Angular False Scattering in Radiative Heat Transfer Analysis Using the Discrete-Ordinates Method With Higher-Order Quadrature Sets

Abstract

The SN quadrature set for the discrete-ordinates method is limited in overall discrete direction number in order to avoid physically unrealistic negative directional weight factors. Such a limitation can adversely impact radiative transfer predictions. Directional discretization results in errors due to ray effect, as well as angular false scattering error due to distortion of the scattering phase function. The use higher-order quadrature schemes in the discrete-ordinates method allows for improvement in discretization errors without an overall directional limitation. In this analysis, four higher-order quadrature sets (Legendre-Equal Weight, Legendre-Chebyshev, Triangle Tessellation, and Spherical Ring Approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Radiative heat fluxes, calculated at low direction number, are compared to the SN quadrature and Monte Carlo predictions to gauge quadrature accuracy. Additionally, investigation into the reduction of angular false scattering with sufficient increase in direction number using higher-order quadrature, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. While higher-order quadrature sets are found to effectively minimize angular false scattering error, it is found to be much more computationally efficient to implement proper phase function normalization for accurate radiative transfer predictions.