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1、7.19PorousMediaConditionsTheporousmediamodelcanbeusedforawidevarietyofproblems,includingflowsthroughpackedbeds,filterpapers,perforatedplates,flowdistributors,andtubebanks.Whenyouusethismodel,youdefineacellzoneinwhichtheporousmediamodelisappliedandthepressurelossintheflowisdeterminedviayourinputsasde
2、scribedinSection7.19.2.Heattransferthroughthemediumcanalsoberepresented,subjecttotheassumptionofthermalequilibriumbetweenthemediumandthefluidflow,asdescribedinSection7.19.3.A1Dsimplificationoftheporousmediamodel,termedtheporousjump,canbeusedtomodelathinmembranewithknownvelocity/pressure-dropcharacte
3、ristics.Theporousjumpmodelisappliedtoafacezone,nottoacellzone,andshouldbeused(insteadofthefullporousmediamodel)wheneverpossiblebecauseitismorerobustandyieldsbetterconvergence.SeeSection7.22fordetails.7.19.1LimitationsandAssumptionsofthePorousMediaModel7.19.2MomentumEquationsforPorousMedia7.19.3Treat
4、mentoftheEnergyEquationinPorousMedia7.19.4TreatmentofTurbulenceinPorousMedia7.19.5EffectofPorosityonTransientScalarEquations7.19.6UserInputsforPorousMedia7.19.7ModelingPorousMediaBasedonPhysicalVelocity7.19.8SolutionStrategiesforPorousMedia7.19.9PostprocessingforPorousMedia7.19.1LimitationsandAssump
5、tionsofthePorousMediaModelTheporousmediamodelincorporatesanempiricallydeterminedflowresistanceinaregionofyourmodeldefinedasporous.Inessence,theporousmediamodelisnothingmorethananaddedmomentumsinkinthegoverningmomentumequations.Assuch,thefollowingmodelingassumptionsandlimitationsshouldbereadilyrecogn
6、ized:Sincethevolumeblockagethatisphysicallypresentisnotrepresentedinthemodel,bydefaultFLUENTusesandreportsasuperficialvelocityinsidetheporousmedium,basedonthevolumetricflowrate,toensurecontinuityofthevelocityvectorsacrosstheporousmediuminterface.Asamoreaccuratealternative,youcaninstructFLUENTtouseth
7、etrue(physical)velocityinsidetheporousmedium.SeeSection7.19.7fordetails.Theeffectoftheporousmediumontheturbulencefieldisonlyapproximated.SeeSection7.19.4fordetails.Whenapplyingtheporousmediamodelinamovingreferenceframe,FLUENTwilleitherapplytherelativereferenceframeortheabsolutereferenceframewhenyoue
8、nabletheRelativeVelocityResistanceFormulation.Thisallowsforthecorrectpredictionofthesourceterms.Formoreinformationaboutporousmedia,seeSections7.19.6and7.19.6.Whenspecifyingthespecificheatcapacity,C,fortheselectedPmaterialintheporouszone,Cmustbeenteredasaconstantvalue.P7.19.2MomentumEquationsforPorou
9、sMediaPorousmediaaremodeledbytheadditionofamomentumsourcetermtothestandardfluidflowequations.Thesourcetermiscomposedoftwoparts:aviscouslossterm(Darcy,thefirsttermontheright-handsideofEquation7.19-1),andaninertiallossterm(thesecondtermontheright-handsideofEquation7.19-1)(7.19-1)whereisthesourcetermfo
10、rtheth(,or)momentumequation,isthemagnitudeofthevelocityandandareprescribedmatrices.Thismomentumsinkcontributestothepressuregradientintheporouscell,creatingapressuredropthatisproportionaltothefluidvelocity(orvelocitysquared)inthecell.Torecoverthecaseofsimplehomogeneousporousmedia(7.19-2)where門isthepe
11、rmeabilityandistheinertialresistancefactor,simplyspecifyandasdiagonalmatriceswithand,respectively,onthediagonals(andzerofortheotherelements).FLUENTalsoallowsthesourcetermtobemodeledasapowerlawofthevelocitymagnitude:園三_仇|訓(xùn)G三仇|創(chuàng)917譏(7.19-3)Cowhereandareuser-definedempiricalcoefficients.Inthepower-lawm
12、odel,thepressuredropisisotropicandtheCounitsforareSI.DarcysLawinPorousMediaInlaminarflowsthroughporousmedia,thepressuredropistypicallyproportionaltovelocityandtheconstantcanbeconsideredtobezero.Ignoringconvectiveaccelerationanddiffusion,theporousmediamodelthenreducestoDarcysLaw:(7.19-4)Thepressuredr
13、opthatFLUENTcomputesineachofthethree(,)coordinatedirectionswithintheporousregionisthen(7.19-5)1/購丁wherearetheentriesinthematrixinEquation7.19-1,arethevelocitycomponentsinthe,anddirections,and,andarethethicknessesofthemediuminthe,anddirections.Here,thethicknessofthemedium(,or)istheactualthicknessofth
