Radiative Transfer as a Propagation Mechanism for Rich Flames of Reactive Suspensions

Abstract

We set up and study a basic model for combustion waves propagating in rich homogeneous mixtures of combustible solid particles and a gaseous oxidizer. These mixtures are viewed as one-temperature absorbing-emitting-reactive media. We assume further that: (i) the rate of the overall heterogeneous “oxidiber + particle” reaction is strongly temperature sensitive, but diffusion-saturated at sufficiently high temperatures, (ii) the only large-scale mechanisms of energy transport are convection and particle black-body radiation, (iii) the radiative transfer follows the Eddington differential approximation. We obtain the structure and burning speed of steady, planar combustion waves analytically by employing the method of matched asymptotic expansions which we use in the double limit of large Zel’dovitch numbers (an activation to thermal energy ratio) and of small Boltzmann numbers (a convective to forward radiant heat flux ratio). Two kinds of propagation regimes are exhibited, and the computation of their burning speed (an eigenvalue) is reduced to solving a small number of transcendental equations. The first kind of regime has a structure which resembles that of (diffusion-free) gaseous flames, heat convection being negligible at the leading order in the reaction zone. For the second kind of regime, the reaction zone includes sublayers where convection is significant, owing to the peculiarities of radiative transfer and its coupling with a strongly temperature-dependent rate of heat release. For some mixtures the two regimes may coexist, giving two burning speeds for the same mixture.