Analytical solution for pressure-coupled combustion response functions of composite solid propellants

This paper extends the classical analytical solution for small perturbation analysis of the pressure-coupled response of a homogeneous propellant to any two-component composite propellant. The solution obtained is general and can be used with any particular model for propellant combustion. As an example, the Cohen and Strand ammonium perchlorate propellant model for a single ammonium perchlorate particle size was used in this work. The results and their mechanistic significance are presented and discussed. It is shown that, for a two-component composite propellant, two forms of pressure exponents arise from the analysis. The significance of the second exponent is that it enables the composite propellant to be viewed as a homogeneous propellant with a frequency-dependent exponent via the coupling coefficients. It is found that the ammonium perchlorate is the main source of instability because of its condensed phase exothermicity and monopropellant flame kinetics. This will be a problem with energetic materials in general. The inert binder provides a stabilizing influence because of its endothermicity and the diffusion flame formed with the ammonium perchlorate. Effects of ammonium perchlorate particle size and pressure stem from the changing flame structure and its effect on burning rate.