A. Rikanati

Vortex-merger statistical-mechanics model for the late time self-similar evolution of the Kelvin–Helmholtz instability

The nonlinear growth, of the multimode incompressible Kelvin–Helmholtz shear flow instability at all density ratios is treated by a large-scale statistical-mechanics eddy-pairing model that is based on the behavior of a single eddy and on the two eddy pairing process. From the model, a linear time growth of the mixing zone is obtained and the linear growth coefficient is derived for several density ratios. Furthermore, the asymptotic eddy size distribution and the average eddy life time probability are calculated. Very good agreement with experimental results and full numerical simulations is achieved.

Scaling in the shock–bubble interaction

The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. In the present study, simple dimensional analysis is used to show that the circulation is linearly dependent on the surrounding material speed of sound c, and the initial bubble radius R. In addition, it is shown that the velocities characterizing the flow field are linearly dependent on the speed of sound, and are independent of the initial bubble radius. The dependence of the circulation on the shock wave Mach number M is derived by Samtaney and Zabusky (1994) as (1 + 1/M + 2/M 2 ) (M - 1). Experiments were performed for slow/fast (air-helium) and fast/slow (air-SF 6 ) interactions. Full numerical simulations were conducted resulting in good agreement. From the results, it is seen that in both cases, according to the proposed scaling, the vortex ring velocity is bubble radius independent. The numerical results for the slow/fast interaction show that the proposed Mach scaling is valid for M < 2. Above M ≅ 2, the topology of the bubble changes due to a competition between the upstream surface of the bubble and the undisturbed shock wave.

An experimental study of the high Mach number and high initial-amplitude effects on the evolution of the single-mode Richtmyer–Meshkov instability

AbstractThe present article describes an experimental study that is a part of an integrated theoretical~Rikanati et al. 2003! andexperiential investigation of the Richtmyer–Meshkov ~RM! hydrodynamic instability that develops on a perturbedcontact surface by a shock wave. The Mach number and the high initial-amplitude effects on the evolution of thesingle-modeshock-wave-inducedinstabilitywerestudied.Todistinguishbetweentheabove-mentionedeffects,twosetsofshock-tubeexperimentswereconducted:highinitialamplitudeswithalow-Machincidentshockandsmallamplitudeinitial conditions with a moderate-Mach incident shock. In the high-amplitude experiments a reduction of the initialvelocity with respect to the linear prediction was measured. The results were compared to those predicted by a vorticitydeposition model and to previous experiments with moderate and high Mach numbers done by others and goodagreement was found.The result suggested that the high initial-amplitude effect is the dominant one rather than the highMach number effect as suggested by others. In the small amplitude–moderate Mach numbers experiments, a reductionfrom the impulsive theory was noted at late stages. It is concluded that while high Mach number effect can dramaticallychange the behavior of the flow at all stages, the high initial-amplitude effect is of minor importance at the late stages.That result is supported by a two-dimensional numerical simulation.Keywords: Richtmyer–Meshkov instability; Shock-tube experiments; Turbulent mixing

A secondary small-scale turbulent mixing phenomenon induced by shock-wave Mach-reflection slip-stream instability

Secondary small-scale Kelvin-Helmholtz instability, developing along the Mach reflection slip-stream, was investigated. This instability is the cause for thickening the slipstream. Growth rates of the large-scale Kelvin-Helmholtz shear flow instability are used to model the evolution of the slip-stream instability in ideal gas. The model is validated through experiments measuring the instability growth rates for a range of Mach numbers and reflecting wedge angles. Good agreement is found for Reynolds numbers of Re > 2 × 104 This work demonstrates, for the first time, the use of large-scale models of the Kelvin-Helmholtz instability in modeling secondary turbulent mixing in hydrodynamic flows, a methodology which could be further implemented in many important secondary mixing processes.

CHAPTER 14 – Shock-Induced Instability of Interfaces

This chapter presents a systematic treatment of shock-wave-induced hydrodynamic mixing instabilities, based on models, simulations, and experiments. The description, based on penetration of the light fluid in the heavy one (bubbles) and the heavy into the light (spikes), provides a comprehensive and understanding of the evolution of the instability for both single-mode and multimode cases. The evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities in the linear and nonlinear stages is also presented. When two fluids of different densities are subjected to an accelerating field, under certain circumstances an instability is created at the contact surface between them. If the acceleration is slowly varied and directed from the heavy fluid to the light one, the Rayleigh-Taylor instability occurs. The theoretical and experimental studies performed regarding the late nonlinear stages of the instability evolution is described. The chapter is devoted to single-mode evolution, but to complete the whole picture, a generalization of the single mode to the multimode case is presented.

Study on the effect of Mach number and initial amplitudes on the evolution of a single-mode shock-induced hydro-dynamic instability

In the present study the Mach number and the high-initial amplitudes effects on the evolution of the single-mode shock wave induced instability were investigated. To distinguish between the above-mentioned effects, two sets of shock-tube experiments were conducted: high-initial amplitudes with a low-Mach incident shock; and small amplitude initial conditions with moderate-Mach incident shock. In the high-amplitude experiments a reduction of the initial velocity with respect to the linear prediction was measured. The results were compared to those predicted by a vorticity deposition model and to previous experiments with moderate and high Mach numbers done by others and good agreement was found. The result suggested that the high-initial amplitude effect is the dominant one rather then the high-Mach number effect as suggested by others. In the small amplitude-moderate Mach numbers experiments a reduction from the impulsive theory was noted at late stages.

Dependence of the Richtmyer-Meshkov instability on the Atwood number and dimensionality: theory and experiments

In order to verify the predictions of the 2D high Atwood number potential flow model for the evolution of the shock wave induced Richtmyer-Meshkov instability, shock-tube experiments were performed with a single-mode perturbation and two competing bubbles as the initial conditions. The experimental results were compared to theoretical model and to numerical simulation. In the present work the dependence of the instability on the Atwood number and the dimensionality of the instability were investigated in a shock tube apparatus. A high speed schlieren photography system were used to monitor the evolution of the unstable contact surface. Different Atwood numbers were achieved by using different gases. The results of those experiments were found to be in very good agreement with the predictions of theoretical model and numerical simulation. These results verify the key elements of the Atwood number scaling of the bubble-merger model used for the prediction of the multi-mode bubble and spike front evolution at all Atwood numbers. The dimensionality investigation of the instability evolution was done using a pyramid like initial perturbation. The results reveal the same two key elements of the bubble-merger model to describe the bubble and spike front evolution as in the 2D case except for different scaling constants.