: Experimental model

Figure 2: Outlet chamber and the gap layout

The talk will summarize our work on the construction of the scale-up model and present our initial experimental results on turbulent drop breakup in the model.

References

[1] Håkansson, A., Fuchs, L., Innings, F., Revstedt, J., Trägårdh, C., Bergenståhl, B., High resolution experimental measurement of turbulent flow field in a high pressure homogenizer model and its implications on turbulent drop fragmentation. Chemical Engineering Science, 66(8), 1790-1801, (2011)

[2] Innings, F., Trägårdh, C., Analysis of the flow field in a high-pressure homogenizer, Experimental Thermal and Fluid Science, 32(2), 345-354 (2007)

[3] Innings, F. and Trägårdh, C., Visualization of the Drop Deformation and Break‐Up Process in a High Pressure Homogenizer. Chem. Eng. Technol.,28:882-891. doi: 10.1002 / ceat. 2005 00080 (2015)


80


DEM SIMULATION OF ASPHALT UNDER FLOW AND COMPACTIONUSING A NEW VISCOELASTIC CONTACT LAW

Erik Olsson1, Denis Jelagin2, Manfred N. Partl3

1Department of Solid Mechanics, KTH, Stockholm, Sweden2Department of Civil and Architectural Engineering, KTH, Stockholm, Sweden

3Laboratory of Road Engineering, Empa Swiss Federal Laboratories for Materials Science and Technology, Dubendorf,Switzerland

To construct durable roads, it is important that the asphalt mixture has an optimal composition of binder and stones of different sizes as well as the right mixture temperature. Here, the particle methods and especially the Discrete El-ement Method (DEM) is a very useful tool to investigate flow and compaction properties of the m ixtures. To obtain accurate predictions from the DEM simulations the contact law, i.e. how the contact forces are calculated between two asphalt particles is of utmost importance.

Asphalt is often modelled in DEM using a viscoelas-tic contact law. However, the existing viscoelastic mod-els in DEM are phenomenological in nature with no clear connection between contact law parameters and the con-stitutive properties of the binder and the stones. Hence, a new viscoelastic contact model, based on contact mechan-ics considerations, has been developed recently [1]. In this work, this model is extended for asphalt materials by mod-elling the asphalt particles as elastic stones surrounded by a viscoelastic layer representing the binder phase. The thick-ness of this layer is chosen to provide the given binder con-tent Figure 1.

Figure 1: Visualization of two asphalt particles at contact.

The accuracy of the extended contact model is validated using FEM. Simulations using DEM are performed us-ing different asphalt mixtures at different temperatures at two different important load cases; gyratory compaction and compaction flow test [2] to critically evaluate the pre-dictability of the DEM model. These two DEM models are shown in Figure 2, where the red surfaces are used to apply the loading.

Figure 2: Visualization of the two DEM models. Top: Com-paction flow test. Bottom: gyratory compaction.

References

[1] E. Olsson and D. Jelagin A, contact model for the nor-mal force between viscoelastic particles in discrete el-ement simulations, Powder Technology 342, 985-991(2018)

[2] E. Ghafoori Roozbahany and M. N. Partl, A new testto study the flow of mixtures at early stages of com-paction. Materials and Structures, 49(9), 3547–3558(2016)


81


A DISCUSSION ON SECOND ORDER RELIABILITY METHODS

Mårten Olsson, Rami Mansour


In reliability analysis, the standard modelling of

‘failure’ is when a ‘performance function’ changes sign from positive to negative. In the ‘design space’, the design variables are the coordinates. Design variables are to be chosen by the designer. However, the failure regions in design space must be avoided, often with some margin of safety. The performance functions are usually denoted gk(yp). Then, the non-admissible failure regions are formed by gi < 0, for any i. The failure set is gi = 0. In high-dimensional spaces, the failure set is a complicated hypersurface. A highly troublesome fact is that the failure set is only implicitly known. In order to determine whether a point in design space is ‘safe’ or not, one has to, in general, perform a large-scale FE-simulation. It is impossible to exactly determine gi = 0, and some approximation must be used. A variety of different approximations exist. Simple approximations are quick and easy to determine, but they have a smaller region of confidence.

Figure 1: Examples of hyperbolic contours of failure limits, approximated by quadratic functions.

Reliability methods, aim to determine the

probability of failure of a chosen design point in the following way: Consider that the design variables are distributed in accordance with some known probability density functions. Coordinate transformations can then be used so that, without lack of generality, the design variables are normally distributed, and statistically independent. A standard

choice is to transform all design variables yp to zero mean values and unit standard deviation. The nominal design (mean value of the design variables) is then at the origin, with some distance to a failure region. Very often it is substantially away from the failure set, so that the probability of failure is very low.

Second order reliability methods, SORMs, are those in which the performance function, gi, is approximated by quadratic functions. SORMs can produce high accuracy in the prediction of failure probability. For problems in high-dimensional space, there are many second order reliability methods available, such as Breitung´s [1], Tvedt´s [2] and Mansour´s [3]. It is not easy to select a suitable method for a specific reliability analysis problem. In the discussion, the SORMs will be discussed with respect to the properties: Capability, Accuracy and Robustness. The SORMs are applied to problems with both quadratic and non-quadratic limit-state functions. Extreme benchmark problems are avoided. The properties are evaluated for a variety of physically reasonable problems that are still demanding. The results are presented in an ‘ensemble sense’, so that the overall SORM-properties can be evaluated.

The capability is evaluated by the ratio of the number of reliable probability of failure to the total number of problems. The accuracy is quantified by the complimentary mean relative error with respect to analytical solutions or those from Monte Carlo simulations, and the robustness is measured by complimentary standard deviation of relative error. The goal of the presentation is to provide a better understanding of the SORMs, and provide guidelines for selecting among them in applications. Some general problems of SORMs will also be discussed.

References [1] Breitung K. Asymptotic approximations for

multinormal integrals. Journal of Engineering Mechanics. 1984;110:357-66.

[2] Tvedt L. Two second-order approximations to the failure probability. Section on structural reliability. 1983.

[3] Mansour R, Olsson M. A closed-form second-order reliability method using noncentral chi-squared distributions. Journal of Mechanical Design. 2014;136:101402.


82


VALIDATING AN EXPERIMENTAL SETUP OF A WING MODELINSIDE A WIND TUNNEL

A. Parikh1, E. Dogan1, F. Mallor1, M. Atzori1, R. Vinuesa1, R. Orlu1, P. Schlatter1

1Linne FLOW Centre, KTH Mechanics, Stockholm SE-100 44, Sweden

The flow around wings is of great interest, but is chal-lenging to study due to the highly complex flow whichexhibits a diverse array of phenomena, including wall-bounded turbulence on curved surfaces, flow subjected toa pressure gradient, incipient flow separation and wake tur-bulence. The main challenge for both experimental andnumerical studies on wings is to establish free-flight condi-tions due to the theoretically infinite domain required. Withadvances in high-performance computing, well-resolvedsimulations that enable detailed investigations of turbulentboundary layers (TBLs) developing over wings are achiev-able. A recent study by Vinuesa et al. [1] reports high-accuracy boundary-layer data and turbulence statistics on aNACA 4412 wing profile. The reference work for this pro-file is a set of experiments conducted by Coles and Wad-cock [2] and Wadcock [3] in the 1970s and 1980s, whereReynolds numbers of up to 1.64 × 106 were achieved. Inconjunction with these studies, the numerical work con-ducted at the Linne FLOW Centre will be used as a basisto perform new – more detailed – experiments with state-of-the-art measurement techniques. The present study de-scribes experiments planned at the Minimum TurbulenceLevel (MTL) wind tunnel at KTH, and the flow around thewing is detailed in detail in a companion abstract.

The wind-tunnel wing model has a chord length of 0.5 min order to achieve a Reynolds-number range similar tothose found in the literature. This chord yields a block-age ratio of around 8% and 14% for angles of attack (α)of 5 and 12 degrees, respectively, in the test section, whichhas a cross-section of 1.2×0.8 m2. In order to mitigate theeffects of blockage on the flow field and model free-flightconditions, wall liners for the side walls of the MTL weredesigned. The wing model has 64 pressure taps to providesurface pressure measurements. Figure 1 shows the stream-wise distribution of the pressure taps, of which 42 are onthe suction surface and 22 are on the pressure surface. Al-though the geometry used in the reference numerical sim-ulations featured a sharp trailing edge, practical considera-tions to reduce manufacturing complexity required that thewind-tunnel model was designed with a blunt trailing edgewith a thickness of 0.1% of the chord. The mechanismsfor mounting the model in the wind tunnel were designedwith future experimental campaigns in mind: one mountingwall is transparent in order to provide optical access for ex-periments using particle image velocimetry (PIV), and theother is designed to support a curvilinear traverse mecha-nism to obtain well-resolved boundary-layer measurementsusing hot-wire anemometry. In order to be able to conductthese measurements at different α, a mechanism for rotat-ing the wing and the traverse was integrated into the setup.

The solution devised is illustrated in Figure 2, which showsthe transparent lower panel on the floor of the wind tunneland the upper panel with the circular insert for α rotation onthe ceiling, along with the rail for the planned curvilinearTBL traverse.

Figure 1: Streamwise distribution of pressure taps on a NACA4412 airfoil profile with a chord length of 0.5 m.

Figure 2: CAD drawing of the wing model mounted in the windtunnel, with flow from right to left.

The full presentation will detail more design consider-ations in the experimental setup and present preliminarymeasurements for cross-validation with the correspondingnumerical work.

