Numerical solutions of radiative heat transfer in combustion systems using a parallel modified discrete ordinates method and several recent formulations of WSGG model

Abstract

The aim of the paper is to perform 3D radiative transfer calculations in combustion gas mixtures. For this purpose, a parallel modified Discrete Ordinates Method with a cell-vertex formulation on unstructured tetrahedral grid is proposed for solving the Radiative Transfer Equation (RTE) in realistic geometries. Several recent formulations of the weighted-sum-of-gray-gases (WSGG) model are implemented. To reduce the false scattering, the cell-vertex formulation is combined with an Exponential scheme and is compared to the Step scheme. The results are then compared with published results on non-isothermal and non-homogeneous gas mixtures. The use of non-gray WSGG models shows a very good level of accuracy for the evaluation of wall heat transfer and radiative heat source. The Exponential scheme is more accurate than the Step scheme. The summation over the wavenumber spectrum of the radiative model is usually carried out after having computed the radiative quantities for each discrete angular direction. By summing first over the wavenumber spectrum, a reduction in the computation time is significantly obtained, up to a factor of 16 on a case study. Also, additionnal significant speedup is obtained with an efficient distributed and multi-threaded parallel algorithm. When the Step scheme is used, the computation time increases very slightly with the number of gray gases. The procedure to speed up the calculations can be applied to any arbitrary numerical method for solving the spectral RTE.