課件教程msc.patran courses課程

1、THERMAL ANALYSISCHAPTER 15THERMAL ANALYSISOVERVIEWHEAT TRANSFERNONLINEARITYMINIMUM ALLOWABLE TIME INCREMENTMINIMUM TIME INCREMENT: PHYSICAL INTERPRETATIONMINIMUM ALLOWABLE TIME INCREMENT (cont)TEMPERATURE VS. POSITION FOR SEVERAL DIFFERENT INCREMENTSTIME INCREMENTATIONTHERMAL STRESS ANALYSISFULLY CO

2、UPLED PROBLEMSEXERCISE 16: TRANSIENT HEAT TRANSFER ANALYSISOVERVIEWThermal Analysis with MSC.AFEAModes of Heat Transfer Available in MSC.AFEAConductionConvectionRadiationTransient Analysis versus Steady State AnalysisLinear versus Nonlinear Thermal AnalysisLoads and Boundary ConditionsTemperaturesFl

3、uxesConvectionRadiationOVERVIEWLinear versus Nonlinear Thermal AnalysisMaterial and Element PropertiesAdaptive Meshing in Thermal AnalysisMinimum Allowable Time IncrementHow to calculate itPhysical InterpretationWhat happens if you violate the formulaHeat Transfer Shell Element Example ProblemTHERMA

4、L ANALYSIS WITH MSC.AFEAHEAT TRANSFERMotivationWhen the solution for the temperature field in a solid (or fluid) is desired, and the temperature is not influenced by the other unknown fields, a heat transfer analysis is appropriate.q= -k dT/dxT1T2T1T2qConductionModes of Heat TransferT2AdvectionRadia

5、tionT1T2T1T2q1q2T1T1T2qConvectionT2Moving Fluid Removes Heat From SolidT1T2qT2T1Heat Moves IN Moving FluidHEAT TRANSFER (CONT.)All three modes of heat transfer may be present in an MSC.AFEA analysis. There are two basic types of analyses:Transient analysis: to obtain the history of the response over

6、 time with heat capacity and latent heat effects taken into account ( 0).Steady state analysis: when only the long term solution under a given set of loads and boundary conditions is sought ( =0).NON-LINEARITYEither type of analysis can be nonlinear.Sources of non-linearity include Temperature depen

7、dence of material properties.Nonlinear surface conditions: e.g. radiation, temperature dependent film (surface convection) coefficients.Loads which vary nonlinearly with temperature. These loads are described using Fields in MSC.PATRAN.Latent heat (phase change) effects.CAPABILITIESSteady State Simu

8、lationTransient Simulation Temperatures can be easily used in uncoupled thermal stress analysis (next section)Coupled Thermal-Structural Analysis (next section)Coupled Thermal-Electric (Joule Heating) NA in MSC.AFEA, only in MSC.MARCCoupled Thermal-Electric-Structural NA in MSC.AFEA, only in MSC.MAR

9、CChoice of Time Step ProceduresFixed Time StepsAdaptive Time StepsCAPABILITIESIsotropic , Orthotropic or Anisotropic All properties may be function of temperature.Latent heat effects included to model phase changesRadiative HeatingView Factor Calculations efficiently done using Monte Carlo methodInt

10、ernal Heating due to plasticity or friction in coupled structural analysis.Thermal Contact in coupled structural analysisParallel ProcessingMATHEMATICAL FORMULATION* energy conservation law:with: mass density: specific heat: gradient operator, MATHEMATICAL FORMULATION (CONT.)Energy flow density is g

11、iven by a diffusion and convection part:where L is the conductivity matrix. Assume that the continuum is pressible and that there is no spatial variation of r and Cp :Without convection this reduces to:where l is the conductivityANALOGY BETWEEN HEAT TRANSFER AND STRESS ANALYSISBOUNDARY CONDITIONSBOU

12、NDARY CONDITIONS (CONT.)CONVECTION HEAT TRANSFER EXAMPLECreate a steady-state temperature distribution across an aluminum plateCreate a spatially varying convection coefficient along one edge using a spacial fieldConvection coefficient is specified under loads/boundary conditionsLOADS AND BOUNDARY C

13、ONDITIONSThe Load/Boundary Conditions form is used to create MSC.AFEA thermal and coupled boundary conditionsDefines the general type of load to appliedDefines what type of region is to be loadedDefines the target element type to which this load will be appliedGenerates an Input Data formSelect Appl

14、ication RegionDefines a general scaling factor for all values defined on this form. The default value is 1.0. This is primarily intended for use when field definitions are used to define the load values. (Not used by MSC.Thermal).When specifying real values in the Input Data entries, spatial fields

15、can be referenced. This area lists all defined spatial fields currently in the database. If the input focus is placed in the Input Data entry, and a spatial field is selected by double clicking in this list, a reference to that field will be entered in the Input Data entry.INPUT DATAInvoked by the I

16、nput Data buttonThe information contained on this form varies By Object By Target Element TypeDefined below is information is standard on this form. LOAD AND BOUNDARY CONDITIONSVarying spacial distributions are specified using FieldsThe Application Region is determined by using the select menu (node

