Two-scale mathematical model of the coal–methane–air particle–gas suspension combustion

This paper presents a mathematical model of combustion of a coal dust particle–gas suspension in a methane–air mixture, which takes into account the inhomogeneity of temperature distribution in the particles. The particle-gas suspension state parameters are determined by the model of the dynamics of a two-phase two-velocity reacting gas-dispersed medium. The combustion of coal dust particles is simulated using a local mathematical model of a heterogeneous reaction on the particle surface and particle heating. A solution to local problems of coal dust particle combustion is used determine the heat release rate of the entire set of particles in the heterogeneous reaction of coal dust with oxygen and the heat exchange with gas. Dependences between the combustion front propagation velocity and the mass concentration of coal dust and the volumetric concentration of methane are determined. The estimated combustion front velocity in a methane-air mixture with no coal dust is in good agreement with experimental data. The comparison of calculating the flame velocity in a coal–methane–air mixture using two models (with and with no account for the inhomogeneity of the temperature distribution in the particles) is given. This comparison shows a significant difference in the values of the estimated combustion front velocity of rapidly burning gas–particle suspensions. For slowly burning particle–gas suspensions, this difference decreases. The developed model explains the shift of the maximum flame propagation velocity in the coal–methane–air mixture toward the excess of fuel in air.