Incorporation of Nonlinear Capabilities in the Standard Stability Prediction Program

Abstract

Predictive algorithms now in general use cannot characterize high-amplitude pressure oscillations that are frequently observed in solid propellant rocket motor combustion chambers. In fact, programs such as the Standard Stability Prediction (SSP) code are based on a linear theory, which has serious shortcomings. Therefore, it is necessary to address both correction of the flawed linear theory and incorporation of models to allow prediction of important nonlinear effects. These include: 1) limit cycle behavior in which the pressure fluctuations may dwell for a considerable period of time near their peak amplitude, 2) elevated mean chamber pressure (DC shift), and 3) a triggering amplitude above which pulsing may cause an apparently stable system to transition to violent oscillations. Culick’s wellestablished nonlinear model provides useful guidance in dealing with the system limit cycle transition. It is demonstrated in this paper that his calculations represent the classical steepening mechanism by which the wave system evolves from an initial set of standing acoustic modes into a shock-like, traveling, steep-fronted wave. However, a very important missing element is the ability to predict the accompanying mean pressure shift; clearly, the program user requires information regarding the maximum chamber pressure that might be experienced during operation of the motor, as well as the peak amplitudes reached by the pressure oscillations. Recent theoretical work has resulted in a firm foundation upon which to build the required predictive capabilities. These are described in detail, and it is demonstrated that the new theory yields results that are in excellent agreement with experimental data.