Nozzle contours for minimum particle-lag loss

Abstract

The flow of a gas-particle mixture through a rocket nozzle is analyzed under the approximation that the particle slip velocity is small compared with the average mixture velocity, using one-dimensional gasdynamics, the Stokes drag law, and corresponding approximations for the heat transfer between solid and gas phase. The variational problem defining the pressure distribution giving the minimum impulse loss due to particle lag is formulated and
\nsolved for nozzles of prescribed mass flow, length, and of given exit pressure or area. The throat section of the optimum nozzle is considerably elongated and more gradual than that of the conventional nozzle. The velocity and temperature lags were much lower (about 1/3) in the throat region than those for the conventional nozzle. The impulse loss of the optimum nozzle was, however, reduced only about 30% below that of the conventional nozzle. It is concluded that contouring of the nozzle to improve gas-particle flow performance will result in only very modest gains. As a direct consequence, the impulse losses calculated herein for optimum nozzles can be used as a rough but convenient approximation for the impulse losses in conventional nozzles having the same area ratio or pressure ratio.