Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder

Abstract

Numerical simulation of Richtmyer–Meshkov instability (RMI) is conducted using an improved localized artificial diffusivity (LAD) method, which is used to treat discontinuities in the form of material interfaces and shocks in the flow-field. The RMI occurs on a cylindrical interface between air and SF6 accelerated by a Mach 1.2 shock initially in air. Navier–Stokes simulation is conducted to accurately predict the mixing between the two fluids. The initial conditions for the two-dimensional simulations are matched to previous experimental work by C. Tomkins et al. [“An experimental investigation of mixing mechanisms in shock-accelerated flow,” J. Fluid Mech. 611, 131 (2008)] and good agreement is found between the experimental data and numerical results. The study on initial condition sensitivity indicates that the initial pressure and density gradient are critical parameters that determine the primary vortex generation responsible for the flow development. A grid convergence study is carried out and the relative contribution of the artificial properties introduced by the LAD method is characterized. Novel to this study is the exploration of the effect of the third species (acetone used as a tracer particle in the experiments to obtain contour fields using planar laser induced florescence). The effect of the presence of the third species on the evolution of the RMI and mixing is shown to be non-negligible and an estimate of the amount of the tracer species that was present in the initial experimental set-up is given.