Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries

Abstract

This article compares predictions of radiative heat transfer in two-dimension al enclosures for several formulations of the discrete ordinates method. The discrete ordinates equations are formulated for an absorbing, isotropically scattering, and re-emitting medium enclosed by gray walls. Control volume based finite element formulations of the radiative transport equation (RTE) are presented for the primitive variable (PV) and even parity (EP) equations. These formulations are compared to the finite element formulation of the EP equations, to the control volume formulation of the PV radiative transport equation, and to exact solutions. Several test enclosures are modeled, including enclosures with either absorbing or isotropically scattering media. Solution accuracy is investigated for two angular discretization schemes: 1) the Sn discrete ordinates approximation and 2) the piece wise constant angular approximation. The PV formulations of the RTE appear to be more accurate than EP formulations. Nomenclature Eh = emissive power, aT4, W/m2 G = incident energy, J477/ dil, W/m2 G* = nondimensional incident energy, GIEh I = intensity, /(r, ft), W/m2- sr M = total number of discrete ordinate directions N = total number of global nodes NJ = basis function N6 = number of divisions in polar direction Nfi = number of divisions in azimuthal direction n = surface normal Q* = nondimensional net wall heat flux, qlEh q =