The free molecule point source and Simons models coupled to the particle Lagrangian trajectory model are employed, respectively, to establish the fast solving method for gas-particle two-phase vacuum plumes. Density, velocity and temperature distributions of gas phase, and velocity and temperature of particles are solved to present the flow properties of two-phase plumes. The method based on free molecule point source model predicts the velocity and temperature distributions of vacuum plumes more reasonably and accurately than the Simons model. Comparisons of different drag coefficients show that Loth's drag formula can calculate exactly particle initial acceleration process for high Rer and Mr two-phase flows. The response characteristics of particles along their motion paths are further analyzed. Smaller particles can easily reach momentum equilibrium, while larger ones accelerate very difficultly. The thermal response is more relaxed than momentum response for different particle sizes. The present study is guidable to consider the effects of two-phase plumes on spacecraft in engineering
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