Hydrodynamic and reactive/diffusive instabilities in a dynamic model of liquid propellant combustion

Abstract

In a classical study of liquid propellant combustion. Landau 1 introduced a simple model in which the liquid/gas interface was assumed to propagate normal to itself with constant velocity. Such a model, applied to the problem of premixed flame propagation, introduced the phenomenon of hydrodynamic flame instability, in which steady, planar deflagration was unstable to steady, but nonplanar (cellular), disturbances. For the case of liquid propellants, it was shown that the inclusion of gravitational and surface tension effects could supress this phenomenon, whereas a later study due to Levich 2 showed that the coupling of gravitational and viscous effects could produce a similar result. In the present work, we show that the assumption of a more realistic pyrolysis burning-rate law, which couples the temperature field to the problem, also is stabilizing with respect to hydrodynamic instability. In addition, this model admits a pulsating type of instability associated with the thermal sensitivity of the chemical reaction, analogous to that which exists for solid propellant combustion and the combustion synthesis of refractory materials. These results parallel recent developments in flame theory, which also suggest that the dynamic coupling of the burning rate with local conditions at the flame front can suppress Landau instability. In addition, however, the present work presents a closed-form expression for the dispersion relation, and predicts regions of stability for steady, planar burning with to both hydrodynamic and reactive/diffusive instabilities.