Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems

The turbulent Rayleigh–Taylor instability is investigated over a comprehensive range of fluid density ratio (R)1.3⩽R⩽50 [0.15⩽A=(R−1)/(R+1)⩽0.96] and different acceleration histories g(t) using the Linear Electric Motor. The mixing layer is diagnosed with backlit photography and laser-induced fluorescence. For a constant acceleration, the bubble (2) and spike (1) amplitudes are found to increase as hi=αiAgt2 with α2∼0.05±0.005 and α1∼α2RDα with Dα∼0.33±0.05. For temporally varying accelerations Ag(t)>0, this can be generalized to hi=2αiAS using S=[∫gdt]2/2 rather than the displacement Z=∫∫gdt′ dt. For impulsive accelerations, S remains constant during the coast phase and the amplitudes obey a power law hi∼tθi with θ2∼0.25±0.05 and θ1∼θ2RDθ with Dθ∼0.21±0.05. These values of Dα and Dθ compare favorably with numerical simulations and mix models. The average diameter at the mixing front for bubbles is found to increase as d2∼h2(1+A)/4 in qualitative agreement with “merger” models, but the associated dhi/dt i...

Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories

Richtmyer–Meshkov instability is investigated for negative Atwood number and two-dimensional sinusoidal perturbations by comparing experiments, numerical simulations and analytic theories. The experiments were conducted on the NOVA laser with strong radiatively driven shocks with Mach numbers greater than 10. Three different hydrodynamics codes (RAGE, PROMETHEUS and FronTier) reproduce the amplitude evolution and the gross features in the experiment while the fine-scale features differ in the different numerical techniques. Linearized theories correctly calculate the growth rates at small amplitude and early time, but fail at large amplitude and late time. A nonlinear theory using asymptotic matching between the linear theory and a potential flow model shows much better agreement with the late-time and large-amplitude growth rates found in the experiments and simulations. We vary the incident shock strength and initial perturbation amplitude to study the behaviour of the simulations and theory and to study the effects of compression and nonlinearity.

Richtmyer–Meshkov instability growth: experiment, simulation and theory

Large-eddy simulations of the Richtmyer–Meshkov instability with reshock are pre- sented and the results are compared with experiments. Several configurations of shocks initially travelling from light (air) to heavy (sulfur hexafluoride, SF6) have been simulated to match previous experiments and good agreement is found in the growth rates of the turbulent mixing zone (TMZ). The stretched-vortex subgrid model used in this study allows for subgrid continuation modelling, where statistics of the unresolved scales of the flow are estimated. In particular, this multiscale modelling allows the anisotropy of the flow to be extended to the dissipation scale, eta, and estimates to be formed for the subgrid probability density function of the mixture fraction of air/SF6 based on the subgrid variance, including the effect of Schmidt number.

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Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock

Results of flow visualization experiments of an impulsively accelerated plane interface between air and SF6 are reported. The shock tube used for the experiments has a larger test section than in previous experiments. The larger extent of uniform test flow relative to nonuniform boundary-layer flow permits unambiguous interpretation of flow-visualization photographs, and the influence of shock-wave/boundary-layer interactions is no longer dominant. The strong wall vortex observed in previous studies is not observed in these experiments. It is found that the thin membrane, which forms the initially plane interface, has a significant influence on the initial growth rate of the interface thickness. However, the measured growth rates after the first reflected shock are independent of membrane configuration and are in good agreement with analytical predictions.

M. Vetter

Papers

Experiments on the Richtmyer-Meshkov instability of an air/SF 6 interface