AccordingtoPatankar,the outletboundary of thesudden expansion case must be positioned at the locationwithout recirculation ("Good" position). It should notbe positioned at the “Bad" location, otherwise the resultsare meaningless.This suggestion not only needs more computermemory but is also not possible for some situations.Openflow systemGooGoodBadBad6/35
6/35 According to Patankar，the outlet boundary of the sudden expansion case must be positioned at the location without recirculation (“Good” position）. It should not be positioned at the “Bad” location, otherwise the results are meaningless. Open flow system Bad Good This suggestion not only needs more computer memory but is also not possible for some situations
If theneglectofthediffusion at anoutflowboundaryappears,forsomcreason,to be serious,then we should conclude that the analyst has placedAparticular badthe outflow boundary at an inappropriate location,A repositioning of theboundary would normally make the outflow treatment acceptable,A partic-choice of anularly bad choice of an outflow-boundary location is the one in which thcre is an"inflow"overapartof it.Anexampleof this is shown inFig.5.12.Forsu-bad choice of the boundary,no meaningful solution can be obtained.outflow-boundaryThis may be a convenient place to review the boundary-conditionpractices for convection-diffusion problems.Wheneverthereis no fluid flowlocation is the oneacross the boundary of the calculation domain,theboundary flux is purelyadiffusion flux,and thepractices described in Chapter 4 apply.For those partsin which there is anof the boundary where the fluid flows into the domain, usually the values ofareknown.(Theproblemisnotproperlyspecifiedif wedonotknowthevalue of that a fluid stream brings with it.)The parts of the boundary"inflow"over awhere the fluid leaves the calculation domain form the outflow boundary,which we havealready discussed.part of it. ... Forsuch a bad choiceof the boundary, nomeaningfulsolution can beobtained.(1980)BadGoodFigure 5.12 Good and bad choices of the location of the outflow boundary.7/35
7/35 A particular bad choice of an outflow-boundary location is the one in which there is an “inflow” over a part of it. . For such a bad choice of the boundary, no meaningful solution can be obtained .(1980)
出口边界Cooling of plate TV screen8/35
8/35 Cooling of plate TV screen
2. Suggestion(1) Outlet normal velocity---treated according to localmassconservation(2) Outlet parallel velocity---treated by homogeneousNeumanncondition（齐次诺曼条件，一阶导数为零）Total mass conservationUu,T.Local massLi.M1conservation个出口边界M1VVM2UUi+1.M212.MLi,M29/35
9/35 (1) Outlet normal velocity-treated according to local mass conservation 2. Suggestion (2) Outlet parallel velocity-treated by homogeneous Neumann condition (齐次诺曼条件,一阶导数 为零) Total mass conservation Local mass conservation
VUi+1,M2 -Ui,M2 = 0 -Vi,M1 -Vi,M2i,M1Ui.MIAxAyAyAylu1Vi,M1i+1,M2i.M2+1.M2iMAxThe resulted Vi,M1 has to bei,M2Axcorrected by total mass conservationcondition.auU.m=UiM2=0Tangential velocityd6.7.4 Methods for outlet normal velocity to satisfytotalmassconservation1. Two situations1) Outlet without recirculation(1) Relative changes of outlet normal velocity =constant10/35
10/35 , 1 , 2 1, 2 , 2 0 i M i M i M i M v v u u y x − − + + = * * * , 1 , 2 1, 2 , 2 ( ) i M i M i M i M y v v u u x + = + − The resulted has to be corrected by total mass conservation condition. i M, 1 v 6.7.4 Methods for outlet normal velocity to satisfy total mass conservation 1. Two situations 1) Outlet without recirculation (1) Relative changes of outlet normal velocity =constant Vi M, 1 , 1 ) 0 i M U y = Tangential velocity * U U i M i M , 1 , 2 = Ui M, 1 x y