Participating Medium (Radiation in Participating Medium 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 heating due to the propagation of the rays, and takes into account the absorbed, the emitted, and the scattered radiation, depending on the Radiation discretization method selected in the Participating Media Settings section of the interface.
It computes the radiative heat source term Q (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).
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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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T is the temperature (SI unit: K)
G is defined by
where
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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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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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is the scattering phase function (dimensionless)
If.the Radiation discretization method is Discrete ordinates method, G is defined by
and
where
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Si is the i-th discrete ordinate.
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Ii is the i-th component of the radiative intensity.
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ωj is the i-th quadrature weight.
If the Radiation discretization method is P1 approximation, G is the solution of the following equation
(6-7)
where DP1 is the P1 diffusion coefficient.
The characteristics of the two available radiation discretization methods are summarized in the following table.
Table 6-3: Discretization methods for Participating Medium (RPM interface)
Option
DOM
P1
Optical thickness validity
All
τ>>1
Absorption modeling
Yes
Yes
Emission modeling
Yes
Yes
Scattering modeling
Linear
Polynomial
Linear
Computational cost
High: up to 80 additional degrees of freedom (Ii)
Medium: 1 additional degree of freedom (G)
If radiative emission may be neglected, the Absorbing-Scattering Medium (Radiation in Absorbing-Scattering Medium Interface) node may be used instead. The table below describes the different effects accounted for by the interfaces found under the Heat Transfer>Radiation branch ().
Table 6-4: Radiation Effects Computed by the Radiation Interfaces
Radiation Effect
RPM
RASM
RBAM
Absorption
Yes
Yes
Yes
Scattering
Yes
Yes
No
Emission
Yes
No
No
Model Input
This section has fields and values that are inputs to expressions that define material properties. If such user-defined property groups are added, the model inputs appear here.
Temperature
This section is available when temperature-dependent material properties are used. The default Temperature is User defined. When additional physics interfaces are added to the model, the temperature variables defined by these physics interfaces can also be selected from the list. The Common model input option corresponds to the minput.T variable, set to 293.15 [K] by default) and all temperature variables from the physics interfaces included in the model. To edit the minput.T variable, click the Go to Source button (), and in the Common Model Inputs node under Global Definitions, set a value for the Temperature in the Expression for remaining selection section.
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, Polynomial anisotropic (only with Discrete ordinates method), or Henyey-Greenstein (only with Discrete ordinates method).
This setting provides options to approximate the scattering phase function φ 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 (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.
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For Henyey-Greenstein it defines the scattering phase function as
where is the anisotropy parameter and K is defined as follows to produce a normalized phase function:
For Linear anisotropic and Polynomial anisotropic, select the Normalize phase function check box to define a phase function such as
The normalization is automatically applied for the Henyey-Greenstein option.
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.
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Theory for Radiation in Participating Media
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Discrete Ordinates Method (DOM)
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P1 Approximation Theory
Radiative Heat Transfer in a Utility Boiler: Application Library path Heat_Transfer_Module/Thermal_Radiation/boiler
Radiative Cooling of a Glass Plate: Application Library path Heat_Transfer_Module/Thermal_Radiation/glass_plate
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>Participating Medium
Ribbon
Physics Tab with Radiation in Participating Media selected:
Domains>Radiation in Participating Media>Participating Medium