密度非均匀流场中冲击加载双模态界面失稳现象的数值模拟

利用可压缩多介质黏性流动和湍流大涡模拟的二维计算程序MVFT-2D,针对初始非均匀流场密度为高斯分布、马赫数Ma=1.27激波作用下的双模态界面失稳现象,进行了数值模拟研究。数值模拟结果表明,处于非均匀流场中的双模态振幅耦合效应较弱,而且低密度区的初始大振幅界面扰动增长最快,高密度区的初始小振幅界面扰动增长最慢。通过进一步分析可知,在一定初始振幅范围内,非均匀流场低密度区的振幅增长率较高,混合区域更宽,湍动能较大,受初始振幅影响较大,导致该区域界面不稳定演化较快。其变化规律与均匀流场呈现相反趋势,说明非均匀流场界面不稳定性的发展规律与均匀流场存在较大差异。     

R-T界面不稳定性及湍流混合的大涡模拟

采用大涡模拟(LES)方法研究R-T(Rayleigh Taylor)不稳定性,显示了不稳定发展的小扰动阶段、变形阶段、规则非线性阶段、不规则非线性阶段和湍流混合阶段界面演化与特征,分析了湍流混合层厚度增长的规律,同时还研究了湍流二阶相关量如动量、质量和能量通量在大尺度和亚格子尺度所占分量,验证了LES方法是处理R-T界面不稳定性和湍流混合的一种有效方法.     

激波冲击V形界面的RM不稳定性实验研究

在激波管中实验研究了二维V形空气/SF6界面在入射激波和反射激波作用下的Richtmyer-Meshkov不稳定性发展规律。实验中采用细针约束肥皂膜的方法形成了精确可控的V形初始界面,利用高速纹影技术获得了受冲击的V形界面演化图像。通过改变初始V形界面顶角表征初始扰动振幅,获得了不同初始振幅条件下的波系和界面演化。结果表明,不同顶角下,入射激波冲击过后,界面形态表现出明显的差异,进一步导致反射激波冲击后界面形态的多样性。当顶角较小时,反射激波在界面内外引起复杂的波系结构,从而对界面形态及反相现象产生较大的影响。反射激波的二次作用使流场快速进入湍流混合状态,并且顶角较小时流场趋于各向同性发展。对反射激波作用后的界面混合宽度进行了测量,并与理论模型预测结果进行对比,发现理论模型不能很好地预测混合宽度的增长,主要是因为反射激波作用之后流场并没有完全达到湍流混合状态,不符合理论模型的适用条件。     

不同界面组分分布对Richtmyer-Meshkov不稳定性的影响

基于二维非定常Euler方程,对平面激波与不同界面组分分布下氦气气柱作用过程所引起的Richtmyer-Meshkov不稳定性现象进行了数值模拟,探讨了激波冲击轻质气柱后气柱界面形态的演变及流场波系结构,定量分析了气柱特征尺度(气柱长度、高度和中轴宽度)和气柱体积压缩率随时间变化.此外,结合流场压强、速度、环量和气体混合率,多角度分析了激波驱动界面气体混合的流动机制,获得了不同界面组分分布对界面不稳定性的影响.结果表明,随着气柱界面从完全扩散界面向间断界面的过渡,界面两侧的声反射系数随之增大,使入射激波与气柱界面的作用由常规透射转变为非常规透射,反射激波逐渐加强,透射激波逐渐减弱,使得Richtmyer-Meshkov不稳定性随之增强;同时,界面两侧阿特伍德数的增大,加强了Rayleigh-Taylor不稳定性和Kelvin-Helmholtz不稳定性的发展.此外,界面不稳定性的加强使得流场环量增大,导致气体混合率的增长速率随之升高.     

波后滑移线引起的界面变形和R-M不稳定性

实验研究复杂波形结构引起平面界面变形和反射激波冲击下的R-M不稳定性的问题.在竖直激波管中生成稳定的N₂/SF₆平面界面,激波在圆柱绕射后,冲击平面界面,由此研究复杂激波引起的界面变形.平面激波在圆柱绕射后的流场,演化成具有初始入射波、三波点、弯曲反射波、Mach波和Mach反射产生的滑移线等复杂结构.研究复杂结构激波对界面的作用,对认识界面扰动的生成具有较大帮助.绕柱激波冲击后,平面界面仅在两对滑移线内部发生变形.绕柱激波冲击界面后,两对滑移线将界面分成"内界面"和"外界面",界面变形形态同滑移线和界面相交位置相关.反射激波二次冲击下,界面扰动的增长与Jacobs-Sheeley涡量模型较吻合.      

