Validation Case: Design Analysis of a Spherical Pressure Vessel
This design analysis of a spherical pressure vessel validation case belongs to thermomechanics. This test case aims to validate the following parameters:
Transient thermostructural analysis
The simulation results of SimScale were compared to the analytical results presented in [Afkar]\(^1\).
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
Table 2: Overview of the mesh, creep formulation, and element technology used for each case
Find below the mesh used for both cases. It’s a standard mesh with first order tetrahedral cells.
Figure 2: First order standard mesh used for cases A and B
Simulation Setup
Material:
Steel (linear elastic)
\(E\) = 190 \(GPa\)
\(\nu\) = 0.305
\(\rho\) = 7750 \(kg/m³\)
\(\kappa\) = 20 \([\frac {W}{m.K}]\) and 22 \([\frac {W}{m.K}]\) for cases A and B, respectively;
Expansion coefficient = 9.7e-6 \(1/K\)
\(T_0\) Reference temperature = 300 \(K\)
Specific heat = 486 \(\frac {J}{kg.K}\)
Initial Conditions
Temperature is 300 \(K\) in the entire pressure vessel.
Boundary Conditions:
Constraints
\(d_x\) = 0 on face ACFE;
\(d_y\) = 0 on face BDFE;
\(d_z\) = 0 on face ACDB.
Surface loads
Pressure boundary condition on face ABE. The pressure increases linearly from 0 \(MPa\) to 1 \(MPa\) according to formula \(P = (0.2e6).t\), where t is time from 0 to 5 seconds;
Fixed temperature value boundary condition on face ABE. Temperature is increasing linearly, from 300 \(K\) to 500 \(K\) according to formula \(T = 40.t + 300\), where t is time from 0 to 5 seconds;
Convective heat flux boundary condition on face CFD. The heat transfer coefficient is 90 \(\frac {W}{K.m^2}\) and \(T_0\) reference temperature is 300 \(K\).
Reference Solution
The analytical solution is given by the equations presented in [Afkar]\(^1\).
Result Comparison
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]\(^1\).
Figure 3: Comparing temperature and von Mises stress results for cases A and B with those from [Afkar]¹.
In Figure 4, we can see how temperature is changing in the sphere’s width, for the last time step:
Figure 4: Temperature on the 1/8th sphere, for time = 5 seconds
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.
