Theoretical Analysis of Oscillatory Burning of Homogeneous Solid Propellant Including Non-Steady Gas Phase Effects

Abstract

This paper presents a theoretical analysis of the linear burning response of an homogeneous solid propellant to pressure fluctuations. The major contribution of this work is to take into account the non-steady effects of the gas phase in a systematic way and thus, eliminate the strong limitation of previous analysis in which the gas-phase is assumed to respond in a quasi-steady manner. Two different response mechanisms are exhibited depending on the frequency range. In agreement with the well known quasi-steady theory, the low frequency response is mainly controlled by the thermal relaxation in the solid phase and is triggered through the pressure dependence of the prefactors in the pyrolysis and burning laws. At high frequencies, the gas temperature fluctuations associated with pressure oscillations, are shown to introduce a new response mechanism of the burning rate independent of the pressure exponents. This response mechanism involves the structure of the gaseous flame. The resulting vibratory instability may be stronger than the low frequency one. A simple one dimensional model is used to study this transition in the frequency dependence of the combustion response. Analytical expressions for the real and imaginary parts of the admittance function vs. frequency are obtained by an asymptotic analysis in the limit of large reduced activation energies. The results differ drastically from the quasi-steady theory in the high frequency range concerned by the vibratory instabilities of acoustic tangential modes. Important quantitative modifications are also obtained in the lower frequency range of longitudinal modes. A parametric study of the theoretical results as well as comparisons with existing experimental data and numerical results are carried out. Simple physical interpretations of phenomena are presented. The general method developed in this paper may be extended to more complex combustion models of solid propellant.