Simulation of unsteady combustion in a solid-propellant rocket motor

Various regimes of combustion in end-burning-grain solid-propellant rocket motors were examined within the framework of the phenomenological theory of unsteady combustion. A system of equations capable of describing the interaction between the process of burning and acoustic waves was derived. A specific feature of the problem is that its formulation involves two characteristic times: the acoustic time and oscillation amplitude variation time. These characteristic times differ by about three orders of magnitude, a circumstance that requires a high accuracy of calculations. Based on the quadratic approximation in oscillation amplitude, a simpler method for solving the problem was proposed, according to which only the effects associated with the oscillation amplitude variation time are taken into account. Numerical results were obtained for the simplest model of propellant burning, which contains the minimum number of parameters and disregards entropy waves in the combustion products. The steady and unsteady regimes of burning were identified. In the latter case, nonlinear effects may generate shock waves in the combustion chamber.