Perturbation analysis of the Heterogeneous Quasi 1-D model – a theoretical framework for predicting frequency response of AP–HTPB composite solid propellants

Abstract

In this paper, the Heterogeneous Quasi 1-D model for steady combustion of AP–HTPB propellants is extended to the unsteady regime. The extended model is used to calculate the pressure-coupled frequency response () of low-smoke (non-aluminised) multi-modal AP–HTPB propellants. The of a multi-modal propellant is expressed in terms of that of the individual binder-matrix coated AP particles constituting the statistical particle path. The weighting function, as expected from the serial burning approach, is the burn-time of particles. A closed-form expression is derived for the of the particles by perturbation analysis of the quasi 1-D burn rate model. In this equation, all except the two parameters that quantify the amplitude () and phase () of fluctuating heat flux on the solid side of the interface, are shown to be from the steady-state model. This result establishes a strong connection between the steady and unsteady framework as compared to earlier models, where (propellant pressure index) as was explicitly imposed. The model is used to predict for a few low-smoke compositions. Effects of AP particle size distribution, mean pressure and initial temperature are brought out. When expressed as vs (non-dimensional frequency based on conduction time scale), the peak response magnitude is of and occurs close to non-dimensional frequency () value of 1. While this conclusion is in line with the earlier results, it does not explain the ubiquitous nature of acoustic instability in tactical missile rockets, which requires the peak response to be at least an order of magnitude higher than n. Burn rate oscillations associated with the binder-melt effect caused by inhibitors is brought out as the most likely mechanism for the observed instabilities. Methods to extend the theory to include this effect is outlined.