Easily computable good approximations for spectral radiative properties of particle-gas components and mixture in pulverized coal combustors

A rather large computational effort is required for calculating the exact values of the spectral radiative extinction, absorption and scattering coefficients in pulverized coal combustors, which contain a polydispersed solid-gas mixture of reactants and combustion products (coal, char, fly ash and soot particles and gaseous components). This computation becomes an especially significant problem in comprehensive modelling of coal combustors, where these properties vary in space and time and where the solution methods are iterative. A number of approximate expressions for calculating these coefficients for each of the particle types, requiring practically insignificant computational effort, are examined for a wide range of size parameters, by comparison with the results of the full Mie equations solved with Mathematica. A set of these approximations, which typically produce errors of <8.9% and <5,1% in the spectral extinction and scattering coefficients respectively, is recommended for use. The spectral absorption coefficient for the gas components is obtained by using the exponential wide-band model. A solution of a comprehensive model of a pulverized anthracite coal combustor shows that the combined error introduced by the recommended radiative property approximations generates an error of < 1.45% in the combustor gas temperature and radiation intensity profile predictions.