Differential Reynolds Stress Modeling for Separating Flows in Industrial Aerodynamics

106 Pages·2015·5.69 MB·English

by  Bernhard Eisfeld (eds.)

Springer Tracts in Mechanical Engineering
Bernhard Eisfeld E ditor
Diff erential Reynolds
Stress Modeling
for Separating
Flows in Industrial
Aerodynamics
Springer Tracts in Mechanical Engineering
Boardofeditors
Seung-BokChoi,InhaUniversity,Incheon,SouthKorea
HaibinDuan,BeijingUniversityofAeronauticsandAstronautics,Beijing,P.R.China
YiliFu,HarbinInstituteofTechnology,Harbin,P.R.China
Jian-QiaoSun,UniversityofCalifornia,Merced,U.S.A
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Bernhard Eisfeld
Editor
Differential Reynolds Stress
Modeling for Separating
Flows in Industrial
Aerodynamics
123
Editor
BernhardEisfeld
GermanAerospaceCenter(DLR)
InstituteofAerodynamicsandFlow
Technology
Braunschweig
Germany
ISSN2195-9862 ISSN2195-9870 (electronic)
SpringerTractsinMechanicalEngineering
ISBN978-3-319-15638-5 ISBN978-3-319-15639-2 (eBook)
DOI10.1007/978-3-319-15639-2
LibraryofCongressControlNumber:2015936036
SpringerChamHeidelbergNewYorkDordrechtLondon
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Preface
Flow separation has attracted fluid mechanics research for a long time, whereas
in industrial aerodynamic design, flow separation is usually avoided due to its
detrimentaleffectontheperformanceoftherespectiveapparatus.Flowseparation
often limits a machine’sperformance,e.g. in terms of maximum aircraftlift or in
termsofthesurgelimitofturbocompressors.Alsoaerodynamicshapeoptimisation
isusuallyboundbytheonsetofseparation.
Currentlythereisatrendinindustrytorelymoreandmoreondataobtainedfrom
numericalflowsimulations,usingComputationalFluidDynamics(CFD)software.
Such CFD-based aerodynamic design therefore heavily depends on the accuracy
with which separating flows can be predicted. As long as the flow stays laminar,
thereisprobablylessdoubtinthereliabilityofCFDpredictions,evenofseparating
flows,butindustriallyrelevantflowsareusuallyturbulent.
Inprinciple,inturbulentflowthegoverningequationsforlaminarflowarestill
valid and could be solved. However, such Direct Numerical Simulations (DNS)
need to accurately resolve the turbulent small-scale motion to get the mean flow
of interest right, thus demanding computational resources that are currently not
affordable in an industrial environment. Resolving only part of the spectrum of
turbulent fluctuations by Large Eddy Simulation (LES) relaxes the computational
requirements, but still is too expensive for an industrial application of boundary-
layerdominatedflowathighReynoldsnumber.
For this reason, the old-fashioned approach based on the Reynolds-averaged
Navier–Stokes(RANS)equationsandemployingcorrespondingturbulencemodels
willremainthestandardtechnologyinmostapplicationsofindustrialaerodynamics
inthenextdecade(s).Unfortunately,today’sstandardmodels,mainlybasedonthe
assumption of a turbulence-generated eddy-viscosity, are considered notoriously
unreliableforthe predictionofseparatedflows. Thereforethereis urgentneedfor
improvement.
Onepossiblepathtowardsanimprovedpredictionofseparatedflowsconsistsin
directlysolvingthetransportequationsfortheindividualReynoldsstressesinstead
of employing a simplified model based on the assumption of an eddy viscosity.
Theseso-calledDifferentialReynoldsStressModels(DRSM)constitutethehighest
v
vi Preface
levelof RANS-based turbulence models. Theyare certainly not a panacea per se,
butoffermorepossibilitiesformodellingindividualeffectsofturbulenceonahigher
levelaccordingtothephysics.Inparticulartheproductionofturbulenceisdefined
exactlyintermsofknownquantities.
Ingeneral,DRSMsareconsideredmuchmoredifficulttohandleinanumerical
flowsolver,inparticularwhenappliedtoindustriallyrelevantflows.Thecontribu-
tions in this book, nevertheless, demonstrate their applicability to separated flows
with different numerical flow solvers that are developed not only at universities
but also at research labs and a company, aiming at industrial use in external
aerodynamics as well as in turbomachinery. Moreover, the applications are not
restricted to one particular model only, but cover a variety of DRSM flavours,
allowingforcross-comparisons.
As might be expected, DRSMs demonstrate advantages when vortices or
anisotropy-driven secondary flows are involved. In other cases improvements are
not always evident compared to established eddy-viscosity models. Nevertheless,
DRSMs perform rarely worse, and since their application still appears to be in
a pioneering state, the presented results are considered encouraging for further
researchindifferentialReynoldsstressmodellingforseparatingflowsinindustrial
aerodynamics.
Braunschweig,Germany BernhardEisfeld
November2014
Contents
ApplicationofaLowReynoldsDifferentialReynoldsStress
ModeltoaCompressorCascadeTip-LeakageFlow......................... 1
ChristianMorsbach,MartinFranke,andFrancescadiMare
Application of Reynolds Stress Models to Separated
AerodynamicFlows.............................................................. 19
ChristopherL.Rumsey
SeparatedFlowPredictionArounda6:1ProlateSpheroid
UsingReynoldsStressModels.................................................. 39
YairMor-Yossef
Influence ofPressure-StrainClosure onthe Predictionof
SeparatedFlows.................................................................. 61
G.A.GerolymosandI.Vallet
