On the Initiation of a Spherical Flame Kernel

Abstract

Using matched asymptotic expansions for large activation energies of the reaction rates, we have studied the structure and stability properties of steady spherical premixed flames which, in this geometry, need not be supported by any source (or sink) of fresh (or burned) gases. The radius of such unsupported flames strongly depends on the differential diffusion of heat and reactant and is interpreted as a flame initiation criterion which corresponds to an unstable equilibrium. This radius must be exceeded for the flame to self-propagate outward. We then focus attention on two means to modify, or even suppress, such a critical flame size, viz.: (i) the effect of a central heal source of constant power, and (ii) the addition of small amounts of a hydrogen-like reactive species with large molecular diffusivity. Multiple steady solutions-including stable, non-propagating flames-or the disappearance of equilibrium solutions are exhibited as are qualitative changes in flame dynamics.