Schemes and Applications of First and Second-Order Discrete Ordinates Interpolation Methods to Irregular Two-Dimensional Geometries

Abstract

This paper presents numerical schemes and comparison of predictions of radiative heat transfer for the first and the second order discrete ordinates methods (DOM1 and DOM2) using an interpolation scheme. The formulations are followed by derivation of numerical schemes for two-dimensional body fitted grids. With varying the optical depths and the numbers of grids and ordinates, radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with the exact solutions for three kinds of two-dimensional enclosures (square, quadrilateral, and J-shaped) containing absorbing/emitting and nonscattering media of known temperature with cold black walls. Emissive power and radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with zonal results for two-dimensional square enclosure containing absorbing/emitting and isotropically scattering medium of known uniform heat source with cold black walls. The results of DOM1 and DOM2 are in good agreement with the exact solutions or the zonal results. DOM1 gives more accurate results than DOM2 for most of the tested optical depths and the numbers of grids and ordinates. These methods appear as powerful candidates of very versatile radiation analysis tool. Their grid and ordinate dependencies are also discussed in depth.