Prediction of the size of aluminum-oxide particles in exhaust plumes of solid rocket motors

The processes of coagulation and aerodynamic fragmentation of liquid particles of aluminum oxide in an accelerating gas flow in the Laval nozzle are analyzed. A formula obtained by an approximate analytical solution of equations of a two-phase flow is proposed to calculate the characteristic particle diameter at the nozzle exit. The limiting particle diameter in the nozzle throat calculated theoretically is close to the mean-mass diameter obtained by numerical simulation of polydisperse two-phase flows with particle coagulation and fragmentation. The formula proposed is in agreement with Hermsen's correlation dependences and is confirmed by numerous published data on measurement of the mean-mass diameter of aluminum-oxide particles in exhaust plumes of small-, medium-, and large-scale solid rocket motors. The formula contains physical parameters whose values are readily calculated and prescribed. The formula is tested by all the parameters that enter into it. Based on a comparison of theoretical calculations and numerous experimental data, the formula is recommended for prediction of the size of aluminum-oxide particles in exhaust plumes of various types of solid rocket motors.