Fundamental development of discrete ordinates interpolation method for solution of radiative energy balance in two-dimensional medium

Abstract

Numerical schemes and comparison of predictions of radiative heat transfer for the first and the second order discrete ordinates interpolation methods (DOIM1 and DOIM2) are presented. The formulations are followed by derivation of numerical schemes for two-dimensional structured body-fitted grids. With varying optical depths and numbers of grids and ordinates, radiative wall heat fluxes by DOIM1 and DOIM2 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 DOIM1 and DOIM2 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 DOIM1 and DOIM2 are in good agreement with the exact solutions or the zonal results. DOIM1 gives more accurate results than DOIM2 for most of the tested optical depths and numbers of grids and ordinates. Their grid and ordinate dependencies are also discussed in depth. Another radiative heat transfer problem for absorbing/emitting and nonscattering medium contained between infinite concentric cylinders is solved by DOIM1. The emissive power and wall heat fluxes by DOIM1 are compared with the results by DOM-OCC (Discrete Ordinates Method in a Orthogonal Curvilinear Coordinate) and Monte Carlo method. Next, the numerical convergence characteristics of the pointwise and the control volume energy balance equations of thermal radiation problems in absorbing, emitting and nonscattering media are examined with DOM and DOIM1. Iteration processes for the solution of temperature are scrutinized and a sufficient condition for convergence is presented. An explicit method using only the diagonal terms in the coefficient matrix A‘ of the radiative energy balance equati...