Rayleigh-Taylor不稳定性的Runge-Kutta间断有限元模拟

 采用发展后的间断有限元方法,对Rayleigh-Taylor不稳定性进行了数值模拟。在计算中采用Level-Set方法进行界面追踪,用虚拟流体方法（Ghost Fluid Method,GFM）对界面附近物理量进行等压装配。对两个典型的Rayleigh-Taylor不稳定性算例的数值研究结果表明,采用该方法计算含有接触间断的多介质流体力学问题是有效的,在交界面附近不出现伪振荡,具有较高的分辨率。     

表面张力对高雷诺数Rayleigh-Taylor不稳定性后期增长的影响

采用多相流的相场格子Boltzmann方法数值研究了微通道内高雷诺数单模Rayleigh-Taylor(RT)不稳定性的后期演化规律,重点分析表面张力对相界面动力学行为以及气泡与尖钉增长的影响.数值实验表明,随着界面张力的增大,可以有效降低演化过程中相界面结构的复杂程度,并抑制不稳定性后期相界面破裂形成离散液滴.另外,...     

界面张力对Rayleigh-Taylor不稳定性的影响

将具有简单速度势的Layzer模型和Zufiria模型推广至非理想流体情况, 并分别利用这两种模型研究了界面张力对Rayleigh-Taylor不稳定性的影响. 首先得到了两种模型下气泡的渐近速度和渐近曲率的解析表达式; 其次系统研究了界面张力对气泡的渐近速度和渐近曲率的影响; 最后将两种模型进行了比较, 并将气泡的渐近速度和数值模拟进行了比较. 研究表明: 界面张力压低了气泡的速度, 但对曲率没有影响; 利用简单速度势的Layzer模型所得的气泡的渐近速度比复杂速度势的Layzer模型的值小, 但是比Zufiria模型的值大; 当阿特伍德数等于1时, 简单速度势的Layzer模型和复杂速度势的Layzer模型给出的结果一致. 关键词： Rayleigh-Taylor不稳定性 界面张力 Layzer模型 Zufiria模型     

耦合界面张力的三维流体界面不稳定性的格子Boltzmann模拟

采用介观格子Boltzmann方法模拟界面张力作用下三维流体界面的Rayleigh-Taylor (RT)不稳定性的增长过程,主要分析表面张力对流体界面动力学行为及尖钉和气泡后期增长的影响机制.首先发现三维RT不稳定性的发生存在临界表面张力(σ_c),其值随着流体Atwood数的增大而增大,且数值预测值与理论分析结果σ_c=(ρ_h-ρ₁)g/k~2一致.另外,随着表面张力的增大,不稳定性演化过程中界面卷吸程度和结构复杂性逐渐减弱,系统中界面破裂形成离散液滴的数目也显著减少.相界面的后期动力学行为也从非对称发展转向始终保持关于中轴线对称.尖钉与气泡振幅在表面张力较小时对其变化不显著,当表面张力增大到一定值后,可以有效地抑制尖钉与气泡振幅的增长.进一步发现,高雷诺数三维RT不稳定性在不同表面张力下均经历4个不同的发展阶段:线性阶段、饱和速度阶段、重加速和混沌混合阶段.尖钉与气泡在饱和速度阶段以近似恒定的速度增长,其渐进速度的值与修正的势流理论模型结果一致.受非线性Kelvin-Helmholtz旋涡的剪切作...     

ICF研究中的Rayleigh-Taylor不稳定性实验用靶

 概述了当前研究Rayleigh-Taylor不稳定性增长实验所用的靶型情况。从实验用靶来看，调制靶的设计正从平面向立体发展，出现了球形和柱形等新靶形，制备手段包括精密机械微加工、激光束、电子束和离子束加工、半导体工艺和微米纳米技术加工等。根据对国外新靶型的研究，结合国内工艺条件和实验需求，对国内可能采用的靶型进行了研究探索。     

