Modeling of nonlinear longitudinal instability in solid rocket motors

Abstract

A comprehensive model of nonlinear longitudinal combustion instability in solid rocket motors has been developed. The two primary elements of this stability analysis are a finite difference solution of the two phase flow in the combustion chamber and a coupled solution of the nonlinear transient propellant burning rate. A new combination finite difference scheme gives the analysis the ability to treat the type of multiple travelling shock wave instabilities that are frequently observed in reduced smoke tactical solid rocket motors. Models for predicting the behavior of both gas ejection and solid ejecta pulses were developed and incorporated into the analysis. Extensive comparisons between model predictions and experimental data from pulsed solid rocket motor firings have been carried out. The nonlinear instability analysis was found to be capable of predicting the complete range of nonlinear behavior observed in actual motor firing data. Good agreement between measured and predicted initial pulse amplitude, pulse evolution, limit cycle amplitude and mean pressure shift was obtained. This investigation has also provided new insight into the nature of nonlinear pulse triggered instability and the factors which influence its occurrence and severity. This new instability analysis should significantly enhance our capability to design tactical solid rocket motors that are free from troublesome and expensive nonlinear combusion instability problems.