Numerical Solution of Solid Propellant Transient Combustion

Abstract

Three thermal theories of solid propellant combustion, [1, 2, 3], all based on the quasi-steady flame assumption, were subjected to a rapidly rising external pressure field simulating a gun combustion chamber. Transient burning rates were computed by four different numerical solution methods; the best results were obtained with an invariant imbedding scheme. The numerical predictions show that (1) burning rate “runaway” is a numerical difficulty and is not a solution to the models, (2) the final state of an intrinsically unstable model at constant pressure is composed of repeating finite-amplitude spikes, and (3) the dynamic burning rate from a linearly-stable model can be many times greater than r = apn.