Documentation
This validation case belongs to heat transfer, with the case of a hollow sphere under release of power condition. The aim of this test case is to validate the following parameters:
The simulation results of SimScale were compared to the numerical results presented in [TPLV06]\(^1\).
The geometry used for the case is as follows:
It represents a section of a hollow sphere with an internal radius of 1 \(m\) and an external radius of 2 \(m\). Face ABCD is the internal face and EFGH is the external face. Axis X passes through the centroid of both faces, making the volume symmetric across the XY and XZ planes.
Tool Type: Code_Aster
Analysis Type: Heat transfer, linear, steady state.
Mesh and Element Types:
Case | Mesh Type | Number of Nodes | Element Type |
---|---|---|---|
A | 1st order hexahedral | 125 | Standard |
B | 2nd order hexahedral | 425 | Standard |
C | 1st order tetrahedral | 2094 | Standard |
D | 2nd order tetrahedral | 14939 | Standard |
The tetrahedral meshes were computed using SimScale’s standard mesh algorithm and automatic sizing. The hexahedral meshes were computed locally and uploaded into the release of power simulation project.
Material:
Boundary Conditions:
The reference solution is of the analytical type, as presented in [TPLV06]\(^1\), originally from [VPCS]\(^2\):
$$ T = T_i + \frac{Q}{6\kappa} \Bigg[ \frac{ (R_e^2 – R_i^2 ) \Big[ \frac{1}{R_i} – \frac{1}{r} \Big] }{ \Big[ \frac{1}{R_i} – \frac{1}{R_e} \Big] } – ( r^2 – R_i^2 ) \Bigg] $$
$$ T_i = 20\ °C $$
$$ Q = 100\ W/m^3 $$
$$ \kappa = 1\ W/(m.K) $$
$$ R_i = 1.0\ m $$
$$ R_e = 2.0\ m $$
The reference solution will be taken at points \( r = \) 1.25, 1.5 and 1.75 \(m\):
$$ T(r = 1.25) = 30.625\ °C $$
$$ T(r = 1.5) = 32.500\ °C $$
$$ T(r = 1.75) = 28.482\ °C $$
Comparison of temperatures at radii \( R = \) 1.25, 1.5 and 1.75 \(m\) with the reference solution is presented:
CASE | R \([m]\) | COMPUTED \([K]\) | COMPUTED \([°C]\) | REFERENCE \([°C]\) | ERROR |
---|---|---|---|---|---|
A | 1.25 | 303.611 | 30.461 | 30.625 | -0.54 % |
1.5 | 305.484 | 32.334 | 32.500 | -0.51 % | |
1.75 | 301.531 | 28.381 | 28.482 | -0.35 % | |
B | 1.25 | 303.79 | 30.64 | 30.625 | 0.05 % |
1.5 | 305.649 | 32.499 | 32.500 | -0.00 % | |
1.75 | 301.621 | 28.471 | 28.482 | -0.04 % | |
C | 1.25 | 303.699 | 30.549 | 30.625 | -0.25 % |
1.5 | 305.576 | 32.426 | 32.500 | -0.23 % | |
1.75 | 301.597 | 28.447 | 28.482 | -0.12 % | |
D | 1.25 | 303.776 | 30.626 | 30.625 | 0.00 % |
1.5 | 305.65 | 32.5 | 32.500 | 0.00 % | |
1.75 | 301.632 | 28.482 | 28.482 | 0.00 % |
Illustration of the temperature distribution from the release of power simulation, case D:
Tutorial: Thermal Analysis of a Differential Casing
References
Note
If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.
Last updated: May 19th, 2021
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