Large-Eddy Simulation of the Flow Over a Circular Cylinder at Reynolds Number 2 × 104 - 图文

FlowTurbulenceCombust(2014)92:673–698DOI10.1007/s10494-013-9509-1

Large-EddySimulationoftheFlowOveraCircularCylinderatReynoldsNumber2×104

DmitryA.Lysenko·IvarS.Ertesv?g·KjellErikRian

Received:8September2012/Accepted:21August2013/Publishedonline:3September2013?SpringerScience+BusinessMediaDordrecht2013

AbstractTheflowoveracircularcylinderatReynoldsnumber2×104waspre-dictednumericallyusingthetechniqueoflarge-eddysimulation(LES).Bothin-compressibleandcompressibleflowformulationswereused.Thepresentresultsobtainedatalow-Machnumber(M=0.2)revealedsignificantinaccuracieslikespuriousoscillationsofthecompressibleflowsolution.Adetailedinvestigationofsuchphenomenawascarriedout.Itwasfoundthatapplicationofblendedcentral-differenceorlinear-upwindschemescoulddampartificialwavessignificantly.However,thistypeofschemeshasatoodissipativenaturecomparedtopurecentral-differences.Theincompressibleflowresultswerefoundtobeconsistentwiththeex-istingnumericalstudiesaswellaswiththeexperimentaldata.BasicflowfeaturesandflowmechanicswerefoundtobeingoodagreementwithexistingexperimentaldataandconsistentwithpreviouslyobtainedLES.Specialemphasiswasputonthespec-tralanalysis.Here,theclassicalFouriertransformaswellasthecontinuouswavelettransformwereapplied.Basedonthelatter,theseparatedshear-layerinstabilitywaspreciselyclarified.ItwasfoundthattheReynoldsnumberdependencybetweenvortexsheddingandshear-layerinstabilitieshadapowerlawrelationwithn=0.5.KeywordsLarge-eddysimulation·Dynamick–equationSGSmodel·Shearlayerinstability·Continuouswavelettransform·Turbulentseparatedflow·Circularcylinder

)·I.S.Ertesv?gD.A.Lysenko(B

DepartmentofEnergyandProcessEngineering,NorwegianUniversityofScienceandTechnology,Kolbj?rnHejesvei1B,7491Trondheim,Norwaye-mail:dmitry.lysenko@ntnu.no

K.E.Rian

ComputationalIndustryTechnologiesAS,7462Trondheim,Norway

674FlowTurbulenceCombust(2014)92:673–698

1Introduction

Thelong-termgoalofthepresentworkistodevelopalarge-eddysimulation(LES)modelforhighReynoldsnumberflowsofpracticalinterestwithfurtheradaptationforturbulentcombustionmodeling.

Previously,amethodicalinvestigationforseveralplainturbulentbluff-bodyflowshasbeencarriedoutwiththegoalofvalidation,verificationandunderstandingofthecapabilitiesofthenumericalmethodusingtheconventionalcompressibleURANSapproach[25],implementedintheOpenFOAM(FieldOperationandManipulation)toolbox.Theseresultswereanalyzedindetailandagreedfairlywellwithexperimentaldata.

Then,themethodwasextendedtoalarge-eddysimulationmodel.ThemainobjectivewastoevaluatetheapplicabilityoftheimplementedLESapproachforpre-dictionsofturbulentseparatedflows.TheflowoveracircularcylinderatReynoldsnumberRe=ρ∞U∞D/μ=3.9×103(whereU∞andρ∞arethefree-streamve-locityandmassdensity,respectively,Disthediameterofthecircularcylinderandμrepresentsthedynamicviscosity)waschosensinceitiswelldocumentedintheliteratureandcanbeviewedasagenericbenchmarkforthesub-criticalregime[34].Themainresults[24],ingeneral,agreedfairlywellwiththeavailableexperi-mentaldata(Norberg[31],PrasadandWilliamson[35],OngandWallace[33]andParnaudeauetal.[34]),aswellaswithDNSstudies[8,53],andgavesomeindicationoftheadequacyandtheaccuracyoftheOpenFOAMtoolboxforpredictionofturbulentseparatedflowsusinglarge-eddysimulations.

