This paper describes supersonic flows of a gas-particle two-phase mixture in considerably complicated situations. For the flow field of gas-particle mixtures such that the gas-phase and the particle-phase interact with each other, the model is constructed by incorporating the particle-trajectory method into the system of gas-phase equations in the two-fluid model. First, the one-phase and two-phase flows of round underexpanded jets exhausted from a sonic nozzle are investigated in detail. The one-phase results are compared with the experimental ones in order to confirm whether the present scheme is reliable or otherwise. For the two-phase results, the particles with the same velocity and temperature as those of the gas-phase are injected at the nozzle exit plane, and the effect of the presence of the particles on the flow field is examined by comparing these two-phase results with the one-phase ones. Second, the results of the numerical experiments in which underexpanded sonic round jets impinge on a flat plate normal to the jet axis are presented and analyzed for both the one-phase and two-phase cases. For the one-phase flow, periodic unstable oscillations have been found to give fairly good agreement with the experimental results. Third, supersonic gas-particle two-phase flows around a sphere are simulated in view of the numerical experiments. The instability in the particle motion near the stagnation region in the shock layer is discussed in detail. A few new findings are also described throughout the present paper
