Appendix Six Thermal Analysis Thermal Analysis Basics of

Appendix Six Thermal Analysis

Thermal Analysis Basics of Steady-State Heat Transfer Training Manual – Temperatures and heat flow rate are usually the items of interest, although heat fluxes can be reported as well. • The general thermal equation is as follows: where t is time and {T} is temperature, [C] is the specific heat (thermal capacitance) matrix, [K] is the conductivity matrix, and {Q} is the heat flow rate load vector. • In a steady-state analysis, all time-dependent terms are removed. However, nonlinearities can be present: ANSYS Workbench – Simulation • A steady-state thermal analysis is performed to determine thermal response under applied steady-state loads August 26, 2005 Inventory #002275 A 6 -2

Thermal Analysis … Elements Used Training Manual – Solid bodies are meshed with 10 -node tetrahedral or 20 -node hexahedral elements • SOLID 87 and SOLID 90 – Surface bodies are meshed with 4 -node quad shell elements • SHELL 57 using real constants • (SHELL 131 or SHELL 132 are currently not used. ) – Line bodies are meshed with 2 -node line elements • LINK 33 using real constants • An equivalent cross-sectional area, as defined in Design. Modeler, is used for LINK 33 – For thermal-stress analyses, a coupled-field element is not used. The thermal-stress analysis is performed sequentially, so the above thermal elements are used, then the temperature field is read into corresponding structural elements. ANSYS Workbench – Simulation • In Simulation, the following elements are used: August 26, 2005 Inventory #002275 A 6 -3

Thermal Analysis … Material Properties Training Manual – For temperature-dependent thermal conductivity, the appropriate MPTEMP and MPDATA commands are issued • Although specific heat may be defined in the “Engineering Data” branch, it is currently unused and not passed to ANSYS – MP, C commands are not written for specific heat ANSYS Workbench – Simulation • Thermal conductivity is input into ANSYS as MP commands. August 26, 2005 Inventory #002275 A 6 -4

Thermal Analysis … Assemblies – Solid Body Contact Training Manual – KEYOPT(1)=2 set for thermal DOF only – KEYOPT(12) is based on contact type used • For example, bonded type is KEYOPT(12)=5. KEYOPT(2), KEYOPT(5), KEYOPT(9), and FKN are also set. These contact settings are most critical for structural contact, so the various default settings are outlined in Chapter 4. – Default thermal contact conductance (TCC) is based on highest value of thermal conductivity of materials and overall geometry size • TCC=KXX*10, 000/ASMDIAG – KXX is of highest thermal conductivity value of used materials ANSYS Workbench – Simulation • Internally, thermal contact for solid faces is defined with CONTA 174 and TARGE 170 elements. – ASMDIAG is diagonal of overall ‘bounding box’ of assembly • TCC is not used for MPC (KEYOPT(2)=2 on CONTA 174) – If Normal Lagrange formulation is set, KEYOPT(2) reset to 0. August 26, 2005 Inventory #002275 A 6 -5

Thermal Analysis … Assemblies – Surface Body Contact Training Manual – Undocumented KEYOPT(1)=2 is set for thermal contact • Contact involving solid edges default to pure penalty method • Contact involving surface edges use MPC formulation. Instead of “target normal, ” if search direction is “pinball region, ” KEYOPT(5)=4 set on companion TARGE 170 element. • For bonded contact (default), both use KEYOPT(12)=5 and KEYOPT(9)=1. • For surfaces in contact with other faces, standard surface-tosurface contact is used, namely CONTA 174 and TARGE 170 CONTA 175 elements ANSYS Workbench – Simulation • Internally, any contact including an edge (solid body edge or surface edge) results in asymmetric contact with CONTA 175 for the edge and TARGE 170 for the edge/face TARGE 170 elements August 26, 2005 Inventory #002275 A 6 -6

