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Radiation Validation Case 2: Closed Ring

Overview

The aim of this project is to validate SimScale radiation results on simple benchmark example, where the analytical solutions exist. The analytical solutions for the net radiative heat flux (Qr) associated with each radiative surface, from the reference literature [1], is compared with the results from SimScale platform.

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Geometry and Setup

Based on the reference literature [1], the ring geometry is a simplified model of the vacuum vessel of a Fusion reactor. As shown below in Fig.1, the geometry contains a small surface (marked in red) representing the upper surface of a specific component maintained at a lower temperature. Rest of the surfaces are at higher temperature. Also, all the radiating surfaces are considered to be black-body with an emissivity of 1. The dimensions for the geometry are:

  • Inner Radius – 6 m
  • Outer Radius – 12 m
  • Height – 11 m

Boundary Conditions

  1. The smaller surface (red) is assigned a wall BC with a fixed lower temperature of 323 K.
  2. All the remaining surfaces are assigned a wall BC with fixed higher temperature of 373 K. As stated emissivity for all surfaces is 1 (Black-body).

Parametric Hexahedral meshes with uniform refinements and different levels of coarseness   were created to get mesh independent results.

Fig. 1 The Ring Geometry

In the figure below (Fig.2) the different surfaces and the nomenclature of the different areas, from A1 – A7, is shown. For all these surfaces the net radiative heat flux values (Qr) will be calculated and compared.

 

Fig. 2 Sufaces of the Closed ring

 

RESULTS COMPARISON

While comparing the analytical results with SimScale results, following points were taken into account:

  1. 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. For this case as the temperatures are not very high (to assume that radiation is the dominant mode of heat transfer), convective losses can not be completely neglected. Also, both laminar and turbulent behaviours were evaluated which provided the same results.
  2. 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”.
  3. 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. The results presented below are for the case where finest radiation resolution was used.

 

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.
  • Unlike the analytical solution where the summation of the net radiative heat transfer from all the surface add up to zero, the results from the platform do not. As mentioned above, this can be attributed to the fact that apart from surface to surface radiation, heat exchange between fluid and surfaces also take place.

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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