Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame

In this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (PN) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of PN and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of PN methods increases with its order, N, but the gain in accuracy reduces with the increase in N, i.e., improvement of P 7 over P 5 is less than that of P 3 over P 1 . This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM's accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers per-form better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P 1 to P 7 approxi-mations for PN, and 2 x 4, 4 x 4, 4 x 8, 8 x 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The PN solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radi-ant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated. (c) 2022 Elsevier Ltd. All rights reserved.