References

[1] Vinuesa, R., Negi, P.S., Atzori, M., Hanifi, A., Hen-ningson, D.S., Schlatter, P., Turbulent boundary lay-ers around wing sections up to Rec= 1,000,000. Int. J.Heat Fluid Flow, 72, 86-99, (2018)

[2] Coles, D., Wadcock, A.J., Flying-hot-wire study offlow past an NACA 4412 airfoil at maximum lift.AIAA J., 17, 321-329, (1979)

[3] Wadcock, A.J., Investigation of low-speed turbulentseparated flow around airfoils. NASA Technical Re-port, NASA CR 177450, (1987)


83


TOWARDS EFFICIENT WALL-BOUNDED TURBULENCE SIMULATIONS

R. Pozuelo1, S. Hoyas2, P. Schlatter1, R. Vinuesa1

1Linne FLOW Centre, KTH Mechanics, Stockholm, Sweden2Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Valencia, Spain

The complex dynamics of wall-bounded turbulence canbe studied through high-fidelity simulations. However, thecomputational cost of such detailed simulations is pro-hibitive at very high Reynolds numbers. In this work wecompare two codes used for wall-bounded turbulence sim-ulations: SIMSON [1] and LISO [2]. The former is apseudo-spectral code developed at KTH for channel andboundary-layer flows, which uses a Chebyshev discretiza-tion in the wall-normal direction. The latter is also apseudo-spectral code, based on compact finite differencesin the wall-normal direction, which was developed for tur-bulent channel flows. Several performance tests have beencarried out for channel flows, and in this study we will fo-cus on the results at a friction Reynolds number of Reτ =950 (based on friction velocity and channel half-height). InFigure 1 we normalize the time required to simulate oneconvective time unit in the various cases with respect to thethe fastest. This figure shows that LISO, with the Cheby-shev mesh, is almost 4 times faster than SIMSON withthe two-dimensional parallelization. Note that, by compar-ing the two LISO cases, it can be inferred that using thecompact-finite-difference mesh allows to improve the com-putational performance (at this Reynolds number) by only4%.

32 64 128 256 512 1024

Cores

1

2

3

4

5

6

7

s1D

s2D

cfd

tch

Figure 1: Performance comparison for turbulent channel flow atReτ = 950. The one- and two-dimensional paral-lelizations of SIMSON are denoted by (s1D) and (s2D),respectively. Two meshes are considered in LISO: (cfd)based on compact finite differences and (tch) the sameChebyshev mesh as the one in SIMSON.

One of the reasons for the higher computational effi-ciency of LISO is the fact that almost all the computationsand communications in this code are performed in singleprecision, while in SIMSON all the operations are in dou-ble precision. Motivated by this, we implemented messagepassing interface (MPI) communications in single preci-sion in SIMSON for both parallelizations. Furthermore, wetested the single-precision MPI with the two communica-

tion strategies in SIMSON, namely MPI ALLTOALL and analternative pairwise implementation based on mpi isend

and mpi recv. Figure 2 shows, for different numbers ofcores, the ratio between the communication times in dou-ble and single precision using the MPI ALLTOALL strategyfor the channel at Reτ = 950. It can be observed that thetime saved by communicating single data compensates thetime spent on making a copy in single precision when atleast 128 cores are used. Note that the communication timecan be reduced by a factor of around 2 for 1,024 cores withthe two-dimensional parallelization of SIMSON.

64 128 256 512 10240

0.5

1

1.5

2Simson 1D parallelization

Simson 2D parallelization

Figure 2: The ratio in communication times of double to singleprecision for turbulent channel flow at Reτ = 950.The dashed line indicates same communication time inboth cases.

The final presentation will include a comparison of thestatistics obtained with the double- and single-precision im-plementations in order to assess the impact of the loss ofaccuracy. We will also show results for turbulent boundarylayer simulations under pressure gradients using differentboundary-condition strategies.

References

[1] Chevalier, M., Schlatter, P., Lundbladh, A. & Henning-son, D. S., A pseudo-spectral solver for incompressibleboundary layer flow. Tech. Rep. TRITA-MEK. KTHMechanics (2007)

[2] Hoyas, S. & Jimenez, J., Scaling of the velocity fluctu-ations in turbulent channels up to Reτ = 2003. Phys.Fluids, 18, 011702, (2006)

[3] Li, Q., Schlatter, P. & Henningson, D. S., Spectralsimulations of wall-bounded flows on massive-parallelcomputers. In Lic. thesis: Simulations of turbulentboundary layers with heat transfer, Li, Q. (2008)


84


REGIMES OF FIBRE DEPOSITION ON FLOW OBSTRUCTIONS WITH APPLICATIONS TO NUCLEAR POWER PLANTS

J.D. Redlinger-Pohn1, M. Liverts1, F. Lundell1


Given the potential risk of nuclear energy it is

mandatory to the operator to review issues associated with operation. Such is for example the deposition of fibres (for example from glass-fibre insulation, or air filters) on screens or upon screen-passage on the fuel assemblies [1,2]. The formed fibre mat then filters suspended particles causing increased pressure loss leading to a drop in coolant flow rate. This fibre mat formation is however yet not fully understood, and reports note screens clogged by fibres larger and smaller than the screen opening [2]. We extended that observation in a preliminary experiment (Figure 1).

Figure 1: Fibre mat formation on screens with small holes and large distance (a,b), and on screens with large holes and small distance (c,d). Snaphot time and filtered volume are stated. The fibre length is

given for comparison in a and c. Unexpectedly, holes smaller than the fibre length

remained uncovered (Figure 1a,b) whilst holes that were 2.5 the fibre length were covered (Figure 1c,d).

The preliminary study was followed up by detail experiments tracking the fibre deposition on screens based on thresholding of the RGB (red green blue) colour values. Screens were designed to probe into the four combination from the two parameters: fibre length to the hole size, LFibre/DOpen, and fibre length to the hole spacing, LFibre/SOpen.

LFibre/DOpen distinguishes between the deposition mechanism, i.e. retention, < 1, and stapling, > 1. The retention rate decreased with decreasing LFibre/SOpen. Distinguishable fibre-screen interaction regimes were found for each combination of the two parameters (Figure 2).

Fibre deposition for regime I screens followed probability retention, i.e. the mechanism of paper production [3]. Coverage and fibre mat growth was comparably fast. For screens in regime II, fibre

stapled on the solid growing inwards and covering the holes with time (Figure 1c,d), which resembles fibre stapling mechanisms [4].

Figure 2: Coverage of screens (solid symbol) differing in the dimensions falling into differing

fibre-screen interaction regimes. For screen in regime III, fibre stapled on the solid

but at a rate and number too low to support the growth of a fibre mat and thus the holes remained open. For screens in regime IV, holes were covered at low approach velocity, but remained open at high approach velocity (Figure 1a,b) showing a significance of hydrodynamic forces, i.e. increased drag, or re-orientation in an extensional flow field in the case of low open screen area, i.e. < 10% of the screen surface.

References

[1] Hart, G.H., A short history of the sump clogging issues and analysis of the problem. Nucl. News, 47, 24-34, (2004)

[2] Suh, J.K., Evaluation of Long Term Core Cooling Capability considering LOCA-generated Debris. PhD Thesis, Seoul National University, (2015)

[3] Parker, J.D., The Sheet-Formin Process (1st ed.). TAPPI (1972)

[4] Olson, J.A., The Effect of Fibre Length on Passage through Narrow Apertures. PhD Thesis, UBC Vancouver, (1996)


85


PREDICTION OF SHOCK AND VIBRATION CAUSED BY A BIRD STRIKE TO AN AIRCRAFT STRUCTURE

A. Rehnberg1, A. Josefsson2, N. Österström2

1Creo Dynamics, Lund, Sweden

2Saab Aeronautics, Linköping, Sweden

In-flight collisions between aircraft and birds, so

called “bird strikes”, are a known hazard in the aviation world. Some of the well-known effects of such incidents are structural damage to transparencies, control surfaces or engines. In addition to such directly damaging effects, the bird impact also causes a mechanical shock that propagates throughout the aircraft structure and may affect sensitive on-board equipment by means of shock and vibration. Hence, the aircraft may be indirectly affected by a bird strike even if the structure and skin is unharmed by the impact. This secondary effect from bird strikes has previously been the subject of much less investigations than the damaging effects to external parts of the airframe.

Due to the large costs involved in bird strike testing and certification, it is highly desirable to investigate more efficient methods for testing of internal effects of bird strike shock. Furthermore, finite element simulations of bird strikes are generally not suitable for shock and vibration because of the high frequency content of induced accelerations. This study therefore aims to predict the internal accelerations caused by a bird impact by combining non-destructive laboratory testing with linear structural dynamics theory.

To this end, the shock severity from a bird strike to an aircraft structure has been studied for a typical test case where the bird impacts the underside of an aircraft fuselage at a shallow angle and relatively low velocity. An existing fuselage section, taken from a decommissioned aircraft, was used as a representative test structure for the investigations.

The transfer functions between possible bird impact points and measurement locations (installation points for on-board equipment) inside the fuselage section were determined using hammer impact tests. These transfer functions were used to compute the impulse response function of each structural transmission path. The impulse response functions were then convoluted with a simplified force function that represents the time history of the bird impact force, derived from the deformation of an equivalent fluid cylinder striking a rigid surface at an angle [1]. The resulting impulse responses thereby represent the predicted secondary accelerations at each equipment location inside the fuselage. As a base for further comparison, shock response spectra (SRS:s) were calculated from the estimated accelerations

In order to verify the predictions, several bird shooting tests were performed on the fuselage

section used for the hammer impact tests, using the same impact points and measurement locations that were used for the hammer impact tests. This was performed using a bird cannon and chicken carcasses of standardised weight and dimensions. Accelerations from the bird impacts were measured and shock response spectra were calculated from the measurements as a base for comparison with predicted values.

