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 one-dimensional 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 k-distribution method is capable of evaluating the heat flux within a one-dimensional system with piecewise constant temperature distribution with line-by-line accuracy with a significant decrease in computational expense. The k-distribution method for treating the spectral properties of an absorbing-emitting medium represents a powerful alternative to line-byline 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 k-distribution method extends the k-distribution method to problems with piecewise constant temperature and optical properties.

The Scaled SLW model of gas radiation in non-uniform media based on Planck-weighted moments of gas absorption cross-section

“…It appears that the Tref = Tmax is the optimal choice of reference temperature for this model. This has been suggested previously [14,28]. The Rank Correlated SLW (RC-SLW) model yields accurate predictions which are insensitive to the choice of source temperature, Tb.…”

“…Because this assumption, in general, is not valid for real spectra, accuracy of the predictions depends critically on the choice of reference state. The reference gas temperature Tref has been chosen from some physical consideration which has included the maximum temperature in the system, the minimum temperature in the system, the volume-averaged temperature, the Planck mean temperature, and the emission-weighted temperature [6,14].…”

“…However, the method remains approximate. A more accurate but more computationally expensive alternative is presented by Tencer and Howell [14]. Their multi-source full spectrum k-distribution method is capable of providing exact results for one-dimensional geometries with piecewise constant temperature and absorption coefficient in the same way that the full spectrum k-distribution method is able to provide exact results for homogeneous media.…”

“…Their multi-source full spectrum k-distribution method is capable of providing exact results for one-dimensional geometries with piecewise constant temperature and absorption coefficient in the same way that the full spectrum k-distribution method is able to provide exact results for homogeneous media. The approach as outlined in [14] provides a significant increase in accuracy when compared to other kdistribution based approaches while remaining significantly less computationally expensive than a standard line-by-line solution. The errors introduced by this method are entirely due to the multilayer approximation.…”

Coupling radiative heat transfer in participating media with other heat transfer modes

“…Band models [121][122][123][124][125][126][127][128][129] accomplish this by defining contiguous wavelength intervals with similar optical properties together and making some assumption on how the properties vary within a given band. The k-distribution [130][131][132][133][134][135][136][137][138][139][140], spectral-line-weighted (SLW) sum-of-gray gases [141][142][143][144][145][146], and cumulative wavenumber (CW) [144,145,147,148] methods work by allowing the wavelength intervals that are grouped together to not be contiguous. Modest and Zhang [134] have shown that the SLW method is a simplified version of the fullspectrum k-distribution method.…”