This validation case belongs to fluid dynamics. The aim of this test case is to validate the following parameter on the radiative surfaces of a cylinder:
Net radiative heat flux, \(Q_r\).
The simulation results obtained from SimScale were compared to the results presented in [1].
The following cylinder was used as the computational domain for this simulation. Faces A1, A3, and A2 mark the bottom flat face, top flat face, and the curvature respectively.
Figure 1: Cylinder geometry description for the radiation test case with faces
The height, \(h\), and radius, \(r\), of the cylinder are 150 \(mm\) and 25 \(mm\) respectively.
Analysis Type and Mesh
Tool type: OpenFoam
Analysis type: Incompressible convective heat transfer with radiation
Turbulence model: Laminar and k-ω SST turbulence model
Time dependency: Steady-state
Mesh and element types: The mesh was created using the standard mesher on the SimScale platform. It has 2.5 million tetrahedral cells.
Figure 2: Final tetrahedral mesh used for all radiation resolutions (closer view on the bottom)
Simulation Setup
Material/Fluid:
Air
Kinematic viscosity \(\nu\) = 1.2784e-5 \(m^2/s\)
Boundary Conditions:
No-slip walls:
Fixed temperature of 300.15 \(K\) on the top surface (A3).
Fixed temperature of 1773 \(K\) on the rest of the faces ( A1 and A2).
All surfaces have a pure black-body behavior, with an emissivity equal to 1.
Reference Solution
The analytical solution for the net radiative heat flux \(Q_r\) makes use of the view factor method as mentioned under reference\(^1\).
Result Comparison
When comparing radiative analytical results and SimScale results, there are a few points that need to be considered:
While the analytical solution takes into account only thermal radiation, in the SimScale platform, radiation is a feature of convective heat transfer. This means that the entire heat exchange will not only happen between the walls, but some part of it will heat the enclosed fluid volume as well. However as radiation is the dominant heat transfer mode with high temperatures, the difference is not significant. Also, laminar and turbulent behaviors were evaluated which provided the same results.
The quantity evaluated is the net radiative heat flux ( \(Q_r\) ) in Watts [ \(W\) ], that a surface emits (or absorbs). The user can easily calculate it by assigning an “Area Integral” to every surface under Result control > Surface data.
The table below summarizes the results for different mesh resolutions along with the analytical results:
\(Q_r\) [\(W\)] SimScale Fine radiation resolution
Relative Error (for finest resolution) [ (%) ]
A1
-28.95
-28.846
-28.847
-28.847
-0.357
A2
-1070.36
-1073.730
-1073.730
-1073.188
0.264
A3
1099.31
1099.619
1099.619
1099.619
0.028
Balance
0
-2.975
-2.975
-2.416
Table 1: Comparative table between analytical and SimScale results for radiative heat
The results for area A2 are the least accurate and SimScale predicts higher heat loss value for this surface. This is due to the fact that A2 being the largest surface is in more contact with the fluid and thus loses more heat. This affects the heat balance, which analytically should be zero.
Overall the results obtained from the SimScale platform are in good agreement with the analytical solutions, and hence this serves as a good validation of the radiation feature.
Figure 3: The net radiative heat flux on the cylinder for the fine radiation resolution and k-omega SST turbulence model