Initial comparisons between shooting tests and predictions showed that the frequency content of the predicted and measured shock response spectra was roughly similar, but that the linear predictions generally seemed to under predict shock amplitudes. Further investigations indicated that this is likely because the force generation of the bird impact is not accurately represented by the simplified force function, which assumes that the target structure behaves as a rigid surface. Furthermore, since the bird impact occurs over a distance rather than a single point, the transfer function is not adequately represented by a single hammer impact measurement.

Finite element simulations, using a validated bird impact model, further revealed that the force generation at bird impact is highly dependent on the structural flexibility at the impact point, and also that force transfer occurs in the longitudinal direction as well as in the vertical.

Using the above information, the force function was updated to match the observations from finite element simulations. This was seen to improve the agreement between predicted and measured shock. Furthermore, the measured transfer functions of the aircraft structure were modified to take into account the behaviour of the target structure at impact. This more representative description of the structural dynamics resulted in further refinement of the prediction model.

References

[1] AFFDL-TR-77-60, 1978, “Bird impact forces and pressures on rigid and compliant targets”, technical report, Air Force Flight Dynamics Laboratory, Ohio, USA.


86


PARTICLE WALL INTERACTION

A. Rinehart 1, U. Lacis1, S. Bagheri1


Particle surface interaction is a common physical phe-nomena that occurs over a wide range of sizes and envi-ronments. An equally wide number of engineering prob-lems; drag reduction, heat transfer, bio-fouling mitigation,and tribology rely on detailed understanding of the particlewall interaction. This research contributes to the under-standing necessary to design functional surfaces. Recentlyelastic and poroelastic surfaces have gained significant at-tention due to their ability to generate lift and resulting non-intuitive particle dynamics. We look at an analogous modelproblem (figure 1) of a 2D cylinder falling freely next to awall where the wall or cylinder surface has inhomogeneousslip properties. We treat slip as the leading order descrip-tion of physical surfaces that could comprise rough, porous,and chemical variations.

V

V⟂

δ

ρμ

ω

xt

x

z

Figure 1: Immersed negatively buoyant cylinder falling freelynext to wall with inhomogeneous slip surface. The wallsurface change results in lift and torque acting on thecylinder due to the broken symmetry in gap pressure.

We derive resistance coefficients and scale estimates forthe motion of the cylinder. Additionally we test severalcases numerically with a finite element method solving thedynamics of the cylinder. We report that the inhomoge-neous surface breaks the lubrication gap pressure symme-try resulting in a lift force. Typical gap pressures are shownin figure 2. The gap pressure can be generated from rota-tion or wall parallel motion. Three categories of surface en-hanced motion arise: migration from the wall (single sur-face transitions), oscillations normal to the wall with netmotion away (patterned surfaces), wall parallel translationgenerated from rotation (single surface transition).

The lift force is obtained through lubrication theory,

f‖z = µfV‖ε−1F ‖z (1)

where µ is the fluid viscosity, V ‖ is cylinder wall parallelvelocity, ε is the ratio of the cylinder wall gap δ over cylin-der radius r, and F ‖z is the resistance coefficient for wallparallel motion.

The resistance coefficient F ‖z is the integral of the gappressure projected on the cylinder surface. It is strictly afunction of the non-dimensional slip length, L = l/δ, phys-ical slip length over gap height as shown in the inset of fig-ure 2. The lift force decays to zero with zero slip lengthand reaches a maximum for large slip lengths.

-10 -5 0 5 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Inhomogeneous Slip

No Slip

Slip

10-4 10-2 100 102 1040

0.5

1

1.5

3

2.5

3.5

Figure 2: Non-dimensional gap pressure distributions are shownas a function of wall position. The inset shows the re-sistance coefficient F ‖

z as a function of L. The inho-mogeneous slip case is indicated by the red circle onthe inset.

The new particle dynamics generated from slip varia-tions could find application in a range of topics; micro flu-idics, tribology, and active matter communities.

References

[1] Salez, T., Mahadevan, L. Elastohydrodynamics ofsliding, spinning and sedimenting cylinder near softwall. J. Fluid Mechanics, 779, 181-196, (2015)

[2] Kaynan, U., Yariv, E. Stokes resistance of a cylin-der near a slippery wall. Physical review of Fluids,2, (2017)

[3] Skotheim, J.M., Mahadevan, L. Soft lubrication:The elastohydrodynamics of nonconforming and con-forming contacts. Physics of Fluids, 17, 92-101,(2005)


87


TOPOLOGY OF COLLOIDAL DISPERSIONS IN EXTENSIONAL FLOWUSING OPTICAL COHERENCE TOMOGRAPHY

C. Rydefalk1, K. Gowda1, F. Lundell1,2

1Department of Mechanics, KTH, Stockholm, Sweden2Wallenberg Wood Science Center, KTH, Stockholm, Sweden

In the pursuit of new bio-based materials researchers arelooking towards cellulose and protein based filaments ob-tained from nano-sized particles. It has been shown thatcolloidal dispersions with protein nano-fibrils (PNF) andcellulose nano-fibrils (CNF) can be used to spin micro-filaments with extraordinary material properties and pos-sibilities[1,2,3]. This has been achieved through the hydro-dynamic alignment of PNF and CNF using the extensionalflow created by a microfluidic flow-focusing device. Fur-thermore, to improve the alignment process, there is a ne-cessity to understand the flow dynamics and the flow field.

Building on a previous study this work employs opticalcoherence tomography (OCT) as the method for studyingthe flow. This is a 3D, non-invasive imaging technique thatcan capture the flow topology of the colloidal dispersion inthe flow-focusing channel with a few micrometre resolu-tions per voxel[4]. In addition to this, by combining thisimaging technique with Doppler acquisition, it is possibleto measure the velocity field.

Figure 1: Top view of the flow-focusing section of the channelcaptured using OCT. Detachment of the core fluid, Q1,from the wall is outlined in green.

Figure 1 shows the top view of the flow-focusing channeldepicting the detachment of the CNF colloidal dispersionfluid from the top wall obtained with OCT. The channelused has a square cross-section of 1 x 1 mm2 and is littleover 20 mm long. The sheath fluid here is water whichenters from side channels with the same dimensions as themain channel and are situated at a 90 angle. The flowrates of core fluid and sheath fluid correspond to Q1 = 6.5mm3s-1 and Q2 = 7.5 mm3s-1. The region occupied by theCNF colloidal dispersion before the detachment is calledwetted region, as highlighted by the green curve. After thedetachment the CNF colloidal dispersion evolves into anelliptical thread shape as depicted in Figure 2.

Figure 2: 3D view of the core fluid thread shape obtained throughOCT.

This study extends to geometric variations of the flow-focus channel. The main focus is on the topology of thewetted region and the shape of the colloidal dispersionthread.

References

[1] Kamada, A. et al., Flow-assisted assembly of nanos-tructured protein microfibers. PNAS, 6, 1232-1237,(2017)

[2] Hakansson, K. et al., Hydrodynamic alignment andassembly of nanofibrils resulting in strong cellulosefilaments. Nature Communications, 5, 4018, (2014)

[3] Mittal, N. et al., Multiscale Control of NanocelluloseAssembly: Transferring Remarkable Nanoscale FibrilMechanics to Macroscale Fibers. ACS nano, 12(7),6378-6388, (2018)

[4] Gowda, K. et al., Effective interfacial tension in flow-focusing of colloidal dispersions: 3D numerical sim-ulations and experiments. eprint arXiv:1901.08939[physics.flu-dyn], (2019)


88


Richtmyer-Meshkov vs Kelvin-Helmholtz instability in an elliptic

inhomogeneity

S.Sembian, M. Liverts, N. Apazidis

Department of Mechanics, KTH, Stockholm, Sweden

When a shock wave interacts with an isolated

density inhomogeneity, strong coupling of several fluid dynamic phenomenon occurs. Predominant among those is the baroclinic deposition of vorticity at the interface between the two fluids resulting in regions of intense mixing, a phenomenon referred to as Richtmyer-Meshkov (RM) instability [1,2]. As the interface becomes more distorted later, shear-induced Kelvin-Helmholtz (KH) instability develops as a secondary effect [3,4]. Due to certain limitations, the inhomogeneities studied thus far were aligned normal to the incident shock wave introducing symmetry along the center axis. In this paper, the effects of inhomogeneity inclination on the instabilities are investigated. In order to enable inclinations, an elliptic inhomogeneity – generated by heating a wire on the basis of ‘Joule heating’ – is employed. The elliptic inhomogeneities are impacted by a Mach 2.15 blast wave.

Fig 1: 0o inclination inhomogeneity interaction Two symmetric counter rotating vortices due to

RMI were observed for the straight (0o inclination) interaction. Since this being a slow/fast configuration, the transmitted shock was seen to travel faster than the incident shock, thereby creating a precursor shock and a Mach stem as seen in Fig 1. When the inhomogeneity is inclined, say at a 24o angle (Fig 2), the first feature to be observed is the asymmetric flow field introduced by it. The transmitted shock wave rotates itself by 24o in the clockwise direction and propagates normal to the inclination axis. The other prominent feature observed is the appearance of a train of vortices similar to KHI. The baroclinic mechanism deposits vorticity at the interface initiating a disturbance. But since they are embedded in a high velocity region following the shock wave, their interaction results in

a velocity discontinuity thereby creating the rolling-up phenomenon of the interface.

Fig 2: 24o inclination inhomogeneity interaction

Circulation, calculated using numerical analysis, showed that the growth of the vortices was linear for the 0o case whereas for the 24o case it followed a quadratic path. Two factors influencing the quadratic nature are: (a) reduction in strength of the transmitted shock thereby generating vortices with reduced strength, and (b) loss of vorticity of the earlier generated vortices.

