Numerical study on Rayleigh-Taylor effect on cylindrically converging Richtmyer-Meshkov instability

Evolution of a two-dimensional air/SF_6 single-mode interface is numerically investigated by an upwind CE/SE method under a cylindrically converging circumstance. The Rayleigh-Taylor effect caused by the flow deceleration on the phase inversion(RTPI)is highlighted. The RTPI was firstly observed in our previous experiment, but the related mechanism remains unclear. By isolating the three-dimensional effect, it is found here that the initial amplitude(a_0), the azimuthal mode number(k_0) and the re-shocking moment are the three major parameters which determine the RTPI occurrence. In the variable space of(k_0, a_0), a critical a_0 for the RTPI occurrence is solved for each k_0, and there exists a threshold value of k_0 below which the RTPI will not occur no matter what a_0 is. There exists a special k_0 corresponding to the largest critical a_0, and the reduction rule of critical a_0 with k_0 can be well described by an exponential decay function. The results show that the occurrence of the RTPI requires a small a_0 which should be less than a critical value, a large k_0 which should exceed a threshold, and a right impinging moment of the re-shock which should be later than the RTPI occurrence. Finally, the effects of the incident shock strength, the density ratio and the initial position of the interface on the threshold value of k_0 and on the maximum critical a_0 are examined. These new findings would facilitate the understanding of the converging Richtmyer-Meshkov instability and would be helpful for designing an optimal structure of the inertia confinement fusion capsule.     

Investigation of the Richtmyer-Meshkov instability with stereolithographed interfaces

A novel method to set highly accurate initial conditions has been designed in the context of shock tube experiments for the Richtmyer-Meshkov instability study. Stereolithography has been used to design the membrane supports which initially materialize the gaseous interface. The visualizations of both heavy-light and light-heavy sinusoidal interfaces were carried out with laser sheet diagnostics. Experiments are in very good agreement with theory and simulations for the heavy-light case, but probably due to the membrane effects, quickly deviate from them in the light-heavy configuration.     

Magnetically driven Rayleigh-Taylor instability with acceleration gradient

We investigate the stability properties of a slab of accelerating, current-carrying, cold, fluid when the accelerating J_ /spl times/ B_ force is nonuniform throughout the slab and leads to a gradient in the slab acceleration. A nonuniform force that squeezes (stretches) the slab while accelerating it increases (decreases) the Magnetic-Rayleigh-Taylor instability growth rate. This effect can explain recent experiments on thin, magnetically driven, imploding liner shells.     

非理想流体中Rayleigh-Taylor和Richtmyer-Meshkov不稳定性气泡速度研究

在随气泡顶端运动的坐标系中, 通过将理想流体模型推广到非理想流体的情况, 研究了流体黏性和表面张力对Rayleigh-Taylor (RT)和Richtmyer-Meshkov (RM)不稳定性气泡速度的影响. 首先得到了RT和RM不稳定性气泡运动的控制方程 (自洽的微分方程组); 其次给出了二维平面坐标和三维柱坐标中气泡速度的数值解和渐近解, 并定量分析了流体黏性和表面张力对RT和RM气泡速度和振幅的影响. 结果表明: 从线性阶段到非线性阶段的全过程中, 非理想流体中的气泡速度和振幅小于理想流体中的气泡速度和振幅. 也就是说, 流体黏性和表面张力对RT和RM不稳定性的发展都具有致稳作用. 关键词： Rayleigh-Taylor不稳定性 Richtmyer-Meshkov不稳定性 气泡速度 非理想流体     

任意Atwood数Rayleigh-Taylor和 Richtmyer-Meshkov 不稳定性气泡速度研究

本文将Layzer气泡模型推广到任意界面Atwood数情形,得到了自洽的微分方程组.该模型描述了气泡从早期的指数增长阶段到气 泡以渐近速度上升的非线性阶段的发展过程,给出了Rayleigh-Taylor(RT)和Richtmyer-Meshkov(RM)不稳定性的二维和 三维气泡速度渐近解,还求出了二维和三维RT不稳定性气泡顶点附近速度的解析解.     

Scaling laws of nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities in two and three dimensions

The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers ( A ) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h∼α·A·gt² with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h∼t^θ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin–Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.     

Solutions to Buoyancy-Drag Equation for Dynamical Evolution of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Zone

With a self-similar parameter b( A_t ) = H_i /λa_i, where A_t is the Atwood number, H_i andλ_i are the amplitude and wavelength of bubble (i = 1) and spike (i =
2) respectively, we derive analytically the solutionsto the Buoyancy-Drag equation recently proposed for dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing zone.Numerical solutions are obtained with a simple form of b(A_t ) = 1/(1 + A_t ) and comparisons with recent LEM (linear electric motor) experiments are made, and an agreement is found with properly chosen initial conditions.     

Granular Rayleigh-Taylor instability: experiments and simulations

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.     

Molecular dynamics simulation of cylindrical Richtmyer-Meshkov instability

The microscopic-scale Richtmyer-Meshkov(RM) instability of a single-mode Cu-He interface subjected to a cylindrically converging shock is studied through the classical molecular dynamics simulation. An unperturbed interface is first considered to examine the flow features in the convergent geometry, and notable distortions at the circular inhomogeneity are observed due to the atomic fluctuation. Detailed processes of the shock propagation and interface deformation for the single-mode interface impacted by a converging shock are clearly captured. Different from the macroscopic-scale situation, the intense molecular thermal motions in the present microscale flow introduce massive small wavelength perturbations at the single-mode interface, which later significantly impede the formation of the roll-up structure. Influences of the initial conditions including the initial amplitude,wave number and density ratio on the instability growth are carefully analyzed. It is found that the late-stage instability development for interfaces with a large perturbation does not depend on its initial amplitude any more. Surprisingly, as the wave number increases from 8 to 12, the growth rate after the reshock drops gradually. The distinct behaviors induced by the amplitude and wave number increments indicate that the present microscopic RM instability cannot be simply characterized by the amplitude over wavelength ratio(η). The pressure history at the convergence center shows that the first pressure peak caused by the shock focusing is insensitive to η, while the second one depends heavily on it.     

Resistive drift instability and Rayleigh-Taylor instability in a dusty plasma

The resistive drift instability and the Rayleigh-Taylor instability are studied self-consistently in a magnetized inhomogeneous dusty plasma. The effect of grain charge fluctuations is taken into consideration. It is found that the presence of the dust grains in the plasma can significantly affect the resistive drift instability but less significantly the Rayleigh-Taylor instability. Further, the grain charge fluctuation has a tendency to stabilize both instabilities.     

Asymptotic behavior of the Rayleigh-Taylor instability

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin and Williams for which we give a simplified demonstration. In particular, we observe that the spike's curvature evolves as t(3), while the overshoot in acceleration shows good agreement with the suggested 1/t(5) law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.