Numerical study on shock–dusty gas cylinder interaction

Abstract

The interaction of a planar shock wave with a dusty-gas cylinder is numerically studied by a compressible multi-component solver with an adaptive mesh refinement technique. The influence of non-equilibrium effect caused by the particle relaxation, which is closely related to the particle radius and shock strength, on the evolution of particle cylinder is emphasized. For a very small particle radius, the particle cloud behaves like an equilibrium gas cylinder with the same physical properties as those of the gas–particle mixture. Specifically, the transmitted shock converges continually within the cylinder and then focuses at a region near the downstream interface, producing a local high-pressure zone followed by a particle jet. Also, noticeable secondary instabilities emerge along the cylinder edge and the evident particle roll-up causes relatively large width and height of the shocked cylinder. As the particle radius increases, the flow features approach those of a frozen flow of pure air, e.g., the transmitted shock propagates more quickly with a weaker strength and a smaller curvature, resulting in an increasingly weakened shock focusing and particle jet. Also, particles would escape from the vortex core formed at late stages due to the larger inertia, inducing a greater particle dispersion. It is found that a large particle radius as well as a strong incident shock can facilitate such particle escape. The theory of Luo et al. (J. Fluid Mech., 2007) combined with the Samtaney–Zabusky (SZ) circulation model (J. Fluid Mech., 1994) can reasonably explain the high dependence of particle escape on the particle radius and shock strength.