Normalization of Various Phase Functions for Radiative Heat Transfer Analysis in a Solar Absorber Tube

Normalization of various phase functions is considered for accurately predicting radiative heat transfer. A solar absorber tube filled with anisotropic scattering working medium is used as an example. Analysis of a previous normalization technique shows that while it does conserve scattered energy exactly after discrete-ordinates method (DOM) discretization, the overall asymmetry factor of the phase function is distorted, leading to substantial changes in overall scattering effect. A new normalization technique that conserves asymmetry factor and scattered energy simultaneously is investigated. The impact of lack of asymmetry factor conservation is analyzed for both the Legendre polynomial and the Henyey–Greenstein phase function approximations. Variations of medium optical thickness, scattering albedo, asymmetry factor, and side-wall emissivity are scrutinized to determine the effects of said parameters on wall heat flux and energy absorbing rate inside the absorber tube. Side-wall heat flux is found to increase with increases in asymmetry factor, optical thickness, and wall emissivity, and with decreases in scattering albedo. Energy absorbing rate profiles are found to depend greatly on optical thickness and scattering albedo.