k-Distribution Thermal Radiation Model Reference

This model is a refinement of the Weighted Sum of Gray Gases Method (WSGGM) for use in combustion simulations. It provides a smoother set of weight functions and so is more easily integrated, though at a higher computational cost.


Theory	See Correlated k Distribution Gray Gases Method.
Provided By	[physics continuum] > Models > Radiation Spectrum (Participating)
Example Node Path	Continua > Physics 1 > Models > k-Distribution Thermal Radiation
Requires	Material: Gas or Multi-Component Gas Space: any Optional Models: Radiation Radiation: Participating Media Radiation (DOM)
Properties	Key properties: Number of Quadrature Points, Gauss Quadrature Shape Factor. See k-Distribution Thermal Radiation Properties.
Activates	Model Controls (child nodes)	Thermal Environments > Radiation Temperature. See Setting the Thermal Environment.
	Materials	See k-Distribution Thermal Radiation Materials and Methods.
	Boundary Inputs	See k-Distribution Thermal Radiation Boundary Settings.
	Field Functions	Absorption Coefficient n, Boundary Emissivity, Boundary Emissivity on External Side, Boundary Reflection Specularity, Boundary Reflection Specularity on External Side, Boundary Reflectivity, Boundary Reflectivity on External Side, Boundary Transmissivity, Scattering Coefficient , User-specified Diffuse Flux See Radiation Field Functions Reference.

k-Distribution Thermal Radiation Properties

Number of Quadrature Points: The value of $n$ in Eqn. (1739) in the Gaussian quadrature scheme used by the k-distribution method.
Gauss Quadrature Shape Factor: The value of $α$ in Eqn. (1740) in the Gaussian quadrature scheme used by the k-distribution method.

k-Distribution Thermal Radiation Materials and Methods

Selecting the k-Distribution Thermal Radiation model adds the Absorption Coefficient and Scattering Coefficient nodes under the material (Gas or Multi-Component Gas) model node.

Absorption Coefficient

The absorption coefficient of the radiative material.

Method	Corresponding Method Node
Correlation Based k-Distribution Method	Correlation Based k-Distribution Method A refinement of the Weighted Sum of Gray Gases method. It provides a smoother set of weight functions and so is more easily integrated, though at a higher computational cost. The method uses a spectral reordering method for specifying the absorption coefficients of gaseous H₂O and CO₂. See Correlated k Distribution Gray Gases Method

Scattering Coefficient

Scattering coefficient of the radiative material

k_{s}

in Eqn. (1734).

k-Distribution Thermal Radiation Boundary Settings

Inflow, Outflow, Wall, and Free Stream Boundaries

Surface Emissivity: The ratio of the power that a body emits to the power it would emit as a black body at the same temperature. See Emissivity.
Surface Reflectivity: The ratio of reflected radiant energy over incident radiant energy at a given surface. See Reflectivity.
Surface Transmissivity: The ratio of transmitted radiant energy over incident radiant energy at a given surface. See Transmissivity.

AMG Linear Solver Defaults

For the k-Distribution Thermal Radiation model, the default value for Cycle Type is Flex Cycle and the Convergence Tolerance is tightened during the first outer iteration by the DO Radiation solver, to propagate the stored spectral solution on the boundary to the participating media. See AMG Linear Solver Reference and The DO Radiation Solver.

Setting the Thermal Environment

When the k-Distribution Thermal Radiation model is used, each continuum is required to have a thermal environment. This thermal environment is a simplified representation of the environment surrounding the continuum, from the standpoint of thermal radiation. The environment is fully defined by ascribing the desired value to the Radiation Temperature.

The thermal environment is modeled as a black body with unity emissivity, and hence can be characterized solely with the Radiation Temperature. This temperature defines the energy that is effectively radiated from the environment. However, since there has to be only one environment, the value of the Radiation Temperature in every continuum must be the same.