17、, element, element edge, or free edges)THERMAL BOUNDARY CONDITIONSOptions for thermal boundary conditionTemperatureConvectionHeat FluxHeat SourceInitial TemperatureRadiationConvective VelocityHEAT FLUX BOUNDARY CONDITIONSInput the heat flux value, or for Template, FluxesInput the Template IDMACRO te

18、mplateThe functional variation is constructed by the templateHeat flux is an elemental quantity in MSC.PatranApplied as Element Uniform (default)Element VariableHEAT FLUX BOUNDARY CONDITION (CONT.)Element Variable heat flux is same as Element Uniform heat flux boundary condition, unless there is a s

19、patial function variation (a field) input for the heat flux data box.If the heat value is spatially varying, the Element Variable type heat flux boundary condition specifies that the data entity will be evaluated at the element nodes, while for Element Uniform type boundary condition, the data entit

20、y is evaluated at the center of the element edge (if scaling is per unit length), element face (scaling is done per unit surface area).VOLUMETRIC HEAT SOURCE BOUNDARY CONDITIONInput the volumetric heat rate value, orUncheck “Fixed” and input the Template IDMACRO templateThe functional variation is c

21、onstructed by this templateHeat rate is an elemental quantity in MSC.PatranApplied as Element Uniform (default)Element Variable VOLUMETRIC HEAT SOURCE BOUNDARY CONDITION (CONT.)Element Variable volumetric heat source is the same as Element Uniform volumetric heat source boundary condition, unless, t

22、here is a spatial functional variation (spatial field) input for “heat source” data boxIf the “heat source” value is spatially varying, the “Element Variable” type volumetric heat source boundary condition specifies that the data entity will be evaluated at the centroid of the elementCONVECTION BOUN

23、DARY CONDITIONOption: Template, ConvectionConstant or spatially varying convection coefficientCheck “Fixed”Enter Coefficient or Select Spatial FieldEnter a single Fluid node IDAssign Temperature LBC to this nodeNode need not be associated with geometryTime or temperature dependent convection coeffic

24、ientConvection Template ID points to a CONV definition in the template.dat.apnd fileConvection coefficient function can be defined in Fields/Material Property/GeneralConvection coefficient can be defined using library of configurationsCONVECTION BOUNDARY CONDITIONCONCLUDEDOption: Fixed CoefficientOn

25、ly uses constant or spatially varying convection coefficientsInput Time or Temperature varying coefficient with Time or Temperature fieldArea for computation comes from “Application Region”ANALYSIS TYPE TABLEThe following table outlines the options when the Analysis Type is set to ThermalObjectTypeO

26、ptionRadiationElement Uniform Gap Radiation via table or User Subroutine View FactorsConvectionElement UniformFixed CoefficientTemperature FieldElement VariableTime FieldUser SubroutineHeatingElement UniformFlux, FixedFluxesElement VariableFlux, Time FieldVolumetric HeatFlux, Temperature TableNodal

27、SourceTemperatureNodalFixedTime FieldInitialPressureNodalFixedTime Table(Hydraulic network LBC)InitialTemplateTemperatureNodalFixedTime FieldCoupledInitialTemplate MATERIAL PROPERTIESUnder the Materials form, Isotropic, 2D or 3D orthotropic and anisotropic materials can be createdOn the Input Proper

28、ties form conductivity, density, specific heat and phase change are specifiedThermal properties can be input as constants or you can select an existing material property fieldFIELDS/MATERIAL PROPERTYVariation of Material Property with Time or Temperature can be defined through Material Property Fiel

29、dsSelect object Material Property and Method TabularSPATIAL FINITE ELEMENT DISCRETIZATIONApproximate temperatures for a set of discrete points (nodes) in space by expressing temperature T(x, t) in terms of locally defined shape functions and nodal valueswhere are the shape functions and are the noda

30、l temperatures.with: heat capacity matrix: conductivity and convection matrix: contribution from convective boundary condition: vector of nodal fluxes* In case of convection:- Upwinding (SUPG method)- Non-symmetric system matrix SPATIAL FINITE ELEMENT DISCRETIZATION (CONT.)Using the Galerkin method,

31、 the heat transfer problem can be written as a coupled set of first order ordinary differential equations:LINEAR HEAT TRANSFER ANALYSISsteady state: solution can be obtained by a single matrix inversion:transient: time discretization by means of finite differences:Approximate nodal temperature at di

32、screte points in time:MARC uses a backward difference scheme is used to approximate time derivative as:Resulting finite difference scheme:NONLINEAR HEAT TRANSFER ANALYSISNonlinearity can be caused by:temperature dependent conductivity or specific heatradiation boundary conditiontemperature dependent

33、 film coefficient or heat fluxConsequently, heat capacity matrix, conductivity matrix, “film matrix” and equivalent nodal flux vector may be temperature dependent.NONLINEAR HEAT TRANSFER ANALYSIS (CONT.)Steady state: applicable in case of mild nonlinearity; e.g. if conductivity is slightly temperatu

