Particle drag model is one of the most important issues in the prediction of particle behavior in the supersonic rarefied gas–particle two-phase flows. However, there is a lack of high-precision drag models at present for the transitional-rarefied flow. Based on free-molecular theory, this study systematically investigates the effects of freestream number density, freestream temperature, particle temperature, and freestream flow velocity on the flowfield and the drag of the particle. The nondimensional model parameters for the molecular kinetic variables are proposed, and a drag model of spherical particles in supersonic transitional–rarefied flow is developed with an applicable range. The proposed model maintains formal consistency with the free-molecular theory, ensuring asymptotic reversion to the free-molecular solution, which reflects the influence of each variable on the particle drag under different degrees of rarefaction. Comparison with experimental data, numerical simulations, and other drag models demonstrates that the proposed model achieves higher prediction accuracy within its applicable range. This model effectively bridges the critical gap by providing a unified, high-precision drag model for supersonic particles from free-molecular flow to transitional flow.
Xue et al. (2026) studied this question.