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.     

Two-Dimensional Rayleigh-Taylor Instability in Incompressible Fluids at Arbitrary Atwood Numbers

The Rayleigh-Taylor instability in two-dimensional incompressible fluids at arbitrary Atwood numbers is studied by expanding the perturbation velocity potential to third order. The second and third harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The mode coupling coefficients are dependent on the Atwood numbers. Our simulations support the weakly nonlinear results. We find that the ratio of the nonlinear saturation amplitude ηs and the perturbation wavelength λ is dependent on the Atwood number AT and the relation is ηs/λ=（1/π）[√2/5/√（1＋3AT2 ）].     

Weakly nonlinear theory for the ablative Rayleigh-Taylor instability

A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in the presence of ablation and thermal transport. The second harmonic generation efficiency of a single-mode disturbance is computed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed. The ablative stabilization can be clearly discussed because the derived formulas for the evanescent ablation rate are in agreement with previously known results for incompressible, inviscid, irrotational, and immiscible fluids [S. W. Haan, Phys. Fluids B 3, 2349 (1991)]; M. Berning and A. M. Rubenchik, Phys. Fluids 10, 1564 (1998)]].     

Rayleigh-Taylor instability for immiscible fluids of arbitrary viscosities: a magnetic levitation investigation and theoretical model

A magnetic field gradient was used to draw down a low density paramagnetic fluid below a more dense fluid in a Hele-Shaw cell. On turning off the field a Rayleigh-Taylor instability was observed in situ, and the growth of the most unstable wave vector was measured versus time. A theory for the instability that permits different viscosities for two immiscible fluids was developed, and good agreement was found with the experimental results. The technique of magnetic levitation promises to broaden significantly the accessible parameter space of gravitational interfacial instability experiments.     

Observation of self-similar behavior of the 3D, nonlinear Rayleigh-Taylor instability

The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation sigma(rms) grows as alpha(sigma)gt(2), where g is the foil acceleration, t is the time, and alpha(sigma) is constant. The number of bubbles evolves as N(t) alpha(omegat sq.rt(9) + C)(-4) and the average size evolves as (t) alpha omega(2)gt(2), where C is a constant and omega = 0.83 +/- 0.1 is the measured scaled bubble-merging rate.     

Rayleigh-Taylor instability experiments with precise and arbitrary control of the initial interface shape

In a Rayleigh-Taylor instability a dense fluid sits metastably atop a less dense fluid, a configuration that can be stabilized using a magnetic field gradient when one fluid is highly paramagnetic. On switching off the magnetic field, the instability occurs as the dense fluid falls under gravity. By affixing appropriately shaped magnetically permeable wires to the outside of the cell, one may impose arbitrarily chosen and well-controlled initial perturbations on the interface. This technique is used to examine both the linear and nonlinear growth regimes for which the perturbation amplitudes, growth rates, and nonlinear growth coefficients are obtained.     

二维Rayleigh-Taylor不稳定性组分剖面与Atwood数相关性

由Rayleigh-Taylor不稳定性引起的湍流混合广泛存在于自然现象和工程应用中.在重力场作用下，将重流体置于轻流体之上，系统处于平衡状态.此时，在轻重流体界面处添加微小扰动，重流体向下形成尖钉，轻流体向上形成气泡，轻重流体进入湍流混合状态，系统失去稳定状态，进入失稳过程.组分剖面揭示了流场在任意时刻任意高度上的成分，从而揭示了Rayleigh-Taylor不稳定性的发展过程.利用计算流体力学软件CFD2模拟常加速度场下二维多模Rayleigh-Taylor不稳定性的发展，研究了重流体组分剖面随Atwood数的变化.文章对比了Atwood数为0.1，0.5，0.9这3种情况下质量分数剖面.在利用气泡高度h_b和尖钉深度h_s对高度做归一化之后，质量分数剖面不依赖于密度比.在不同密度比下，质量分数曲线都满足f_m~$\frac{1}{2}{\mathop{\rm erf}\nolimits} \left( {4\left( {\frac{{y-{h_{\rm{s}}}}}{{{h_{\rm{b}}}-{h_{\rm{s}}}}}-\frac{1}{2}} \right)} \right) + \frac{1}{2}$.      

