Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

Linear analysis of Atwood number effects on shear instability in the elastic–plastic solids

The evolution of shear instability between elastic–plastic solid and ideal fluid which is concerned in oblique impact is studied by developing an approximate linear theoretical model. With the velocities expressed by the velocity potentials from the incompressible and irrotational continuity equations and the pressures obtained by integrating momentum equations with arbitrary densities, the motion equations of the interface amplitude are deduced by considering the continuity of normal velocities and the force equilibrium with the perfectly elastic–plastic properties of solid at interface. The completely analytical formulas of the growth rate and the amplitude evolution are achieved by solving the motion equations. Consistent results are performed by the model and 2D Lagrange simulations. The characteristics of the amplitude development and Atwood number effects on the growth are discussed. The growth of the amplitude is suppressed by elastic–plastic properties of solids in purely elastic stage or after elastic–plastic transition, and the amplitude oscillates if the interface is stable. The system varies from stable to unstable state as Atwood number decreasing. For large Atwood number, elastic–plastic properties play a dominant role on the interface evolution which may influence the formation of the wavy morphology of the interface while metallic plates are suffering obliquely impact.

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

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.

A New Approach to the Rayleigh–Taylor Instability

In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the constitutive laws we formulate a general criterion for the existence of infinitely many weak solutions which reflect the turbulent mixing of the two fluids. Our criterion can be verified in the case that initially the fluids are at rest and separated by a flat interface with the heavier one being above the lighter one—the classical configuration giving rise to the Rayleigh–Taylor instability. We construct specific examples when the Atwood number is in the ultra high range, for which the zone in which the mixing occurs grows quadratically in time.