14、eporousregioninyourmodel.Thusifthethicknessesusedinyourmodeldifferfromtheactualthicknesses,youmustmaketheadjustmentsinyourinputsforInertialLossesinPorousMedia6Athighflowvelocities,theconstantinEquation7.19-1providesacorrectionforinertiallossesintheporousmedium.Thisconstantcanbeviewedasalosscoefficie
15、ntperunitlengthalongtheflowdirection,therebyallowingthepressuredroptobespecifiedasafunctionofdynamichead.Ifyouaremodelingaperforatedplateortubebank,youcansometimeseliminatethepermeabilitytermandusetheinertiallosstermalone,yieldingthefollowingsimplifiedformoftheporousmediaequation:(7.19-6)orwhenwritt
16、enintermsofthepressuredropinthe,directions:陽31若兔噸碼Ml韜ai(7.19-7)呵嗎I創(chuàng)ATIjtAgain,thethicknessofthemedium(,or)isthethicknessyouhavedefinedinyourmodel.7.19.3TreatmentoftheEnergyEquationinPorousMediaFLUENTsolvesthestandardenergytransportequation(7.198)(Equation13.2-1)inporousmediaregionswithmodificationst
17、otheconductionfluxandthetransienttermsonly.Intheporousmedium,theconductionfluxusesaneffectiveconductivityandthetransienttermincludesthethermalinertiaofthesolidregiononthemedium:魯仙P冋十卩加風(fēng))何用十p)三VcffVT-wheretotalfluidenergytotalfluidenergy77totalsolidmediumenergyporosityofthemediumtotalfluidenergytotal
18、fluidenergy77sfeffectivethermalconductivityofthemediumfluidenthalpysourcetermEffectiveConductivityinthePorousMediumTheeffectivethermalconductivityintheporousmedium,iscomputedbyFLUENTasthevolumeaverageofthefluidconductivityandthesolidconductivity:Ai-J-:A(7.19-9)whereporosityofthemediumcontribution,fl
19、uidphasethermalconductivity(includingtheturbulent払)=solidmediumthermalconductivityThefluidthermalconductivityandthesolidthermalconductivitycanbecomputedviauser-definedfunctions.Theanisotropiceffectivethermalconductivitycanalsobespecifiedviauser-definedfunctions.Inthiscase,theisotropiccontributionsyk
20、ffromthefluid,areaddedtothediagonalelementsofthesolidanisotropicthermalconductivitymatrix.TreatmentofTurbulenceinPorousMediaFLUENTwill,bydefault,solvethestandardconservationequationsforturbulencequantitiesintheporousmedium.Inthisdefaultapproach,turbulenceinthemediumistreatedasthoughthesolidmediumhas
21、noeffectontheturbulencegenerationordissipationrates.Thisassumptionmaybereasonableifthemediumspermeabilityisquitelargeandthegeometricscaleofthemediumdoesnotinteractwiththescaleoftheturbulenteddies.Inotherinstances,however,youmaywanttosuppresstheeffectofturbulenceinthemedium.Ifyouareusingoneoftheturbu
22、lencemodels(withtheexceptionoftheLargeEddySimulation(LES)model),youcansuppresstheeffectofturbulenceinaporousregionbysettingtheturbulentcontributiontoviscosity,equaltozero.Whenyouchoosethisoption,FLUENTwilltransporttheinletturbulencequantitiesthroughthemedium,buttheireffectonthefluidmixingandmomentum
23、willbeignored.Inaddition,thegenerationofturbulencewillbesettozerointhemedium.ThismodelingstrategyisenabledbyturningontheLaminarZoneoptionintheFluidpanel.Enablingthisoptionimpliesthatiszeroandthatgenerationofturbulencewillbezerointhisporouszone.Disablingtheoption(thedefault)impliesthatturbulencewillb
24、ecomputedintheporousregionjustasinthebulkfluidflow.RefertoSection7.17.1fordetailsaboutusingtheLaminarZoneoption.EffectofPorosityonTransientScalarEquationsFortransientporousmediacalculations,theeffectofporosityonthetime-derivativetermsisaccountedforinallscalartransportequationsandthecontinuityequatio
25、n.Whentheeffectofporosityistakenintoaccount,thetime-derivativetermbecomes,whereisthescalarquantity(,etc.)andistheporosity.Theeffectofporosityisenabledautomaticallyfortransientcalculations,andtheporosityissetto1bydefault.UserInputsforPorousMediaWhenyouaremodelingaporousregion,theonlyadditionalinputsf
26、ortheproblemsetupareasfollows.Optionalinputsareindicatedassuch.Definetheporouszone.Definetheporousvelocityformulation.(optional)Identifythefluidmaterialflowingthroughtheporousmedium.Enablereactionsfortheporouszone,ifappropriate,andselectthereactionmechanism.EnabletheRelativeVelocityResistanceFormula