ModelingofReynolds-StressAugmentationinShearLayers
withStronglyCurvedVelocityProfiles ........................................ 85
René-DanielCécora,RolfRadespiel,andSuadJakirlic´
vii
Application of a Low Reynolds Differential
Reynolds Stress Model to a Compressor
Cascade Tip-Leakage Flow
ChristianMorsbach,MartinFranke,andFrancescadiMare
Abstract The tip-leakage flow of a low speed compressor cascade at MaD0:07
and Re D 400;000 was simulated employing the Jakirlic´/Hanjalic´-!h (JH-!h)
differential Reynolds Stress model (DRSM) and results are presented. The pre-
dictions are compared with those obtained using the SSG/LRR-! DRSM and the
MenterSSTk-!lineareddyviscositymodel(LEVM).Inadditiontothemeanflow
quantities,thefocusisontheReynoldsstressesandtheiranisotropy.BothDRSMs
show significant improvementscompared to the LEVM with respect to the mean
flow quantities; however, details of the turbulence structure are more accurately
predictedbytheJH-!h model.
1 Introduction
The flow in axial compressor rotors is highly complex due to, amongst other
phenomena, the vortical motions which develop in the gap between the blades
and the machine’s casing (tip-gap) [16]. Numerical simulations of such flows
often rely on highly tuned linear eddy viscosity models (LEVM) despite the high
anisotropywhichcharacterisestheturbulencefieldandplaysamajorroleinmany
phenomenaof practicalinterest. It would appearsensible to adopt,in these cases,
an anisotropy-resolving modelling approach. Differential Reynolds stress models
(DRSM) belong to this class of closures; however, reports on their application to
realisticconfigurationsarescarce.
Gerolymosandco-workerswereamongthefirsttoemployDRSMstoinvestigate
complexconfigurations,rangingfromcascades[7]tomulti-stagecompressors[6].
C.Morsbach((cid:2))(cid:129)F.diMare
DepartmentofNumericalMethods,GermanAerospaceCenter(DLR),InstituteofPropulsion
Technology,LinderHöhe,51147Cologne,Germany
e-mail:[email protected];[email protected]
M.Franke
DepartmentofNumericalMethods,GermanAerospaceCenter(DLR),InstituteofPropulsion
Technology,Müller-Breslau-Str.8,10623Berlin,Germany
e-mail:[email protected]
©SpringerInternationalPublishingSwitzerland2015 1
B.Eisfeld(ed.),DifferentialReynoldsStressModelingforSeparatingFlows
inIndustrialAerodynamics,SpringerTractsinMechanicalEngineering,
DOI10.1007/978-3-319-15639-2_1
2 C.Morsbachetal.
TheydevelopedaDRSMwithspecialfocusonindependencefromgeometryrelated
parameterssuchasdistancefromthewallandwallnormalvectors.Theycompared
performancedata as well as radial distributions of flow angles, total pressure and
temperature,etc.toresultsobtainedbyastandardk-(cid:2) approach.Whiletheycould
show only marginal improvements over LEVMs using DRSMs for flows which
are not dominated by large separation, the flows dominated by large separation
were predicted in better agreement with experimental data [6]. Rautaheimo [25]
conducted simulations of a centrifugal compressor using a DRSM combined of
a high and a low Reynolds model. He found that the LEVMs were superior in
predictingtheintegralvalueswhereastheDRSMperformedbetterinregionswith
secondaryflows. A linear compressorcascade with tip-clearance was investigated
byBorelloetal.[2]usingtheDRSMofHanjalic´ andJakirlic´ [9].Inalltheabove-
mentioned studies, results obtained using DRSMs were found to be superior to
thoseofanLEVMtakenasreference,especiallyforcomplex3Dflowfeatureswith
anisotropicturbulence.Yet,despitetheobviousadvantagesofDRSMs,theyarestill
notpopularinindustrialdesignapplications.
In a previous paper, the present authors applied the SSG/LRR-! DRSM to a
compressorcascadeflowandcomparedtheresultstothoseobtainedwithanLEVM
and an explicit algebraic Reynolds stress model [22]. It could be shown that the
prediction of secondary velocities in the tip-gap flow and the shape of the tip-
gap vortex could be improved by the DRSM. However, there was still potential
for improvement in the representation of the mean velocities and especially of
theReynoldsstresses nearthewall.Thismotivatedthepresentinvestigationusing
the low Reynolds DRSM of Jakirlic´ and Hanjalic´ in a formulationemploying the
specifichomogeneousdissipationrate!hasscaledeterminingvariable[18].
2 TurbulenceModelling
In a Reynolds averaged Navier-Stokes (RANS) framework, the objective of tur-
bulence modelling is to determine the Reynolds stress tensor (cid:3)u00u00. This can be
i j
accomplishedusing closures entailing differentlevels of complexity.For standard
industrial CFD applications, the Boussinesq approximation is generally invoked,
which defines a turbulent viscosity (cid:4)T to relate the Reynolds stresses directly to
the trace-free rate of strain S(cid:2). A prominent example of such an approach is the
ij
MenterSSTk-!model[20],whichwillbeusedasreferenceinthispaper.However,
althoughthelinearstress-straincouplingcanbejustifiedforcertainflowtopologies,
itcannotbeexpectedtoholdingeneral.Infact,itisthereasonfortheinabilityof
LEVMstopredicthigherordereffectssuchasstreamlinecurvature,rotationorthree
dimensionalboundarylayers[10].Inthesecases,individualcomponentsoftherate
ofstraintensorinfluencedifferentlyanddistinctivelythevarioustermsappearingin
theReynoldsstressbudget,particularlytheturbulenceproduction.Thismechanism
cannotbecapturedbyLEVMssincetheproductionofturbulentkineticenergyina
Boussinesqcontextreliesonthenormoftherateofstraintensoronly.