Thermal Analysis … Assemblies – Spot Weld Training Manual – The LINK 33 elements use same thermal conductivity as underlying materials but with a circular cross-section with radius=5*thickness of underlying shells – Figure on right shows two spot welds between two sets of shell elements, which are made translucent for clarity. ANSYS Workbench – Simulation • Internally, spot welds are defined as a set of LINK 33 elements. The spot weld is defined with one link element, and the top and bottom of the spot weld is connected to the shell or solid elements with a ‘spider web’ of multiple links. August 26, 2005 Inventory #002275 A 6 -7

Thermal Analysis … Thermal Loads in ANSYS Training Manual – Heat flow for an edge or vertex is a heat flow rate (F, , HEAT) – Heat flux or heat flow for a surface is surface load (SF, , HFLUX) – Internal heat generation is applied as a body load (BFE, , HGEN) – Given temperature is applied as a constraint (D, , TEMP) – Perfectly insulated condition internally removes any loads applied in Simulation on those surface(s). – Convection is defined by surface effect SURF 152 elements • Bulk temperature and film coefficient is applied on the surface effect elements (SF, , CONV, film, bulk) • If temperature-dependent film coefficients exist, these are defined with a temperature-dependent HF material property (MPDATA, HF). The film coefficient value applied will be “–HF_number, ” and ANSYS knows to use the referenced HF material property number. ANSYS Workbench – Simulation • The internal representation of loads in ANSYS: • KEYOPT(8) is set to be consistent with temperature evaluation of h(T), such as evaluate h(T) based on surface temperature. August 26, 2005 Inventory #002275 A 6 -8

Thermal Analysis … Solution Options in ANSYS Training Manual – The solvers used are either the direct sparse solver (EQSLV, SPARSE) or the PCG solver (EQSLV, PCG) • The JCG solver is not used in thermal analyses – A simplified discussion between the two solvers: • If given the linear static case of [K]{x} = {F}, Direct solvers factorize [K] to solve for [K]-1. Then, {x} = [K]-1{F}. – This factorization is computationally expensive but is done once. • Iterative solvers use a preconditioner [Q] to solve the equation [Q][K]{x} = [Q]{F}. Assume that [Q] = [K]-1. In this trivial case, [I]{x} = [K]-1{F}. However, the preconditioner is not usually [K]-1. The closer [Q] is to [K]-1, the better the preconditioning is, and this process is repeated - hence the name, iterative solver. – For iterative solvers, matrix multiplication (not factorization) is performed. This is much faster than matrix inversion if done entirely in RAM, so, as long as the number of iterations is not very high (which happens for well-conditioned matrices), iterative solvers can be more efficient than sparse solvers. – The main difference between the iterative solvers in ANSYS — PCG, JCG, ICCG — is the type of pre-conditioner used. ANSYS Workbench – Simulation • The solver selection for direct vs. iterative: August 26, 2005 Inventory #002275 A 6 -9

Thermal Analysis … Solution Options in ANSYS Training Manual – The ANSYS input file is written as “ds. dat” in the solver directory. The output file is “solve. out” and can be viewed in the “Worksheet” tab of the “Solution Information” branch. – ANSYS is executed in batch mode (-b) as a separate process. During solution, the results file. rth is written. The results are also read in and XML results files are generated in batch mode. The XML files are then read into Simulation. – All associated ANSYS files have default jobname of “file” and are deleted after solution, unless changed in “Tools > Options… > Simulation: Solution > Save Ansys Files”. ANSYS Workbench – Simulation • Solver working directory: August 26, 2005 Inventory #002275 A 6 -10

Thermal Analysis … Solution Options in ANSYS Training Manual – Solution control is used • This is different from structural analyses in Simulation where Solution Control is turned off – ANSYS shape checking is turned off (SHPP, OFF) – If nonlinear, the number of substeps (NSUBST, 1, 10, 1) and number of equilibrium iterations (NEQIT, 20) are defined • CNVTOL also set, where minimum reference heat flow rate is defined as 1 e-6 W – Only Simulation-supported results is output with OUTRES, not everything by default • Results are later written to XML files in /POST 1, which are then read back into Simulation. Hence, Simulation does not directly read the results from the. rth file ANSYS Workbench – Simulation • Some solution options are also defined: August 26, 2005 Inventory #002275 A 6 -11

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