34、re dependent* Solution can be obtained iteratively:start with:next approximations are obtained by successivesubstitution:continue until:NONLINEAR HEAT TRANSFER ANALYSIS (CONT.)Transient analysis: necessary in case of severe non- linearity; e.g. radiation boundary conditionSolution can be obtained us

35、ing nonlinear backward difference scheme:where is the average nodal temperature vector in time increment Dt first iteration within an increment n, is taken as an extrapolated value of the previous two increments:for the next iterations i, follows from:iterations are stopped ifCONTROL VALUES HEAT TRA

36、NSFER ANALYSISDTtol1: maximum incremental temperature change at node (def = 20); if the automatic time stepping scheme is selected, the time step will be automatically increased or decreased if necessaryDTtol2: maximum nodal temperature change before properties are reevaluated and matrices reassembl

37、ed (def=100)DTtol3: maximum error in estimated nodal temperature; used for property reevaluation (def = 0, test is bypassed)MINIMUM ALLOWABLE TIME INCREMENTIn transient heat transfer there is a minimum allowable incrementthe mesh refinement determines how small a time increment can be analyzed.A sim

38、ple formula provides the minimum allowable incrementThis minimum is only a requirement for second order elements but it is good to use it as a guideline for all meshes.INITIAL TIME STEP ESTIMATESometimes oscillatory behaviour if time step is too small; e.g. heat penetration in an originally iso-ther

39、mal blockMINIMUM TIME INCREMENT:PHYSICAL INTERPRETATIONThis equation describes the physical limitation on the amount of heat that can be moved a distance Dl in an amount of time DtThink of the temperature at each node representing the amount of heat in the physical region of that nodeThen think of t

40、he amount of heat associated with each individual nodeMINIMUM TIME INCREMENT:PHYSICAL INTERPRETATION (CONT.)If you numerically specify the temperature at node A (as a boundary condition) heat must be removed from nodes B and C to comply with the specified temperature boundary conditionIf Dt is too s

41、mall, or Dl too large, to allow enough heat to move to node A, the extra heat required to comply with the specified temperature boundary condition must come from the region of node B. If too much heat is removed from node B this way the temperature drops below the physically realistic valueMINIMUM A

42、LLOWABLE TIME INCREMENTWhat happens if you violate this formula? Consider the following 1 dimensional case:TEMPERATURE VS. POSITION FOR SEVERAL DIFFERENT INCREMENTS:The first time increment solution violates the minimum allowable time increment relationshipThe solution at this time (which shows the

43、temperature dropping below the baseline value) is invalidTIME INCREMENTATIONSymptoms of time increments being too smallTemperature increases when it should decreaseTemperature decreases when it should increaseResolutionUse larger time increments (do not accept early transient solution) orRefine mesh

44、 near surfaceElement selectionUse second-order elements for smooth diffusion and conductionUse first-order elements for highly nonlinear, discontinuous conduction such as phase changes (latent heat effects).INITIAL TIME STEP ESTIMATE (CONT.)Better approximation can be obtained if:time step is INCREA

45、SEDmesh is refinedheat capacity matrix is lumped (linear elements)Further MSC.AFEA capabilities:User subroutines for non-linear boundary conditions tyings and heat transfer shell element with parabolic distribution in thickness direction phase transitionsADAPTIVE MESHINGLocal Adaptive Meshing can ta

46、rget areas of high thermal gradients that typically occur in welding simulations. SIMULATION OF WELDING PROCESSv2002THERMAL RADIATIONNew Radiation LBCRadiation Viewfactor calculationUses Monte Carlo Simulation2DAxisymmetric3DNew Convective Velocity LBCThermal or Coupled analysisv2002RADIATION OVERVI

47、EWBasic equation: q = s F A (Ti4 Tj4)T is in absolute unitsKelvin or Rankines is the Stefan Boltzmann Constant5.6696E-8 Watt/(m2-K4)1.7140E-9 Btu/(hr-ft2-R4)F (script-F) is the gray body configuration factorF is a function of Fij, the geometric view-factor from surface-i to surface-jei, the emissivi

48、ty of surface-iej, the emissivity of surface-j12BGv2002VIEW FACTOR ILLUSTRATIONF1-2 approaches 1F1-BG approaches 012BGv2002VIEW FACTOR ILLUSTRATION (CONT.)F1-2 approaches 0F1-BG approaches 11-eieiAi1-ejejAj1AiFijv2002RADIOSITY CONCEPTRadiosity node added for each surface nodeFA is separated into two

49、 termsA “space” resistance which is a function of only FijEach “surface” resistance a function of either ei and ej onlyThis technique facilitates Change in surface properties without new view factor runIndependently variable emissivity valuese = 1.0 will eliminate radiosity nodesFacilitates debugging of surface-to-surface connectionsv2002NODE ELEMENTAL SUB-AREAThe portion of an element face associated with a particular node.v2002NODE ELEMENTAL SUB-AREA (CONT.)The portion of an element face associated with a particular node.v2002SIMPLE RADIOSITY NETWORKHEAT TRA