橢球體集合曳力的統(tǒng)計學(xué)分析獲獎科研報告

橢球體集合曳力的統(tǒng)計學(xué)分析獲獎科研報告

ABSTRACT：Inthisstudy，Particle-ResolvedSimulations（PRS）areperformedforsuspensionsofdifferentellipsoidsthatarerandomlyorientedandthedragforcesarecalculatedforeachindividualparticleintheflow.TheinvestigatedconditionsincludeReynoldsnumberfrom10to200，solidvolumefractionfromlow（0.1）tointermediate（around0.3）withellipsoidaspectratios（AR）of2.5，5and10.

Keywords：Particlesuspensions;Particle-ResolvedSimulation;prolateellipsoids;dragforce;statisticalanalysis.

1.INTRODUCTION

Fluiddragforcesactingonparticlesinsuspensionareofcriticalimportanceforcapturingthedynamicsoffluid-particlesystemsaccurately.Inthispaper，particle-resolvedsimulationsareperformedforsuspensionsofellipsoidswithaspectratio（definedastheratiobetweenlengthoftheparticlealongrotationalsymmetryaxisandthediameteroftheequatorialplane）of2.5，5and10.Reynoldsnumberrangeof[10，200]withsolidfractionof[0.1，0.35]，[0.1，0.3]and[0.1，0.2]forthesethreeellipsoids，respectivelyareinvestigatedwithderivationofdragforceforeachindividualparticleinthesuspensions.Togetabetterunderstandingofthedragforcedistribution.StatisticalanalysisarecarriedoutincludingthePDF，standarddeviationtoprovidemoreinsightinsuchproblemasidefromtheensemblemeandragforce.

2.METHODS

Detailedexplanationaboutthecomputationalalgorithmandvalidationcanbefoundin[1]TheparticlesuspensionsaregeneratedusingaphysicalsimulationenginePhysXdevelopedbyNvidia[2]whichhasbeenimplementedinthepreviousworks[3，4].DetailedprocedurecanbefoundintheworkofHeetal.[3]，whichcontainstheprocessofparticlecollisiondetection，resolvingthepost-collisiontranslationalandrotationalvelocityandkineticenergydecayingtofinallyreachastationarystate.ExamplesoftheparticlesuspensionforAR5ellipsoidundersolidfractionof0.1areshowninFigure1.Thetotalamountofparticlerequiredforaspecificsolidfractioniscalculatedby：

Whererepresentstheamountofparticlesneededunder.isthevolumeofthedomainthatcontainstheparticleswithadimensionof.

3.RESULTS

3.1DragForceDistributionintheWholeSuspension

AsisdemonstratedinthestudyofRongetal.[5]，dragforceofspheresinsuspensionfollowanapproximateGaussiandistribution.Inthiswork，thegeometryisextendedtoellipsoidsofaspectratioof2.5，5and10.ThedragforceatReynoldsnumberof10withsolidfractionof0.1isshowninFigure2.Figuresontherightsharethesamey-axistitleasthefiguresontheleft.Theleftthreeplotspresentthedragforcedistributionwithrespecttotheparticleinclinationangle.Consideringellipsoidswithaspectratioof2.5，theanalysisofHeandTafti[4]indicatesthatincreaseofpressureforceanddecreaseofviscousforceresultsinanalmostconstanttotaldragwithrespectto.Besides，itcanbeobservedthatthedatahasinsignificantvariationofspreadunderdifferent，whichisduetothealmostconstantdispersityofviscousdragundervaryinganditsdominanteffectonthetotaldragforce.However，fordataofellipsoidswithaspectratioof5and10，asignificantincreasingtrendindragforcecanbeobservedwithrespectto.

UnlikesphericalparticlesuspensionsthatshowGaussiandistributionofthedragforce[5]，thecurrentresultsforellipsoidsexhibitvaryingdegreesofskewnessatvaluesof0.50，0.92and0.86forellipsoidswithaspectratioof2.5，5and10，respectively.Asdiscussedpreviously，thedragofAR2.5ellipsoiddoesntshowsignificantvariationwithrespectto，howeverthePDFindicatesthatthedragshowspreferenceforlessthantheaverage.AstheaspectratioincreasestoAR5andAR10，thedragdataexhibitslargerskewness.Thisisbecauseforsmall，thespreadofdragissmall.Asinclinationangleincreases，dispersityofdragincreasestotheextentthataparticleatinclinationangleof90°canexhibitthesamedragforceasaparticleatinclinationangleof0°.Thepropensityforlowdragvaluesthatappearsatalmostall，resultsinanoveralllowdragpreferenceinthesuspensions.

ResultsatReynoldsnumberof200andthehighestsolidfractionforeachaspectratioarealsoanalyzedandtheresultsareshowninFigure3.TheresultsforAR2.5ellipsoidsatRe=200，=0.35showanincreasingtrendinmagnitudeanddispersitywithrespectto.ThePDFplotshowsasimilartrendastheresultsforRe=10，=0.1withaskewnessof0.45.Therefore，thisindicatesthatthechangeinReanddoesnothaveasignificantinfluenceonthedragforcePDFdistributioninthesuspensionsofAR2.5ellipsoids.ForthesuspensionofAR5ellipsoidsatRe=200，=0.3，thePDFalsoshowsatrendsimilartotheresultsatRe=10，=0.1，butwithalowerskewnessvalueof0.69.Thelowerskewnessindicatesthatthedragtendstowardsamoreuniformdistribution.Actually，afterinvestigatingtheresultsatdifferentReand，adecreasingtrendinskewnesswithrespecttoRecanalwaysbeobservedatdifferent.ThisisattributedtotheobservationthatasReincreases，aparticleinthesuspensionwillhaveastrongerinfluenceonthesurroundingfluid.Asaresult，themixingeffectoftheflowbecomesmoreprominentandthedragforcetendstoamoreuniformdistribution.ForAR10ellipsoids，thedraghasaskewnessof1.04，whichisslightlylargerthanthecasewithRe=10，=0.1.

4.CONCLUSIONS

ThispaperinvestigatesthestatisticalpropertiesofdragforcevariationinsuspensionsofAR2.5，AR5andAR10ellipsoid.Thelargerangeofcalculateddragforceindicatesthatevenusingtheaveragedragconfinedinasmallrangebasedonaspectratio，Reynoldsnumber，solidfraction，andinclinationangleisaroughapproximationoftheactualdragforceexperiencedbydifferentparticles.Thusthestatisticalnatureofdragforcedistributionatdifferentinclinationanglesisinvestigated.Basedontheresults，wecandrawtheconclusionas：unlikethesphericalsuspensionsthatshowanapproximateGaussiandistribution，dragforceonellipsoidsshowsabiaseddistributionwithpositiveskewness.Thisindicatesthatmoreparticlestendtohavedragbelowtheaveragevalue.Largeraspectratioellipsoidstendtohavehigherskewness.BothReanddonothavemucheffectontheskewnessofAR2.5ellipsoidsuspensions.However，skewnessdecreaseswithincreasingReforAR5andAR10ellipsoids.ThiscanberelatedtothestrongermixingeffectofthefluidathigherReynoldsnumbers.

REFERENCES

[1]Cao，Z.，Tafti，D.K.，andShahnam，M.，2020，