A HYBRID SOLVER FOR THE RADIATIVE TRANSFER EQUATION IN NONGRAY COMBUSTION GASES

Abstract

The discrete ordinates method (DOM) or its variant, the finite angle method (FAM), is a popular solution method for the radiative transfer equation (RTE). Accurate solution to the RTE using the DOM or FAM requires many solid angles (directions) in multidimensional geometry. In combustion gases, where the absorption coefficient oscillates wildly and the RTE must be solved repeatedly, this method becomes computationally intractable. Here, the FAM is hybridized with the P₁ approximation, which is efficient since it requires solution to a single partial differential equation as opposed to a set of directional RTEs in the FAM. The P₁ approximation is accurate when the intensity field is fairly isotropic, as evidenced in optically thick media. Hence, the hybridization employs the FAM for optically thin and intermediate spectral intervals and employs the P₁ approximation for optically thick spectral intervals. The objective of the present study is to determine optimal parameters for hybridization that can provide the best compromise between accuracy and efficiency. Using a narrowband-based box model for carbon dioxide and water vapor, the nongray radiative transfer equation is solved in media with nonuniform properties enclosed in multidimensional enclosures. Two different approaches-cutoff and filter optical thickness-are investigated for hybridizing. Several problems, both two- and three-dimensional, and with and without coupling to other modes of heat transfer are considered. The filter approach was found to be the best choice for prediction of the radiative source and temperature (in the case of a coupled mode), while the cutoff approach was found to be the best for prediction of wall radiative heat fluxes.