Stability of a deflagration front in compressible media

A two-dimensional linear analysis of the planar flame front stability for a compressible fluid is presented. The analysis shows that there are two types of perturbations. The first type, corresponding to waves in incompressible media, has already been studied by Landau. It predicts absolute instability of the flame front. The second type of perturbations is due to fluid compressibility and the dependence on upstream flow parameters of the flame front velocity. Three different regimes for these perturbations are possible: stable, acoustically unstable, and absolutely unstable. The instability results in a pronounced pressure wave generation.A one-dimensional analysis of the interaction of the flame front with flow boundaries is performed. Under some circumstances, this interaction is shown to cause exponential growth of the perturbations.