TheaimofthisworkisfurthervalidationoftheOpenFOAMcapabilitiesfortheapplicationsofLEStoflowsofengineeringinterest.Wehaveextendedthevalidationeffortandperformedlarge-eddysimulationsforamodestsub-criticalcircularcylinderflowataReynoldsnumberofRe=2×104whilethesameflowconfigurationasin[24]wasconsidered.Inthepresentstudybothanincompressibleandacompressible(ataMachnumberM=U∞/c∞=0.2,wherec∞isthespeedofsoundinthefreestream)treatmentoftheflowwasused.Sincemostpracticalcombustiondevices(forexample,gasturbinecombustionchambers)operateatlow-Machnumbers,investigatingthebehaviorofthecompressibleflowalgorithmatthelow-Machnumbersbecomesofspecialinterest.

Anotherscopeofthisworkisaninvestigationofthephysicalfeaturesoftheflowbasedonthepresentwell-resolvedLESresults.Thus,afrequencyoftheshear-layerinstabilitywasassessedqualitativelyusingwaveletdecomposition.Visualizationsofthecoherentstructuresinthevicinityofthecylindertogetherwiththewavelettrans-formallowedtobetterunderstandtheintermittentnatureofthistypeofinstabilities.Fromtheexperimentalpointofview,severalmeasurementsareavailableforthisparticulartestcase.Availableexperimentaldatacoverthemostimportantintegralfeaturesoftheflow(suchasforces,wakedynamics,primaryandsecondaryseparationanglesandrecirculationbubbles)andlocalfeaturesoftheflow(pressurecoefficient,velocity,vorticityandReynoldsstresses)allowingtoassessanumer-icalmethodbothqualitativelyandquantitatively.SonandHanratty[43]usedelectrochemicaltechniquestomeasurethevelocitygradientsatthesurfaceofacircularcylinderforReynoldsnumbersfromRe=5×103toRe=5×105.Schewe[39]conductedforcesmeasurementsfromsub-criticaluptotrans-criticalReynoldsnumbers2.3×104

FlowTurbulenceCombust(2014)92:673–698675

fluctuatingpressureandskinfrictionaroundacircularcylinderincross-flowinthesub-criticalReynoldsnumberrange,104?105.Particleimagevelocimetry(PIV)measurementsforRe=1.6×104andRe=2.4×104weredocumentedbyLimandLee[23].Norberg[32]providedadetailedinvestigationconcerningfluctuatingliftactingonastationarycylinderincross-flowaswellasacomprehensivereviewofmeasurementsmethods.1.1Paperoverview

Previously,theLESstudyoftheflowoveracircularcylinderatRe=3.9×103wascarriedoutusingthe‘classical’O-typegridonacomputationaldomainof50×D[24].AfurtherinvestigationoftheOpenFOAMcapabilitiesforLESforhighReynoldsnumberswasperformedfortheflowpastacircularcylinderatthemodestsub-criticalReynolds(Re=2×104)number.AtthisReynoldsnumber,thebound-arylayersarestilllaminar,andtransitiontakesplaceinthefreeshearlayersduetoboundarylayerseparation.Itiswellknownfromtheboundarylayer√theory[40]thattheboundarylayer(BLhereafter)thicknessbehaveslikeδ/r≈1/Re(whereristheradialcoordinate),andthegridspacingshouldbesmallerbyafactorof2toachievethesamequalityofresolutionasinthepreviouscomputations.However,suchgridwillgiveapproximately600×600×128=4.6×108computationalcellswhichwillbetoocomputationallyexpensiveforpracticalpurposes.Inthepresentstudywethereforedecidedtoadoptameshwiththeresolutionof440×440×64.Itisworthnoticing,thatthereisonlyasmallnumberofLESresultsforthisparticularReynoldsnumber.WefoundthestudiesbySalvaticiandSalvetti[38]andWornometal.[54].Thefirstone[38]wasdatedby2003anddiscussedtheresultsobtainedatgridswithmaximumresolutionof128×128×32.Theotherone[54]waspublishedrecentlyandreportedresultsfortheReynoldsnumbersRe=3.9×103,Re=104andRe=2×104.

Thepaperisorganizedasfollows:AgeneraltestcasedescriptionisgiveninSection2.InSection3themainfeaturesoftheemployednumericalmethodaresum-marized.Computationalresultsarepresented,analyzedanddiscussedinSection4,andconcludingremarksaregiveninSection5.

2TestCaseDescription

ThecurvilinearO-typeorthogonalgrid(Fig.1)wasusedwith440×440controlvolumes(CVs)inthecross-sectionalplaneand64CVsinthespan-wisedirection(atotalof1.24×107CVs).Theentirecomputationaldomainhadaradialextensionof25×Dinthecross-section.Thegridpointswereclusteredinthevicinityofthecylinder(??r/D=5.6×10?4)withagridexpansionfactorintheradialdirectionof1.06.

Thegridhadaspan-wiseextensionLz=π×D.Itiswellknownfromexperi-mentalstudies[27,52],thatthewavelengthofthestream-wisestructures(??Z)inthenearwakeofacircularcylinderscalesas??Z/D≈25Re?1/2.Fartherdownstreaminthewake,largerscalestructureswithwavelengths??Z/D≈1wereidentifiedbyWilliamsonetal.[52].Inthepresentsimulationsweused64gridpointsoverthe

676FlowTurbulenceCombust(2014)92:673–698

Fig.1Generalscheme(a),descriptionofthegrid(b)andzoomintothecylinderregion(c)fortheflowoveracircularcylinderatRe=2×104:θisthethecircumferentialcoordinate,x,yandzarethedomaincoordinatesinstream-wise,transverseandspan-wisedirections

span-wiselengthofπ×Dtoresolvethestructuresobservedintheexperiments.Thespan-wiselengthofthecomputationaldomainwassettoπ×D,asinourpreviousstudy[24].Recently,WissinkandRodi[53]performedaseriesofDNSatRe=3.3×103withdifferentspan-wisesizesofthecomputationaldomainvaryingthespan-wisedirectionfrom4×Dto8×D.Theyfoundthatthespan-wisesize(Lz=4×D?8×D)onlymarginallyaffectedthetime-averagedstatisticsinthecylinderwake.However,thefurtheranalysisofthespan-wiseautocorrelationofthestream-wisevelocityindicatedthatitdidnotconvergetozeroforLz→8×D.Thesedatashowedthatevenaspansizeof8×Dmightnotbelargeenoughtoaccommodate

??

allspan-wisestructures.Norberg[32]suggestedalsotouseCltoassessthedegreeofthree-dimensionalityinthesheddingflow.Tomeasurethisthree-dimensionality,thespan-wisecorrelationlength(L??/D)maybeused.Norberg[32]speculatedthatthespan-wisecorrelationalsohasagreatimportanceforvortex-inducedsoundgenerationandforthequestionofthenecessaryspan-wiselengthincomputationaldomaintocapturesignificantflow-dynamicfeaturesin3Dsimulations.BasedonthecompilationofL??/DversusRereportedbyNorberg[32],avalueofL??/D≈3forRe=2×104wasfound.Thisisconsistentwiththespan-wiselengththatweusedinthepresentsimulations.

3BriefDescriptionofNumerics

Large-eddysimulationswerecarriedoutusingtheOpenFOAMcode[49].DetailsofsolversforcompressibleandincompressibleflowsandtheirimplementationinOpenFOAMaswellassomeaspectsofthespectralanalysisareoutlinedbelow.3.1Incompressibleflowsetup

ThefilteredNavier-Stokesequationsforincompressibleflowswereconsidered.Thesolverwasbasedonthefinite-volumemethod[11]andthepressure-implicitwithsplittingofoperators(PISO)algorithmforthepressure-velocitycoupling[14].Thecentral-differencescheme(CDS-2[11,47])wasappliedforallconvective-term