Reynolds-Averaged Turbulence Modeling Using Type I and Type II Machine Learning Frameworks with Deep Learning

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1、Reynolds-AveragedTurbulenceModelingUsingTypeIandTypeIIMachineLearningFrameworkswithDeepLearningChih-WeiChangandNamT.DinhDepartmentofNuclearEngineeringNorthCarolinaStateUniversity,RaleighNC27695-7909cchang11@ncsu.edu,ntdinh@ncsu.eduAbstractDeeplearning(DL)-basedReynoldsstresswithitscapabilityt

2、oleveragevaluesoflargedatacanbeusedtocloseReynolds-averagedNavier-Stoke(RANS)equations.TypeIandTypeIImachinelearning(ML)frameworksarestudiedtoinvestigatedataandflowfeaturerequirementswhiletrainingDL-basedReynoldsstress.Thepaperpresentsamethod,flowfeaturescoveragemapping(FFCM),toquantifythephy

3、sicscoverageofDL-basedclosuresthatcanbeusedtoexaminethesufficiencyoftrainingdatapointsaswellasinputflowfeaturesfordata-driventurbulencemodels.ThreecasestudiesareformulatedtodemonstratethepropertiesofTypeIandTypeIIML.ThefirstcaseindicatesthaterrorsofRANSequationswithDL-basedReynoldsstressbyTyp

4、eIMLareaccumulatedalongwiththesimulationtimewhentrainingdatadonotsufficientlycovertransientdetails.ThesecondcaseusesTypeIMLtoshowthatDLcanfigureouttimehistoryofflowtransientsfromdatasampledatvarioustimes.ThecasestudyalsoshowsthatthenecessaryandsufficientflowfeaturesofDL-basedclosuresarefirst-

5、orderspatialderivativesofvelocityfields.ThelastcasedemonstratesthelimitationofTypeIIMLforunsteadyflowsimulation.TypeIIMLrequiresinitialconditionstobesufficientlyclosetoreferencedata.ThenreferencedatacanbeusedtoimproveRANSsimulation.Keywords:data-driventurbulencemodeling,Reynoldsstress,deeplea

6、rning,TypeImachinelearningframework,TypeIImachinelearningframework1.IntroductionReynolds-averagedNavier-Stokes(RANS)equationsarewidelyusedinfluidengineeringsimulationandanalysisduetoitscomputationalefficiency.ReynoldsstressisessentialtocloseRANSequations.Lineareddyviscositymodels(LEVMs)areatt

7、ractivetorepresentReynoldsstressduetotheircomputationalefficiency.LEVMsincludeSpalart-Allmaras[1],k-ε[2],andk-ω[3]modelsthatrequireextensivelyevaluatedandcalibratedfordifferentflowcharacteristics.Consequently,performanceofdifferentmodelsislim