Calculation of acoustic admittance at a burning surface

Abstract

During the past fifteen years many papers have been devoted to calculation of the admittance function for a solid propellant burning surface. Most of the theoretical models have been based on the special assumptions of non-steady burning zone structure, such as those concerned with kinetics of the surface decomposition reactions and the temperature and pressure sensitivities of the gas-phase reaction rate. This paper describes the method of calculation which is based on the theory of non-steady burning of solid propellant proposed by Soviet scientists. This theory does not require a detailed knowledge of the burning zone structure. It uses the steady-state burning rate and steady-state burning surface temperature data as functions of pressure and initial temperature for deducing the appropriate unsteady burning laws. It is also assumed that the only delay process is heat conduction in the condensed phase; all other processes are presumed quasisteady. In this paper the simple analytical expression is derived which relates the acoustic response function with some parameters characterizing the pressure and the initial temperature sensitivities of the steady-state burning rate and steady-state burning temperature. The calculation gives the acoustic admittance and permits analysis of the acoustic instability domains. The results are compared with available experimental data. The paper includes as well a short review of the other papers which are based on the same theoretical approach to description of the unsteady burning rate.