Unsteady Spherical Flames in Dusty Gases

Abstract

Abstract We examine an expanding spherical premixed flame propagating in a mixture containing inert dust. The presence of the dust generates a significant radiative energy flux that influences the flame speed. With the adoption of a hydrodynamic description in which stretch effects are accounted for using an empirical formula, and with the use of the Eddington approximation to describe the radiation, a simple numerical problem is formulated valid for that initial time interval in which the flame-temperature changes by O(e) amounts where c is the small inverse activation energy. Solutions are constructed using parameter values appropriate to lean CH^/air mixtures, and for modest particle loadings. We describe the competition between the Zeldouich-Spalding effect in which radiative losses on the diffusive scale tend to quench the flame, and the Joulin effect in which radiative preheating on the scale of the Planck length tends to strengthen the flame.