27、tion.Bydefault,thisoptionisalreadyenabledandtakesthemovingporousmediaintoconsideration(asdescribedinSection7.19.6).Settheviscousresistancecoefficients(inEquation7.19-1,orinEquation7.19-2)andtheinertialresistancecoefficients(inEquation7.19-1,orinEquation7.19-2),anddefinethedirectionvectorsforwhichthe
28、yapply.Alternatively,specifythecoefficientsforthepower-lawmodel.Specifytheporosityoftheporousmedium.Selectthematerialcontainedintheporousmedium(requiredonlyformodelsthatincludeheattransfer).Notethatthespecificheatcapacity,fortheselectedmaterialintheporouszonecanonlybeenteredasaconstantvalue.Setthevo
29、lumetricheatgenerationrateinthesolidportionoftheporousmedium(oranyothersources,suchasmassormomentum).(optional)Setanyfixedvaluesforsolutionvariablesinthefluidregion(optional).Suppresstheturbulentviscosityintheporousregion,ifappropriate.Specifytherotationaxisand/orzonemotion,ifrelevant.Methodsfordete
30、rminingtheresistancecoefficientsand/orpermeabilityarepresentedbelow.Ifyouchoosetousethepower-lawapproximationoftheporous-media-momentumsourceterm,youwillenterthecoefficientsandinEquation7.19-3insteadoftheresistancecoefficientsandflowdirection.YouwillsetallparametersfortheporousmediumintheFluidpanel(
31、Figure7.19.1),whichisopenedfromtheBoundaryConditionspanel(asdescribedinSection7.1.4).Figure7.19.1:TheFluidPanelforaPorousZoneDefiningthePorousZoneAsmentionedinSection7.1,aporouszoneismodeledasaspecialtypeoffluidzone.Toindicatethatthefluidzoneisaporousregion,enablethePorousZoneoptionintheFluidpanel.T
32、hepanelwillexpandtoshowtheporousmediainputs(asshowninFigure7.19.1).DefiningthePorousVelocityFormulationTheSolverpanelcontainsaPorousFormulationregionwhereyoucaninstructFLUENTtouseeitherasuperficialorphysicalvelocityintheporousmediumsimulation.Bydefault,thevelocityissettoSuperficialVelocity.Fordetail
33、saboutusingthePhysicalVelocityformulation,seeSection7.19.7.DefiningtheFluidPassingThroughthePorousMediumTodefinethefluidthatpassesthroughtheporousmedium,selecttheappropriatefluidintheMaterialNamedrop-downlistintheFluidpanel.Ifyouwanttocheckormodifythepropertiesoftheselectedmaterial,youcanclickEdit.t
34、oopentheMaterialpanel;thispanelcontainsjustthepropertiesoftheselectedmaterial,notthefullcontentsofthestandardMaterialspanel.Ifyouaremodelingspeciestransportormultiphaseflow,theMaterialNamelistwillnotappearintheFluidpanel.Forspeciescalculations,themixturematerialforallfluid/porouszoneswillbethemateri
35、alyouspecifiedintheSpeciesModelpanel.Formultiphaseflows,thematerialsarespecifiedwhenyoudefinethephases,asdescribedinSection23.10.3.EnablingReactionsinaPorousZoneIfyouaremodelingspeciestransportwithreactions,youcanenablereactionsinaporouszonebyturningontheReactionoptionintheFluidpanelandselectingamec
36、hanismintheReactionMechanismdrop-downlist.Ifyourmechanismcontainswallsurfacereactions,youwillalsoneedtospecifyavaluefortheSurface-to-VolumeRatio.ThisvalueisthesurfaceAyareaoftheporewallsperunitvolume(),andcanbethoughtofasameasureofcatalystloading.Withthisvalue,FLUENTcancalculatethetotalsurfaceareaon
37、whichthereactiontakesplaceineachcellbymultiplyingbythevolumeofthecell.SeeSection14.1.4fordetailsaboutdefiningreactionmechanisms.SeeSection14.2fordetailsaboutwallsurfacereactions.IncludingtheRelativeVelocityResistanceFormulationPriortoFLUENT6.3,caseswithmovingreferenceframesusedtheabsolutevelocitiesi
38、nthesourcecalculationsforinertialandviscousresistance.Thisapproachhasbeenenhancedsothatrelativevelocitiesareusedfortheporoussourcecalculations(Section7.19.2).UsingtheRelativeVelocityResistanceFormulationoption(turnedonbydefault)allowsyoutobetterpredictthesourcetermsforcasesinvolvingmovingmeshesormov
39、ingreferenceframes(MRF).Thisoptionworkswellincaseswithnon-movingandmovingporousmedia.NotethatFLUENTwillusetheappropriatevelocities(relativeorabsolute),dependingonyourcasesetup.DefiningtheViscousandInertialResistanceCoefficientsTheviscousandinertialresistancecoefficientsarebothdefinedinthesamemanner.