斜激波与物质界面相互作用的数值模拟

当斜激波与多种物质分界面相互作用时，会出现Richtmyer-meshkov不稳定性现象，以及由于斜压性导致的涡量产生。研究激波与物质界面相互作用在燃料混合和激光质性约束聚变方面有着重要意义。有研究平面界面扰动演化的实验，研究柱面和球面界面的实验。数值模拟方面的研究也有很多。但激波与界面相互作用的理论研究很不完善，如Richtmyer。提出的不稳定性线性理论仅对激波与穿过界面很短的时间内有效，Sturtevant就发现实验结果与线性理论相差很大。     

可压流体Rayleigh-Taylor不稳定性的离散Boltzmann模拟

使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题:Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性,所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究,得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用,一开始扰动界面被"抹平",演化较慢;随着模式互相耦合而减少,演化开始加速,并经历非线性小扰动阶段和不规则非线性阶段,而后发展成典型的"蘑菇状",后期进入湍流混合阶段.由于扰动模式的耦合与发展,轻重流体的重力势能、压缩能与动能相互转化,系统先是趋于热动平衡态,而后偏离热动平衡态以线性形式增长,接着再次趋于热动平衡态,最后慢慢远离热动平衡态.     

反应性RM不稳定混合特性研究: 反应活性与介质不均匀性的影响

预混火焰界面的RM（Richtmyer-Meshkov）不稳定现象在自然界和工程实践中十分常见,但目前关于反应性RM不稳定的研究主要集中于均匀介质的情况,而实际中的预混气体往往是非均匀的,因此开展非均匀介质中火焰界面演化和混合特性的研究十分必要。采用带单步化学反应的Navier-Stokes方程和高精度数值格式,研究了预混火焰界面在入射激波及反射激波作用下的RM不稳定过程,考察了化学反应活性以及介质非均匀性对RM不稳定过程中火焰界面混合特性的变化规律的影响。结果表明,在入射激波作用后的阶段,在均匀介质中的火焰界面形态呈现典型的"钉-帽-泡"结构,化学反应活性越强,界面的"泡"结构和"钉-帽"结构增长越快;而在非均匀介质中,火焰界面形态则呈现"钉-钉"结构,界面在流向速度差的诱导下被更大程度地拉伸。在第一次反射激波作用后的阶段,混合区的增长速率不依赖于反应活性和均匀性,仅与流动特性有关。时间尺度的研究表明,大尺度流动是反应性RM不稳定的主导因素,其次是化学反应,最后是小尺度混合,化学反应的强化会抑制大尺度流动,非均匀性会强化大尺度流动。      

Rayleigh-Taylor不稳定性弱非线性阶段界面效应对谐波的影响

为了更好地理解不同空间坐标系下流体界面对Rayleigh-Taylor（RT）不稳定性弱非线性阶段谐波的影响,文章采用3阶小扰动展开法,解析研究了球坐标空间经典RT不稳定性弱非线性阶段谐波的演化规律,并和柱坐标空间以及直角坐标空间相应结果进行了对比研究.当球坐标系和直角坐标系中RT不稳定性界面扰动波长相同,球坐标系中初始扰动半径为无穷大时（即球坐标下RT不稳定性初始扰动半径相对于扰动波长为无穷大时）,球坐标下RT不稳定性前4次谐波的结果和直角坐标系下的相应结果相同.研究表明:由初始界面曲率引起的Bell-Plesset（BP）效应和空间效应（直角坐标空间、柱坐标空间和球坐标空间）对谐波发展有较大的影响.即在不同正交曲线坐标系下,不同曲率的流体界面效应对RT不稳定性谐波发展有较大的影响.对于柱坐标空间和球坐标空间,2阶对0次谐波的反馈加强了界面向内收缩.研究还表明:界面效应增加了2次谐波的负反馈,然而,对于基模和3次谐波却有不同的影响.      

