乱流基础工学2

乱流基础工学2

乱流基礎工学"求一卜Areviewofparticle-turbulenceinteractionandcloudsinengineering2.Parameterspertinenttoparticle-turbulenceinteractionTheparticle-flowinteractionisatwo-waycoupling;thatis,theturbulentflowmayinfluencethespatialdistributionoftheparticleswhiletheparticlesmayalsomodifythepropertiesoftheflow.Inthisreview,wewillmostlystudythefirstissueandbrieflydiscusswhythesecondissueislesspertinenttocloudphysics.Particlesinteractwiththeflowthroughthedragforce(mechanicalcoupling)andthroughthermodynamiceflects.Thedragforceisnonzerowhenevertherelativevelocitybetweentheparticleandtheflowisnonzero.Thisarisesbecauseparticlesfallundertheinfluenceofgravityandbecausetheypossessinertiasothattheydonotrespondinstantaneouslytoaccelerationsoftheflow.Thermodynamiceffectsmaybeimportantwhenphasechangesoccur(e.g・，growingclouddroplets)orforchemicallyreactingflows(e.g.,combustion).Wewillnotdiscusschemicallyreactingflowshereandjustbrieflycommentonthepossibilitythatparticleslikeclouddropletsmayinfluencetheturbulentflowthroughlatentheatexchanges.Thefbllowingfourdimensionlessparametersareusefultopredictthenatureordegreeoftheparticle-flowmechanicalcouplingofindividualparticlesortheoveralleflectofagroupofparticlesontheflow:A.theratiod/1,wheredistheparticlediameterandlisacharacteristiclengthscaleoftheflow[eithertheKolmogorovlengthscale(q)ortheintegralscale(L)];B・theparticle'sReynoldsnumber,ReP=UR/v,whereUistherelativevelocity\nbetweentheflowandtheparticle,Ristheradiusoftheparticle,andvisthekinematicviscosityofthefluid;C.theStokesnumber,whichistheratiobetweentheparticle^sresponsetime(tP)andacharacteristictimescaleoftheflow(iF),St=tP/tF;andD.themassloading(Mp/Mf),thatis,theratioofthetotalmassofparticles(Mp)andthemassofthecarrierfluid(Mf).Particles,assumedspherical,areessentiallydescribedbytheirmass(mp)andradius(R).Withthesetwoparameters,andthedynamicviscosityofthecarrierfluid,p,wecancalculatetheparticle'sresponsetimetP(alsocalledtherelaxationorStokestimescale).ThetimescaletPisthecharacteristictimetheparticletakestoreacttochangesintheflow.ForparticleswithdensitymuchlargerthanthatofthesurroundingfluidandsmallReynoldsnumber(definedinsection2c),theequationofmotioninvolvesonlythedragforceandgravity.Whenthereisnomotioninthefluid,thesolutionoftheequationofmotionoftheparticleisV(t)=VT[1一exp-t/ip],whereVT=xPgistheparticle'sterminalvelocity(ordriftvelocityorStokessettlingvelocity)andtP=mp/(67rR|i)=2pwR2/9gisthetimeforthevelocityoftheparticletoreachabout63%[1一(1/exp)]ofitsterminalvelocity.Thesymbolpwdenotesthedensityofwaterandgisthegravitationalacceleration.Aswillbeshownlater,theresponseoftheparticletothefluidismostsignificantwhenthemagnitudeofthecharacteristictimescaleofthefluidisofthesameorderas卬・Turbulencedevelopsinrotationalflows.Itarisesfromdiffusionandstretchingofvorticitycreatedbyvariousmeansrelatingtoeithershearorthermalgradients.A\nturbulentflow,whichexhibitscomplexchaoticspatialandtemporalbehavior,canbedescribedasaweaklycorrelatedrandomfieldwithstronglycorrelatedyethighlylocalizedstructures(coherentvortices)thatarelargelyresponsibleforintermittenteffects(Sheetal.1990,1991).Theyhavebeenshowntomodifythespatialdistributionofparticlesinlaboratoryexperiments.3.ResultsfromlaboratoryworkandmodelsimulationsinengineeringDuetotheirfiniteinertia,particleswithahigherdensitythanthesurroundingcarrierfluidwillnotfbllowtheflowexactlyAsaconsequence,particlestendtodivergeoutofregionsofhighvorticesandconvergepreferentiallyinregionsoflowvorticessuchasstagnationpoints[seeFig.1ofEatonandFesler(1994)forvisualexplanation].Asaresult,regionswithmuchhigherandlowerconcentrationthanpredictedfromarandomPoissonspatialdistributioncandevelop・Thishascometobeknownasclusteringorpreferentialconcentration.Thisphenomenonhasbeenanactiveareaofresearchforthelastdecadeorso.Earlierworkonparticle-flowinteractionconcentratedonthedifferenceindispersionbetweentheparticlesandfluidpoints.\noSquiresandEaton(1991)・DNS△WangandMaxey(1993)・DNS□SundaramandCollins(1997)•DNS▼Fessleretal.(1996)・LAB▼23456StCD▼ODOBCD□▼ODOB£=.09iifs234561O-1.O234561Q0.0234561Q1.O2345678Figure1Stokesnumber(St)-velocityratio(Sv)diagramshowinglocationofdirectnumericalsimulations(DNS)andlaboratoiyexperiments(LAB)forparticlesin3Dturbulence・TheSt-Svregionforclouddropletsof5-25-(imradiusisshownfbranappropriaterangeofeddydissipationrates(10-4-0.09m2s-3).Thedashedlinesareforconstanteddydissipationrates(10—4,10-3,10-2,and0.09m2s-3)andradiivaryingfrom5to25pm,whilethesolidlinesareforconstantradii(5,10,15,20,and25pm).\n0-1JStreamlineswithusingfourturbulencemodelswereshownintheFigure2.Itisseenthattherearetwobiggereddycornerswithusingk-wmodelandBSLmodelthank-£model.Inkw-modelandBSLmodel,thejetflowfromtheinletcannotmovealongtheceilingsofarasink-emodelandthereturnflowclosetothefloorisseparatedearlierthanink-emodel.ThestreamlinewithusingSSTmodelisquitediflerentfromtheothers.Figure3showsthestreamlineinexperiment.Itisseenthattherearetwoeddyrecirculationattheupperrightcomerandlowerleftcomer,butitishardtosaywhichturbulencemodelisbetterinthiscaseaccordingtoFigure3.(a)streamlinewithusingstandardk一£model(b)streamlinewithusingstandardkw-modell5.23009|m»A-1|[m$*-1|(c)streamlinewithusingkw-BSLmodel(d)streamlinewithusingkw-SSTmodelFigure2streamlinewithusingdiflerentturbulencemodel\nFigure3streamlineinexperiment(PeterV.NielsenPhDthesis,1974)