热流科学与工程西步文源大学E教育部重点实验室Numerical HeatTransfer（数值传热学）Chapter6PrimitiveVariableMethodsforEllipticFlowandHeatTransfer(3)oInstructorTao,Wen-QuanKeyLaboratoryofThermo-FluidScience&EngineeringInt.JointResearchLaboratoryofThermalScience&EngineeringXi'anJiaotongUniversityInnovativeHarborofWestChina,Xian2022-OCT.-26CFD-NHT-EHTΦ1/34CENTER
1/34 Instructor Tao, Wen-Quan Key Laboratory of Thermo-Fluid Science & Engineering Int. Joint Research Laboratory of Thermal Science & Engineering Xi’an Jiaotong University Innovative Harbor of West China, Xian 2022-OCT.-26 Numerical Heat Transfer (数值传热学) Chapter 6 Primitive Variable Methods for Elliptic Flow and Heat Transfer（3）
热流科学与工程西步文源大堂G教育部重点实验室6.7Boundary condition treatmentsforopen system6.7.1Selectionsforoutletboundary6.7.2Treatment of outlet boundary conditionwithoutrecirculation1. Local one-way2. Fully developed6.7.3 Treatment of outlet boundary condition withrecirculation1. Example with recirculation ; 2. Suggestion6.7.4Methodsfor outlet normal velocity satisfyingtotalmassconservation1. Two cases;2. Application中CFD-NHT-EH'2/34CENTER
2/34 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
热流科学与工程西步文源大堂G教育部重点实验室6.7 Boundary condition treatments for open system6.7.1Selectionsforoutletboundaryposition1. At the location without recirculation (回流)--Suggested byPatankar2 .At the location with recirculation---special attentionshouldbepaidforboundaryconditiontreatment6.7.2Treatment ofB.C.without recirculationUi,Mi1. Local one-way assumptionui+IM1ui,M（局部单向化假设）+1-M2Di,M2CFD-NHT-EHTG3/34CENTER
3/34 6.7 Boundary condition treatments for open system 6.7.1 Selections for outlet boundary position 1. At the location without recirculation (回流)- Suggested by Patankar 2 .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
热流科学与工程西步文源大堂E教育部重点实验室adDi,Mi2. Fully developed,MI=0ui+1M1ui,Man(1) Updating (更新)boundary valueIsM中,m -d.M2 = 0Pi,MI=gDUi,M2i.M2(8y)b(2) ASTM:adTaking= as givenheatflux conditionanFor both methods, the outlet normal velocity mustsatisfy thetotal mass conservation condition6.7.3Treatment ofoutletboundaryconditionwithrecirculation1.Necessity（必要性）for such selectionRequired from somepractical problemsΦCFD-NHT-EHT4/34CENTER
4/34 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
热流科学与工程亚步文源大堂E教育部重点实验室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 also is not possible for some situations.Openflow systemGooGoodBadBadΦCFD-NHT-EHT5/34CENTER
5/34 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 also is not possible for some situations