Solid Rocket Motor Combustion Instabilities: Analysis of the Transition to the First Limit Cycle

A nonlinear multi time-scale analysis of the solid propellant rocket motor transition to the first limit cycle is presented and the motor behavior subsequent to some relevant transition scenarios is investigated. Important physical parameters characterizing the transition to limit cycle are then put in evidence and their cross-effects are studied. The analysis takes into account the effects of acoustic-vorticity-entropy wave coupling, waves steepening, rotational and viscous flow losses due to the steep-fronted waves, energy losses in the steepened state, nonlinear energy pathways and includes the study of the oscillatory energy losses in the nozzle, the unsteady combustion and the combustion chamber geometry changes resulting from the grain regression. The analysis provides evidence that in the investigated instability regions the wave amplitude evolution in the combustion chamber as well as the actual intrinsic motor stability is influenced by the time-history of selected parameter interactions.