Radiation

Radiation is defined as the transference of energy using electromagnetic waves. When these waves impact on any type of matter, they become heat. All bodies with a temperature greater than absolute zero emit radiation, and in contrast to conduction or convection, this phenomenon requires no medium.

In SimScale, radiation is modelled using a Diffuse View Factors Model. This approximation implies several assumptions that can be applied to most of the engineering problems:

  • Diffuse radiation is hemispheric and uniform. For every surface, its emission is independent of direction.
  • View Factors only consider the radiative heat exchange between surfaces. Thus, the medium (air) is supposed to have no interference. This is true when there are no particles suspended in the fluid which make it less transparent (like dust or fog). The View Factor of two surfaces measures the proportion of the total radiation that is exchanged between them. It only depends on geometrical parameters.

The different surfaces of the model will exchange heat between them, and they will also provide or subtract heat from the adjacent fluid. Coupling of both convection and radiation will be achieved once the simulation converges.

In SimScale, Radiation is available in Convective Heat Transfer simulations. If we switch the radiation interruptor on, two additional fields appear when assigning the Boundary Conditions: the Radiative Behavior and Additional Radiative Source.

Radiative Behavior

The Radiative Behavior specifies the relationship between the Net Radiative Heat per Surface Unit Qr [W/m²] and the Temperature of every surface Ts [K]:

  • A Transparent surface establishes no relation between Qr and Ts. This means that the surface temperature remains unaffected by the net radiative heat that the surface emits or receives. This implies that Ts is determined by other heat transport means (conduction or convection) or by a boundary condition. This option is mainly applied to surfaces that are not solid, like inlets or outlets (for example, an open window).

    Transparent surface boundary condition for radiation.
  • A Grey-Body behavior couples Qr and Ts using the Stefan-Boltzmann Law for diffuse and hemispheric radiation. Supposing two different surfaces S and S’, the Qr that S provides to S’ is:

Qr(S→S’) = F𝝐 𝝈(Ts-Ts)⁴

F is the View Factor between S and S’, 𝝈 is the Stefan-Boltzmann constant (𝝈 = 5.6696 ·10-8 W /m²K), and 𝝐 is the emissivity of the surface S. This value depends on the material of the surface, and it measures its capability to emit radiation. The default value that appears is 0.9, which is a good approximation for walls made of brick or concrete.

Grey body boundary condition for radiation.

 

Additional Radiative Source

Apart from the radiative heat interchange that the surfaces will perform, we can set an additional radiative source. This source represents any additional (mainly external) source of radiation that goes through the surface and it will not heat it up. The best example is the solar radiation getting into the domain through an open window (Radiative behavior: Transparent; Additional radiative source different from zero).

Additional Notes

  • Radiation becomes more important when the simulation has high Temperatures.
  • To save time and avoid mistakes, Transparent radiative behavior is assigned by default to all inlets and outlets.
  • Simulations which include radiation often need more iterations to converge because of this additional heat transference. It is advisable to switch off the “Compressible” option in SimScale.
  • Emissivity is considered constant for every material. In reality, it depends on the wavelength of the radiation that is being emitted. In CFD simulations, the total emissivity is specified, which is the integrated emissivity over all wavelengths.
  • Solar radiation is usually directional. However, it can be considered diffuse in cloudy days.
  • Currently, radiation is only included in Convective Heat Transfer simulations, so absorption or transmission of radiative energy are not considered. Also, symmetric boundary conditions are not supported by the current radiation solver.

To read more about supported radiation check out this documentation page. 

Validation cases

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