Differential Reynolds Stress Modeling for Separating Flows in Industrial Aerodynamics PDF
Preview Differential Reynolds Stress Modeling for Separating Flows in Industrial Aerodynamics
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 AboutthisSeries Springer Tracts in Mechanical Engineering (STME) publishes the latest developments in Mechanical Engineering - quickly, informally and with high quality.Theintentistocoverallthemainbranchesofmechanicalengineering,both theoreticalandapplied,including: • EngineeringDesign (cid:129) MachineryandMachineElements (cid:129) Mechanicalstructuresandstressanalysis (cid:129) AutomotiveEngineering (cid:129) EngineTechnology (cid:129) AerospaceTechnologyandAstronautics (cid:129) NanotechnologyandMicroengineering (cid:129) Control,Robotics,Mechatronics (cid:129) MEMS (cid:129) TheoreticalandAppliedMechanics (cid:129) DynamicalSystems,Control (cid:129) Fluidsmechanics (cid:129) EngineeringThermodynamics,HeatandMassTransfer (cid:129) Manufacturing (cid:129) Precisionengineering,Instrumentation,Measurement (cid:129) MaterialsEngineering (cid:129) Tribologyandsurfacetechnology Within the scopes of the series are monographs, professional books or graduate textbooks,editedvolumesaswellasoutstandingPhDthesesandbookspurposely devoted to support education in mechanical engineering at graduate and post- graduatelevels. Moreinformationaboutthisseriesat http://www.springer.com/series/11693 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 ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia (www.springer.com) 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.
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