Investigation of a gas flow with solid particles in a supersonic nozzle

A two-phase flow with high Reynolds numbers in the subsonic, transonic, and supersonic parts of the nozzle is considered within the framework of the Prandtl model, i.e., the flow is divided into an inviscid core and a thin boundary layer. Mutual influence of the gas and solid particles is taken into account. The Euler equations are solved for the gas in the flow core, and the boundary-layer equations are used in the near-wall region. The particle motion in the inviscid region is described by the Lagrangian approach, and trajectories and temperatures of particle packets are tracked. The behavior of particles in the boundary layer is described by the Euler equations for volume-averaged parameters of particles. The computed particle-velocity distributions are compared with experiments in a plane nozzle. It is noted that particles inserted in the subsonic part of the nozzle are focused at the nozzle centerline, which leads to substantial flow deceleration in the supersonic part of the nozzle. The effect of various boundary conditions for the flow of particles in the inviscid region is considered. For an axisymmetric nozzle, the influence of the contour of the subsonic part of the nozzle, the loading ratio, and the particle diameter on the particle-flow parameters in the inviscid region and in the boundary layer is studied.