Gas dynamics of stationary supersonic gas jets with inert particles exhausting into a medium with low pressure

Issues related to the development of tools for mathematical modeling of stationary supersonic flows of an ideal compressible gas with inert particles are considered. A mathematical model is constructed that describes the flow of an inviscid compressible gas with inert particles in a jet flowing from an axisymmetric nozzle into a flooded space. Provided that the flow is supersonic along one of the spatial coordinates, the Euler equations are hyperbolic along this coordinate. For numerical calculations of the gas flow field, the finite volume method and the marching method are used. For integration over the marching direction, the three-step Runge–Kutta scheme is used. The procedure for calculating the flows includes the reconstruction of the values of the desired functions on the faces of the control volumes from the average values over the control volumes and the solution of the problem of the decay of an arbitrary discontinuity (the Riemann problem). The Lagrangian method of test particles is used to describe the dispersed phase. The effects of the reverse influence of particles on the flow of the carrier gas are not taken into account. The effects of viscosity and rarefaction of the gas flow are taken into account only when the gas interacts with particles. Calculation of the trajectories of inert particles is carried out in a known flow field of the carrier gas. The motion trajectories of discrete inclusions in jet flows with strong underexpansion are presented. The influence of the particle size and the coordinates of the particle entry point into the flow on the features of their transfer by the jet stream are discussed. Efficient means of numerical simulation of stationary supersonic flows of an ideal compressible gas with particles in nozzles and jets have been developed. The calculation results are of interest for studying supersonic gas suspension flows around bodies and for calculating oblique shock waves.