Nonlinear combustion in solid propellant rocket motors

The combustion-acoustics problem in combustion chambers is examined in the framework of nonlinear acoustics and nonlinear propellant burning response to varying pressure. As an example, a combustion chamber having a rigid head-end and an aft-end nozzle is considered. To reduce a number of governing parameters, the simplest propellant model is used. The first two longitudinal acoustic modes are considered with the second-order acoustics and combustion non-linearity. To write boundary conditions for an acoustic field at the propellant surface, the idea of nonlinear gas velocity response functions to oscillatory pressure is used. A set of the governing differential equations is obtained for the complex amplitudes of the acoustic modes, These equations are analyzed to obtain the possible limit cycles and to study their stability. Numerical calculations are performed to find the amplitude-time history that may include triggering phenomena. It has been shown when both acoustic non-linearity and non-linearity of solid propellant burning rate response to oscillatory pressure are considered new qualitative effects arise as compared to the case when only acoustic non-linearity is accounted for.