On the interaction of a finite amplitude pressure pulse with a combustion region

Abstract

The present work is concerned with the study of the interaction of a finite amplitude pressure pulse with the combustion region at the surface of a burning solid propellant. The problem is assumed to be one dimensional with the propagation of the pulse taking place normal to the plane of the surface of the propellant. The combustion region is divided into three zones: a decomposition zone, an induction zone, and a flame zone. Large amounts of heat are assumed to be released in the decomposition and flame zones with the heat-release rates governed by Arrhenius-type functions. The induction zone is assumed to be a preparation zone where heating of the gases takes place. The propellant, which is assumed to decompose directly from a solid to a gas at its surface, is treated as an elastic solid of semi-infinite extent. The only transport process included in the analysis is heat transfer, since preliminary calculations indicated that the effects of molecular diffusion and bulk viscosity upon the amplification of the pulse were of higher order. The unsteady conservation equations applicable to the solution of the problem and the transformed conservation equations employed in making the numerical integration are given. The properties and physical characteristics for the combustion region were assigned based upon the assumption that the propellant being burned was composed of 80 per cent ammonium perchlorate and 20 per cent polybutadiene-acrylic acid by weight. Numerical results were obtained for initial pulse amplitudes ranging from 2.5 to 50 psi and for combustion pressures of 250, 500, and 1000 psia. Results of the analysis indicate that for a given initial pulse amplitude the amplification of the pulse decreases with increasing combustion pressure, and that for a given combustion pressure the amplification of the pulse decreases with increasing initial pulse amplitude. An investigation of the mechanism which produces amplification of the pulse by the combustion region revealed that the main effect amplifying the pulse is the heat addition in the combustion region. The main attenuating effects are the absorption of heat by the propellant and the attenuation of the pulse upon reflection from the propellant surface. It was also noted that the amplifying effect of the heat addition was multiplied by the expression γ-1, which indicates that if the gas mixture in the combustion region has a specific heat ratio near unity, the pulse should experience little amplification upon interaction with that combustion region. The over-all results of the analysis are in qualitative agreement with available experimental data.