BEHAVIOUR AT ACOUSTIC WAVE FRONTS IN A LAMINAR DIFFUSION FLAME

Abstract

The set of linear first-order partial differential equations which governs propagation of infinitesimal disturbances through the spatially non-uniform field of a diffusion flame of reaction-broadened type is derived. Attention is focused on the jump in the normal derivative of flow quantities, like pressure and density, which can occur at a wave-front propagating at the local frozen sound speed, and a result is obtained which exhibits the general effects of both spatial non-uniformity and of the chemical dis-equilibrium which is a feature of the reaction-broadened flame. Amplification of disturbances can occur, especially from the latter source, and the importance of this result for an understanding of extinction is commented upon. Two special cases give specific results which help to illuminate the general theory.