References

[1] Richtmyer, R. D., Taylor instability in shock acceleration of compressible fluids, Commun. Pure. Applied. Maths. 13, 297-319 (1960).

[2] Meshkov, E. E., Instability of the interface of two gases accelerated by a shock wave, Fluid Dyn. 4, 101-104 (1969)

[3] Brouillette, M., The richtmyer-meshkov instability, Annu. Rev. Fluid Mech. 34, 445-468 (2002).

[4] Ranjan, D., Oaklay, J., Bonazza, R., Shock-bubble interactions, Annu. Rev. Fluid Mech. 43, 117-140 (2011)


89


Inelastic mechanical behaviour of granite under spherical indentation test

H. Shariati, M. Saadati, P.-L. Larsson


The inelastic behaviour of Bohus granite is

investigated based on experimental and numerical results. The yield surface and related dilation angle are determined based on quasi-oedometric tests performed in an earlier work [1]. In the constitutive modelling, a Drucker-Prager law [2] is employed together with a variable dilation angle. The constitutive model is first applied to simulate the quasi-oedometric test and the stress and strain fields are obtained. Furthermore, the validation of the model is investigated by simulation of the spherical indentation test.

The inelastic behaviour of the material is investigated based on quasi-oedometric compression tests. As it can be seen in Figure 1, a cylindrical specimen enclosed within a confinement cell is axially loaded in compression. Both axial and radial stresses increase during loading as the material expands in the lateral direction. This gives an indication of the strength of the material at different levels of hydrostatic pressure.

Figure 1: Experimental quasi-oedometric

compression test setup

Figure 2: Schematic illustration of the spherical

indentation test

Quasi-static indentation tests, schematically shown in Figure 2. Rock blocks are indented by means of a tungsten carbide spherical indenter.

In order to investigate the reason behind the detected load-drops in the experimental Force-Penetration response, a high speed camera is utilized to capture images of the rock specimen surface

before and after the load-drops. It is found that each load-drop in Force-Penetration response during that test corresponds to a material removal occurrence on the specimen surface, see [3].

Linear Drucker-Prager model is employed in order to numerically simulate the experiments, see Eq. (1).

𝐹 = 𝑞 − 𝑝 𝑡𝑎𝑛 𝛽 − 𝑑 = 0 (1)

where F is yield function, d the cohesion of the material, β the friction angle, q von Mises equivalent stress and 𝑝 pressure.

𝐺 = 𝑞 − 𝑝 𝑡𝑎𝑛 𝛹 (2)

As for inelastic yielding, the flow potential (G) can be seen in Eq. (2), where 𝛹 is dilation angle.

The resulting Force-Penetration responses by the numerical simulations as well as one of the experimental results are plotted in Figure 3 for comparison purposes. Good agreement between experiments and the present model is found.

Figure 3: Force-Penetration simulation results using different material models compared to

experimental results

References

[1] Saadati M, Forquin P, Weddfelt K, Larsson P, Hild F. On the Mechanical Behavior of Granite Material with Particular Emphasis on the Influence From Pre-Existing Cracks and Defects. Journal of Testing and Evaluation 2018; 46(1):1-13.

[2] Drucker DC, Prager W. Soil mechanics and plastic analysis or limit design. Quarterly of applied mathematics 1952; 10(2):157-165.

[3] Shariati H, Saadati M, Bouterf A, Weddfelt K, Larsson P.L, Hild F. On the Inelastic Mechanical Behavior of Granite: Study Based on Quasi-oedometric and Indentation Tests. Rock Mechanics and Rock Engineering 2019; 52(3):645-657.


90


FRICTION INDUCED DRIVE TRAIN VIBRATIONS

J. Sjostrand 1, I. Lopez Arteaga1,2, L. Kari2

1The Marcus Wallenberg Laboratory for Sound and Vibration Research (MWL), KTH, Stockholm, Sweden2Department of Mechanical Engineering, Section Dynamics and Control, TUE, Eindhoven, The Netherlands

An analysis of the frictional stick-slip behavior in a re-duced drive train system of a heavy-duty truck will be pre-sented. The stick-slip behavior is due to an overload ofthe torque transmitting capacity of the dry friction clutchinstalled in the drive line. Drive line systems connectedto combustion engines usually contains some switchingmechanism that is able too turn the torque transmissionon or off in order to carry out gear-shifts etc. The dryfriction clutch is a common choice of this mechanism inheavy-duty trucks. The drive line model is comprised oflumped torsional inertias, I1, I2 ... In, connected by eithera dry-friction path, Tf , or discrete spring/damper elements,Kn,m, Cn,m. The system is excited by a mean torque withsuperimposed oscillating terms, Te(t), and also a resistingtorque, Td, representing, for instance, the air- and rollingresistance that is acting on the truck, see Figure 1.

Figure 1: Example of a reduced drive line model, Following theright hand rule the positive direction of rotation iscounter-clockwise.

The frictional interface introduces some computationaldifficulties. Whenever a state-transition occurs (sticking toslipping or vice versa) the topology of the system changes.This calls for state-by-state solutions of the equations ofmotion in order to obtain the correct response. An algo-rithm proposed by Duan and Singh [1] will be presented.Figure 2 shows a typical stick-slip behavior computed witha state-by-state solution algorithm.

Numerically this calls for more work and a common wayto circumvent this problem is to introduce different smooth-ing procedures which transforms the discontinuous equa-tions of motion into a set of continuous equations. A typi-cal choice of smoothing procedure could be the hyperbolictangent function

Tf (δ) = Tsf tanh(σδ) (1)

Where Tsf is the friction saturation torque, δ the relativeangular velocity in the friction interface and σ is a parame-ter governing the steepness of the transition from negativeto positive relative velocity. The σ-parameter affects thesubtle measure of ”stiffness” of the equations. A large σ-value yields stiff equations and hence the solving techniqueof the continuous equations should be changed accordingly.

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Time [s]

-30

-20

-10

0

10

20

30

40

An

gu

lar

ve

locity [

rad

/s]

Figure 2: Time-domain simulations of a drive line model. Theplot shows the relative angular velocity, δ, in the fric-tion interface.

The numerically more heavy state-by-state solution of thediscontinuous equations can serve as a benchmark for thesmoothend system. Lastly, state-by-state analytical solu-tions to the equations will be compared to the numericalcalculations

References

[1] Duan, Chengwu, and Rajendra Singh. ”Dynamics ofa 3dof torsional system with a dry friction controlledpath.” Journal of sound and vibration 289.4-5 (2006):657-688.

[2] Moler, Cleve. ”Stiff differential equa-tions.” Retrieved March 12, 2019,https://se.mathworks.com/company/newsletters/articles/stiff-differential-equations.html


91


PLASMA DRAG REDUCTION METHODOLOGYFOR EFFECTIVE ENERGY USAGE — PROMETHEUS

P. Sujar-Garrido1, R. Orlu1, P. Elofsson2, P. H. Alfredsson1

1Linne FLOW Centre, KTH Mechanics, Royal Institute of Technology, Stockholm, SE-100 44, Sweden2Scania CV AB, SE-15187 Sodertalje, Sweden

Aerodynamic drag accounts for more than 20% of thetotal energy loss of heavy duty vehicles and around half ofthis drag is induced by the tractor when considering a zerodegree yaw angle. The flow separation in the region of theA-pillars substantially increase the overall drag of the truckunder side-wind conditions. Active methods with feedbackcontrol would probably improve the situation when consid-ering that trucks on the road are subjected to varying yawangles. Dielectric Barrier Discharge (DBD) plasma actua-tors have shown effectiveness in controlling flow separationfor geometries such as airfoils or cylinders by ‘injecting’momentum in the streamwise direction close to the sepa-ration line [1, 2]. However, they are only effective for lowflow velocities and the effect of actuation is strongly depen-dent on the relative position between the separation line andthe position of the actuator. To overcome these limitationsan array of DBD plasma actuators creating streamwise vor-tices similar to those induced by physical vortex generators(VGs) has been suggested as an alternative [3]. Recently,based on previous work performed within the Linne FLOWCentre [1, 2, 3], a DBD-VG array has been mounted on theA-pillar of a 1:6 scale truck model and balance measure-ments in an aerodynamic wind tunnel have been performedto directly assess the drag for various velocities and yawangles, with the actuators on and off [4]. This proof-of-concept experiment resulted in significant drag reductionunder actuation that increases with the yaw angle. Above 5degree yaw even net drag reduction, i.e. when also takingthe power consumption of the actuator into account, wasachieved.

Building on the success from the proof-of-concept ex-periment, the project PROMETHEUS (Plasma drag Re-ductiOn METHodology for effectiveEnergy USage) hasbeen initiated with the aim to develop and optimise plasmaactuators for the purpose of aerodynamic drag reductionon heavy duty trucks. In this project various geometrical(length and spacing) and operational parameters (duty cy-cle) will be investigated in order to find an optimal balancebetween control performance and actuator power consump-tion. The presentation will provide an outline of recent ef-forts in flow control on truck aerodynamics in light of theaforementioned progress within the Linne FLOW Centre incollaboration with Scania CV AB and present the plannedwork within PROMETHEUS.

References

[1] Vernet, J. A., Orlu, R. and Alfredsson, P. H. Separa-tion control by means of plasma actuation on a half

cylinder approached by a turbulent boundary layer. J.Wind. Eng. Ind. Aerod. 145, 318–326 (2015).

[2] Vernet, J. A., Orlu, R. and Alfredsson, P. H. Flow sep-aration control by dielectric barrier discharge plasmaactuation via pulsed momentum injection. AIP Ad-vances 8, 075229 (2018).

