论多孔介质中流体流动问题的数值模拟方法

:2000205217::(1975-),(),,,:100025870(2000)0520111206,,(,100084):,,:;;;;:O357.3:A,(),1856Darcy,[1],1,,(REV)REV,REV;,1REV,1Vm,VfVm,Darcy’V,’Vf,(intrinsicav2eragevelocity)ˆvDupuitForchheimer:’V=ˆv,(1),,,Darcy’V2,,,200024()Vol.24No.55JournaloftheUniversityofPetroleum,ChinaOct.2000,,REV,,,:5(f)5t+¨(f’V)=0.(2),fDarcy:V=-k5p5x,(3),V;;k(,k,,k),Darcy,,,k,Darcy,2050,,,Darcy(1)DarcyN2S,Wood2ing[2]:f-15’V5t+-2(’V¨)’V=-¨p-k’V.(4)Nield[3],,(’V¨)’V,[4],,,k/t0(t0)(2)Darcy2Forchheimer1901,Forch2heimer,(Rep1),Darcy,,¨p=-k’V-cFk-1/2f|’V|’V.(5),cF(5)Darcy2ForchheimerPascalJ.PascalH.[5,6],,,Darcy.,,,,|’V|’V,,,Darcy-ForchheimerLage[7],(Rep100),cF,3(3)Brinkman1947,BrinkmanDarcy:¨p=-k’V+‰¨2’V.(6)(6)Brinkman‰¨2’VN2SLaplacianBrinkman,(0.7)BrinkmanSomerton[811],,‰=(4)Binkman2ForchheimerVaifai[12,13]N2SREV,,Brinkman2Forchheimer:f-15’V5t+-1¨’V’V=-1¨(p)+f¨2’V-k’V-1kcFf|’V|’V.(7),‰=/(f),(7)(4)(5)(6),BrinkmanForchheimerDarcy,(5)Klinkenberg1941,Klinkenberg211()200010Klinkenberg,,,:kg=k1+bp.(8)k,KlinkenbergReda[14,15],,Klinkenberg,,,Wu[16]Klinkenberg,,,,,(2),,,,,(),,keff[11]3,50010,1.5[17],,PatankarSpalding[18],,Sha[19],Karayannis[20,21],[22],PrithivirajAn2drews[17](),,22V,Vf,A,Affv,fs(fs=Af/A),Vf=VfvdV,Af=AfsdA.(9)Vf55t()dV+Af’VˆndA=AfˆnFsdA+VfFbdV.(10),Fs,Fb,’V(9)(10)V55t()fvdV+A’VˆnfsdA=-AˆnFsfsdA+VFbfvdV.(11)(11)1,,:55t(fv)+¨(fs’V-fs¨)=fvS.(12),S(12),,(12)N-S,311245:42080,BaerNunziato[23],(),,REV,(),(),(),[2430],5:,(3),3,,,(1)DarcyForchheimerBeaversJoseph[31]N2S:d2udy2=dpdx;Darcy:-k^u=d^pdxDarcy(,4(a)),Beavers,(4(b)),4,u-^u=kdudy|y=0.(13),,Beavers,(2)BrinkmanBrinkman2Forchheimer,[32],Brinkman(6)DarcyBrinkman4NealeN2SBrinkman,Beavers:411()200010u=^u,dudy=^d^udy,limy-^u=-kd^pdx.(14)[3335],Vafai[36]Al2Nimr[37]Alkam[11],Brinkman2Forchheimer(14)Salinger[38],DarcyBrinkman,,Beckermann[39,40],Brinkman2Forchheimer,BrinkmannForchheimerDarcy,,N2S,Brinkman2Forchheimer,,,Poulikakos[9]Beckermann,Beckermann,6,,:[1]NieldDA,BejanA.ConvectioninPorousMedia[M].NewYork:Springer2VelagInc,1999.[2]WoodingRA.Steadystatefreethermalconvectionofliquidinasaturatedpermeablemedium[J].J.FluidMech,1957,(2):273-285.[3]NieldDA.Modelinghigh2speedflowofacompressiblefluidinasaturatedporousmedium[J].TransportinPorousMedia,1994,14:85-88.[4]NieldDA.Effectsoflocalthermalnonequilibriuminsteadyconvectiveprocessesinasaturatedporousmedi2um:forcedconvectioninachannel[J].J.PorousMedi2a,1998,(1):181-186.[5]PascalJP,PascalH.Pressurediffusioninunsteadynon2Darcianflowsthroughporousmedia[J].EurJMech,B/Fluids,1995,14(1):75-90.