Instabilities of a circular moderately dense particle cloud impacted by an incident shock

Abstract

Shock-driven gas-particle flows exist in a wide variety of physical systems, covering the range from dilute to dense regime. There are a lot of fundamental questions remaining to be answered, like the evolutions of flow instability, two-phase interactions, and inter-particle collision effects. In this work, the Eulerian-Lagrangian approach with gas-particle four-way coupling is applied to model two-dimensional shock-driven gas-particle flow under the moderately dense regime. For the gas flow, the formation mechanism of primary and secondary vortexes is discussed. The primary vortex is caused by the roll-up of slip line, while the secondary vortexes are induced by the velocity and density difference between the penetrating flow of particle-laden zone and the outside mainstream. Parametric studies of different Mach numbers, particle diameters and initial volume fractions have been performed to investigate the effects on shock behaviours and slip line instabilities. For the particle phase, a high-volume-fraction compression region forms at the upstream cloud zone, which blocks the penetrating gas, and results in the formation of slip line. The cloud tail is mainly composed of the upstream edge particles. The inter-particle collisions have impact on the particle distributions, and greatly affect the slip line stability at the upstream cloud edge. This work provides valuable insights into the instability mechanism of compressible gas-solid flow and the particle dispersion behaviours. However, it is important to note that our analysis is based on a two-dimensional configuration. In a real three-dimensional context, the generation of vortices is likely to differ, and may affect the particle dynamics to a certain degree.