高雷诺数下非混相Rayleigh-Taylor不稳定性的格子Boltzmann方法模拟

本文采用相场格子Boltzmann方法研究了竖直微通道内中等Atwoods数流体的单模Rayleigh-Taylor不稳定性问题,系统分析了雷诺数对相界面动力学行为以及扰动在各发展阶段演化规律的影响.数值结果表明高雷诺数条件下,不稳定性界面扰动的增长经历了四个不同的发展阶段,包括线性增长阶段、饱和速度阶段、重加速阶段及混沌混合阶段.在线性增长阶段,我们计算获得的气泡与尖钉振幅符合线性稳定性理论,并且线性增长率随着雷诺数的增加而增大.在第二个阶段,我们观察到气泡与尖钉将以恒定的速度增长,获得的尖钉饱和速度略高于Goncharov经典势能模型的解析解[Phys.Rev.Lett.200288134502],这归因于系统中产生了多个尺度的旋涡,而涡之间的相互作用促进了尖钉的增长.随着横向速度和纵向速度的差异扩大,气泡和尖钉界面演化诱导产生的Kelvin–Helmholtz不稳定性逐渐增强,从而流体混合区域出现许多不同层次的涡结构,加速了气泡与尖钉振幅的演化速度,并在演化后期阶段,导致界面发生多层次卷起、剧烈变形、混沌破裂等行为,最终形成了非常复杂的拓扑结构.此外,我们还统计了演化后期气泡与尖钉的无量纲加速度,发现气泡和尖钉的振幅在后期呈现二次增长规律,其增长率系数分别为0.045与0.233.而在低雷诺条件下,重流体在不稳定性后期以尖钉的形式向下运动而轻流体以气泡的形式向上升起.在整个演化过程中,界面变得足够光滑,气泡与尖钉在后期的演化速度接近于常数,未观察到后期的重加速与混沌混合阶段.     

Ablation effects on weakly nonlinear Rayleigh-Taylor instability with a finite bandwidth

A weakly nonlinear but numerically tractable model (to third order in amplitude and including bandwidth effects) has been developed for the ablative Rayleigh-Taylor (RT) instability. Model results clearly show growth reduction from linear ablative RT values and even amplitude saturation in some realistic cases. For excitation of a band of wave numbers near the cutoff for growth, the behavior is dominated by the mode with the largest linear growth rate, and not by the mode with the largest initial amplitude. This type of model is likely to be important for the future assessment of the RT effects on specific target designs of the inertial confinement fusion.     

Nonlinear analysis of the Rayleigh-Taylor instability at the charged interface

An asymptotic solution to the problem of analyzing the nonlinear stage of the Rayleigh-Taylor instability at the uniformly charged interface between two (conducting and insulating) immiscible ideal incompressible liquids is derived in the third order of smallness. It is found that the charge expands the range of waves experiencing instability toward shorter waves and decreases the length of the wave with a maximum growth rate. It turns out that the characteristic linear scale of interface deformation, which arises when the heavy liquid flows into the light one, decreases as the charge surface density increases in proportion to the square root of the Tonks-Frenkel parameter characterizing the stability of the interface against the distributed self-charge.     

High-amplitude single-mode perturbation evolution at the Richtmyer-Meshkov instability

The single-mode Richtmyer-Meshkov hydrodynamic instability at light/heavy (air/SF6 and air/CO2), close density (air/N2), and heavy/light (air/He) interfaces has been experimentally studied for a low incident shock wave Mach number. Two identical 2D half sinusoidal initial perturbations, with a relatively high initial amplitude, were considered in order to rapidly reach the nonlinear regime and check the reduction of the initial growth rate compared to that predicted by the small-amplitude theory. The growth rate measurements for the air/SF6 and air/CO2 cases are in excellent agreement with the nonlinear model of Sadot et al. coupled with a reduction factor suggested by Rikanati et al. In the air/N2 case, the reversal phase can be precisely described by the linear theory. Finally, the heavy/light experiment is well described by the Vandenboomgaerde model also coupled with a smaller reduction factor.     

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.     

双锥对撞点火机制2020年冬季实验中的瑞利-泰勒不稳定性分析

直接驱动激光聚变通过整形后的纳秒脉冲激光辐照氘氚(DT)球壳靶,经球对称压缩加速后,在中心转滞获得高温等离子体热斑,实现聚变点火.在球壳靶受到压缩和加速过程中等离子体界面的流体力学不稳定性,特别是瑞利-泰勒不稳定性的增长有可能会对压缩壳层造成破坏,导致点火的失败.本文通过理论解析和数值模拟,对基于Zhang等提出的双锥对撞点火方案(2020 Philos.Trans.A Math.Phys.Eng.Sci.378 20200015)在2020年冬季实验条件下的流体力学不稳定性增长进行了分析.结果显示理论模型与一维数值模拟中对整体压缩和加速过程的描述基本一致,在当前的近等熵波形下金锥中的壳层靶实现了低熵压缩,同时瑞利-泰勒不稳定性增长导致的最危险时刻扰动振幅和壳层厚度比可以达到约0.25,壳层依然处于安全状态,但当初始壳层表面扰动均方根振幅大于22 nm时,则可能出现壳层的破裂.因此,未来实验中的靶设计与驱动激光脉冲波形设计中可以通过增加靶壳层厚度、提高预脉冲强度、减小靶表面的粗糙度和提高激光辐照的匀滑度等方式来抑制不稳定性增长.