[6]PascalJP,PascalH.Non2lineareffectsonsomeun2steadynon2Darcianflowsthroughporousmedia[J].IntJNon2LinearMechanics,1997,32(2):361-376.[7]LageJL,AntoheBV,NieldDA.Twotypesofnonlin2earpressuredropversusflow2raterelationobservedforsat2uratedporousmedia[J].ASMEJ.FluidsEngng,1997,119:701-706.[8]SomertonCW,Catton.Onthethermalinstabilityofsu2perposefluidandporouslayers[J].J.HeatTransfer,1989,111:357-362.[9]PoulikakosD.Forcedconvectioninfaductpartiallyfilledwithaporousmaterial[J].ASMEJournalofHeatTrans2fer,1987,109:653-662.[10]NishimuraT,TakumiT,ShiraishiM,KawamuraYandOzoeH.Numericalanalysisofnaturalconvectioninarectangularenclosurehorizontallydividedintofluidandporousregions[J].Int.J.HeatMassTransfer,1986,29:889-898.[11]AlkamMK,Al2NimrMA.Transientnon2Darcianforcedconvectionflowinapipepartiallyfilledwithaporousmaterial[J].Int.J.HeatMassTransfer,1998,41(2):347-356.[12]VafaiK,TienCL.Boundaryandinertiaeffectsonflowandheattransferinporousmedia[J].Int.J.HeatTransfer,1981,(24):195-203.[13]HsuCT,ChengP.Thermaldispersioninaporousmedium[J].Int.J.HeatMassTransfer,1990,33:1587-1597.[14]RedaDC.Slipflowexperimentsinweldedtuff:theknudsondiffusionproblem[A].Chin2FuTsang.Cou2pledprocessesAssociatedwithNuclearWasteReposito2ries[C],1987,485-493.[15]PersoffP,HulenJB.HydrologicCharacterizationoffourcoresfromthegeyserscoringproject[J].Proc511245:Twenty2FirstWorkshoponGeothremalEngineering,StanfordUniversity,CA,January22-24,1996.[16]Yu2ShuWu,PruessK,PersoffP.GasflowinporousmediawithKlinkenbergeffects[J].TransportinPorousMedia,1998,32:117-137.[17]PrithivirajM,AndrewsMJ.Threedimensionalnumer2icalsimulationofshell2and2tubeheatexchangers[J].1998,33(8):799-816,817-828.[18]PatankarSV,SpaldingDB.Acalculationprocedureforthetransientandsteadystatebehaviorofshell2and2tubeheatexchangers[A].AfganNF,SchlunderEV.Heatexchangers:DesignandThearySourceBook[C].New2York:McGraw2Hill,1974.155-176.[19]ShaWT,YangCI,KaoTT,ChoSM.Multidimen2sionalnumericalmodelingofheatexchangers[J].J.HeatTransfer,1982,104:417-425.[20]KarayannisN,MarkatosNCG.Mathematicalmodel2ingofheatexchangers[A].BerrymanRJ.ProceedingsoftheTenthInternationalHeatTransferConference[C],Brighton,UK,TheIndustrialSessionsPapers,13-18,1994.[21]HuangLY,WenJX,KaraynannisTG,MathewsRD.CFDmodelingoffluidflowandheattransferinashell2and2tubeheatexchanger[J].PhoenicsJ.CFDAp2pl,1996,9(2):189-209.[22].[D].,1995.[23]BaerMR,NunziatoJW.ATwo2phasemixturetheoryforthedeflagrationtodetonationtransition(DDT)inre2activegranularmaterialsm[J].IntJMultiphaseFlow,1986,(12):861-889.[