Numerical simulation of shock wave propagation over a dense particle layer using the Baer-Nunziato model

The present study examines the possibility of numerical simulation of a strong shock wave propagating over the surface of a dense layer of particles poured onto an impermeable wall using the Baer-Nunziato two-phase flow model. The setting of the problem follows the full-scale experiment. The mathematical model is based on a two-dimensional system of Baer-Nunziato equations and takes into account intergranular stresses arising in the solid phase of particles. The computational algorithm is based on the Harten-Lax-van Leer-Contact method with a pressure relaxation procedure. The developed algorithm proved to be workable for two-phase problems with explicit interfacial boundaries and strong shock waves. These issues are typical of problems arising from the interaction of a shock wave with a bed or a layer of particles. A comparison with the simulations and full-scale experiments of other authors is carried out. A reasonable agreement with the experiment is obtained for the angles of the transmitted compaction wave and granular contact, including their dependency on the intensity of the propagating shock wave. The granular contact angle increases with the incident shock wave Mach number, while the transmitted compaction wave angle decreases. An explanation is given of the phenomenon of the decrease in thickness of the compacted region in the layer with the increase in intensity of the propagating shock wave. The main reason is that the maximal value of the particle volume fraction in the plug of compacted particles in the layer rises with the increase in shock wave intensity.