In this work, the particle jetting behavior in a blast-driven dense particle bed is studied at early times. Four-way coupled Euler–Lagrange simulations are performed using a high-order discontinuous Galerkin spectral element solver coupled with a high-order Lagrangian particle solver, wherein the inter-particle collisions are resolved using a discrete element method collision model. Following the experiments of Rodriguez et al. [“Formation of particle jetting in a cylindrical shock tube,” Shock Waves 23(6), 619–634 (2013)] and the simulations of Osnes et al. [“Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell,” Shock Waves 28(3), 451–461 (2018)], the simulations are performed in a quasi-two-dimensional cylindrical geometry (Hele-Shaw cell). Parametric studies are carried out to assess the impact of the coefficient of restitution and the strength of the incident shock on the particle jetting behavior. The deposition of vorticity through a multiphase (gas–particle) analog of Richtmyer–Meshkov instability is observed to play a crucial role in channeling the particles into well-defined jets at the outer edge of the particle bed. This is confirmed by the presence of vortex pairs around the outer jets. Furthermore, the effect of the relaxation of the relative velocity between the two phases on the vorticity generation is explored by analyzing the correlation between the radial velocity of particles and the radial velocity of the gas at the particle location.

A research area emerging in the multiphase flow community is the study of shock-driven multiphase instability (SDMI), a gas–particle analog of the traditional fluid-fluid Richtmyer–Meshkov instability (RMI). In this work, we study the interaction of planar air shocks with corrugated glass particle curtains through the use of numerical simulations with an Eulerian–Lagrangian approach. One objective of this study is to compare the simulated particle curtains to a comparable set of shock tube experiments performed to analyze traditional RMI of a gas curtain. The simulations are set to match the experimental shock Mach numbers and perturbation wavelengths (3.6 and 7.2 mm) while also matching the Atwood number of the experiments to the multiphase Atwood number of the simulations. Varying particle diameters are tested in the simulations to explore the impact of particle diameter on the evolution of the particle curtain. This simulation setup allows for a one-to-one comparison between RMI and SDMI under comparable conditions while also allowing for a separate study into the validity of the use of the multiphase Atwood number to compare the single-phase and multiphase instabilities. In particular, we show that the comparison depends on the diameter of the particles (thus, dependent on the Stokes number of the flow). A second objective of this study is to analyze the effect of the initial particle volume fraction on the evolution of the curtain and the behavior of the instability. This is done through analyzing the effect of the multiphase terms of the vorticity evolution equation on the vorticity deposition in SDMI. Also discussed is the effect of the particle diameter on the multiphase generation terms as well as in the baroclinic vorticity generation term in SDMI as the shock passes over the curtain.

In this paper, we present the results of the explosive dispersal of particles in high-speed environments. We carry out Euler–Lagrange numerical simulations of a source at quiescent ambient conditions as well as moving at Mach numbers of 3 and 6. Particle volume fractions of 0%, 1%, and 4.5% are presented. The detonation profile is computed with the Jones–Wilkins–Lee equation of state using a reactive burn model. Non-static cases provide a framework to consider the effect of a bow shock and pre-existing high-speed flow conditions on the dispersal process. We also compute averages of both static and dynamic pressures, as well as impulse density histories on virtual probe planes to characterize the momentum of the flow and particles that would deposit on a target. Results suggest that the presence of the particles can have a substantial effect on the pressure average of the virtual target planes.

We study the interaction of a planar air shock with a perturbed, monodispersed, particle curtain using point-particle simulations. In this Eulerian-Lagrangian approach, equations of motion are solved to track the position, momentum, and energy of the computational particles while the carrier fluid flow is computed in the Eulerian frame of reference. In contrast with many Shock-Driven Multiphase Instability (SDMI) studies, we investigate a configuration with an initially high particle volume fraction, which produces a strongly two-way coupled flow in the early moments following the shock-solid phase interaction. In the present study, the curtain is about 4 mm in thickness and has a peak volume fraction of about 26%. It is composed of spherical particles of d = 115μm in diameter and a density of 2500 kg.m−3, thus replicating glass particles commonly used in multiphase shock tube experiments or multiphase explosive experiments. We characterize both the evolution of the perturbed particle curtain and the gas initially trapped inside the particle curtain in our planar three-dimensional numerical shock tube. Control parameters such as the shock strength, the particle curtain perturbation wavelength and particle volume fraction peak-to-trough amplitude are varied to quantify their influence on the evolution of the particle cloud and the initially trapped gas. We also analyze the vortical motion in the flow field. Our results indicate that the shock strength is the primary contributor to the cloud particle width. Also, a classic Richtmyer-Meshkov instability mixes the gas initially trapped in the particle curtain and the surrounding gas. Finally, we observe that the particle cloud contribute to the formation of longitudinal vortices in the downstream flow.

A research area emerging in the multiphase flow community is the study of Shock-Driven Multi-phase Instability (SDMI), a gas-particle analog of the traditional fluid-fluid Richtmyer-Meshkov instability (RMI). In this work, we study the interaction of planar air shocks with corrugated glass particle curtains through the use of numerical simulations with an Eulerian-Lagrangian approach. This approach has simulations track computational particle trajectories in a Lagrangian framework while evolving the surrounding fluid flow on a fixed Eulerian mesh. In addition to observing the evolution of the perturbed particle curtain in the simulations, we also observe the evolution of the curtain of gas which is initially trapped inside of the particle curtain as the simulation progresses. The objective of this study is to compare the evolving simulation curtains (both particle and gas) to a comparable set of shock tube experiments performed to analyze traditional fluid RMI evolution. The simulations are set to match the experimental shock Mach numbers and perturbation wavelengths (3.6 and 7.2 mm) while matching the Atwood number of the experiments to the multiphase Atwood number of the simulations. However, multiple particle diameters are tested in the simulations to get a view into the impact of the particle diameter on the evolution of the particle curtain. This simulation setup allows for a one-to-one comparison between RMI and SDMI under comparable conditions while also allowing for a separate study into the validity of the use of both the multiphase Atwood number and the fluid-only Atwood number to compare the single-phase and multiphase instabilities. In particular, we show that this validity is at least partly dependent on the diameters of the particles in the curtain (thus, dependent on the Stokes number of the flow). We also analyze the effect of the multiphase terms of the vorticity evolution equation on the vorticity deposition in SDMI. Also discussed is the effect of the particle diameter on the multiphase generation terms as well as in the baroclinic vorticity generation term in SDMI as the shock passes over the curtain.