[3] Vernet, J. A., Orlu, R. and Alfredsson, P. H. Flowseparation control behind a cylindrical bump usingdielectric-barrier-discharge vortex generator plasmaactuators. J. Fluid Mech. 835, 852–879 (2018).

[4] Vernet, J.A., Orlu, R., Soderblom, D., Eloffson, P. andAlfredsson, P. H., Plasma streamwise vortex genera-tors for flow separation control on trucks. A proof-of-concept experiment. Flow Turbul. Combust. 100,1101–1109 (2018).


a)

b)

Figure 1: a) A 1:6 scale model of a truck in the “Lola Cars Inter-national 50% Scale Wind Tunnel”. The right A-pillaris equipped with DBD-VG array. b) A close-up ofthe actuators under actuation, the violet light show theplasma. Reprinted from Vernet et al. [4].

92


A TOPOLOGY OPTIMIZATION METHOD FOR AS-BUILT METAL ADDITIVE MANUFACTURING

S. Suresh, C.-J. Thore, A. Klarbring

Solid Mechanics, Department of Management and Engineering, Linköping University, Sweden

It is generally found that mechanical properties, such as stiffness, static strength and fatigue behaviour of metal additive manufactured (AM) components are size dependent in that thin structural members tend to have lower relative stiffness and inferior fatigue and strength properties compared to thicker members [1]. However, it is also found that this tendency is largely reduced by surface treatments such as machining and polishing while it is highly present in specimens with rough as-built surface. This implies that these reduced mechanical properties can be attributed to surface morphology where a surface layer is a large part of the cross section of a structural member. Since machining and polishing is sometimes not possible or unpractical (e.g., due to interior surfaces) there is demand for topology optimization (TO) methods for as-built structures where size dependency due to rough surface layers is considered. We have developed such a TO formulation where regions close to the surface of an optimized structure are identified and given a lower stiffness than the bulk material. The formulation is density-based and utilizes two density-like fields obtained from an optimization variable field by linear filtering. The first such density is the shape density that defines the geometry of the structure and which is penalized to be essentially black and white by, e.g., SIMP penalization. The second density field is a surface layer identifier for which a larger filter radius, that gives the width of the surface roughness effect, is utilized. The stiffness deterioration could be a function of this density, utilizing damage mechanics, or could be set as constant in the surface region identified by a non-zero density gradient. In a simple model we assume different but constant Young’s moduli in the bulk material and in the surface layer, denoted 𝐸𝐸𝐵𝐵 and 𝐸𝐸𝑆𝑆, respectively. The interpolation of Young’s modulus, using SIMP penalization for the shape density, is

𝐸𝐸 = 𝜌𝜌𝑞𝑞𝐻𝐻(|∇𝜌𝜌𝐷𝐷|)𝐸𝐸𝑆𝑆 + 1 −𝐻𝐻(|∇𝜌𝜌𝐷𝐷|)𝐸𝐸𝐵𝐵,

where the shape density 𝜌𝜌 is obtained from the optimization variable by linear filtering. Similarly, the surface layer identifier 𝜌𝜌𝐷𝐷 is also obtained by linear filtering but using a larger filter radius. The surface layer is defined by |∇ρD| ≠ 0 and the material is interpolated using the Heaviside step function 𝐻𝐻. Although the developed method can allow for stress as well as fatigue constraints, as a first study we present results for pure stiffness optimization. In

the figures below optimal topologies for a cantilever beam are shown and the green surface layer represents regions having lower Young’s modulus. The difference in the set-up used to obtain the two figures is the size of the radius of the filtering giving the surface layer identifier 𝜌𝜌𝐷𝐷 . Figure 1 is the optimal topology for a smaller such radius, i.e., for a thinner surface layer, than in Figure 2. Note that a thicker surface layer supresses the presence of thin structural members.

Figure 1: Optimal topology for a cantilever beam problem having lower Young’s modulus in the

green surface layer than in the red bulk material.

Figure 2: Same problem as in Figure 1 but for a slightly thicker surface layer. Note the changed

topology.

References

[1] Magnus Kahlin, Fatigue performance of additive manufactured TI6AI4V in aerospace applications, Linköping Studies in Science and Technology, Licentiate Thesis No. 1775, 2017.


93


TOPOLOGY OPTIMIZATION USING AN EVOLUTION-BASEDANISOTROPIC HIGH-CYCLE FATIGUE CONSTRAINT

S. Suresh, S.B. Lindstrom, C.-J. Thore, B. Torstenfelt, A. KlarbringSolid Mechanics, Department of Management and Engineering, Linkoping University, Sweden

We propose a new topology optimization (TO) methodfor the design of elastic continua that includes high-cyclefatigue of anisotropic materials as a constraint. The fatigueconstraint is based on a continuous-time model [1] in theform of differential equations governing the time-evolutionof fatigue damage at each point in the design domain. Suchevolution occurs when the stress state lies outside a so-called endurance surface, which moves in stress space de-pending on the current stress and a back-stress tensor. Withthis type of model, fatigue damage can be predicted for ageneral, multiaxial load history including non-proportionalloads, without the use of cycle-counting algorithms.

The TO method should be applicable to design for ad-ditive manufacturing (AM). The use of AM leads to di-rectional dependencies in the mechanical properties. Wepropose two methods to account for anisotropic materialproperties in the fatigue model, particularly for transverselyisotropic material.

In the first method, the predicted fatigue-damage followsthe fatigue model as defined in [1] without changing thedifferential equations, but the stresses are calculated froman anisotropic elastic analysis. Now the calculated stressσ = σ(t) from the anisotropic elastic analysis is consid-ered as given and the endurance function is defined as

β1(σ,α) =1

S0[σ +Atr(σ) − S0] , (1)

where α is the back-stress tensor, σ is the effective stress,S0 > 0 is the endurance stress and A > 0 is a dimension-less parameter.

In the second method, the definition of the endurancefunction in (1) is changed to account for anisotropy, in thiscase, transversely isotropic material. The key idea is to splitthe stress tensor σ into longitudinal σL and transverse σT

parts, i.e., σ = σL + σT . Following [2], the endurancefunction is redefined as

β2(σL,σT ,α) =1

ST[σ +AT tr(σT ) +ALtr(σL)

− ((1 − ξ)ST + ξSL)],

(2)

where the parameter ξ is used to reflect the average loadingdirection that is defined in terms of stress ratio. The param-eters AL > 0, SL > 0 and AT > 0, ST > 0 correspond tomaterial parameters defined in longitudinal and transversedirections, respectively. However the evolution equationsof the back-stress tensor and the damage development fol-low the original formulation [1].

We consider maximizing stiffness with bounds on themass and the maximum fatigue damage using the materialdistribution method and penalization to enforce discrete-

valued solutions. The maximum fatigue damage is ap-proximated using an aggregation function in the form ofa p-norm. The problem is solved using a gradient-basedmethod and the sensitivities are determined by adjoint sen-sitivity analysis. For the fatigue constraint, the sensi-tivities require the solution of a terminal value problem,which turns out to be the most computationally expensivepart of the optimization process. Several numerical exam-ples demonstrating both proportional and non-proportionalloads and effects of anisotropy are given.

We consider transversely isotropic material, particularlyAISI-SAE 4340 alloy steel. The optimization problem istested for an cantilever beam with a proportional periodicload history of 1-cycle using the first method, as men-tioned earlier. In Fig.1, we can see optimized result for thecantilever beam, where the stiffness is maximized with anevolution-based anisotropic high-cycle fatigue constraint.

Ex

EZ

Figure 1: Optimized model of cantilever beam with anisotropicmaterial properties

References

[1] N. S. Ottosen, R. Stenstrom, and M. Ristinmaa. Con-tinuum approach to high-cycle fatigue modeling. In-ternational Journal of Fatigue, 30(6):996–1006, 2008.

[2] S. Holopainen, R. Kouhia, and T. Saksala. Con-tinuum approach for modelling transversely isotropichigh-cycle fatigue. European Journal of Mechanics -A/Solids, 60:183–195, 2016.


94


FULL SCALE MODELING AND VALIDATION OF WEAR IN A POWER SHOVEL BUCKET

A. Svanberg1,2, P. Jonsén1

1Department of Engineering Sciences and Mathematics, LTU, Luleå, Sweden

2Boliden Minerals AB, Aitik, Sweden

Wear in heavy mining equipment is one of the key factors for unexpected and expected machine down time due to failure and maintenance in the Aitik copper mine. Abrasive wear from both sliding and impact is fundamental modes of wear in the power shovel buckets in the mine. Being able to numerically predict how wear in the power shovel buckets takes place is a step towards decreasing the machine down time, both through better planning of the maintenance but also to improve wear behavior by e.g. repositioning of wear components. In the experimental part of this study, a bucket belonging to a Bucyrus 495 power shovel located in the Aitik copper mine have been extensively studied through one duty cycle. A three dimensional laser scanning of the bucket was initially performed to receive the bucket geometry which can be seen in Figure 1. A number of predefined positons on the bucket’s wear plates were measured with an ultrasonic thickness gauge, the tooth length was measured for all teeth. The measurements were done with a constant interval of loaded tons during the whole duty cycle from a newly renovated to a worn out bucket. The abrasive wear behavior from both sliding and impact was considered: To study the wear from sliding between wear plates

and copper ore a wear drum test was used in a similar way as described in [1].

The impact wear was studied by the use of a novel experimental setup consisting of a box filled with ore which was lined with wear plates. A uni-directional translation movement with a certain frequency was then applied, and the wear on the plates caused be impact was studied.

