High-Frequency Combustion Instability in Solid Propellant Rockets. Part 2

A theory of unstable high-frequency oscillations in solid propellant rockets is advanced with the mechanism of self-excitation based on the following simplified model. Both the rate of primary decomposition of solid propellant element and the rate of activation of the intermediate products during the time lag are assumed to depend upon the gas oscillations. Both interactions are expressed in terms of the instantaneous pressure according to power law with exponent n and m, respectively. The dependence of the rate of decomposition on drifting velocity is shown to be not of fundamental importance in determining the stability of oscillations in the combustion chamber. Analysis shows that a simplified over-all pressure index of interaction S = m — (n/2) must be bigger than certain minimum value if unstable oscillation is to be possible. Unstable oscillation further requires the time lag to be in proper range. The most unstable mode is shown to be the fundamental spiral mode, and its tangential component with exactly the acoustical frequency is the one which is most easily observed at finite magnitudes because of its rapid amplification. Several configurations of the propellant grain with radial burning surfaces have been investigated. Rod grain becomes more stable while other grain shapes become less stable in the course of firing. Rod grain is the most stable while tubular grain is the most unstable configuration. The stabilizing effect of inserting a nonburning solid rod into tubular grain is verified by the theory. Several other aspects have also been treated. Solid rocket with end burning grain also becomes less stable in the course of operation. Both the spiral and the longitudinal modes in rocket with endburning grain are briefly investigated.