Low-Probability Events Leading to Rocket Engine Combustion Instability

Abstract

A new method is proposed for calculations of rare-event rocket combustion instabilities. Acceleration of the combustion chamber is modeled as a stochastic process of long duration and moderate amplitude. Using a simplified model for the effect of acceleration on the evolution of the first tangential mode of pressure within the chamber, a modified sampling distribution is obtained that yields higher occurrence of the rare event: in this case, growth to instability. Statistics are then calculated for the original distribution of the stochastic process using an importance sampling procedure. Knowledge of the likelihood ratios between the real and modified probability density functions allows a low-cost computation of the probability of the rare event of triggering the combustion instability by low-amplitude acceleration fluctuations. There are two distinct regimes of high and low probabilities of triggering, with a critical acceleration amplitude threshold between them; in the low-probability regime, the probability of triggering increases exponentially with increasing acceleration amplitude. The probability of triggering increases with increasing duration of the stochastic acceleration. This method of low-probability event analysis can be extended to other instability-triggering mechanisms.