The reason behind the thoroughly planned experimental program was to have a sufficient validation case for the numerical models as well as calibrate the numerical model. For the numerical model, a combined model consisting of the Finite element method (FEM) and the discrete element method (DEM). FEM was used to model the elastic behavior of the bucket, and DEM was used for modeling the copper ore material. Several critical parameters for the internal interaction between discrete elements as well as the interaction with the bucket was calibrated with angle of repose tests. The particle size distribution (PSD) from the ore in the Aitik mine [2] was applied to the DEM distribution in simulations. Wear is modeled with a combined wear law which treats both sliding and impact wear and is calibrated from the previous mentioned wear tests. The kinematic behavior of the bucket and excavator was captured through live video recordings and data analysis of several loading cycles with different operators and working conditions in order to capture an averaged loading cycle. The kinematic behavior was then used in the numerical model. Preliminary results from the numerical model shows significant possibilities to better understand the behavior of wear in the buckets. The novel wear calibration procedure where a sliding and impacting wear law is combined and calibrated from realistic experiments shows interesting results in capturing the multi-modal wear occurring in the bucket. The numerical results compared to the experimental results shows a good agreement on a qualitative as well as a quantitative level considering both wear and kinematic behavior of the copper ore-bucket interaction. References [1] Forsström, D., et al. Engineering Failure

Analysis. Calibration and validation of a large

scale abrasive wear model by coupling DEM-

FEM: Local failure prediction from abrasive

wear of tipper bodies during unloading of granular material, 66, 274-283, (2016)

[2] Petropoulset, N., et al. Improved blasting results

through precise initiation: results from field

trials at the Aitik open pit mine. Swebrec report, no. 2013:1, ISSN: 1653-5006.


Figure 1: Isometric view from 3D-scan of the studied bucket.

95


A STUDY OF THE FRACTURE BEHAVIOUR OF ULTRATHIN COATINGS ON A POLYMER SUBSTRATE

M. V. Tavares da Costa1, J. Bolinsson 2, P. Fayet3 E.K. Gamstedt1

1 Uppsala University, Division of Applied Mechanics, Uppsala, Sweden.2 Tetra Pak Packaging Solutions AB, D & E, Lund, Sweden. 3 Adhemon Sarl, Thin Technology, Lausanne, Switzerland.

Metal oxide coating with a nanometer scale thickness on flexible polymer substrates is a viable material combination for food packaging applications. This combination can provide an enhancement of the barrier performance in the package [1]. A concern is the cracking of the brittle coating when subjected to tension and bending in the manufacturing process. Such cracks can affect the permeability.

This presentation focuses on examining multiple cracking in metal oxide coatings through fragmentation tests [2] by in-situ tensile loading in a table-top scanning electron microscope. This allow for tracking of the crack accumulation and subsequently to calculate adhesive and cohesive properties, such as the interfacial shear strength and the distribution of the coating tensile strength. Furthermore, we will present high-resolution microscopy images of ridge cracking [3], which is mainly caused by compressive deformation due to the transverse Poisson contraction. It will also be demonstrate how to obtain an interfacial fracture toughness parameter between coating and substrate, making use of a micromechanical model and ridge crack dimension. These parameters are compared with results from finite element simulations. The advantages and disadvantages of the experimental methods and numerical simulation will be addressed, as well as the accuracy of the assumptions in their underlying models. Finally, it will also be discussed how the obtained mechanical properties can be used in predicting coating cracking under more complex loadings in manufacturing, and how relevant barrier properties, such as the oxygen transmission rate, may be predicted.

Figure 1: TiO2 coating of 20 nm thickness on top of PET substrate stretched at 10% of tensile strain

References [1] P. Fayet, C. Neagu, E.K. Gamstedt, Mechanics-

driven material design for optimized barrierfilms, In: Proceedings of the AIMCAL WebCoating and Handling Conference, Naples, USA(2015).

[2] Y. Leterrier, Y. Wyser, J.A.E. Månson, J.Hilborn, A method to measure the adhesion ofthin glass coatings on polymer films, The

Journal of Adhesion, 44, 213–227 (1994).[3] M.D. Thouless, Combined Buckling and

Cracking of Films, Journal of the American

Ceramic Society, 76 (1993)._________________________________________ Corresponding author email: [email protected]

96


A GENERALIZATION OF A COHESIVE MIXED MODE MODEL

J. Tryding1,2, M. Ristinmaa1, E. Borgqvist2

1Division of Solid Mechanics, LU, Lund, Sweden 2Tetra Pak, Lund, Sweden

A thermodynamically consistent interface model is generalized to predict arbitrary mixed mode loading histories. The model, only, makes use of a normal cohesive traction-separation law defined by the material’s fracture energy, tensile strength and a dimensionless parameter. A master curve is established from these three quantities, with the shape of the law given by the dimensionless parameter. Calibrating the interface model for normal mode loading, it is demonstrated that the interface model predicts experimentally obtained cohesive traction-separation curves reported for a polyurea and two epoxy adhesives subjected to different temperatures and loading rates at shear mode loadings. The dimensionless parameter is found to determine the shape of the fracture curve and is invariant to mixed mode loading, temperatures and loading rates. __________________________________________ Corresponding author email: [email protected]

97


TOWARDS THE DISCRETE ELEMENT MODELING OF ROCK DRILLING

A. Wessling 1, P. Jonsen1, J. Kajberg1

1Department of Solid Mechanics, Lulea University of Technology, Lulea, Sweden

Rock drilling is involved in a lot of areas today, e.g.in mining-, oil- and geothermal industries. Depending onthe conditions, different drilling methods are used. Twoprevalent methods for drilling in rock are the regular rotarydrilling method, where the rock is crushed by a weight-on-bit and rotation, and the percussive rotary drilling method,where the rock is initially crushed by the impact energy andexperiences further splitting from the rotary motion of thebit.

In the GeoFit project, the main goal is to develop costeffective enhanced geothermal systems on energy efficientbuilding retrofitting. As a part of this project, LTU willlead the simulation work regarding the application of noveldrilling techniques. This involves the development anddemonstration of modeling strategies, based on particlebased methods and FEM, of the drilling and excavation pro-cess. The work is focused on virtual predictions of the drillbit in terms of wear rate, pressure distribution and vibra-tions in the adjacent soil and rock. From this prediction,the drilling parameters, tool performance and selection ofmaterials will be improved in order to reduce tool damageand predict maintenance.

Using the Discrete Element Method of the rock and arigid FEM formulation of the drill bit, LTU has conductedsimulations of the aforementioned drilling methods. Thewear has been evaluated using two different wear laws; Ar-chard’s and Finnie’s law.

The Discrete Element Method, as initially formulated byCundall (1971), is a discontinuous method where the ma-terial of interest is modeled using discrete rigid spheres, allof which follow the Newtonian laws of motion. This inher-ent discontinuous behavior is what makes this method suit-able for modeling problems of large deformations, which ishighly relevant in the rock drilling process.

In the current applications, the LS-Dyna software hasbeen used. Here, each particle contact is realized by us-ing a penalty-based contact. Friction is also included at theperimeters of the particles based on the Coulombs frictionlaw. In order to model the cohesion between particles forthe rock model, the parallel bond model [1] has been used.Here, the cohesion is represented by contact forces in thenormal- and tangential direction, given by

Fn = Knun

|Fs| = Ks|us|(1)

where un is the gap (or overlap) between the spheres, us isthe relative displacement and Kn and Ks are the normal-and tangential contact stiffnesses. A bond breaks instan-taneously once the normal or tangential force exceeds itsmaximum value, σc or τc respectively.

A challenge with the DEM is how to relate the macro-scopic parameters, e.g elastic modulus and Poisson’s ratio,

to the microscopic parameters, Kn, Ks, σc and τc. Forthe present applications, parameters from previous researchhas been used [2,3].

Future work consists of laboratory experiments, usinge.g. the unconfined stress test, Brazilian test and Split-Hopkinson bar, in order to calibrate the different types ofrocks often encountered during drilling in geothermal ap-plications. Further, the constitutive relationships for thedrill bit will be determined in order to model wear and ge-ometry changes.

Figure 1: Broken particle bonds from percussive rotary drilling.

The Geofit project is a acknowledged for financial sup-port, grant agreement number 792210.

References

[1] Potyondy, D., Cundall, P. A bonded-particle modelfor rock. International Journal of Rock Mechanics andMining Sciences 41, 1329-1364. Elsevier (2004)

[2] Rojek, R., Labra, C., Okan S., Onate. Comparativestudy of different discrete element models and eval-uation of equivalent micromechanical parameters. In-ternational Journal of Solids and Structures 49, 1497-1517. Elsevier (2012)

[3] Larsson, S. Characterization and modeling of rockimpact on steel plates. Master’s thesis, Departmentof Engineering Sciences and Mathematics Divisionof Mechanics of Solid Materials, Lulea University ofTechnology. 2014.


98


INFLUENCE OF SYSTEM DYNAMICS ON EXHAUST VALVE FLOWS

P. M. Winroth1,2 and P. H. Alfredsson1,2

1Department of Mechanics, KTH, Stockholm, Sweden2Competence Center of Gas Exchange, KTH, Stockholm, Sweden

As the energy consumption of our society is constantlyincreasing, so is the anthropogenic emissions of green-house gases, such as carbon dioxide (CO2). A large portionof the CO2 emissions are caused by the transportation sec-tor. The way to decrease the CO2 emissions of an internalcombustion engine is to make it more fuel efficient. Themost common way to realize this is through ‘downsizing’,where a turbocharger is used to increase the power outputof a small, low weight, engine. In order to maximize theusefulness of the turbocharger, it is necessary to understandthe flow physics related to the exhaust valves. Traditionallythe exhaust-valve flow has been studied under steady con-ditions, as it is easier to perform such experiments. Thismeans that the flow is assumed to be quasi-steady, i.e. thatthe steady flow experiments accurately captures the essen-tial flow physics of the real, dynamic, process. To increasethe understanding of the flow past the exhaust valves an ex-perimental investigation of the flow past the exhaust valvewas undertaken.

