Propagating Flames and their Stability

Abstract

Viewed on a hydrodynamical scale, a flame may be considered as a surface of discontinuity, separating burned from unburned gas. Unlike earlier treatments, which ignored the flame structure, the present study accounts for the interaction of the fluid flow with the transport processes and chemical reactions occurring inside the thin flame zone. Thus we derive, rather than prescribe, jump conditions across the flame front and an equation for the flame speed. The model, derived in coordinate invariant form, describes the dynamics of flame fronts including their stability. Particular attention is focused on the stability of curved flames, which reveal some characteristics that do not exist in the corresponding analysis of plane flames. Due to the stabilizing effect of curvature, disturbances of circular flames grow more slowly than those for plane flames. As in the case of plane flames, when the mass diffusivity of the deficient reactant component is sufficiently smaller than thermal diffusivity, curved flames can be stabilized. Finally, in contrast to plane flames, the effect of viscosity on curved flames is comparable to that of diffusion and is destabilizing. This dependence decreases with increasing radius of curvature and disappears entirely for plane flames.