流体最小熵产生原理与最小能耗率原理Ⅰ

20035SHUILIXUEBAO5:20020912:(59979020):(1956-),,,,,:05599350(2003)05003506()徐国宾1,2,练继建1(1.,300072;2.,300222):100,(YangC.T.),,,,;,:;;;;;:TV131:A1(Helmholtz)1868,,,[1]2050,(Be!∀#∃%..),(,),,2070,(YangC.T.)(ChangH.H.)[2][3~5],,[4],,,,,,,,,,,[6],[8~10],,,,,,,[4,7]::35-1(h)xi+1ijxj=vit+vjvixii,j=1,2,3(1):vi;h;;ij,:ij=-ijp+(+)vixj+vjxi(2):p;ij;;,(1)(),(2)(1),:xi(h+p)=xj(+)vixj+vjxi(3):vi/xi=0(4):=12(+)vixj+vjxi2(5)[4]vi(3)(4),(vi+vi)(3),(4)(vi+vi)(5),:(vi+vi)=(vi)+(vi)+(+)vixj+vjxivixj+vjxi(6),:(vi+vi)=(vi)+(vi)(7)vi,,:(vi)=(vi+vi)-(vi)(vi+vi)(8),[7]:=QJ(9):Q;J,:QJ=(10):(1),,,,,,,,(2),[4,7],,,,,,,,,,,,,36,,,,,,(3)(3)(3),,2(PrigogineI.)1945[9,10],,[6,11,12],21,S,dS[8,9],dS/dt=deS/dt+diS/dt(11):deSdt,,,;diS/dt,,P,diSdt,P=diS/dt0(12)22[8,9],,,n,S,SV:SV=SV({j(r,t)})(13):SV,(13),SVt=nj=1SVjjt(14)23n,,nm1,m2,,mj,mnjr,kwk,kjk[8]jt=-divJj+rk=1jkwk(j=1,2,,n)(15):jj;Jjj,24[6],:TdSV=de+pdVm-d(16):SV();T;;Vm,37,Vm=Vm=1(17),,(16)[8]SVj=-jT(18)(18)(14),SVt=-nj=1jTjt(19)(15),SVt=(nj=1jTJj)-nj=1JjjT+rk=1(-nj=1jTjk)wk(20)-divJs=nj=1jTJj,(s=1,2,,n)=-nj=1JjjT+rk=1AkTwk(21)Js,;,;Ak,Ak=-nj=1jkj(21)(20),SVt=-divJs+(22)dSdt=tVSVdV=-VdivJsdV+VdV=-nJsd+VdV(23)(11)(23),deSdt=-nJsd(24)diSdt=VdV(25)[8,12]=mi=1JiXi(26):Ji;Xi(26),[10,12]25dxidt=f(t,{xi})(i=1,2n)(27):1:(27)V(t,{xi}),DVdVdt0,(27);2:V({t,{xi}),DVdVdt0,(27);3:V(t,{xi}),DVdVdt0,(27)V(t,{xi}),,,,,,38,,26,,:Jk=Jk({Xl})JkXl[8],Jk({Xl})=Jk(0)+ml=1JkXl0Xl+12ml=1ms=12JkXlXs0XlXs+(28),,,,Jk=ml=1LklXl(29)Lkl=Jk/Xl0(30)(29),,,()Lkl,,,Lkl=Llk(31)(31)(OnsagerL.),XlJkXkJl27,,(),,,,,P=diSdt0,P,P,dP/dt,[8],dP/dt0(32),(32),,,,,,,,,[8,9],,,,,3,[13~18],,,,,,,()39:[1].[M].:,1982.[2].[J].,1994,(4):50-58.[3].[J]..1992,(1):12-22[4]YangCT,SongCCS.TheoryofMinimumEnergyandEnergyDissipationRate[A].In:EncyclopediaofFluidMechaniss,Vol.1,Chapter11.GulfPublishingCulfPublishingCompany,1986:353-399.[5]SongCCS,YangCT.MinimumEnergyandEnergyDissipationRate[J].JournaloftheHydraulicsDivision.1982,108(HY5):690~706[6].[M].:,1998.[7]YangCT,SongCCS.TheoryofMinimumRateofEnergyDissipation[J].JournaloftheHydraulicsDivision.1979,105(HY7):769-784.[8]NicolisG,PrigogineI.SelfOrganizationinNonEquilibriumSystems[M].NewYork:WileyInterscience.1977(:.,.:.1986.[9],,.[M].:,1982.[10].[M].:,1986.[11].[M].:,1988.[12]S,B,R.[M].,,.:.1988.[13]YangCT,AlbertMolinas.SedimentTransportandUnitStreamPowerFunction[J].JournaloftheHydraulicsDivision,1982,108(HY6):774-793.[14]ChangHH.AnalysisofRiverMeanders[J].JournalofHydraulicEngineering,1984,110(HY1):37-50.[15].[J].,1992,(3):65-69.[16].[J].,1993,(4):65~71.[17].[J].,1993,():567-570.[18].[J].,1996,(7):61-66.Theoriesoftheminimumrateofenergydissipationandtheminimumentropyproductionofflow()XUGuobin1,2,LIANJijian1(1.CollegeofCivilEngineering,TianjinUniversity,Tianjin300072,China;2.TianjinInvestigation,DesignandResearchInstituteofWaterConservancyandHydropowerTianjin300222,China)Abstract:Thetheoryofminimumrateofenergydissipationhasattractedreserchersattentionsinceitwasproposedinthemiddleofthe19thcentury.Itwasnotuntiltheearly1970sthatC.T.Yangandothersmadesignificantprogressinthisdirection.TheauthorsanalyzedC.T.Yangstheoryofminimumrateofenergydissipationandfoundoutsomeimperfection.Anexpressionofminimumrateofenergydissipationofflowwasrederivedbasedonthetheoryofminimumentropyproductionofnonequilibriumthermodynamics.Theresultispresentedintwoparts.Inthefirstpart,thetheoreticalbasiswaspresentedforthemathematicalderivationofminimumrateofenergydissipation.Keywords:riverflows;opensystem;theoryofminimumentropyproduction;theoryofminimumrateofenergydissipation;nonequilibriumthermodynamics40