Numerical HeatTransfer（数值传热学）Chapter6PrimitiveVariableMethodsforEllipticFlowandHeatTransfer (3)1/35
1/35 Numerical Heat Transfer (数值传热学) Chapter 6 Primitive Variable Methods for Elliptic Flow and Heat Transfer（3）
6.1 Source terms in momentum equations and two keyissuesin numerically solvingmomentum equation6.2 Staggered grid system and discretization ofmomentumequation6.3 Pressure correction methods for N-S equation6.4ApproximationsinSIMPLEalgorithm6.5Discussionon SIMPLEalgorithmand criteriaforconvergence6.6DevelopmentsofSIMPLEalgorithm6.7Boundaryconditiontreatmentsforopensystem6.8 Fluid flow & heat transfer in a closed system2/35
2/35 6.1 Source terms in momentum equations and two key issues in numerically solving momentum equation 6.2 Staggered grid system and discretization of momentum equation 6.3 Pressure correction methods for N-S equation 6.4 Approximations in SIMPLE algorithm 6.5 Discussion on SIMPLE algorithm and criteria for convergence 6.6 Developments of SIMPLE algorithm 6.7 Boundary condition treatments for open system 6.8 Fluid flow & heat transfer in a closed system
6.7Boundary conditiontreatmentsforopen system6.7.1Selectionsforoutletboundary6.7.2Treatment of outlet boundaryconditionwithoutrecirculation1. Local one-way2. Fully developed6.7.3Treatment of outletboundary conditionwithrecirculation1. Example with recirculation ; 2. Suggestion6.7.4Methods for outlet normal velocity satisfyingtotalmassconservation1. Two cases;2. Application3/35
3/35 6.7.1 Selections for outlet boundary 6.7.2 Treatment of outlet boundary condition without recirculation 6.7.3 Treatment of outlet boundary condition with recirculation 1. Local one-way 2. Fully developed 1. Two cases； 2. Application 1. Example with recirculation ; 2. Suggestion 6.7 Boundary condition treatments for open system 6.7.4 Methods for outlet normal velocity satisfying total mass conservation
6.7 Boundary condition treatments for open system6.7.1Selectionsforoutlet boundaryposition1. It should be at the location without recirculation (回流)--Suggested by Patankar2 .If it is at the location with recirculation---specialattention should bepaidforboundaryconditiontreatment6.7.2Treatment ofB.C.withoutrecirculationUi,M11. Local one-way assumptionui+1M1Ui,Mi（局部单向化假设）1M2D,M24/35
4/35 6.7 Boundary condition treatments for open system 6.7.1 Selections for outlet boundary position 1. It should be at the location without recirculation (回流)- -Suggested by Patankar 2 .If it is at the location with recirculation-special attention should be paid for boundary condition treatment 6.7.2 Treatment of B.C. without recirculation 1. Local one-way assumption (局部单向化假设) , 2 ( ) 0 N i M a =
adDi,Mi2. Fully developed=0ui+1M1ui,MIM1an(1) Updating (更新)boundary value1M2diM1 - dj,M2 = 0n=ΦDUi,M2i.M2i.M1(8y)b(2) ASTM:adTaking= O as given heat flux conditionanFor both methods, the outlet normal velocity mustsatisfy thetotal mass conservation condition6.7.3Treatment ofoutletboundary condition withrecirculation1.Necessity（必要性）for such selectionRequired fromsomepractical problems5/35
5/35 2. Fully developed , 1 ) 0 i M n = (1) Updating (更新)boundary value , 1 , 2 0 ( ) i M i M B y − = * i M i M , 1 , 2 = (2) ASTM： Taking , 1 ) 0 i M n = as given heat flux condition For both methods，the outlet normal velocity must satisfy the total mass conservation condition. 6.7.3 Treatment of outlet boundary condition with recirculation 1. Necessity (必要性) for such selection Required from some practical problems