瑞利-泰勒不稳定性中尺度效应的数值模拟研究

 瑞利-泰勒不稳定性是一种由于密度梯度引起的界面不稳定性，在惯性约束聚变中具有重要的意义。利用被动标量输运模型对包含不同尺度初始扰动的界面演化过程进行数值模拟。计算结果表明界面的初始形状对不稳定性的发展具有很大的影响，狭长型扰动比正方型扰动发展慢。另外，不同尺度扰动的相互作用一般会减小沿界面发展方向运动的动能，使能量更多地用于平行于界面方向的运动。     

Direct Numerical Simulation of Three-Dimensional Richtmyer--Meshkov Instability

Direct numerical simulation （DNS） is used to study flow characteristics after interaction of a planar shock with a spherical media interface in each side of which the density is different. This interracial instability is known as the Richtmyer-Meshkov （R-M） instability. The compressible Navier-Stoke equations are discretized with group velocity control （GVC） modified fourth order accurate compact difference scheme. Three-dimensional numerical simulations are performed for R-M instability installed passing a shock through a spherical interface. Based on numerical results the characteristics of 3D R-M instability are analysed. The evaluation for distortion of the interface, the deformation of the incident shock wave and effects of refraction, reflection and diffraction are presented. The effects of the interracial instability on produced vorticity and mixing is discussed.     

Nonlinear instability of elementary stratified flows at large Richardson number

Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319-350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin-Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. (c) 2000 American Institute of Physics.     

Experimental study of initial condition dependence on turbulent mixing in shock-accelerated Richtmyer–Meshkov fluid layers

Experimental evidence is needed to verify the hypothesis that the memory of initial conditions is retained at late times in variable density flows. If true, this presents an opportunity to “design” and “control” late-time turbulence, with an improved understanding in the prediction of inertial confinement fusion and other general fluid mixing processes. In this communication, an experimental and theoretical study on the effects of initial condition parameters, namely, the amplitude δ₀ and wavenumber κ₀ , where λ₀ is the initial wavelength) of perturbations, on late-time turbulence and mixing in shock-driven Richtmyer–Meshkov (R-M) unstable fluid layers in a 2D plane is presented. Single and multi-mode membrane-free initial conditions in the form of a gas curtain having a light-heavy-light configuration (air-SF₆-air) with an Atwood number of A= 0.57 were used in our experiments. A planar shock wave with a shock Mach number M= 1.21 drives the R-M instability, and the evolution of this instability after incident shock is captured using high resolution simultaneous planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV) diagnostics. Time evolution of statistics such as amplitude of the mixing layer, 2D turbulent kinetic energy, Reynolds number, rms of velocity fluctuations, probability density functions, and density-specific volume correlation were observed to quantify the amount of mixing and understand the nature of turbulence in this flow. Based on these results, it was found that the R-M mixing layer is asymmetric and non-Boussinesq. There is a correlation between initial condition parameters and large-scale, and small-scale mixing at late times, indicating an initial condition dependence on R-M mixing.     

Evaluating the modulated gradient model in large eddy simulation of channel flow with OpenFOAM

Recently, a new family of subgrid-scale (SGS) models, termed as gradient-based models, has been introduced to calculate the SGS stresses in large eddy simulation (LES). In the present work, the modulated gradient model (MGM) was implemented in the OpenFOAM package, and the pimpleFoam solver was improved to be adopted with non-eddy viscosity models. The MGM is a new, nonlinear model that uses the local equilibrium hypothesis to assess the SGS kinetic energy and the velocity gradient tensor to calculate the relative weight of the different components of the SGS stress tensor. To evaluate the accuracy of the MGM along with the modified pimpleFoam solver, a turbulent channel flow was simulated at the three different frictional Reynolds numbers of 180, 395 and 590. Furthermore, the results were compared with direct numerical simulation data, as well as the numerical results obtained by the established SGS models such as the dynamic Smagorinsky model (DSM). A suitable accuracy for the first- and second-order turbulence parameters was reported. Moreover, it was demonstrated that MGM is computationally efficient compared to the DSM in treating channel flow.     

A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier–Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin–Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ? 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures.     

