Documentation
This design analysis of a spherical pressure vessel validation case belongs to thermomechanics. This test case aims to validate the following parameters:
The simulation results of SimScale were compared to the analytical results presented in [Afkar]\(^1\).
The geometry consists of 1/8th of a sphere, with an inner radius of 0.19 \(m\) and an outer radius of 0.2 \(m\).
The coordinates for the points in the sphere are as tabulated below:
A | B | C | D | E | F | |
x | 0 | 0.19 | 0 | 0.2 | 0 | 0 |
y | 0.19 | 0 | 0.2 | 0 | 0 | 0 |
z | 0 | 0 | 0 | 0 | 0.19 | 0.2 |
Tool Type: Code_Aster
Analysis Type: Transient thermomechanical, linear
Mesh and Element Types: The mesh for cases A and B was created with the standard algorithm, with first order elements.
The setup from cases A and B is the same, except for the thermal conductivity \(\kappa\).
Case | Mesh Type | Nodes | Thermal Conductivity \(\kappa\) | Element Type |
(A) | 1st order standard | 172833 | 20 \([\frac {W}{m.K}]\) | Standard |
(B) | 1st order standard | 172833 | 22 \([\frac {W}{m.K}]\) | Standard |
Find below the mesh used for both cases. It’s a standard mesh with first order tetrahedral cells.
Material:
Initial Conditions
Temperature is 300 \(K\) in the entire pressure vessel.
Boundary Conditions:
The analytical solution is given by the equations presented in [Afkar]\(^1\).
Since no value for thermal conductivity \(\kappa\) was provided, the values of 20 \(\frac {W}{m.K}\) and 22 \(\frac {W}{m.K}\) were used. For the final time step, the SimScale results for von Mises stress \([MPa]\) and temperature \([K]\) over the edge EF are compared to those from [Afkar]\(^1\).
In Figure 4, we can see how temperature is changing in the sphere’s width, for the last time step:
Last updated: November 7th, 2023
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