On a multi-block method for transonic turbulent flows past a wing-fuselage configuration PDF
Preview On a multi-block method for transonic turbulent flows past a wing-fuselage configuration
ONAMULTI-BLOCKMETHOD FORTRANSONICTURBULENTFLOWS PASTAWING-FUSELAGECONFIGURATION By CHAU-LINLEE ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1991 ACKNOWLEDGEMENTS IwishtoexpressmydeepappreciationtoDr.Chen-ChiHsuforhis constantguidancethroughoutthisresearchandforhisinvaluablehelpinthe writingofthisdissertation. Also,IwishtothankDr.WeiShyyformakinga numberofveryconstructivecommentsandsuggestionsduringthecourseofthis research. Iamalsoindebtedtomembersofmydissertationcommittee,Dr. UlrichH.Kurzweg,Dr.DavidW.Mikolaitis,andDr.GeraldJ.Micklow,fortheir interestinthesubjectandvaluablecriticismonthedraftofthisdissertation. Finally,IwouldliketoextendmyacknowledgementstoDr.Nae-Haur ShiauandDr.Shu-ChengYangfortheirpreviousworkonthecomputercodeand plottingpackagesemployedinthisstudyandtoFloridaStateUniversityfor providingthesupercomputerCrayY-MPresources. ii TABLEOFCONTENTS page ACKNOWLEDGEMENTS ii ABSTRACT v CHAPTERS I INTRODUCTION 1 LIBackground 2 1.2LiteratureSurvey 4 L3Objectives 9 L4Overview 9 n FORMULATIONOFPROBLEM 10 2.1DescriptionofProblem 10 2.2NondimensionalizedNavier-StokesEquations 13 2.3TransformedNavier-StokesEquations 16 2.4Thin-LayerNavier-StokesEquations 18 2.5TurbulenceModel 19 2.6BoundaryConditions 23 2.7InitialConditions 24 m NUMERICALMETHODOFSOLUTION 25 3.1GridTopology 26 3.2FlowSolver 32 IV GRIDGENERATION 47 4.1VolumeGridGeneration 49 4.2SurfaceGeneration 55 iii V RESULTSANDDISCUSSION 67 5.1EffectofSolution-Adaptation 71 5.2EffectofGridRefinement 80 5.3ComplexFlowPhysics 86 VI SUMMARY 92 REFERENCES 95 BIOGRAPfflCALSKETCH 100 '-'•-> . , ' '' \_ s. * - t iv AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ONAMULTI-BLOCKMETHOD FORTRANSONICTURBULENTFLOWS PASTAWING-FUSELAGECONFIGURATION By Chau-LinLee August1991 Chairperson:Chen-ChiHsu MajorDepartment:AerospaceEngineering,Mechanics andEngineeringScience Amulti-blockmethodbeingexploredisfurtherdevelopedandinvestigated forthesimulationofMach0.8transonicturbulentflowpastawing-fuselage configurationat-3.0degreeangleofattack. Inthismethodtheflowfieldof interestisfirstdividedintosixcontiguousblocksinsuchawaythateachblockis partiallyboundbyasolidsurface. Accordinglythesolidsurfaceismappedontoa completerectangularboundaryplaneinthecomputationaldomainforeffective calculationofalgebraiceddyviscosityaswellasfordirectapplicationofathin- layerNavier-Stokescode. Then,inthesolutionprocess,eachblockistreatedas anindependentflowproblem,modeledbytheunsteadyReynolds-averagedthin- layerNavier-Stokesequations,withtheinterfaceboundaryconditionsupdatedat everytimestep. TheturbulenceclosuremodelemployedistheBaldwin-Lomax eddyviscositymodel. Themulti-blockmethodbeinginvestigatedhasadistinctadvantagein designapplicationinthatalocalchangetotheconfigurationrequiresonlythe relatedblockgridtoberegenerated. However,theexcessivedistortiononblock domaintransformation,inparticularthewingblocks,imposedbythespecial featuresofthemethodmakesitdifficulttogenerategoodblockgridsforaccurate flowsimulation. Accordingly,specialmeasuresandpropertechniquesforquaUty blockgriddingshavetobedevelopedandinvestigated. Inthisstudyaone-dimensionaladaptivegridgenerationtechniquebased onavariationalapproachhasbeenemployedtogeneratewingsurfacesadaptive tomeasuredsurfacepressuregradients. Withthesolidsurfaceandthe correspondingoutersurfacegenerated,thesixblockgridsaregeneratedbyan algebraicTwo-BoundaryMethodbasedontransfiniteinterpolation. Theblending functionusedisaHermitepolynomialwhichcanprovidegoodorthogonalgrids nearthesurface. Also,ahyperbohctangentclusteringfunctionhasbeenusedto provideeffectivegridpointdistributionandsufficientgridresolutioninthe viscousboundarylayer. Fortheadaptiveblockgridsgenerated,theJacobianof transformationevaluatedbyfinite-differenceapproximationsispositiveatevery