The influence of the valve motion (and thus system dy-namics) were investigated by comparing data from steadyflow measurements to those taken from a dynamically dis-charging cylinder, with a moving valve. The static-valveexperiments were performed using a high-pressure flowbench that could deliver a mass-flow rate of 0.5 kg/s at apressure of 500 kPa. In the dynamic-valve experiments thecylinder was pressurised and the exhaust valve was openedusing a linear motor. The experiments were designed insuch a way that the valve-opening speed could be variedand the valve-opening duration corresponded to equivalentengine speeds in the range from 800 to 1350 rpm (valveopening duration of the order of 10 ms).

By comparing mass-flow rates under steady conditionsto those found under dynamic conditions it has been shownthat the static-valve experiments vastly underpredicts theflow losses of the exhaust process. It has also been shownthat the flow losses tend to decrease as the engine speedis increased. To explain this phenomenon a new non-dimensional number (called the QS-number) has been for-mulated, which was used to quantify the “steadiness” ofthe process at any one point in time. Using the QS-numberit has been shown that the faster moving valve actually is“more” quasi-steady than the slower moving ones. Theseresults are reported in Ref. [1].

Furthermore, the influence of the system dynamics onthe shock patterns, developing in the exhaust port, has beeninvestigated. This was studied using high-speed Schlierenimaging of the flow in the exhaust port. Large differencesbetween static and dynamic-valve operations were found.The flow in dynamic experiments were found to belong toone of three different flow states (depending on valve lift):

Figure 1: Images highlighting the differences between the shockstructures in the dynamic (top) and the static-valve pro-cess (bottom).

i) An overexpanded jet with two free surfaces (for low valvelifts). ii) A wall-bounded overexpanded jet with one freesurface (medium valve lifts). iii) A fully expanded super-sonic nozzle flow (for large valve lifts). For some valvelifts, the static valve flows was shown to go from flow stateii) to flow state iii) if enough upstream pressure was ap-plied, whereas the dynamic experiments remained in flowstate ii), for the same valve lifts, even for very large cylin-der pressures. The difference in flow patterns is illustratedin Fig. 1, where the shock patterns of the dynamic-valveexperiments are shown in the top image (for 1350 rpm) andthe shocks of the static-valve experiments are shown in thebottom image (flow state iii). These results are reported inRef. [2].

From these studies it can be concluded that experimentsconcerning exhaust valve flows need to include the systemdynamics and should be carried out at relevant pressure ra-tios. If these two criterion are not fulfilled, the experimentswill not include the right physics and will thus be inaccu-rate.

References

[1] Winroth, P. M., Ford, C. L., Alfredsson, P. H., Ondischarge from poppet valves: effects of pressureand system dynamics. Experiments in Fluids, 59:24,(2018)

[2] Winroth, P. M., Alfredsson, P. H., On shock structuresin dynamic exhaust valve flows. Physics of Fluids, 31,026107, (2019)


99


A PLEA FOR USE OF HYDROGEL SPHERES FOR INVESTIGATINGDENSE MULTIPHASE FLOWS

Sagar Zade1, Fredrik Lundell1, Luca Brandt1

1Linne Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden

Experiments performed at the Fluid Physics Lab of KTHMechanics since March 2016 have increasingly proven theeffectiveness of super-absorbent (polyacrylamide based)hydrogel particles as model spheres for use in studies ofparticle-laden liquid flows. The inspiration to use thesetransparent gel-like spheres was due to a number of origi-nal studies including [1]. These authors went a step furtherand embedded tracer particles inside the hydrogel spheresso as to track their rotation in the flow. Our own per-sonal experience suggests that this technique can be advan-tageously used only up to a small volume fraction or (to beprecise) across few fluid-particle interfaces. Even withoutembedded tracers, these spheres are suitable to investigatecomplex velocity field in multiphase flows e.g. squeezingflow between approaching particle(s), flow between a par-ticle(s) and the bounding wall, etc. while rendering them-selves useful at much higher concentrations. From a practi-cal standpoint, these particles are inexpensive and are usu-ally procured in a dry form, thereby occupying minimalstorage space. Once mixed with water and left submergedfor around one day, they grow to a fairly mono-disperseequilibrium size. Their availability in a range of millime-ter size generates the opportunity to span a wide parameterspace.

In the following paragraphs we briefly present three newstudies that to investigate the influence of large sphericalparticles on flow of Newtonian and non-Newtonian sus-pending medium. The same experimental set-up is usedin all these experiements: a long transparent square duct(50 mm x 50 mm x 5 m) through which the desired fluid-particle mixture is recirculated at varying flow rates bymeans of a gentle disc pump to minimize any damage,to these particles and to minimize any degradation of thestructured non-Newtonian fluid. Particle Image Velocime-try (PIV) is performed using a continuous wave laser anda high speed camera. In order to differentiate the hydrogelparticles from the surrounding fluid in the PIV images, atiny amount (in ppm) of fluorescent Rhodamine dye is ab-sorbed inside each particle during swelling. The flow rate(and hence, the bulk velocity) is measured using an electro-magmetic flow meter and the pressure drop (and hence, theaverage wall-shear stress) is measured using a differentialpressure transducer. Measurements are performed at thefar downstream end of the duct to ensure a fully developedturbulent flow.[2] Turbulent duct flow of a Newtonian suspending fluid (tap water) at varying Reynolds number Re2H ∈ (10000, 27000), 2H being the duct full height, is explored in presence of three particle sizes: 2H/dp = 40, 16 and 9, dp being the particle diameter, at multiple volume frac-

tions Φ up to 20%. Since the particles are slightly heav-ier than the fluid, sedimentation effects are observed at the lowest Re2H while the particles are almost fully sus-pended at the highest Re2H . Velocity profiles for both fluid and particle (only translational velocity), fluid tur-bulence statistics and particle concentration profiles are reported. The pressure drop dispays an intriguing be-haviour as a function of particle size and volume frac-tion.

[3] Experiments similar to the ones above were pursued, now in a turbulent flow of a viscoelastic fluid. Viscoelas-ticity is known to produce drag reduction, implying di-rect energy savings in transport processes. Comparison was done with a corresponding particle laden flow of a Newtonian fluid at the same Re2H ≈ 10000 and the same 2H/dp = 10 up to Φ = 20%. The most interest-ing feature was the increased rate of excess pressure drop with Φ in the viscoelastic fluid.[4] Sedimentation is inevitable when the there is a den-sity difference between the carrier (fluid) phase and dis-crete (particle) phase. Under sedimenting conditions, at a low yet turbulent Re2H = 5600, experiments and di-rect numerical simulations were compared for Φ = 1%to investigate the flow physics and validate both meth-ods. Additional experiments up to Φ = 5% quantified the role of volume fraction on the overall flow dynamics. The latest study in progress deals with the effect of par-ticle phase on flow of yield stress fluid thus, extending theapplicability of these versatile particles to more complexfluid flows.

References

[1] Bellani, G and Byron, M L and Collignon, A G and Meyer, C R and Variano, E A, Journal of Fluid Me-chanics, 712, 41-60, (2012).

[2] S Zade, P Costa, W Fornari, F Lundell, L Brandt, Journal of Fluid Mechanics, 857, 748-783 (2018)

[3] S Zade, F Lundell, L Brandt, International Journal of Multiphase Flow, 112, 116-129 (2019)

[4] S Zade, W Fornari, F Lundell, L Brandt, Physical Re-view Fluids, 4(2), (2019)


100


A FEM FOR TWO FIBRE FAMILY REINFORCED FINITEHYPERELASTICITY

A. Zdunek 1 and W. Rachowicz2

1HB Ber-Rit, Solhemsbackarna 73, SE 163 56 Spanga, Sweden2Institute of Computer Science, Cracow University of Technology, Pl 31-155 Cracow, Poland

This presentation concerns the numerical solution ofmechanical boundary value problems in the proximity ofincompressible finite hyperelasticity involving a materialwhich may be strongly anisotropic or may develop a stronganisotropy due to a finite stretching of its fibre reinforce-ment. The material is allowed to transform from beingisotropic to being virtually inextensible in one or two pre-ferred directions due to fibre stretching. In human arteries,for example, the evolution is exponential with raising bloodpressure and it takes place in tension only. The material re-mains essentially isotropic in compression. Considering allthese features together makes the class of problems verychallenging.

A decoupled perturbation approach for evolving inexten-sibility is inappropriate. Moreover, a simple inextensibilityis incompatible with a small dilatation. A description ofthe anisotropy in terms of an isochoric integrity basis be-comes inadmissible, [1, 4, 5]. We developed a so-calledgeneralised metric approach [6] which spans the wholerange, from the unconstrained weakly anisotropic state tothe strongly anisotropic inextensible limit. It extends theconcurrent theory of simple internal kinematic constraints[2, 3]. In [5] we show that exceeding a certain anisotropicstiffness contrast (Γ/µ & 105) the computational problemmay become unsolvable using a H1 based pure displace-ment method. Polynomial extensions p ≥ 4 do not neces-sarily restore convergence with respect to Γ/µ. Our remedyis a mixed H1/L2 finite element formulation. h-adaptivityis shown to resolve oscillations (checker-boarding) in a se-vere elongational locking problem [6], Figure 1. A possibledeformation stiffening reinforcement by one- or two-fibrefamilies (f = 1, 2) is considered [5, 6]. The convergencecharacteristics of the H1

p/[L2p−1]2f element constructs with

p ≥ 1, will be shown. Fibre tensions %f and fibre stretchesλf are in L2

p−1 and the displacement increment ∆u ∈ H1p .

