SIMPLE MODELING OF PARTICLE TRAJECTORIES IN SOLID ROCKET MOTORS

An ultrasimplistic, rapidly executed procedure (with modest computational requirements) is presented for estimating the aluminum-oxide-particle field within a long-bore solid rocket motor. The motor has a partially star-configured grain and a re-entrant (submerged) nozzle. The composite grain is of aluminum-particle/ammonium-perchlorate-crystal/rubber-binder type. The first step of the procedure is to obtain an approximate Eulerian solution for the gas-phase flowfield by adapting a simple quasisteady counterflow model; the spatial extent of any recirculatory flow is a parameter of the model, and an axisymmetric equivalent geometry is introduced for the azimuthally periodic corrugations of the star-configured section of the grain. Lagrangian particle tracking within this quasisteady gas-phase flowfield then permits the identification of 1) what fraction of the oxide particles fails to exit the motor and 2) what properties characterize the two-phase flow at the entrance to the sonic nozzle. The sequential calculation outlined here is intended to hold for any degree of velocity slip between the particles and the gas flow, provided the particle loading is not too heavy; in the absence of definite knowledge of the size distribution of the aluminum oxide particles, results are presented in terms of a finite spectrum of discrete particle sizes. Finally, the analysis is generalized to encompass burns during which the rocket motor undergoes rotation about its axis of symmetry.