ABSTRACT
In the modelling of combustion and flames, the stability question is of major importance. Detonations are, by nature, unstable. Exchange of stability often arises in pre-mixed flames, as shown by the classical thermo-diffusive model for the Lewis number close to 1. In this framework, the famous Kuramoto-Sivashinsky equation exhibits cellular instabilities. As far as diffusion flames are concerned, chambered flames present S-shaped response curves for arbitrary Lewis numbers. Away from laminar combustion, turbulence may stabilize the flame and lead to extinction/reignition phenomena. Solid combustion should not be forgotten: clearly, instabilities in the combustion of solid propellants can endanger the rocket propulsion.