燃烧系统的离散Boltzmann建模与模拟研究进展

燃烧系统的诸多模拟依托于流体建模, 离散Boltzmann方法(discrete Boltzmann method, DBM) 是近年来发展起来的一种新的流体介观建模方法. 本文简要评述DBM发展的两个方向——Navier-Stokes等偏微分方程的数值逼近解法和复杂系统的微介观动理学建模. 主要介绍在燃烧系统模拟方面DBM已有的工作、新近的思路、与传统流体建模的异同以及近期的研究成果. 本文重点传递的信息为: 作为复杂系统微介观动理学建模出现的DBM在模拟过程中同时给出“流动”及其相伴随的、关系最密切的那部分“热动”非平衡效应; 它为燃烧等复杂系统中各类非平衡行为的描述、非平衡信息的提取、非平衡程度的度量提供了一种简洁、有效的方法; 它所提供的热动非平衡测量量有两类: 一类是直接比较分布函数和平衡态分布函数的动理学矩关系得到的, 一类是来自于Chapman-Enskog多尺度分析给出的热传导和黏性项. 基于第二类DBM, 可以实现(燃烧等)一大类复杂流体系统的多尺度物理建模.     

可压缩流体的Rayleigh-Taylor和Kelvin-Helmholtz不稳定性

可压缩流体界面不稳定性的小扰动研究中，往往首先规定具体的状态方程形式，然后给出色散关系。这使得所给出的结果仅适用于该状态方程的具体形式，具有特殊性。由于这种特殊性，使得某些机理的讨论变得复杂，且结论相互矛盾。     

辐射烧蚀界面的单模Rayleigh-Taylor不稳定性分析

首先对惯性约束聚变(ICF)遇到的流体力学界面不稳定性作了简要的分析;其次讨论了Rayleigh-Taylor(RT)不稳定性在ICF中所起的作用;第三,根据一维数值计算结果,按照考虑密度梯度和烧蚀致稳的RT不稳定性增长的定标规律对不稳定性增长作了估计。最后在计算结果的讨论中,对有关实验测量提出某些倾向性的建议。     

斜界面Rayleigh-Taylor不稳定性混合实验研究

 实验研究了不相溶流体斜界面Rayleigh-Taylor（R-T）不稳定性湍流混合区的混合不对称性特征。利用高压气体加速装有不同液体的箱体,加速度方向由轻液体指向重液体,此时界面是R-T不稳定性的。利用阴影测试技术,研究了初始倾角9°的ZnCl₂溶液/正己烷斜界面的演化规律,得出混合区内混合不对称、斜界面倾角渐增的规律。     

柱几何Rayleigh-Taylor不稳定性的数值模拟

给出了柱几何中流体力学方程组及其在数值模拟中采用的计算方法。对二维柱几何Rayleigh-Taylor不稳定性进行数值模拟,在线性阶段与线性理论符合得很好;不稳定性增长进入非线性区域的阈值依赖于界面的位置,并且明显不同于平面情况。     

Lattice Boltzmann modeling and simulation of compressible flows

In this mini-review we summarize the progress of Lattice Boltzmann (LB) modeling and simulating compressible flows in our group in recent years. Main contents include (i) Single-Relaxation-Time (SRT) LB model supplemented by additional viscosity, (ii) Multiple-Relaxation-Time (MRT) LB model, and (iii) LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model supplemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross-Krook (LBGK). So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a completely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.     

Rayleigh-Taylor instability under multi-mode perturbation: Discrete Boltzmann modeling with tracers

The two-dimensional Rayleigh-Taylor Instability (RTI) under multi-mode perturbation in compressible flow is probed via the Discrete Boltzmann Modeling (DBM) with tracers. The distribution of tracers provides clear boundaries between light and heavy fluids in the position space. Besides, the position-velocity phase space offers a new perspective for understanding the flow behavior of RTI with intuitive geometrical correspondence. The effects of viscosity, acceleration, compressibility, and Atwood number on the mixing of material and momentum and the mean non-equilibrium strength at the interfaces are investigated separately based on both the mixedness defined by the tracers and the non-equilibrium strength defined by the DBM. The mixedness increases with viscosity during early stage but decreases with viscosity at the later stage. Acceleration, compressibility, and Atwood number show enhancement effects on mixing based on different mechanisms. After the system relaxes from the initial state, the mean non-equilibrium strength at the interfaces presents an initially increasing and then declining trend, which is jointly determined by the interface length and the macroscopic physical quantity gradient. We conclude that the four factors investigated all significantly affect early evolution behavior of an RTI system, such as the competition between interface length and macroscopic physical quantity gradient. The results contribute to the understanding of the multi-mode RTI evolutionary mechanism and the accompanied kinetic effects.     

