Modeling of nonlinear combustion instability in solid propellant rocket motors

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. Although quasi-one dimensional, the model has been generalized to treat realistic variable cross-section and partial length grains. An excellent finite difference shock capturing technique—a combination of the Lax-Wendroff, Hybrid and Artificial Compression schemes—gives the analysis the ability to treat the multiple shock-wave type of instabilities that are frequently observed in reduced smoke solid rocket motors. Ad hoc velocity coupling models were also incorporated into the analysis. Solutions are presented demonstrating that pressure oscillations in unstable solid rocket motors (with metallized as well as unmetallized propellants) reach the same limit cycle (amplitude and waveform) independent of the characteristics of the initiating disturbance. Results obtained with the velocity coupling models demonstrate the ability to analytically predict triggering, DC pressure shifts, modulated amplitude limit cycle, and strongly nonlinear waveforms; phenomena that have all been observed in actual solid rocket motor firings.