Finite-amplitude axial instability in solid-rocket combustion

Abstract

The driving mechanism of high-amplitude axial-mode solid-rocket combustion instability, that appears as an oscillating shock wave in the combustion chamber, is considered. The pressure pulse associated with the traveling shock wave induces a burning rate-perturbation as the wave passes over the propellant surface. Of primary interest, in this paper is the interaction mechanism through which this burning-rate response supports the shock wave, causing combustion instability. A simplified analysis of this complex interaction provides a first-order estimate of the minimum combustion response that will drive the oscillating shock wave. Empolying a theoretical treatment of the propellant response, the, analysis predicts the limits of the stable operating regime on the basis of two criteria: (1) the traveling wave must oscillate at a frequency near the predicted resonant response frequency of the propellant and (2) the predicted response amplitude at the resonant frequency must exceed the theoretical minimum value required to drive the shock wave. The theoretical treatment is compared with data from motors 15 in., 23 in., 40 in., and 82 in. in length, using a range of propellants, and is shown to provide a consistent explanation of the experimental observations.