A full spectrum k-distribution based non-gray radiative property model for unburnt char

By using the concept of weighted sum of four gray particles and spectrum k-distribution (WSGP-SK), a non-gray radiative property model for unburnt char particles is developed. Based on the carbon burnout kinetic model for structure during oxidation, and the linear mixed approximation theory for complex index of refraction, spectral radiative properties of unburnt char particles are first calculated as function of the burnout ratio by Mie theory. Referring to the full spectrum k-distribution model, k-distribution is applied to reorder absorption and scattering efficiencies of particles. Then, weighting factors and efficiency factors of the non-gray radiative property model are directly obtained from Gaussian integral points of k-distribution. The model is validated against the benchmark solutions of line-by-line (LBL) model. Maximum relative errors of this model are 3% and 15% for radiative heat fluxes and source terms in non-isothermal inhomogeneous particulate media, respectively. The assumption of linearly varying radiative properties with burnout ratio (Lockwood et al. 1986) will result in a predicted deviation of 53% for radiative source terms. Results also show that this non-gray model is remarkably better than the Planck mean method. Moreover, a satisfactory comparison with LBL solutions is achieved in the gas and particle mixture by combining the non-gray WSGG-SK model (Guo et al. 2015). As a radiation sub-model, this non-gray radiative property model can significantly improve prediction accuracy of radiative heat transfer in oxy-fuel combustion.