Comparison of Phase Function Normalization Techniques for Radiative Transfer Analysis Using DOM

Five phase-function (PF) normalization techniques are compared using the discrete-ordinate method (DOM) for modeling diffuse radiation heat transfer in participating media. Both the mathematical formulation and the impact on the conservation of both scattered energy and PF asymmetry factor for both Henyey-Greenstein (HG) and Legendre PF distributions are presented for each technique. DOM radiation transfer predictions generated using the five normalization techniques are compared to high-order finite-volume method, to gauge their accuracy. The commonly implemented scattered energy averaging technique cannot correct asymmetry factor distortion after angular discretization, and thus large errors due to angular false scattering are prevalent. Another three simple techniques via correction of one or two terms in the PF are shown to reduce normalization complexity whilst retaining diffuse radiation computation accuracy for HG PFs. However, for Legendre PFs, such simple normalization is found to result in unphysical negative PF values at one or few correction directions. The relatively complex Hunter and Guo 2012 technique, in which normalization is realized through a correction matrix covering all discrete directions, is shown to be highly applicable for both PF types.