A Gas-Particle Analogue to the Richtmyer-Meshkov Instability: Comparing Multiphase Simulations to Shock Tube Experiments

Abstract

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.