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椭球体集合曳力的统计学分析获奖科研报告
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,
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