Diffusional/Thermal Coupling and Intrinsic Instability of Solid Propellant Combustion

Abstract

Intrinsic instability in the steady, planar deflagration of a homogeneous solid propellant is considered through an asymptotic analysis for large values of nondimensional overall activation energies for the surface pyrolysis and gas-phase combustion processes. It is shown that the previously known pulsating instability is essentially connected with condensed-phase pyrolysis, and that new instability phenomena, which are associated with intrinsic gas-flame instability and which are sensitive to the value of the gas-phase Lewis number and to the distance of the gas flame from the propellant surface, arise. These results are obtained by relaxing the usual assumptions of quasi-steadiness and quasi-planarity for the gas phase, so that the coupling of intrinsic diffusional/thermal instabilities in the gas and solid phases becomes an integral feature of the model. The steady, planar deflagration thus may be unstable not only to pulsating disturbances, but also to (time-independent, nonplanar) cellular perturbations as well. It is shown that the onset of pulsating instability has a dual character which is related to the intrinsic instabilities of both the deflagrating solid and the gas flame. In contrast, the onset of cellular instability, apparently not predicted by previous theories for solid propellants, is clearly related to the stability of the gas flame. Appropriate limiting cases of the model retrieve the well-known pulsating and cellular neutral stability boundaries for strictly gaseous combustions, and the pulsating neutral stability boundary for strictly condensed phase combustion.