Evaluation of angular resolution requirements in the finite-volume-method solution of the radiative transfer equation

Abstract

The performance of the finite volume method (FVM) used to solve the radiative transfer equation (RTE) is investigated in a simple benchmark configuration corresponding to a hot plate radiating towards sensors located at various separation distances. The study is performed using the Fire Dynamics Simulator (FDS). The objective of this study is to evaluate angular resolution requirements in the FVM-RTE solver to provide suitable accuracy and to avoid ray effects. The FDS-simulated radiative heat fluxes are compared to exact analytical expressions based on view factors. It is found that the numerical error has spatial and angular discretization components. The spatial discretization error is controlled by the size of computational cells and is generally small. The angular discretization error is controlled by the number of radiation angles (NRA) and becomes large in the far-field unless NRA is sufficiently large. A design criterion is proposed to select suitable values of NRA to achieve converged numerical solutions. This criterion is applied to the case of radiant emissions from a benchmark pool fire configuration; this application illustrates how the choice of NRA should be adjusted depending on the size of the region where accurate calculations of radiative heat fluxes are expected.