40、ThebasicapproachfordefiningthecoefficientsusingaCartesiancoordinatesystemistodefineonedirectionvectorin2Dortwodirectionvectorsin3D,andthenspecifytheviscousand/orinertialresistancecoefficientsineachdirection.In2D,theseconddirection,whichisnotexplicitlydefined,isnormaltotheplanedefinedbythespecifieddi
41、rectionvectorandthe一directionvector.In3D,thethirddirectionisnormaltotheplanedefinedbythetwospecifieddirectionvectors.Fora3Dproblem,theseconddirectionmustbenormaltothefirst.Ifyoufailtospecifytwonormaldirections,thesolverwillensurethattheyarenormalbyignoringanycomponentoftheseconddirectionthatisinthef
42、irstdirection.Youshouldthereforebecertainthatthefirstdirectioniscorrectlyspecified.Youcanalsodefinetheviscousand/orinertialresistancecoefficientsineachdirectionusingauser-definedfunction(UDF).Theuser-definedoptionsbecomeavailableinthecorrespondingdrop-downlistwhentheUDFhasbeencreatedandloadedintoFLU
43、ENT.NotethatthecoefficientsdefinedintheUDFmustutilizetheDEFINE_PROFILEmacro.Formoreinformationoncreatingandusinguser-definedfunction,seetheseparateUDFManual.Ifyouaremodelingaxisymmetricswirlingflows,youcanspecifyanadditionaldirectioncomponentfortheviscousand/orinertialresistancecoefficients.Thisdire
44、ctioncomponentisalwaystangentialtotheothertwospecifieddirections.Thisoptionisavailableforbothdensity-basedandpressure-basedsolvers.In3D,itisalsopossibletodefinethecoefficientsusingaconical(orcylindrical)coordinatesystem,asdescribedbelow.Notethattheviscousandinertialresistancecoefficientsaregenerally
45、basedonthesuperficialvelocityofthefluidintheporousmedia.Theprocedurefordefiningresistancecoefficientsisasfollows:1.Definethedirectionvectors.TouseaCartesiancoordinatesystem,simplyspecifytheDirection-1Vectorand,for3D,theDirection-2Vector.Theunspecifieddirectionwillbedeterminedasdescribedabove.Thesedi
46、rectionvectorscorrespondtotheprincipleaxesoftheporousmedia.Forsomeproblemsinwhichtheprincipalaxesoftheporousmediumarenotalignedwiththecoordinateaxesofthedomain,youmaynotknowapriorithedirectionvectorsoftheporousmedium.Insuchcases,theplanetoolin3D(orthelinetoolin2D)canhelpyoutodeterminethesedirectionv
47、ectors.Snaptheplanetool(orthelinetool)ontotheboundaryoftheporousregion.(FollowtheinstructionsinSection27.6.1or27.5.1forinitializingthetooltoapositiononanexistingsurface.)Rotatetheaxesofthetoolappropriatelyuntiltheyarealignedwiththeporousmedium.Oncetheaxesarealigned,clickontheUpdateFromPlaneToolorUpd
48、ateFromLineToolbuttonintheFluidpanel.FLUENTwillautomaticallysettheDirection-1Vectortothedirectionoftheredarrowofthetool,and(in3D)theDirection-2Vectortothedirectionofthegreenarrow.Touseaconicalcoordinatesystem(e.g.,foranannular,conicalfilterelement),followthestepsbelow.Thisoptionisavailableonlyin3Dca
49、ses.TurnontheConicaloption.(b)SpecifytheConeAxisVectorandPointonConeAxis.TheconeaxisisspecifiedasbeinginthedirectionoftheConeAxisVector(unitvector),andpassingthroughthePointonConeAxis.Theconeaxismayormaynotpassthroughtheoriginofthecoordinatesystem.(c)SettheConeHalfAngle(theanglebetweentheconesaxisan
50、ditssurface,showninFigure7.19.2).Touseacylindricalcoordinatesystem,settheConeHalfAngleto0.Forsomeproblemsinwhichtheaxisoftheconicalfilterelementisnotalignedwiththecoordinateaxesofthedomain,youmaynotknowapriorithedirectionvectoroftheconeaxisandcoordinatesofapointontheconeaxis.Insuchcases,theplanetool
