A theory of low-frequency combustion instability in solid rocket motors

A theoretical investigation of low-frequency combustion instability is conducted where the mechanism of instability is the lag of burning-rate response to pi essure disturbances near the propellant surface due to the temperature gradient just below the surface and its interaction with lag in exhausting the chamber due to nozzle flow The pei iod of low-frequency chamber fluctuations is considered large compared to any time lags in the gas-phase burning process The burning-rate perturbations and pressure perturbations are related through a closed-loop feedback system analysis The burning-rate fluctuations cause pressure fluctuations through the chamber transfer function These pressure fluctuations are, in turn, fed back to the burning-rate fluctuations thiough the combustion transfer function Expressions are derived for the two transfer functions, and an instability criterion is developed by the application of Cauchy's theorem, resulting in the correlation of the critical pressure for a given propellant and chamber characteristic length L* The results are compared with experimental data obtained at the Jet Propulsion Laboratory