The flow field in the slender combustion chambers of solid propellant rockets

Abstract

We analyse the near inviscid flow field generated in a slender non-axisymmetric cylindrical cavity by the gasification and combustion reactions of a surrounding solid propellant grain. These reactions are confined to a thin layer adjacent to the surface of the solid propellant, so that the flow is non-reacting in most of the cavity, and of the same form as the flow in slender ducts due to fluid injection through lateral porous walls. The non-reacting flow can be described in terms of self-similar solutions of the Navier -Stokes equations that we calculate numerically for star-shaped grain configurations, with Reynolds numbers only moderately large for the flow to remain laminar and steady. The self-similar flows for non-axisymmetric configurations show strong axial vortices that we analyze using the Euler simplified form of the flow equations for large Reynolds numbers, and the general solution of the Burgers equation for strained vortices that describes their viscous cores; a logarithmic singularity could then be encountered at their center line