Radiation in Participating Media (RPM Interface)
This node should be used when radiation occurs in a medium not completely transparent, in which the radiation rays interact with the medium. It computes the radiative heat source term Qr (SI unit: W/m3), defined by:
where
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κ is the absorption coefficient (SI unit: m-1).
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G is the incident radiation (SI unit: W/m2), defined by
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 I(Ω) is the radiative intensity (SI unit: W/(m2·sr)) at a given position following the Ω direction, that satisfies the radiative transfer equation
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Ib(T) is the blackbody radiative intensity (SI unit: W/(m2·sr)), defined as
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 nr is the refractive index (dimensionless).
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σ is the Stefan-Boltzmann constant (SI unit: W/(m2·K4)).
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β = κ + σs is the extinction coefficient (SI unit: 1/m).
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σs is the scattering coefficient (SI unit: 1/m).
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φ(Ω′, Ω) is the scattering phase function (dimensionless).
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T is the temperature (SI unit: K).
It takes into account the absorbed, emitted, and scattered radiation of the participating medium.
Two approximation methods are available for the radiation discretization method. The characteristics of each of them are summarized in the following table.
Table 6-2: Discretization methods for Radiation in Participating Media (RPM interface)
Option
Discrete ordinates method
P1 approximation
Optical thickness validity
All
τ>>1
Scattering modeling
Linear
Polynomial
Linear
Computation of G
Computational cost
High: up to 80 additional degrees of freedom (Ii)
Medium: 1 additional degree of freedom (G)
Models Inputs
There is one standard model input — the Temperature T. The default is 293.15 K and is used in the blackbody radiative intensity expression.
Absorption
The Absorption coefficient κ should be specified. It defines the amount of radiation, κI(Ω), that is absorbed by the medium.
Scattering
This section sets the scattering property of the participating medium.
The Scattering coefficient σs should be specified.
Choose in addition the Scattering type: Isotropic, Linear anisotropic, or Polynomial anisotropic (only with Discrete ordinates method). This setting provides options to approximate the scattering phase function using the cosine of the scattering angle, μ0:
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Isotropic (the default) corresponds to the scattering phase function φ(μ0) = 1.
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For Linear anisotropic it defines the scattering phase function as φ(μ0) = 1 + a1μ0. Enter the Legendre coefficient a1.
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For Polynomial anisotropic it defines the scattering phase function as
Enter each Legendre coefficient a1, …, a12 as required.
Initial Values
When Discrete ordinates method is selected as the Radiation discretization method for the physics interface, the Initial radiative intensity I should be specified. The default is rpm.Ibinit, which is the blackbody radiative intensity at initial temperature.
When P1 approximation is selected as the Radiation discretization method for the physics interface, the Initial incident radiation G should be specified. The default is (4*pi)*rpm.Ibinit, computed from the blackbody radiative intensity at initial temperature.
Theory for Radiation in Participating Media
Discrete Ordinates Method (DOM)
P1 Approximation Theory
Radiative Heat Transfer in a Utility Boiler: Application Library path Heat_Transfer_Module/Thermal_Radiation/boiler
Radiative Heat Transfer in Finite Cylindrical Media: Application Library path Heat_Transfer_Module/Verification_Examples/cylinder_participating_media
Radiative Heat Transfer in Finite Cylindrical Media—P1 Method: Application Library path Heat_Transfer_Module/Verification_Examples/
cylinder_participating_media_p1
Location in User Interface
Context menus
 Radiation in Participating Media>Radiation in Participating Media
Ribbon
Physics Tab with Radiation in Participating Media selected:
Domains>Radiation in Participating Media>Radiation in Participating Media