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外文翻译--干燥过程中多尺度方面的传热传质 英文版.pdf

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外文翻译--干燥过程中多尺度方面的传热传质 英文版.pdf

TranspPorousMed20076659–76DOI10.1007/s1124200690222ORIGINALPAPERMultiscaleaspectsofheatandmasstransferduringdryingPatrickPerréReceived30November2005/Accepted26March2006/Publishedonline30August2006©SpringerScienceBusinessMediaB.V.2006AbstractThemacroscopicformulationofcoupledheatandmasstransferhasbeenwidelyusedduringthepasttwodecadestomodelandsimulatethedryingofonesinglepieceofproduct,includingthecaseofinternalvaporization.However,moreoftenthanexpected,themacroscopicapproachfailsandseveralscaleshavetobeconsideredatthesametime.Thispaperisdevotedtomultiscaleapproachestotransferinporousmedia,withparticularattentiontodrying.Thechangeofscale,namelyhomogenization,ispresentedfirstandusedasagenericapproachabletosupplyparametervaluestothemacroscopicformulation.Theneedforarealmultiscaleapproachisthenexemplifiedbysomeexperimentalobservations.Suchanapproachisrequiredassoonasthermodynamicequilibriumisnotensuredatthemicroscopicscale.Astepwisepresentationisproposedtoformulatesuchsituations.KeywordsChangeofscaleComputationalmodelDryingDualscaleHomogenizationPorousmediaWood1IntroductionThispaperfocusesonmultiscalemodelingofcoupledtransferinporousmedia.Nowadays,thecomprehensivesetofequationsgoverningthesephenomenaatthemacroscopicleveliswellknownandhasbeenwidelyusedtosimulateseveralconfigurations,particularlythedryingprocess.However,thismacroscopicdescriptionhassomedrawbacksitgeneratesadramaticdemandinphysicalandmechanicalcharacterizationandfailsinsome,notespeciallyunusualconfigurations.Thesedrawbacksareprobablythemainmotivationformultiscaleapproaches.Differentstrategies,hencepossibilities,canbeapplied.Inthecaseoftimescaleseparation,thecouplingbetweenscalesP.PerréBLERMABIntegratedWoodResearchUnit,UMR1093INRA/ENGREF/UniversityH.PoincaréNancyI,ENGREF,14,rueGirardet,54042Nancy,Franceemailperrenancyengref.inra.fr60PatrickPerréissequentialthemultiscaleapproachreducestoachangeofscale.Whenthetimescalesoverlap,aconcurrentcouplinghastobetreatedthisisarealmultiscaleconfiguration,moredemandingincomputationalresourcesandinappliedmathematics.ThefollowingcontentisproposedinthispaperSequentialcouplingTechniquesareavailablethatallowmacroscopicpropertiestobecomputedusingthepropertiesandmorphologyofthesocalledunitcell.Homogenizationisapartofthesetechniquesandcanbeappliedsuccessfullyonactualporousmediasuchaswood,fibrousmaterials,solidfoams,etc.,providedtherealmorphologyistakenintoaccount.Examplesofmechanicalpropertiesofoak,includingshrinkage,willbeconsidered.Finally,ithastobenotedthathomogenizationassumesthatbothscalesareindependent,whichallowsthesolutiontobecomputedonlyonceandsubsequentlyusedinthemacroscopicsetofequations.ConcurrentcouplingThepreviousassumptionoftenfailsinreallifesituations.Insuchcases,thescalelevelcannotbeconsideredasindependentandamultiscaleapproachbecomesnecessary.Someformulationsarepresentedheretoexplainhowseveralscalescanbeconsideredsimultaneously,fromasimplecouplingbetweenmicroscopicphasestoacomprehensiveformulationinwhichthetimeevolutionsofthemacroscopicvaluesandmacroscopicgradientsareconsideredovertheRepresentativeElementaryVolume.Suchstrategiesaremuchmoredemandingintermsofdevelopmentandcomputationaltime.Someconfigurationshavealreadybeencomputedandareusedheretopicturetheequations.However,thereadershouldbeawarethatthisisanewandopenfield,especiallyinthedomainofcoupledheatandmasstransfer,whichisthesubjectofongoingresearchwork.Inthefollowing,themacroscopicscalealwaysreferstothescaleweareinterestedin,whereasallsmallerscalesarereferredtoasmicroscopicscales.Thisindicationisthereforeindependentoftherealsizeofthesescales.Forexample,whenpredictingshrinkageofawoodtissue,themacroscaleisthecellulararrangementtypicallysomehundredsofmicrometersandthemicroscalesarethecellwalltypicallysomemicrometersandthescaleofthemacromoleculessometensofnanometers.Attheoppositeend,whendealingwithastackapproach,themacroscaleisthestacksizesomemetersandthemicroscaleistheboardsectionsomecentimeters.2MacroscopicformulationSeveralsetsofmacroscopicequationsareproposedintheliteratureforthesimulationofthedryingprocess.However,thispartwilljustfocusonthemostcomprehensivesetofequationsusedatthemacroscopiclevel,whichdescribesthesystemusingthreeindependentstatevariables.Atpresent,researchersusingathreevariablemodelagreewiththeformulationtobeused.Thesetofequations,asproposedbelow,originatesforthemostpartfromWhitakers1977workwithminorchangesrequiredtoaccountforboundwaterdiffusionanddryingwithinternaloverpressurePerréandDegiovanni1990.Inparticular,thereadermustbeawarethatallvariablesareaveragedovertheREVRepresentativeElementaryVolumeSlattery1967,hencetheexpressionmacroscopic.Thisassumestheexistenceofsucharepresentativevolume,largeenoughfortheaveragedquantitiestobedefinedandsmallenoughtoavoidvariationsduetomacroscopicgradientsandnonequilibriumconfigurationsatthemicroscopiclevel.Multiscaleaspectsofheatandmasstransferduringdrying61Waterconservation∂∂tparenleftbigεwρwεgρvρbparenrightbig∇parenleftbigρw¯vwρv¯vgρbvbparenrightbig∇parenleftBigρgDeff∇ωvparenrightBig.1AirConservation∂∂tparenleftbigεgρaparenrightbig∇parenleftbigρa¯vgparenrightbig∇parenleftBigρgDeff∇ωaparenrightBig.2Energyconservation∂∂tparenleftBigεwρwhwεgρvhvρahaρbhbρohs−εgPgparenrightBig∇parenleftbigρwhwvwρvhvρahavghbρbvbparenrightbig∇parenleftBigρgDeffhv∇ωvha∇ωaλeff∇TparenrightBigPhi1,3wherethegasandliquidphasevelocitiesaregivenbytheGeneralisedDarcyLawvlscript−Klscriptklscriptµlscript∇ϕlscript,∇ϕlscript∇Plscript−ρlscriptg∇χ,wherelscriptw,g.4Thequantitiesϕareknownasthephasepotentialsandχisthedepthscalar.Allothersymbolshavetheirusualmeaning.BoundaryconditionsFortheexternaldryingsurfacesofthesample,theboundaryconditionsareassumedtobeofthefollowingformJw|x0ˆnhmcMvlnparenleftbigg1−xv∞1−xv|x0parenrightbigg,Pgvextendsinglevextendsinglex0Patm,Je|x0ˆnhT|x0−T∞,5whereJwandJerepresentthefluxesoftotalmoistureandtotalenthalpyattheboundary,respectively,xdenotesthepositionfromtheboundaryalongtheexternalunitnormalandxvthemolarfractionofvapor.Inalltheseequations,subscripteffdenotestheeffectivepropertythathastobedeterminedexperimentallyorbyusingapredictivescalingapproachseethenextsection.Theaveragedvalueofvariableϕ,indicatedbyabar,isdefinedas¯ϕ1VREVintegraldisplayREVϕdV.6AmoredetaileddescriptionoftheseequationsandrelatedassumptionscanbefoundelsewherePerré1996,1999.SincethisformulationtakescareoftheinternalpressurethroughtheairbalanceEq.2,thesetofequationsprovedtobeverypowerfulandabletodealwithnumerousconfigurationsinvolvingintensetransfershightemperatureconvectivedrying,vacuumdrying,RF/vacuumdrying,IR/vacuumdrying,etc.Forexample,thesimulationofconvectivedryingathightemperature,withsuperheatedsteamormoistair,canbepredictedwithgoodaccuracywhendryinglightconcretePerréetal.1993.Themostimportantmechanismsandtrendsarealsowellpredictedinthecaseofwood,inspiteofitsstronganisotropyanditsbiological62PatrickPerré00.10.20.30.4Pressure05101520Widthcm024Thickness505254565860Temperature05101520Widthcm024Thickness051015Power05101520Widthcm0001234Thickness0.51Moisturecontent05101520Widthcm24ThicknessDryingtime20hoursFig.1ExampleofdryingsimulationcomprehensivemodelingofconvectivedryingwithRadioFrequencyheatingPerréandBucki2004variability.Amongthespecificbehaviorsofwood,theinternalgaseouspressuregeneratedbyinternalvaporizationisabletodrivemoistureinthelongitudinaldirection.ThiseffectiseasilyobservedandprovedexperimentallybytheendpiecetemperatureandwassimulatedbyusingthissetofequationsinthedryingmodelPerréetal.1993Perré1996.Asanotherexampleofintricatephysicalmechanisms,Fig.1depictsthevariablefieldsvolumetricpower,temperature,moisturecontent,andinternalpressureobtainedafter20hoursofconvectivedryingofanoaksectionwithradiofrequencyheating.Inthiscase,thepowerfieldiscomputedbysolvingMaxwellsequations.Thisfielddependsonthedielectricpropertiesofwood,henceonthetemperatureandmoisturecontentfields.Similarly,thetemperatureandmoisturecontentfieldsdependonthepowerfield.Tosolvethistwowaycouplingefficiently,requiresatrickycomputationalstrategy.3HomogenizationAlthoughthesetofmacroscopicequationspresentedintheprevioussectionisapowerfulfoundationforcomputationalsimulationofdrying,itrequiresknowledgeofseveralphysicalparameters,mostofthembeingafunctionofbothtemperatureandmoisturecontent.Consequently,supplyingthecomputermodelwithallphysicalcharacterizationsisatedioustask,whichrestrainstheuseofmodeling.Thefirstgoalforamultiscaleapproachistousemodelingtopredictonepartoftheparameters

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