Numerical analysis of vortex formation and particle dispersion in a supersonic compressible particle-laden mixing layer

In the study, the quasi 2D-direct numerical simulations (DNS) approach of a supersonic mixing layer of hydrogen–nitrogen flow (upper high-speed) and air (bottom low-speed) with solid particles are performed. Navier–Stokes equations are taken for the multispecies gas phase combined with system of ordinary differential equations for solid particles (Eulerian–Lagrangian approach). Both dynamics of the unsteady vortex system formation and its effect on the solid particles distribution in the mixing layer for two values of the convective Mach number (ratio between the difference of flow velocities and sound speed) low 0.4 and high 0.8, also influence of the various hydrogen and nitrogen mass fractions in the upper flow on the particle dispersion in the mixture layer are studied. The similarity behavior of the particle dispersion for two convective Mach number M_c is consist, a namely, the particles accumulate around the vortex circle and along the spit between two vortices, which leads to some “empty” area inside the vortex due to the influence of centrifugal force, whereas the local eddy shock wave (shocklets) in the flow is formed for high convective Mach number M_c and the particle dispersion is not only controlled by turbulent vortex structures but also is complicated due to intersect this local shocklets. That result is in an additional curvature of the particle trajectory in the region shocklets. In addition, the hydrogen mass fraction variations in mixture show that the heavier the mixture, the smaller number of shocklets are formed, respectively, and the thickness of the mixing layer is growth.