Mechanical Engineering

ThePennsylvaniaStateUniversityTheGraduateSchoolDepartmentofMechanicalandNuclearEngineeringUNSTEADYANALYSISOFBLUFFBODIESUSINGTHENONLINEARDISTURBANCEEQUATIONSAThesisinMechanicalEngineeringbyRobertP.Hansen2001RobertP.HansenSubmittedinPartialFulfillmentoftheRequirementsfortheDegreeofDoctorofPhilosophyAugust2001WeapprovethethesisofRobertP.Hansen.DateofSignatureLyleN.LongProfessorofAerospaceEngineeringThesisAdvisorCo-ChairofCommitteeGaryH.KoopmannDistinguishedProfessorofMechanicalEngineeringCo-ChairofCommitteeJohnH.MahaffyAssociateProfessorofNuclearEngineeringPhilipJ.MorrisBoeingProfessorofAerospaceEngineeringGaryS.SettlesProfessorofMechanicalEngineeringRichardC.BensonProfessorofMechanicalEngineeringHeadoftheDepartmentofMechanicalandNuclearEngineeringABSTRACTAcomputationalstudyofunsteady,separated,low-ReynoldsnumberfluidflowismadeusingamodifiedformoftheNavier-Stokesequations.ThemodificationinvolvesthedecompositionofallvariablesintheNavier-Stokesequationsintotime-independentandtime-dependentcomponents.Theresultingequationsarenottime-averaged,asintheReynoldsAveragedNavier-Stokesequations,butareinsteadsuppliedthemeancomponentsasaninputandsolvedforthetime-dependentcomponents.Thebenefitsofthisformulation,calledthenonlineardisturbanceequations,areinvestigatedusingbothinviscidandviscoustestcases.Asecond-orderaccurate,cell-centeredfinite-volumemethodwithexplicittime-marchingisusedtonumericallysolvethenonlineardisturbanceequations.Whiletheprimaryemphasisisonthedescriptionofthethree-dimensionalformulationdesignedforunstructuredgrids,thedescriptionandresultsforatwo-dimensionalversiondesignedforstructuredgridsisalsoprovided.Thethree-dimensionalsimulationsincludeturbulencemodelingusingLargeEddySimulationwithafixed-coefficientSmagorinskysubgrid-scalemodel.ParalleloperationusingtheMessagePassingInterfacelibraryofsubroutinesisemployedinthethree-dimensionalcodetoincreasethespeedofcalculations.Theparalleloperationonunstructuredgrids,includinggriddecompositionandsynchronizationofdataacrosszonalboundaries,isdescribedindetail.Anevaluationofparallelperformanceondifferentdistributed-memoryparallelcomputersystemsisalsomade.ivAcomparisonismadebetweenastandardNavier-Stokesformulationandthetwo-dimensionalnonlineardisturbanceequationformulationforacircularcylinderatReynoldsnumber1000,basedonfreestreamvelocityandcylinderdiameter.Threedifferenttypesofmeanflowinputtothenonlineardisturbanceequationalgorithmareevaluatedfortheiraffectontheaccuracyofthecylinderflowsolution.Itisfoundthatusingthefreestreamconditionsasthemeanflowimprovestheaccuracyofthepredictedsheddingfrequencyandrequiresfeweriterationsbeforeunsteadinessandperiodicitybegin.Thethree-dimensionalnumericalmethodusesRoe'sapproximateRiemannsolvertocalculateupwindedfluxvalues.AcomparisonismadebetweenthestandardNavier-Stokesformulation,thestandardformulationwiththeSmagorinskysubgrid-scalemodel,andthenonlineardisturbanceequationformulationwiththeSmagorinskysubgrid-scalemodel.Keyparameters,includingReynoldsstresses,arecomparedforthedifferentcaseswithexperimentsforthetime-averagedflowoveracircularcylinderatReynoldsnumber3900andMachnumber0.2.Comparisonsarealsomadewithselectedthree-dimensionalnumericalcalculationsdoneonstructuredgrids.Whilethesheddingfrequencyisingoodagreementwithexperiment,allcasesarestronglyaffectedbythenumericaldissipationinherentinupwindbiasing,causingincreasedbasepressure,shortenedrecirculationzonesinthecylinderwake,andexcessivedragcomparedtoexperiment.Theresultsofthecurrentunstructuredmethodarefoundtobeverysimilartotheresultsobtainedonstructuredgridsthatuseacomparableupwindingscheme.Thevnonlineardisturbanceequationformulationdemonstratednosignificantadvantageswhenemployedinthethree-dimensionalcases.TABLEOFCONTENTSLISTOFFIGURES......................................................................................................ixLISTOFTABLES.......................................................................................................xiiACKNOWLEDGMENTS............................................................................................xiiiNOMENCLATURE.....................................................................................................xivChapter1Introduction.................................................................................................11.1Motivation.......................................................................................................11.2ScopeandObjectives......................................................................................31.3RelatedWorks.................................................................................................61.3.1TheNonlinearDisturbance(NLD)Equations......................................61.3.2ModelingofHighlySeparatedTurbulentFlows..................................71.3.3DetailsofCircularCylinderFlow........................................................13Chapter2GoverningEquationsandTurbulenceModeling.........................................182.1GoverningEquations..