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Radiation Validation Case 1: Cylinder

Overview

The aim of this project is to validate SimScale radiation results on simple benchmark example, where the analytical solutions exist. The analytical solution method in the reference literature [1] makes use of view factor method to calculate the net radiative heat flux (Qr) associated with each radiative surface.

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Geometry and Setup

Height (h) and radius (r) of the cylinder are 150 and 50 mm, respectively. All surfaces have a pure black-body behaviour, with an emissivity equal to 1 . The bottom and side surfaces (A1 and A2) of the cylinder is assigned a wall boundary condition with a fixed temperature of 1500 ºC. The top surface (A3) is exposed to surrounding and also has a wall boundary condition with a temperature of 27 ºC.

Different meshes with uniform region refinements were created to get mesh independent results.

Cylinder geometry description for radiation test case.

RESULTS COMPARISON

When comparing radiative analytical results and SimScale results, there are a few points that have to be taken into account:

  • 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 behaviours were evaluated which provided the same results.
  • The quantity evaluated is the Net radiative heat flux (Qr) 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” and “Surface Data”.
  • In SimScale, the user can choose the computational power assigned to the radiative calculation. User can choose a “Coarse Radiation Resolution” (faster results) or a “Fine Radiation Resolution” (slower results) in “Numerics”, in the “Advanced Concepts” section.

The table below summarises the results with different radiation resolutions along with the analytical results.

Comparative table between analytical and SimScale results for radiative heat.
  • 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.
  • The results for area A2 are the least accurate and SimScale predicts higher heat loss value for this surface. This also has an effect on the heat balance, which analytically should be zero. This is due to the fact that  A2 being the largest surface is in more contact with the fluid and thus loses more heat.

References

[1] https://www.intechopen.com/books/heat-transfer-models-methods-and-applications/use-of-cfd-codes-for-calculation-of-radiation-heat-transfer-from-validation-to-application

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