Evaluation of different gray gas formulations against line-by-line calculations in two- and three-dimensional configurations for participating media composed by CO2, H2O and soot

Abstract

This paper presents an assessment of the performance of different gray gas (GG) formulations in participating media composed by carbon dioxide, water vapor and soot for two- and three-dimensional configurations, considering prescribed temperature and species concentration distributions typical of fires and combustion problems. Results for the radiative heat source and the wall radiative heat flux obtained by each GG formulation are compared to solutions employing the more accurate method of line-by-line integration. The radiative transfer equation is solved in a modified version of the Fire Dynamics Simulator base-code, into which all necessary models have been implemented. For mixtures without soot, the majority of the GG formulations performs poorly, some presenting domain-average errors above 100%; however, as soot is introduced and its volume fraction fv increases, there is a significant improvement in accuracy, with almost all formulations yielding errors of about 5% for cases with fv=10−5. Among the tested models, those based on the weighted-sum-of-gray-gases correlations have lower errors than those developed from curve-fittings of the Planck-mean absorption coefficient for weakly sooting mixtures, while the opposite is verified for strongly sooting media.