Validation Case: Heat Transfer in a Perforated Plate
This project belongs to the heat transfer analysis type. The aim of this test case is to validate the following parameter using a transient thermal solver, with a surface and a convective heat flux boundary condition on a perforated plate:
Temperature \([K]\) on a single node for 12 consecutive timesteps.
The simulation results of SimScale were compared to the results presented in case B of [TTLP301]\(^1\).
The geometry used for the analysis with the highlighted node N1 can be seen below. It is a random thick plate with straight and curved edges.
Figure 1: Geometry of a perforated plate with highlighted node N1 (red)
The coordinates for each vertex of the plate are displayed in the following table:
A
B
C
D
E
F
G
H
I
J
x \([m]\)
0.635
0.9395
0.9395
0.5427
0.3175
0.635
0.9395
0.9395
0.5428
0.3175
y \([m]\)
0
0
0.8338
0.9401
0.5499
0
0
0.8338
0.9401
0.5499
z \([m]\)
0
0
0
0
0
0.2
0.2
0.2
0.2
0.2
Table 1: The coordinates of the main geometry points
Analysis Type and Domain
Tool type : Code_Aster
Analysis type : Heat transfer, linear
Time dependency: Transient
Mesh and element types: Four mesh cases were considered for the analysis of the perforated plate; with 1st order and 2nd order tetrahedral, as well as 1st order and 2nd order hexahedral elements. The hexahedral mesh was locally computed and uploaded to the SimScale Workbench.
Case
Mesh type
Number of nodes
Number of 3D elements
Element type
(A)
1st order tetrahedral
5340
25676
Standard
(B)
2nd order tetrahedral
16807
10976
Standard
(C)
1st order hexahedral
1210
840
Standard
(D)
2nd order hexahedral
4433
840
Standard
Table 2: The mesh characteristics for all the cases
Below, the 1st order tetrahedral mesh for case A is visualized:
Figure 2: The mesh used for case A, created with SimScale’s standard meshing algorithm
And the mesh that was uploaded for case C is presented below:
Figure 3: The mesh used for case C, created externally with 1st order hexahedral elements
Simulation Setup
Material/Solid
Isotropic:
Density \(ρ\) = 1 \( kg \over \ m³ \),
Thermal conductivity \(\kappa\) = 0.1 \( W \over \ m \ K\),
Specific heat = 1 \( J \over \ kg \ K\)
Initial conditions
Initial Temperature = 273.15 \(K\)
Boundary conditions
Surface heat flux on face AFJE:
Heat flux value = 1 \(W \over \ m²\)
Convective heat flux on face CHID
Reference temperature \(T_{0}\) = 273.15 \(K\)
Heat transfer coefficient = 1 \(W \over \ m² \ K\)
Results Comparison
The temperature values at node N1 for 12 time steps obtained with SimScale are compared against the results presented in case B of [TTLP301]\(^1\).
Timesteps \([s]\)
[TTLP301] \([K]\)
Case A \([K]\)
Error [%]
Case B \([K]\)
Error [%]
Case C \([K]\)
Error [%]
Case D \([K]\)
Error [%]
0.1
274.195
274.201
2.19E-03
274.203
2.92E-03
274.198
1.09E-03
274.204
3.28E-03
0.2
274.597
274.601
1.46E-03
274.604
2.55E-03
274.6
1.09E-03
274.604
2.55E-03
0.3
274.892
274.895
1.09E-03
274.898
2.18E-03
274.894
7.28E-04
274.898
2.18E-03
0.4
275.132
275.135
1.09E-03
275.138
2.18E-03
275.134
7.27E-04
275.138
2.18E-03
0.5
275.339
275.342
1.09E-03
275.345
2.18E-03
275.341
7.26E-04
275.345
2.18E-03
0.6
275.523
275.526
1.09E-03
275.529
2.18E-03
275.525
7.26E-04
275.529
2.18E-03
0.7
275.691
275.695
1.45E-03
275.697
2.18E-03
275.694
1.09E-03
275.697
2.18E-03
0.8
275.848
275.852
1.45E-03
275.854
2.18E-03
275.851
1.09E-03
275.854
2.18E-03
0.9
276.996
275.999
1.09E-03
276.001
1.81E-03
275.998
7.25E-04
276.001
1.81E-03
1.0
276.136
276.14
1.45E-03
276.142
2.17E-03
276.139
1.09E-03
276.142
2.17E-03
1.1
276.27
276.274
1.45E-03
276.276
2.17E-03
276.273
1.09E-03
276.276
2.17E-03
1.2
276.398
276.403
1.81E-03
276.404
2.17E-03
276.402
1.45E-03
276.404
2.17E-03
Table 3: Temperature results for all cases at different time steps
All of the cases are in a good agreement with the reference results.
You can see the temperature distribution on the plate for the last time step of Case A below:
Figure 4: Temperature distribution on the plate for Case A at time 1.2s
This website uses cookies so that we can provide you with the best user experience possible. Cookie information is stored in your browser and performs functions such as recognising you when you return to our website and helping our team to understand which sections of the website you find most interesting and useful.
Strictly Necessary Cookies
Strictly Necessary Cookie should be enabled at all times so that we can save your preferences for cookie settings.
If you disable this cookie, we will not be able to save your preferences. This means that every time you visit this website you will need to enable or disable cookies again.