gridpoint. Togainfurtherinsightandunderstandingonthemulti-blockmethod forcomplexflowsimulation,fivedifferentsetsofsixblockgridshavebeen generatedandinvestigatedforthewing-fuselageflowsimulation. Numerical vi resultsobtainedshowthatthemulti-blockmethodinvestigatedisaverypromising approachwhichcanbefurtherdevelopedforcomplexconfigurationaerodynamics simulation. vu CHAPTERI INTRODUCTION Withtheadventofsupercomputersandtheadvancementinsolution algorithmsfornonlinearproblems,computationalfluiddynamics(CFD)has becomeapowerfultoolforanalyzingpracticalfluidflowproblems. Eventhough muchprogresshasbeenmadeinCFD,furtheradvancesareneededinorderto effectivelyuseitforsimulatinghighspeedturbulentflowspastcomplex aerodynamicconfigurations. Asuccessfulnumericalsimulationofflowpasta complexconfigurationrequiresnotonlyanaccurateandrobustflowsolverbut alsoagoodgridsystem. Inthisstudy,acomputationalmethodutilizingamulti- blockgridsystemisdevelopedandinvestigatedforsimulatingtransonicturbulent flowspastawing-fuselageconfiguration. Webeginthisintroductorychapterwithsomegeneralbackground informationongridgeneration. Afterwards,aliteraturesurveyisgivenfortopics relevanttothemulti-blockcomputationalmethodsdevelopedinthisstudy. This chapterconcludeswithadescriptionoftheobjectivesofthepresentstudyandan overviewofthisdissertation. 1 2 1.1Background Gridgenerationisconcernedwiththemappingofunequallydistributed gridpointsinthespatialdomainontoacomputationaldomainwhereallofthe gridpointsareuniformlydistributed. MuchoftherapidprogressinCFDcanbe directlyattributedtothedevelopmentofgridgenerationtechniques,becausethey, inconjunctionwithmethodssuchasthefinite-differencealgorithm,haveenabled onetostudyflowproblemsincomplexgeometriesefficientlyandaccurately[1-8]. EisemanandErlebacher[7]classifiedallpossiblegridsystemsthatcanbe usedbyfinite-differencemethodasfollows: Atthebroadestlevel,agridsystem canbeclassifiedasstructured,unstructured,ormixeddependinguponhowthe gridpointsareconnectedtoeachother. Astructuredgridsysteminturncanbe classifiedasasinglegridoramulti-blockgrid. Asinglegridisonethatisbased onasingleboundary-fittedcoordinatesystemwhereasamulti-blockgridismade upoftwoormoresinglegridspatchedtogetherwitheachsinglegridhavinga differentboundary-fittedcoordinatesystem. Ofthegridsystemsmentionedabove,theunstructuredandmixedgrid systemsaremoreversatile,especiallyforcompHcated-shapedspatialdomains; buttheuseofthesegridsystemswithafinite-differencemethodisstillinastate ofdevelopment[8,9]. Presently,mostfinite-differencemethodsusethe structuredgridbecauseofitsinherentcompatibilitywithsuchmethods. Inthis research,thestructuredgridisused. 3 Methodsforgeneratinggridsystemscanbedividedintotwomajorclasses- differentialequationmethodsandalgebraicmethods. Differentialequation methodsgenerategridsystemsbysolvingasystemofpartialdifferentialequations whichdescribehowgridpointsaretobedistributedwithinthespatialdomain. Manyofthesemethodsrequireasubstantialamountofcomputationaleffort, sincethesystemofpartialdifferentialequationsthatmustbesolvedisquasilinear andoftenascomplicatedasthepartialdifferentialequationsthatgovernthefluid flowproblem. Algebraicmethodsgenerategridsystemsbyinterpolatingbetween boundariesofthespatialdomainandusingstretchingfunctionstocontrolthe distributionofgridpoints. Here,forthepurposeofgridgeneration,interpolation meansaprocessofinferringgridpointlocationsbetweenpointswhere informationisknownexactly. Sincethedesiredgridpointlocationsarean algebraiccombinationofknownquantities,nopartialdifferentialequationneeds tobesolvedinthisgridgenerationprocess. A "quality"gridsystem,whethergeneratedbydifferentialequationor algebraicmethods,isusuallyonethatisreasonablyorthogonalandsmoothwith thegridpointsconcentratedinregionswheretheyaremostneeded. By strategicallypositioningthegridpoints,thetotalnumberofgridpointsneededto obtainaccuratesolutionscanbereduced. Thisreducescomputermemoryand CPUtimerequirements.
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