Pseudo-turbulence in inviscid simulations of shock interacting with a bed of randomly distributed particles

Abstract

Particle-resolved 3-D inviscid simulations of a planar shock interacting with a bed of randomly distributed spherical particles are carried out. The aim of this study is to investigate the importance of flowfield fluctuations caused by a random distribution of particles during shock–particle interaction. We present the volume-averaged governing equations. The volume-averaging process results in the appearance of the Reynolds stress term in the momentum equation, and similar terms also arise in the energy equation. These terms are generally neglected in the Euler–Lagrange or the Euler–Euler simulations of shock–particle interaction, and hence, the motivation for this study is to determine the importance of these stresses. The spatiotemporal evolution of the flow inside the particle bed is studied by presenting the mean and the fluctuating flow properties. We compute the RMS velocity, the magnitude of pseudo-turbulent Reynolds stress, and the magnitude of fluctuations in the pressure and total energy. We compare our results with previous studies involving shock interaction with a curtain of cylindrical particles. It is found that the strength of the fluctuating field is much weaker for the spherical particle case compared with the cylindrical particle case. Our results are also in good agreement with the recent study on a planar shock interacting with a random bed of spherical particles under viscous conditions.