Absorbing-Scattering Medium (Radiation in Absorbing-Scattering 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 and the scattered radiation, depending on the Radiation discretization method selected in the Participating Media Settings section of the interface. In particular, it can be used for the modeling of light diffusion in a non-emitting medium.
It computes the radiative heat source term Qr (SI unit: W/m3), defined by:
where
•
κ is the absorption coefficient (SI unit: m–1).
•
G is the incident radiation (SI unit: W/m2), defined by
where
•
 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 with no emission term
•
β = κ + σs is the extinction coefficient (SI unit: 1/m).
•
σs is the scattering coefficient (SI unit: 1/m).
•
is the scattering phase function (dimensionless)
If the Radiation discretization method is Discrete ordinates method, G is defined by
and
(6-1)
where
•
Si is the ith discrete ordinate.
•
Ii is the ith component of the radiative intensity.
•
ωj is the ith quadrature weight.
If the Radiation discretization method is P1 approximation, the incident radiation G is the solution of the following equation
(6-2)
where DP1 is the P1 diffusion coefficient.
When Wavelength dependence of radiative properties is Solar and ambient or Multiple spectral bands in the Participating Media Settings section of the interface, Equation 6-1 and Equation 6-2 are solved for each spectral band k: Ii,k is the ith component of the radiative intensity for spectral band k, and Gk is the incident radiation for spectral band k.
The characteristics of the two available radiation discretization methods are summarized in the following table.
Table 6-1: Discretization methods for Radiation in Absorbing-Scattering Media (RASM interface)
Option
DOM
P1
Optical thickness validity
All
τ>>1
Absorption 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 should be considered as well, the Participating Medium (Radiation in Participating Medium Interface) node should be used instead. The table below describes the different effects accounted for by the interfaces found under the Heat Transfer>Radiation branch ().
Table 6-2: 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 Default 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.
The Absorption coefficient κ (SI unit: 1/m) uses values From material by default.
For User defined, set a value or expression. You may set a temperature-dependent absorption coefficient through the use of the variable rasm.T.
If Wavelength dependence of radiative properties is Solar and ambient or Multiple spectral bands, the wavelength may be accessed through the rasm.lambda variable. Any expression set for the absorption coefficient is then averaged on each spectral band to obtain a piecewise constant absorption coefficient. If the average value of the absorption coefficient on each band is known, you may use instead the User defined for each band option to avoid the evaluation of the average.
When Absorption coefficient is set to User defined for each band, enter a value for the Absorption coefficient for each spectral band in the table displayed underneath. Within a spectral band, each value is supposed to be wavelength-independent.
Scattering
This section sets the scattering property of the participating medium. The Scattering coefficient σs should be specified.
The Scattering coefficient σs (SI unit: 1/m) uses values From material by default.
For User defined, set a value or expression. You may set a temperature-dependent scattering coefficient through the use of the variable rasm.T.
If Wavelength dependence of radiative properties is Solar and ambient or Multiple spectral bands, the wavelength may be accessed through the rasm.lambda variable. Any expression set for the scattering coefficient is then averaged on each spectral band to obtain a piecewise constant scattering coefficient. If the average value of the scattering coefficient on each band is known, you may use instead the User defined for each band option to avoid the evaluation of the average.
When Scattering coefficient is set to User defined for each band, enter a value for the Scattering coefficient for each spectral band in the table displayed underneath. Within a spectral band, each value is supposed to be wavelength-independent.
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 using the cosine of the scattering angle, μ0:
•
Isotropic (the default) corresponds to the scattering phase function (μ0) = 1.
•
For Linear anisotropic it defines the scattering phase function as (μ0) = 1 + a1μ0. Enter the Legendre coefficient a1.
•
For Polynomial anisotropic it defines the scattering phase function as
Enter each Legendre coefficient a1, …, a12 as required.
•
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.
For Linear anisotropic, Polynomial anisotropic, and Henyey-Greenstein, select the Wavelength-dependent scattering type check box to average each Legendre coefficient a1, …, a12 or the Anisotropy parameter μ to obtain piecewise constant coefficients on each spectral band.
•
Theory for Radiation in Participating Media
•
Discrete Ordinates Method (DOM)
•
P1 Approximation Theory
•
Radiation in Absorbing-Scattering Media Theory
Location in User Interface
Context Menus
 Radiation in Absorbing-Scattering Media>Absorbing-Scattering Medium
Ribbon
Physics Tab with Radiation in Absorbing-Scattering Media selected:
Domains>Absorbing-Scattering Medium