Understanding DPMFoam_MPPICFoam英文文献资料

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1、UnderstandingDPMFoam/MPPICFoamJeroenHofmanMultiscalemodelingformultiphasereactorsDepartmentofchemicalengineeringEindhovenUniversityofTechnologyMay20,2015InthisdocumentIintendtoclarifytheMPPICFoam owsolver.Itisbynomeanscompleteandit'scomposedofseveralseparatereportsIwrote,sotheremightbedisco

2、ntinuitiesinthedescription(andIdon'thavetimetorewritethewholething).Itdoesn'tonlycontainthingsspecictoMP-PIC,butitalsoincludesremarksonthemoregeneralsolvingofthe uid-phasebyusingPIMPLEandemployingRhie-Chowinterpolation.IngeneralitincludesclaricationsIstumbleduponwhiletryingtounderstandthe

3、solver.1TheFlowSolverInthissectionwerstsetuptheincompressibleNavier-Stokesequationsforthegas owsolver,thenwedescribethederivationofthepressureequationinsemi-discretizedform,whichisusedinthePIMPLEalgorithmemployedbyOpenFOAMinthelastsection.1.1IncompressibleNavier-StokesWestartwiththeincompr

4、essibleNavier-Stokesequationforlaminar owwithgasvolumefraction,constantviscosity,gasdensity,gravityg,stresstensorandmomentumtransfertermF:@u+r
(uu)r
=rp+gF(1)@twherethestresstensorwithunittensorandkinematicviscosity=isgivenby:T2=ru+(ru)+(r
u)(2)31Theinterphasemomen

5、tumtransfertermFcontainsbothmomentumtransferduetodragandbuoyancy[2],detailswillbegiveninsection1.2.Thereforeitisnotfullyasourcetermsincethedragisproportionaltou.WhendividingbythedensityanddeningthekinematicpressureaspP=weobtain:@uF+r
(uu)r
=rP+g(3)@tWealsodenethecontinuityequati

6、onas:@+r
(u)=0(4)@t1.2MomentumtransferInthissectionwelookatdierentwaysofdeningmomentumtransfertoeithertheparticleorthe uidphase.ByswitchingfromthediscreteparticledescriptiontoacontinuumdescriptionwetrytolinkthedierentwaysofdeningthemomentumtransfertermsinceregardlessofdenitionofFequa

7、tion3theresultingPDEsshouldbeequal.Wewillrstlookatthewaythemomentumtransfertermisusuallydenedasacombinationofbuoyancyanddragforparticlesinacomputationalcell:X1X1XF=f=(fdragVprpi)=FdragVprpi(5)VVpppwhereVisthevolumeofthecomputationalcell,Vpthevolumeof