Conservation of asymmetry factor in phase function discretization for radiative transfer analysis in anisotropic scattering media

A new phase function normalization technique is developed for use with anisotropic scattering media and is applied to the conventional discrete-ordinates method. The new approach is shown to ensure conservation of both scattered energy and phase function asymmetry factor after directional discretization when considering the Henyey-Greenstein phase function approximation. Results show the necessity of conservation of the asymmetry factor as well as of the scattered energy. Lack of either conservation can lead to false results for radiation analysis in highly anisotropic media. Wall flux profiles predicted by the normalized DOM in a highly anisotropic scattering cylinder are compared with FVM and isotropic scaling profiles. The effect of scattering albedo and optical thickness is examined. For the tested benchmark problem, it is found that heat flux profiles generated with the present normalization approach conform more accurately to both FVM and isotropic scaling profiles than when the previous normalization techniques are implemented.