A shock wave model of unstable rocket combustors

A periodic solution describing the nonlinear waveform of the fundamental longitudinal mode of combustion instability has been obtained. The waveform consists of shock discontinuities followed by exponential decays in pressure and gas velocity. The theory predicts an explicit relationship between the functional nature of the combustion laws and the functional form of the wave shape in the combustion chamber. Therefore, this allows the possibility of investigating the forcing function or driving mechanism of the instability in a quantitative manner by experimentally determining the wave shape in the chamber. The theory applies to any instability where the physical phenomenon that provides that the forcing function contains no phasing effect. Specifically, a model of the combustion zone dynamics has been studied which considers chemical kinetics as the important factor in the forcing function. The results of the analysis on this model have been compared with the experimental results on the Princeton gas rocket research program. The method may be applied to other forms of the forcing function as well.