Modeling combustion of lycopodium particles by considering the temperature difference between the gas and the particles

The effect of the temperature difference between the gas and the particles on propagation of premixed flames in a combustible mixture containing volatile fuel particles uniformly distributed in an oxidizing gas mixture is analyzed in this paper. It is presumed that the fuel particles vaporize first to yield a gaseous fuel, which is oxidized in the gas phase. The analysis is performed in the asymptotic limit, where the value of the characteristic Zel’dovich number is large, which implies that the reaction term in the preheating zone is negligible. Required relations between the gas and the particles are derived from equations for premixed flames of organic dust. Subsequently, the governing equations are solved by an analytical method. Finally, the variation of the dimensionless temperatures of the gas and the particles, the mass fraction of the particles, the equivalence ratio $\phi_g$ as a function of $\phi_u$, the flame temperature, and the burning velocities of the gas and the particles are obtained. The analysis shows that the calculated value of $\phi_g$ is smaller than unity for certain cases, even though $\phi_u\ge1$.