51、canhelpyoutodeterminetheconeaxisvectorandpointcoordinates.Onemethodisasfollows:(a)Selectaboundaryzoneoftheconicalfilterelementthatisnormaltotheconeaxisvectorinthedrop-downlistnexttotheSnaptoZonebutton.ClickontheSnaptoZonebutton.FLUENTwillautomaticallysnaptheplanetoolontotheboundary.ItwillalsosettheC
52、oneAxisVectorandthePointonConeAxis.(NotethatyouwillstillhavetosettheConeHalfAngleyourself.)Analternatemethodisasfollows:(a)Snaptheplanetoolontotheboundaryoftheporousregion.(FollowtheinstructionsinSection27.6.1forinitializingthetooltoapositiononanexistingsurface.)(b)Rotateandtranslatetheaxesofthetool
53、appropriatelyuntiltheredarrowofthetoolispointinginthedirectionoftheconeaxisvectorandtheoriginofthetoolisontheconeaxis.Oncetheaxesandoriginofthetoolarealigned,clickontheUpdateFromPlaneToolbuttonintheFluidpanel.FLUENTwillautomaticallysettheConeAxisVectorandthePointonConeAxis.(Notethatyouwillstillhavet
54、osettheConeHalfAngleyourself.)2.UnderViscousResistance,specifytheviscousresistancelidcoefficientineachdirection.UnderInertialResistance,specifytheinertialresistancecoefficient_ineachdirection.(Youwillneedtoscrolldownwiththescrollbartoviewtheseinputs.)Forporousmediacasescontaininghighlyanisotropicine
55、rtialresistances,enableAlternativeFormulationunderInertialResistance.TheAlternativeFormulationoptionprovidesbetterstabilitytothecalculationwhenyourporousmediumisanisotropic.Thepressurelossthroughthemediumdependsonthemagnitudeofthevelocityvectoroftheithcomponentinthemedium.UsingtheformulationofEquati
56、on7.19-6yieldstheexpressionbelow:s.-77.1r.(7.19T0)WhetherornotyouusetheAlternativeFormulationoptiondependsonhowwellyoucanfityourexperimentallydeterminedpressuredropdatatotheFLUENTmodel.Forexample,iftheflowthroughthemediumisalignedwiththegridinyourFLUENTmodel,thenitwillnotmakeadifferencewhetherornoty
57、ouusetheformulation.Formoreinfomationaboutsimulationsinvolvinghighlyanisotropicporousmedia,seeSection7.19.8.Notethatthealternativeformulationiscompatibleonlywiththepressure-basedsolver.IfyouareusingtheConicalspecificationmethod,Direction-1istheconeaxisdirection,Direction-2isthenormaltotheconesurface
58、(radial(嚴(yán))directionforacylinder),andDirection-3isthecircumferential()direction.In3Dtherearethreepossiblecategoriesofcoefficients,andin2Dtherearetwo:Intheisotropiccase,theresistancecoefficientsinalldirectionsarethesame(e.g.,asponge).Foranisotropiccase,youmustexplicitlysettheresistancecoefficientsinea
59、chdirectiontothesamevalue.When(in3D)thecoefficientsintwodirectionsarethesameandthoseinthethirddirectionaredifferentor(in2D)thecoefficientsinthetwodirectionsaredifferent,youmustbecarefultospecifythecoefficientsproperlyforeachdirection.Forexample,ifyouhadaporousregionconsistingofcylindricalstrawswiths
60、mallholesinthempositionedparalleltotheflowdirection,theflowwouldpasseasilythroughthestraws,buttheflowintheothertwodirections(throughthesmallholes)wouldbeverylittle.Ifyouhadaplaneofflatplatesperpendiculartotheflowdirection,theflowwouldnotpassthroughthematall;itwouldinsteadmoveintheothertwodirections.
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