On Multilayer Modeling of Radiative Transfer for Use With the Multisource k Distribution Method for Inhomogeneous Media

Abstract

A nonisothermal medium is modeled using the multilayer approach in which the continuous temperature distribution in a onedimensional system as modeled as being piecewise constant. This has been shown to provide accurate results for a surprisingly small number of layers. Analysis is performed on a nonisothermal gray medium to attempt to characterize the ways in which the errors introduced by the multilayer modeling change with various physical parameters namely, the optical thickness and the temperature or emissive power gradient. A demonstration is made of how the multisource kdistribution method is capable of evaluating the heat flux within a onedimensional system with piecewise constant temperature distribution with linebyline accuracy with a significant decrease in computational expense. The kdistribution method for treating the spectral properties of an absorbing–emitting medium represents a powerful alternative to linebyline calculations by reducing the number of radiative transfer equation (RTE) evaluations from the order of a million to the order of 10 without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the kdistribution method is formally exact. However, when no appropriate reference temperature can be defined, the method results in errors. The multisource kdistribution method extends the kdistribution method to problems with piecewise constant temperature and optical properties.