Discrete Boltzmann model for implosion- and explosion-related compressible flow with spherical symmetry

To kinetically model implosion- and explosion-related phenomena, we present a theoretical framework for constructing a discrete Boltzmann model (DBM) with spherical symmetry in spherical coordinates. To achieve this goal, a key technique is to use localCartesian coordinates to describe the particle velocity in the kinetic model. Therefore, geometric effects, such as divergence and convergence, are described as a “force term”. To better access the nonequilibrium behavior, even though the corresponding hydrodynamic model is one-dimensional, the DBM uses a discrete velocity model (DVM) with three dimensions. A new scheme is introduced so that the DBM can use the same DVM regardless of whether or not there are extra degrees of freedom. As an example, a DVM with 26 velocities is formulated to construct the DBM at the Navier–Stokes level. Via the DBM, one can study simultaneously the hydrodynamic and thermodynamic nonequilibrium behaviors in implosion and explosion processes that are not very close to the spherical center. The extension of the current model to a multiple-relaxation-time version is straightforward.     

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.     

Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method

Rayleigh–Taylor (RT) instability widely exists in nature and engineering fields. How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value. At present, abundant results of RT instability have been obtained by traditional macroscopic methods. However, research on the thermodynamic non-equilibrium (TNE) effects in the process of system evolution is relatively scarce. In this paper, the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability. The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region. Firstly, as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region, the average TNE intensity first increases and then reduces, and it increases with the specific heat ratio decreasing; the specific heat ratio has the same effect on the global strength of the viscous stress tensor. Secondly, the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure. Thirdly, under the competition between the temperature gradients and the contact area of the two fluids, the average intensity of the non-equilibrium quantity related to the heat flux shows diversity, and the influence of the specific heat ratio is also quite remarkable.     

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin–Helmholtz instability (KHI) via an efficient discrete Boltzmann model. Technically, two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes. One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures; the other is to evaluate the growth rate of KHI from the slopes of morphological functionals. Physically, it is found that the time histories of width of mixing layer, TNE intensity, and boundary length show high correlation and attain their maxima simultaneously. The viscosity effects are twofold, stabilize the KHI, and enhance both the local and global TNE intensities. Contrary to the monotonically inhibiting effects of viscosity, the heat conduction effects firstly refrain then enhance the evolution afterwards. The physical reasons are analyzed and presented.     

Rayleigh-Taylor instability of multi-fluid layers in cylindrical geometry

Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically.The growth rates and the amplitudes of perturbation on the two interfaces are obtained. The feedback factor from outer to inner interface is larger than that from inner to outer interface under the same conditions. The growth rate on the initially unstable interface is larger than the corresponding result in planar geometry for low mode perturbation. The two interfaces are decoupled for a larger mode number perturbation. The dependencies of the amplitudes of perturbation on different initial conditions are analyzed. The negative feedback effect from initially stable interface to another unstable interface is observed. In the limit of infinity inner radius and finite shell thickness, the results in planar geometry are recovered.     

Directly driven Rayleigh—Taylor instability of modulated CH targets

Directly driven ablative Rayleigh-Taylor (R-T) instability of modulated CH targets was studied using the face- on X-ray radiography on the Shen-Guang II device. We obtained temporal evolution images of the R-T instability perturbation. The R-T instability growth factor has been obtained by using the methods of fast Fourier transform and seeking the difference of light intensity between the peak and the valley of the targets. Through comparison with the the theoretical simulation, we found that the experimental data had a good agreement with the theoretical simulation results before 1.8 ns, and was lower than the theoretical simulation results after that.