Steady Flows in the Slender, Noncircular, Combustion Chambers of Solid Propellant Rockets

Abstract

An analysis of the steady flows with axial vortices in slender, cylindrical, nonaxisymmetric cavities generated by injection from their porous walls is presented. This problem is encountered in the description of the flow in slender combustion chambers of solid-propellant rocket motors associated with the gasification of the solid propellant surrounding the combustion chamber. Nonreacting flow can be described in terms of self-similar solutions of the Navier-Stokes equations and the solution, calculated numerically for noncircular grain configurations, shows strong axial vortices, with a viscous vortex core that has been analyzed asymptotically for large Reynolds numbers. It was found that the important property of the flow, namely, C 1/2 S/Π, where C is a constant determining the axial pressure gradient, S and n are the cross section area and its perimeter, respectively, becomes unexpectedly close to π/2 at large Reynolds numbers, independently on the geometry of the cross section of the cavity. One can suppose that C 1/2 S/Π = π/2 for any cavities in the invicsid limit, a conjecture that also obtained a support from numerical calculations of flows in rectangular cavities generated by injection from their porous walls.