Richtmyer-Meshkov不稳定性强化混合参变机理

在不同参数条件下, 计算分析了H₂O和N₂等混合物界面上激波诱导Richtmyer-Meshkov(R-M)不稳定性过程.采用有限差分方法数值求解了二维可压缩Navier-Stokes方程, 对流项以5阶特征紧致-WENO混合格式离散, 输运项以6阶对称紧致格式离散, 时间方向以3阶显式Runge-Kutta方法推进.研究表明, 界面振幅和激波强度增大, 均可增强界面附近涡量场, 强化混合.      

Numerical simulation of the hydrodynamic instability experiments and flow mixing

Based on the numerical methods of volume of fluid (VOF) and piecewise parabolic method (PPM) and parallel circumstance of Message Passing Interface (MPI), a parallel multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and performed to study the hydrodynamic instability and flow mixing. Firstly, the MVPPM code is verified and validated by simulating three instability cases: The first one is a Riemann problem of viscous flow on the shock tube; the second one is the hydrodynamic instability and mixing of gaseous flows under re-shocks; the third one is a half height experiment of interfacial instability, which is conducted on the AWE’s shock tube. By comparing the numerical results with experimental data, good agreement is achieved. Then the MVPPM code is applied to simulate the two cases of the interfacial instabilities of jelly models accelerated by explosion products of a gaseous explosive mixture (GEM), which are adopted in our experiments. The first is implosive dynamic interfacial instability of cylindrical symmetry and mixing. The evolving process of inner and outer interfaces, and the late distribution of mixing mass caused by Rayleigh-Taylor (RT) instability in the center of different radius are given. The second is jelly layer experiment which is initialized with one periodic perturbation with different amplitude and wave length. It reveals the complex processes of evolution of interface, and presents the displacement of front face of jelly layer, bubble head and top of spike relative to initial equilibrium position vs. time. The numerical results are in excellent agreement with that experimental images, and show that the amplitude of initial perturbations affects the evolvement of fluid mixing zone (FMZ) growth rate extremely, especially at late times.     

Parallel computation and numerical visualization for non-uniform particles included in gas and liquid flows

A parallel computation method has been proposed for the mixing and segregation of granular mixture included in gas and liquid flows. In this method, a three-dimensional (3D) computational volume is decomposed into multiple sub-blocks and their geometries are represented by 3D body-fitted coordinates. The fluid-particle interactions are treated by two types of models: a two-way model for liquid-solid flows and a one-way model in case of gas-solid flows. The computations of the particle motions in the multiple sub-blocks are executed simultaneously on the basis of the distinct element method (DEM). Since a graphic process is also executed as one of the parallel jobs, the particle distributions can be visualized during the computations. The computational method was applied to the gas-solid flows consisting of different diameters and densities in the horizontal and inclined cylinders rotating around their axes. From the comparison with the experimental results, nearly uniform mixing and particle segregation are successfully predicted in the oscillating liquid flows. In addition, it has been indicated that the particle pathline is very effective to visualize and understand the flow patterns of the particles with different properties. The result of the computations for the liquid-solid flows demonstrated that the vertical segregation of the non-uniform particles is reasonably reproduced.     

二维槽道湍流拟序结构的大涡模拟

本文采用大涡模拟的方法,对二维槽道湍流流动进行了数值模拟。采用Chorin的分步投影法求解大尺度涡运动的Navier-Stokes方程,小尺度涡采用三种亚格子（SGS）模式分别模拟,给出了不同亚格子涡粘性模式下的模拟结果。对固壁面采用了壁函数。模拟结果再现了二维槽道流动拟序结构的发展演变过程。通过对不同入口速度下的瞬态流场的比较,揭示了入口速度分布对流场的影响。     

Eulerian mean flow from an instability of convective plumes

The dynamical origin of large-scale flows in systems driven by concentrated Archimedean forces is considered. A two-dimensional model of plumes, such as those observed in thermal convection at large Rayleigh and Prandtl numbers, is introduced. From this model, we deduce the onset of mean flow as an instability of a convective state consisting of parallel vertical flow supported by buoyancy forces. The form of the linear equation governing the instability is derived and two modes of instability are discussed, one of which leads to the onset of steady Eulerian mean flow in the system. We are thus able to link the origin of mean flow precisely to the profiles of the unperturbed plumes. The form of the nonlinear partial differential equation governing the Eulerian mean flow, including nonlinear effects, is derived in one special case. The extension to three dimensions is outlined. (c) 2000 American Institute of Physics.