Propellant non-steady burning effects on controllable solid rocket motor internal ballistics

An analysis of the unsteady non-linear behavior of the controllable solid propellant rocket motor (CSRM) consequent to rapid and relevant nozzle operation is presented. The study includes a development of a non-linear unsteady combustion model able to handle relevant and rapid chamber pressure changes typical of CSRMs. The CSRM nonlinear unsteady model is implemented according to a main solver - sub models architecture and uses different time scales. The formulation of the combustion gas mass flow rate is developed considering the propellant density, the unsteady combustion, the regression of the combustion surface and the outflow through the variable nozzle. The grain surface involved in the combustion is obtained by a regression model of the chamber walls, in reliance on the unsteady burning rate, on the initial grain geometry and integrates the history of performed nozzle operations. The CSRM is described by a system of differential equations that is reduced in sub systems and solved numerically in the main solver sub model frame.