Influence of a hydrodynamic field on laminar flame stability

Abstract

The hydrodynamic stability of a plane flame front has been studied by L. D. Landau in [1], where it was shown that it is absolutely unstable. The aim of this note is to clarify the influence of the hydrodynamic field curvature on flame stability. Flame stability is analyzed within the framework of Landau's theory, in which the flame front is represented by a surface on which the velocity, density, and temperature values experience discontinuities. Viscosity, diffusion, and heat conduction are neglected. The front moves at a given constant velocity relative to the gas. The gas is assumed to be incompressible in front of and behind the front. It is shown that fields exist which will both stabilize and destabilize the gas. A cylindrical flame formed by a concentrated source of given intensity is examined (two-dimensional problem). Flame stability is studied for the case of a perturbed flame front. It is shown that in this case, the hydrodynamic field has the effect of stabilizing the flame. For the first perturbation harmonics, the destabilizing effect of gas expansion appears to be relatively weak compared to the stabilizing effect of the velocity field. The first perturbation harmonics attenuate. The destabilizing effect of the velocity field is demonstrated by an example in which the radial flow of the fresh mixture is applied externally, and there exists a concentrated sink flow for the combustion products.