The rank correlated SLW model of gas radiation in non-uniform media

- Development of possible reference approaches in modelling of radiation transfer in non-uniform gaseous media within the framework of the Generalized SLW Model.
- The concept of rank correlation of full scale absorption cross-section is introduced.
- A novel rank correlated SLW Model is presented.
- The rank correlated SLW Model does not require specification of a reference gas thermodynamic state, and it preserves the emission term in the spectral integration of the Radiative Transfer Equation.

A comprehensive theoretical development of possible reference approaches in modelling of radiation transfer in non-uniform gaseous media is developed within the framework of the Generalized SLW Model. The notion of absorption spectrum “correlation” adopted currently for global methods in gas radiation is critically revisited and replaced by a less restrictive concept of rank correlated spectrum. Within this framework it is shown that eight different reference approaches are possible, of which only three have been reported in the literature. Among the approaches presented is a novel Rank Correlated SLW Model, which is distinguished by the fact that i) it does not require the specification of a reference gas thermodynamic state, and ii) it preserves the emission term in the spectrally integrated Radiative Transfer Equation. Construction of this reference model requires only two absorption line blackbody distribution functions, and subdivision into gray gases can be performed using standard quadratures. Consequently, this new reference approach appears to have significant advantages over all other methods, and is, in general, a significant improvement in the global modelling of gas radiation. All reference approaches are summarized in the present work, and their use in radiative transfer prediction is demonstrated for simple example cases. Further, a detailed rigorous theoretical development of the improved methods is provided.