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A new Full-Spectrum Correlated-k Distribution has been developed, which provides an efficient means for accurate radiative transfer calculations in absorbing/emitting molecular gases. The Full-Spectrum Correlated-k Distribution can be used together with any desired solution method to solve the radiative transfer equation for a small number of spectral absorption coefficients, followed by numerical quadrature. It is shown that the Weighted-Sum-of-Gray-Gases model is effectively only a crude implementation of the Full-Spectrum Correlated-k Distribution approach. Within the limits of the Full-Spectrum Correlated-k Distribution model (i.e., an absorption coefficient obeying the so-called “scaling approximation”), the method is exact. This is demonstrated by comparison with line-by-line calculations for a one-dimensional CO2-N2 gas mixture as well as a two-dimensional CO2-H2O-N2 gas mixture with varying temperature and mole fraction fields.

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The weighted-sum-of-gray-gases approach for radiative transfer in nongray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (nonscattering media within a black-walled enclosure), any nongray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-I approximation for the equivalent gray media solutions. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95 percent) that are achieved.