Sheet Music

A numerical method for solving three-dimensional generalized Newtonian free surface flows

Description
A numerical method for solving three-dimensional generalized Newtonian free surface flows
Categories
Published
of 32
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  NASAContractorReport198159ICASEReportNo.95-38 S A NUMERICAL METHODFORSOLVING THETHeE-DIMENSIONAL PARABOLIZEDNAVIER-STOKESEQUATIONSDomenicD'AmbrosioRobertoMarsilio  NASA-CR-198159 ANUMERICALMETHODFORSOLVING THE THREE-DIMENSIONALPARABOLIZEDNAVIER-STCKESEQUATIONSFinalReport(ICASE)24 p G313_N95-27917 Unclas 0050224 ContractNo.NAS1-19480May1995InstituteforComputerNASALangleyResearchCenterHampton,VA23681-,clence ng]neenng  ANumericalMethodforSolvingtheThree-DimensionalParabolizedNavier-StokesEquations* DomenicD'AmbrosioDipartimentodiIngegneriaAeronauticaeSpazialePolitecnicodiTorino10129Torino,ItalyRobertoMarsilioInstituteforComputerApplicationsinScienceandEngineeringNASALangleyResearchCenterHampton,VA 23681, USA. AbstractAnumericaltechniquethat solves theparabolizedformoftheNavier-Stokesequa-tionsispresented.SuchamethodmakesitpossibletoobtainverydetaileddescriptionsoftheflowfieldinarelativelymodestCPUtime.Thepresentapproachisbasedonaspace-marchingtechnique,usesafinitevolumediscretizationandanupwindflux-differencesplittingschemefortheevaluationoftheinviscidfluxes.Secondorderac-curacyisachievedfollowingtheguidelinesofthetheENOschemes.Themethodologyisusedtoinvestigatethree-dimensionalsupersonicviscousflowsoversymmetriccor-ners.Primaryandsecondarystreamwisevorticalstructuresembeddedintheboundarylayerandoriginatedbytheinteractionwithshockwavesaredetectedandstudied.Forpurposeofvalidation,resultsarecomparedwithexperimentaldataextractedfromliterature.Theagreementisfoundtobesatisfactory.Inconclusion,thenumericalmethodproposedseemstobepromisingasitpermits,atareasonablecomputationalexpense,investigationofcomplexthree-dimensionaiflowfleldsingreatdetail.*This research wassupportedinpartbyMPI40%anditwasalsosupportedinpartbytheNationalAeronauticsand"SpaceAdministrationunderNASAContractNo.NAS1-19480whilethesecondauthorwasinresidenceattheInstituteforComputerApplicationsinScience and Engineering,(ICASE),NASALangleyResearchCenter,Hampton,VA,23681  1Introduction In the study of three-dimensionalsupersonicflowsitiscommon to befacedwithcomplexinteractionsconcerningshockwavesandviscouslayers.Suchoccurrencesoftenprovokedramaticchangesintheflowfieldfeatures,bothqualitativelyandquantitatively.Shock-inducedseparationsof the viscouslayermake the flowvortex-dominatedclosetothewall,andvorticalstructuresarealsolikely to appear,forsufficientlyhighReynoldsnumbers,inzoneswhereconvectiveeffectsarepreponderant,due the instabilityof the slipsurfacesresultingfromshock/shockinteractions.Importantconsequencesof these interactionsareincreasesinheatfluxes,skinfrictioncoefficientsandpressuresatthewallincorrespondencewith the reattachmentoftheseparatedflow;inadditiontransition,shockwaveshapesandtheefficiencyoftheair-intakesthatmightswallowsuchstreamsareaffected.Numericaltestsareusuallyhelpfulintheinvestigationsofsuchcomplicatedfluid-dynamicpatterns,astheyprovideatooltoobserveandpossiblytounderstandtheoriginsandtheeffectsofthenumerousphenomenatriggeredbyshock/shockandshock/viscouslayerinteractions.Itisclear,however,thatinordertoobtaingoodnumericalresultscomparablewithexperimentaldata,afairlydetaileddescriptionoftheflowfieldisnecessary,especiallywhenmultiplevorticalstructuresarepresent.Theonlycompletelycorrectwayofsolvingnumericallythree-dimensionalcompressibleviscousflowsistointegrateintimethefullNavier-Stokesequationsuntilasteady-state(ifoneexists)isreached.Thisapproachiscertainlyaffordabletoday,but,ifmanygridpointsareneededtosolveindetailcomplexfluid-dynamicfeatures,itcouldbeexcessivelytimeandmemoryconsuming.Inthecaseofsupersonicsteady-stateflows,however,thispracticaldifficultycanbepartiallycircumventedwiththeaidoftheapproximateformofthefullNavier-Stokesequationsknownas ParabolizedNavier-Stokesequations. Aswillbepointedoutinthenextsections,theadvantageoftheParabolizedNavier-Stokes(PNS)equationsisthattheycanbesolvedusingaspace-marchingtechnique,acharacteristicwhichallowsonetospendrelativelyshortcomputationaleffortandalsoresultsinnoticeablememorysavings.Therefore,itispossibletoreinvesttimeandmemoryinmorerefinedgrids,thuspermittingabetterresolutionoftheflowfield.Asadrawback,theparabolizingassumptionrequiresthefreestreamMachnumbertobesupersonicandthestreamwisevelocitytobealwayspositive(streamwiseflowseparationsarethusexcluded,whilecrossflowseparationsarepermitted);moreover,thestreamwisepressuregradientmustbealteredinthesubsonicpartoftheflowfield[1].Intheapproachpresentedhere,thegoverningequationsareintegratedinanexplicitfash-ionandthephysicaldomainisdiscretizedaccordingtoafinitevolumetechnique.Thecon-vectivepartoftheequations(inviscidfluxes)istreatedfollowingaflux-difference-splittingmethodwithanapproximatesolutionofaRiemannproblemateachcellinterface[2][3]whilethediffusiveterms(viscousfluxes)arecalculatedusingacenteredscheme.SecondorderaccuracyisachievedbymeansofanEssentiallyNonOscillatoryscheme[4]withlinearreconstructionofthesolutionateachstepofintegration.Presently,onlyinertgasesinlam-inarregimeareconsidered,butafutureextensiontoincludethermochemicalorturbulenceeffectsiscertainlypossible.Tovalidatethemethod,numericalresultsarecomparedwithexperimentaldataex-tractedfromtheliterature.Supersoniccornerflowsconfigurationshavebeenchosenasa
Search
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks