Hydrodynamic stability of solid and liquid propellant combustion

We derive a model which describes the dynamics of a multiphase system consisting of a gas flame attached to a pyrolyzing solid or liquid propellant. We consider the case in which the multiphase flame, which includes the propellant interface, the preheat zone and the gas-phase reaction zone, is thin compared to some characteristic hydrodynamic length. An asymptotic analysis of the inner structure then yields jump conditions on the fluid and transport variables across the multiphase flame, which is treated as a surface of discontinuity separating the unburned condensed-phase propellant from the burned gas. The resulting model, which describes the evolution of this surface, is then used to investigate the hydrodynamic (Landau) stability of propellant deflagration. In particular, it is shown that this type of instability is completely suppressed for solid propellants, whereas for liquid propellants, a cellular instability arises which is similar to that which occurs in premixed flame propagation.