Computational analysis of a dense granular system driven by a propagating shock wave in an Eulerian–Eulerian framework

Abstract

Numerical simulations using an Eulerian–Eulerian approach are performed to investigate the problem of a dense granular bed driven by a propagating shock wave with special emphasis on the particle-phase behavior. Validation of the granular model based on the kinetic theory of granular flow is performed by comparing the simulation results with experimental data on the shock-particle curtain interaction by Ling et al. [Phys. Fluids 24, 113301 (2012)]. Then, simulations of a Mach-1.92 shock propagating into an infinite-long granular system are tested, where the particle diameter, density, and volume fraction are 115 μm, 2520 kg/m3, and 21%, respectively. The simulations demonstrate that as the gas-phase shock interacts with the granular system, a reflected shock, a contact surface, and a transmitted shock wave form instantly. Meanwhile, a dilute region, a densely packed region, and an “excitation and relaxation” region behind the granular shock are observed. The physics of the granular shock structures are elucidated through an evaluation of forces and pseudo-thermal energy (PTE) fluctuations. It is shown that the combination of a positive drag force and Archimedes force are responsible for the particle motion, while the intergranular stress has a negative contribution in most of the region. The PTE is generated in the initial stage owing to the velocity slip (ϕslip) then dissipates primarily due to particle inelastic collisions (−γ̇l) until particles reach an equilibrium state in the later stages. Finally, the effects of particle parameters including the initial particle packing (αs) and the coefficient of restitution (e) are elucidated and discussed. The results show that the particle concentration greatly affects the granular shock velocity, and as the collisions become less ideal, particle clusters are observed in the dilute region.