Grouping the wall spectral bands for an effective computation of the radiative transfer in participating media bounded by non-gray walls

Abstract

This study presents a methodology to solve the radiative transfer in participating media bounded by non-gray walls for direct use with global gas models. The method is based on grouping the wall emissivity/absorptivity spectral bands (GWB) to employ the total emissivity and absorptivity, instead of their spectral distributions, in the integration of the radiative transfer equation (RTE). The total emissivity is calculated from the wall surface temperature, whereas the concept of a reference medium temperature is introduced for determining the total absorptivity. Though the assumptions involved in the method are analyzed in the framework of the weighted-sum-of-gray-gases (WSGG) model, they can be readily extended to any global gas model. The performance of the GWB method is assessed for two test cases, consisting of a non-homogeneous, non-isothermal, one-dimension medium slab bounded by walls with different spectral emissivities and absorptivities. For these cases, choosing the medium-averaged temperature as the reference temperature to compute the wall total absorptivity led to an accurate prediction of the radiative heat transfer, with errors below 4% relative to a reference solution obtained by line-by-line integration.