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Heat Transfer: Perforated plate

Overview

The aim of this test case is to validate the following functions:

  • Transient thermal solver
  • Surface heat flux boundary condition
  • Convective heat flux boundary condition

The simulation results of SimScale were compared to the results presented in case B of [TTLP301]. Four of the mesh cases were considered; linear and quadratic tetrahedrals, linear and quadratic hexahedrals.

Import validation project into workspace

Geometry

HeatTransferInAPerforatedPlate-geometry

Geometry of a perforated plate

  A B C D E F G H I J
x [m] 0.635 0.9395 0.9395 0.542749683 0.3175002537 0.635 0.9395 0.9395 0.542749683 0.3175002537
y [m] 0 0 0.83376 0.9400690251 0.5499259849 0 0 0.83376 0.9400690251 0.5499259849
z [m] 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2

Analysis type and Domain

Tool Type : CalculiX, Code-Aster

Analysis Type : Transient thermal analysis

Mesh and Element types :

Case Mesh type Number of nodes Number of 3D elements Element type Tool type
(A) linear tetrahedrals 3167 14857 3D isoparametric CalculiX
(B) quadratic tetrahedrals 22411 14857 3D isoparametric CalculiX
(C) linear hexahedrals 1210 840 3D isoparametric CalculiX
(D) quadratic hexahedrals 4433 840 3D isoparametric CalculiX
(E) linear tetrahedrals 3167 14857 3D isoparametric Code_Aster
(F) quadratic tetrahedrals 22411 14857 3D isoparametric Code_Aster
(G) linear hexahedrals 1210 840 3D isoparametric Code_Aster
(H) quadratic hexahedrals 4433 840 3D isoparametric Code_Aster
HeatTransferInAPerforatedPlate-mesh-caseB

Mesh used for the SimScale Case B

HeatTransferInAPerforatedPlate-mesh-caseD

Mesh used for the SimScale Case D

Simulation Setup

Material:

  • isotropic: \(\rho\) = 1 kg/m³, \(\kappa\) = 0.1 W/(m K), Specific heat \(c\) = 1 J/(kg K)

Initial Condition:

  • Initial Temperature \(T_{initial}\) = 273.15 K

Heat flux:

  • Surface heat flux on face AFJE with a surface heat flux \(q\) = 1 W/(m²)
  • Convective heat flux on face CHID with a temperature \(T_{CHID}\) = 273.15 K and a convection coefficient \(h\) = 1 W/(m² K)

Results

Comparison of the temperature on node N1 for 12 timesteps obtained with SimScale and the results presented in case B of [TTLP301] ¹ and [TTLP301] ². The Error was calculated with respect to [TTLP301] ¹.

Comparison of the temperature on node N1 [K]
Timesteps [s] [TTLP301] ¹ [K] [TTLP301] ² [K] Case A [K] Error [%] Case B [K] Error [%] Case C [K] Error [%] Case D [K] Error [%] Case E [K] Error [%] Case F [K] Error [%] Case G [K] Error [%] Case H [K] Error [%]
0.1 274.20 274.22 274.19 1.82E-03 274.19 1.82E-03 274.19 1.82E-03 274.19 1.82E-03 274.15 1.64E-02 274.15 1.64E-02 274.15 1.64E-02 274.15 1.64E-02
0.2 274.60 274.60 274.60 1.09E-03 274.60 1.09E-03 274.59 2.55E-03 274.6 1.09E-03 274.57 9.83E-03 274.57 9.83E-03 274.57 9.83E-03 274.57 9.83E-03
0.3 274.89 274.90 274.89 7.28E-04 274.89 7.28E-04 274.89 7.28E-04 274.89 7.28E-04 274.87 8.00E-03 274.87 8.00E-03 274.87 8.00E-03 274.87 8.00E-03
0.4 275.13 275.13 275.13 7.27E-04 275.13 7.27E-04 275.13 7.27E-04 275.13 7.27E-04 275.11 8.00E-03 275.12 4.36E-03 275.11 8.00E-03 275.12 4.36E-03
0.5 275.34 275.34 275.34 3.63E-04 275.34 3.63E-04 275.34 3.63E-04 275.34 3.63E-04 275.32 6.90E-03 275.33 3.27E-03 275.32 6.90E-03 275.33 3.27E-03
0.6 275.52 275.53 275.52 1.09E-03 275.52 1.09E-03 275.52 1.09E-03 275.52 1.09E-03 275.51 4.72E-03 275.51 4.72E-03 275.51 4.72E-03 275.51 4.72E-03
0.7 275.69 275.70 275.69 3.63E-04 275.69 3.63E-04 275.69 3.63E-04 275.69 3.63E-04 275.68 3.99E-03 275.68 3.99E-03 275.68 3.99E-03 275.68 3.99E-03
0.8 275.85 275.85 275.85 7.25E-04 275.85 7.25E-04 275.85 7.25E-04 275.85 7.25E-04 275.84 2.90E-03 275.84 2.90E-03 275.84 2.90E-03 275.84 2.90E-03
0.9 276.00 276.00 276.00 1.45E-03 276.00 1.45E-03 276 1.45E-03 276 1.45E-03 275.99 2.17E-03 275.99 2.17E-03 275.98 5.80E-03 275.99 2.17E-03
1.0 276.14 276.14 276.14 4.00E-04 276.14 4.00E-04 276.14 4.00E-04 276.14 4.00E-04 276.13 3.22E-03 276.13 3.22E-03 276.13 3.22E-03 276.13 3.22E-03
1.1 276.27 276.27 276.27 0.00E+00 276.27 0.00E+00 276.27 0.00E+00 276.27 0.00E+00 276.26 3.62E-03 276.26 3.62E-03 276.26 3.62E-03 276.26 3.62E-03
1.2 276.40 276.40 276.40 7.24E-04 276.40 7.24E-04 276.4 7.24E-04 276.4 7.24E-04 276.39 2.89E-03 276.39 2.89E-03 276.39 2.89E-03 276.39 2.89E-03

References

[TTLP301](1, 2, 3, 4, 5, 6, 7, 8) TTLP301 - Transfert de chaleur dans une plaque perforée

¹ Results by Donea as mentioned in [TTLP301]: Donea, J. (1974), On the accuracy of finite element solutions to the transient heat-conduction equation. Int. J. Numer. Meth. Engng., 8: 103–110

² Code_Aster results as mentioned in case B of [TTLP301]