Evolution of particle cloud after being impacted by a planar shock: Particle-resolved simulation and theoretical model

Interaction between shock and particle cloud is numerically investigated by using a conservative sharp interface method. At the early stage of the interaction, reflected shock waves at the upstream of the particle cloud merge into a shock front, accompanied by local compression of the particle cloud. When high-speed flow passes through the particle cloud, the particles effectively serve as connected Laval nozzles. Consequently, rarefaction waves and shocklets are formed among the particles. Particularly, supersonic expansion occurs at the downstream of the particle cloud, which is partly responsible for the diffusion of the particle cloud at the late stage of the interaction. To quantitatively analyze the evolution of the flow field in the particle cloud, we calculate the spanwise average of flow quantities as well as the local volume fraction of the particles. The effect of the particle cloud on the evolution of the flow field is then approximated by a one-dimensional variable cross section pipe model, especially when the particle structure remains more or less the same as the initial arrangement. The model takes the initial particle arrangement and the Mach number of incident shock into account and also estimates the pressure drop across the particle cloud based on fractal theory. Furthermore, the macroscopic deformation (such as compression and diffusion) of the particle cloud is evaluated based on a semi-permeable approximation of and the estimation of pressure drop across the particle cloud. The theoretical prediction of the models is compared against the numerical results, and good agreement is achieved.