Unsteady flows in a tube with combustion reaction

A method for the calculation of flow field and piston motion for unsteady tube flows with combustion is treated. The principal relations of thermodynamics and an introduction to the Abel state equation are presented. The equations are applied to a homogeneous two-phase mixture. Using the streamline theory for flows in tubes with small cross section variations, the unsteady balance equations for friction and heat-conduction-free flows with mass and energy supply are simplified. Simple equations for a homogeneous mixture of gas and particles in which the two phases have equal velocity are obtained. Based on these equations and the approximation of a perfect entrainment of the propulsion powder by the gaseous flow, a simulation model for the interior ballistics phenomena is developed. For the numerical solution a characteristics method in Lagrangian coordinates is proposed, supposing a spatially and temporally uniform ignition of the propulsion powder. Taking into account the simplifications of the model, the numerical results agree well with the known characteristics of the utilized materials.