Nonlinear Combustion Instability in Solid Rocket Motors: A Numerical Study of Longitudinal Oscillations with Pressure and Velocity Coupling.

Abstract

Abstract : An existing nonlinear instability model has been extended and improved to allow it to more realistically treat the longitudinal shock wave type of combustion instability frequently encountered in tactical solid rocket motors. Results obtained utilizing this model to investigate limiting amplitude and velocity coupling phenomena in solid rocket motors are presented. An advanced finite difference integration technique capable of accurately describing shocks and contact discontinuities has been incorporated into the computer program, as well as an improved heat conduction solution, an heuristic velocity coupling model, and a spectral analysis capability. Solutions of wave propagation and shock formation and propagation in a variable area duct and a solid propellant rocket motor are presented; as are a number of solutions demonstrating that limiting amplitude is independent of the characteristics of the initial disturbance. Results of a preliminary study of nonlinear velocity modulated limit cycles are presented, as are results that demonstrate the primarily traveling wave nature of nonlinear wave propagation in solid rocket motors, and the complexity of the phase relationships between pressure, burning rate, and velocity oscillations are presented. Finally, the effect of a threshold velocity on non-linear velocity coupled instability was explored, and some of the results are also presented. (Author)