The cumulative wavenumber method for modeling radiative transfer in gas mixtures with soot

Recently, the cumulative wavenumber method was formulated and its viability demonstrated for the prediction of radiative heat transfer in high temperature CO2 and H2O. This paper presents enhancements to the cumulative wavenumber method, formalizing a mathematical definition for the cumulative wavenumber distribution function, introducing the joint cumulative wavenumber for gas mixtures, extending the method to non-homogenous, non-isothermal media, and demonstrating its application to gas mixtures with non-gray particles. The methodology for applying the cumulative wavenumber method to mixtures is explored using several different theoretical approaches. Model predictions are compared with line-by-line benchmark integration of the RTE. Finally, the relationship between the cumulative wavenumber and previously proposed spectral distribution functions is summarized.