A simple a posteriori residual error estimation procedure isdeveloped. It is used to guide h-adaptive mesh refinement.Its usefulness is illustrated in a number of case studies em-ployed to verify the approach presented.

References

[1] R.J. Flory Thermodynamic relations for highly elasticmaterials. T. Fraday Soc. 57, 829–838, (1961)

[2] C. Truesdell and W. Noll, The Nonlinear Field The-ories of Mechanics, Vol 3, Springer–Verlag, Berlin-Heidelberg, New York, (1965)

[3] D.E. Carlson, E. Fried, D.A. Tortorelli, Geometricallybased consequenses of internal constraints, J. Elastic-ity, 70, 1001–1009, (2003)

Figure 1: Corner region. Two fibre families. Fibre tension%1. Checker board pattern. 64×64 mesh with lin-ear displacement-constant tension/extension elements,H1

1/[L20]

4.

[4] D.R. Nolan, A.L. Gower, M. Destrade, R.W. Ogdenand J.P. McGarry, A robust anisotropic hyperelasticformulation for the modelling of soft tissue, J. Mech.Behav. Biomed., 39, 48–60, (2014)

[5] A. Zdunek, W. Rachowicz, A 3-field formulation forstrongly transversely isotropic compressible finite hy-perelasticity, Comput. Methods. Appl. Mech. Engrg.,315, 478–500, (2017)

[6] A. Zdunek, W. Rachowicz, A mixed finite elementformulation for compressible finite hyperelasticitywith two fibre family reinforcement, Comput. Meth-ods. Appl. Mech. Engrg., 345, 233–262, (2019)


101


Computation of the Stable Atmospheric Boundary Layer Using the ExplicitAlgebraic Reynolds-Stress Model

Velibor Zeli1, Geert Brethouwer1, Stefan Wallin1, Arne Johansson1

1Department of Mechanics, Linne FLOW Centre, KTH Royal Institute of Technology, 10044 Stockholm, Sweden

Despite ongoing intensive study, understanding andmodelling stably stratified turbulence in atmosphericboundary layers remains at the forefront of turbulence re-search. Complex dynamics in stable boundary layers (SBL)make it hard to relate moderately strong stratification withproduction of weak and anisotropic turbulence in a simplemanner. Due to the wide spectrum of turbulent length andtime scales, it is not possible to resolve the dynamics of tur-bulence in a computationally efficient way (such that it canbe used in weather forecast and climate models) thereforeturbulence models are used to relate turbulent mixing withthe profiles of mean forecast variables [1].

The aim of the present study is to validate the per-formance of a recently developed atmospheric turbulencemodel, the so-called, explicit algebraic Reynolds-stress(EARS) model and to better understand the model be-haviour in moderately stratified SBL. The EARS modelis considered to be one of the more advanced turbulencemodels that take into an account, aside from the mean at-mospheric variables, many atmospheric properties relatedto turbulence (e.g., turbulent kinetic energy (TKE), shearand buoyancy production as well as the dissipation of TKE)and where the turbulent fluxes do not necessarily have tobe aligned with the mean gradients, see [2] for detailedmodel description. It is derived from the turbulence modelfor full prognostic equation (differential Reynolds-stressmodel, Mellor and Yamada level 4 model) so it does notrequire modeling of shear and buoyancy production terms.Furthermore, it contains a weak-equilibrium assumptionwhich makes it explicit and somewhat similar to the Mel-lor and Yamada level 3 model. This means that it is morecomplex than the standard eddy-viscosity/eddy-diffusivityapproach and contains transport equation for temperaturevariance beside the equations for TKE and dissipation, andat the same time does not depend on any empirical functionnor ad-hoc correction specifically for SBL.

Simulations were ran for the case of a developing SBLfor the course of 9 physical hours during which the surfacetemperature was constantly cooled with the cooling rateCr= (0.25, 0.375, 0.5, 1) K h−1 for each of the four simu-lations. The simulations correspond to night-time coolingof the atmospheric boundary layer. Surface forcing is di-rectly responsible for the stratification intensity in the SBLand for the damping of turbulence. This numerical experi-ment was proposed in a high-resolution large-eddy simula-tion (LES) study, see [3], and the LES results are used as avalidation reference for the EARS model.

Results of the EARS model show good agreement withthe LES data for the profiles of mean atmospheric proper-ties (e.g., horizontal wind speed and potential temperature).

Predefining a linear change of the surface temperature dur-ing the simulation dose not impose any limits on the changeof surface momentum and heat flux. The model capturesthe essence of SBL, such as the inversion layer, the strongdamping of the vertical mixing, although the surface fluxand vertical mixing are slightly over predicted in all sim-ulations. Aside from validating the results of the EARSmodel, the set-up is also used for studying the intricate na-ture of the EARS model and it’s performance when strati-fication in SBL changes, such as studying the scaled turbu-lence production as a function of Richardson number.

In summary, it was shown that the EARS model is afully explicit turbulence model with a more comprehen-sive and accurate description of turbulence, in the strat-ified SBL, than the commonly used eddy-viscosity/eddy-diffusivity models.

References

[1] Holtslag, A., and Coauthors, Stable atmosphericboundary layers and diurnal cycles: challenges forweather and climate models, Bulletin of the AmericanMeteorological Society, 94(11), 1691-1706 (2013)

[2] Zeli, V., Brethouwer, G., Wallin, S., Johansson, A.,Consistent boundary-condition treatment for compu-tation of the atmospheric boundary layer using theexplicit algebraic Reynolds-stress model, Boundary-Layer Meteorology, 171, 53-77 (2019)

[3] Sullivan, P., Weil, J., Patton, E., Jonker, H., Mironov,D., Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundarylayer, Journal of the Atmospheric Sciences, 73(4),1815-1840 (2016)


102

Deltagarlista

Alfredsson, P. Henrik KTHAlzweighi, Mossab KTHArrhen, Fredrik RISEAsp, Leif ChalmersAthanasopoulos, Stefanos LUBard-Hagberg, Delphine LTHBerg, Niclas KTHBengtsson, Rhodel UUBoij, Susann KTHBondesson, Johan ChalmersBoasen, Magnus KTHBrandberg, August KTHChai, Guocai SandvikChen, Song KTHCrone, Philip KTHDahlberg, Carl F O KTHDe Vincentiis, Luca KTHEkh, Magnus ChalmersEkre, Fredrik ChalmersEmami, Nazanin LTUEnelund, Mikael ChalmersEspadas Escalante,

Juan Jose UUFerrante, Gioele KTHFiusco, Francesco KTHFransson, Jens KTHFredholm, Jens StudentlitteraturFureby, Christer FOIGaborit, Mathieu KTHGamstedt, Kristofer UUGe, Zhouyang KTHGholamisheeri, Masumeh ScaniaGibanica, Mladen ChalmersGodonou, Patrice UUGomez, Erik Scania/KTHGowda, Krishne KTHGudmundson, Peter KTHGutkin, Renaud Volvo CarsHalilovic, Armin KTHHallberg, Hakan LUHallstrom, Stefan KTHHenningson, Dan KTHHolmberg, Joakim LIUIreman, Tomas SaabIsaksson, Per UUIvarsson, Niklas LUJansson, Per-Ake ChalmersJonsen, Par LTUJosefson, Lennart ChalmersJungstedt, Erik KTHKao-Walter, Sharon BTHKato, Kentaro KTHKhodashenas, Niloofar KTHKlarbring, Anders LIUKleine, Vitor Gabriel KTHKumaraswamy, Siddhart Volvo Cars/KTHLarsson, Fredik ChalmersLarsson, Per-Lennart KTHLeidermark, Daniel LIU

Lemetayer, Julien KTHLeskovec, Martin KTHLiefvendahl, Mattias FOILind, Petter KTHLindstrom, Stefan LIULindstrom, Thomas LIULiverts, Michael KTHLundell, Fredrik KTHLundgren, Jonas LIUMallor, Fermin KTHMamidala, Santhosh Babu KTHMansour, Rami KTHManzari, Luca KTHMao, Huina KTHMariani Raffaello KTHMeliani, Mostafa KTHMeyer, Knut Andras ChalmersMorfin, Andres KTHMousavi, Mahmoud KAUMukha, Timofey ChalmersMartensson, Hans GKNNa, Wei KTHNorling, Daniel ScaniaNygren, Johan KTHOddy, Carolyn ChalmersOlad, Peyman LTHOlsson, Erik KTHOlsson, Marten KTHParikh, Agastya KTHPozuelo, Ramon KTHPrahl Wittberg, Lisa KTHRamanenka, Dmitrij Volvo TrucksRedlinger-Pohn, Jakob D KTHRehnberg, Adam Creo DynamicsRevstedt, Johan LTHRinehart, Aidan KTHRistinmaa, Matti LURumpler, Romain KTHRunesson, Kenneth ChalmersRydefalk, Cecilia KTHShariati, Hossein KTHSjostrand, Jakob KTHSujar-Garrido, Patricia KTHSundarapandian, Sembian KTHSuresh, Shyam LIUSvanberg, Andreas Boliden Minerals/LTUTavares da costa,

Marcus Vinıcius UUTryding, Johan Tetra Pak/LUTunay, Tural KTHUcel, Ibrahim Bugra KTHWessling, Albin LTUWinroth, Marcus KTHZade, Sagar KTHZdunek, Adam HB Ber-RitZeli, Velibor KTHAkermo, Malin KTH

Orlu, Ramis KTH

Ostlund, Soren KTH

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