The influence of magnetic field on the physical explosion of a heavy gas cloud

Richtmyer–Meshkov (RM) instability arises during the eruption of heavy gas cloud. In this study, we numerically study the effects of magnetic fields on the RM instability induced by the ionised cylindrical and spherical heavy gas cloud eruption using corner transport upwind + constrained transport algorithm. Our numerical results show that magnetic fields can suppress the formation of spike and bubble structures induced by the eruption in both cylindrical and spherical cases. The magnetic pressure of the interface along the perpendicular direction of magnetic field is the main factor to control the distortion of the interface. Even weak magnetic fields can drastically alter the evolution of the cloud and result in different distributions and amplifications of the magnetic pressure, which will affect further transformation of RM instability during the ionised gas eruption. Meanwhile, the magnetic pressure on the interface decreases gradually when the initial magnetic field is relatively large; when the initial magnetic field is small enough, the opposite results will occur.     

A design of a two-dimensional,supersonic KH experiment on OMEGA-EP

An experiment meant to investigate the evolution of single mode Kelvin–Helmholtz (KH) instability in the supersonic regime is presented and theoretically analyzed. This experiment is intended to provide a direct measurement of the two-dimensional vortex evolution so that the high-Mach-number effects can be measured. The proposed design takes advantage of the ability of OMEGA-EP to drive experiments for up to 30 ns to produce steady conditions for KH that endure long enough to observe substantial growth. KH growth for the proposed design has been analyzed using two-dimensional numerical simulations. The results were compared to synthetic temporal KH numerical simulations using non-dimensional scaling in the low and high Mach number regime. The comparisons show that the growth in the high Mach number regime is expected to be suppressed by up to a factor of two. The effects of two-dimensional rarefactions from the lateral boundaries of the experimental system were also investigated. It was found that they introduce no major uncertainties or hazards to the experiment. We produced simulated radiographs, which show that the proposed experimental system will enable observation of the KH structures. An experiment of this kind has not yet been performed, and therefore would serve to validate numerical results and analytical models presented here and in the literature.     

RM不稳定过程中预混火焰界面演化及混合区增长预测

预混火焰界面的RM (Richtmyer-Meshkov)不稳定导致的界面混合区增长过程在自然界和工程实践中十分常见,但化学反应对其增长的影响机理仍不明确,反应性界面混合区增长速率的预测也未见报道, 因此,开展RM不稳定过程中火焰界面演化和混合区预测的研究十分必要.本文采用带单步化学反应的Navier-Stokes方程和高精度数值格式,研究了正弦形预混火焰界面在平面入射激波及其反射激波作用下的RM不稳定过程.结果表明, 在入射激波作用后的阶段,除RM不稳定本身导致的界面演化为"钉-帽"和"泡"形结构外,化学反应一方面以预混火焰传播的方式促进了界面中"泡"结构的增长,另一方面通过与涡结构的复杂相互作用促进了"钉-帽"结构的增长.化学反应活性越强, 火焰界面的"泡" 结构和"钉-帽"结构的增长越快.在第一次反射激波作用后的阶段,化学反应以相同的火焰传播方式对"泡"和"钉-帽"结构产生影响, 两者效应相抵,因而导致反射激波作用后的阶段中界面混合区增长不受化学反应活性的影响.根据以上分析,分别针对入射激波和第一次反射激波作用后的火焰界面混合区增长速率提出了相应的预测模型,为探索反应性RM不稳定过程的理论预测方法提供了有益参考.      

INTERFACE EVOLUTIONS AND GROWTH PREDICTIONS OF MIXING ZONE ON PREMIXED FLAME INTERFACE DURING RM INSTABILITY 1)

预混火焰界面的RM (Richtmyer-Meshkov)不稳定导致的界面混合区增长过程在自然界和工程实践中十分常见,但化学反应对其增长的影响机理仍不明确,反应性界面混合区增长速率的预测也未见报道, 因此,开展RM不稳定过程中火焰界面演化和混合区预测的研究十分必要.本文采用带单步化学反应的Navier-Stokes方程和高精度数值格式,研究了正弦形预混火焰界面在平面入射激波及其反射激波作用下的RM不稳定过程.结果表明, 在入射激波作用后的阶段,除RM不稳定本身导致的界面演化为"钉-帽"和"泡"形结构外,化学反应一方面以预混火焰传播的方式促进了界面中"泡"结构的增长,另一方面通过与涡结构的复杂相互作用促进了"钉-帽"结构的增长.化学反应活性越强, 火焰界面的"泡" 结构和"钉-帽"结构的增长越快.在第一次反射激波作用后的阶段,化学反应以相同的火焰传播方式对"泡"和"钉-帽"结构产生影响, 两者效应相抵,因而导致反射激波作用后的阶段中界面混合区增长不受化学反应活性的影响.根据以上分析,分别针对入射激波和第一次反射激波作用后的火焰界面混合区增长速率提出了相应的预测模型,为探索反应性RM不稳定过程的理论预测方法提供了有益参考.     

激波诱导下的气体界面不稳定性实验研究

界面不稳定性, 特别是Richtmyer–Meshkov (RM) 不稳定性, 是流体
力学中一项重要的研究内容, 无论在学术研究领域还是工程应用领域都有着
重要的研究价值和应用背景. RM 不稳定性问题自提出以来, 得到了学术界
广泛的关注, 其研究无论是在实验方法、数值模拟还是在理论分析方面都取
得了很大的进展. 在激波管中开展激波与界面相互作用的实验研究, 即研究
界面初始扰动在激波诱导下的演化规律, 是目前研究RM 不稳定性的重要手
段. RM 不稳定性实验研究包括3 个部分, 分别是激波的产生、界面的形成
以及流场的观测. 综述了RM 不稳定性的实验研究进展, 并针对目前研究的
局限性提出了RM 不稳定性今后实验研究的重点和方向: 汇聚激波作用下界
面不稳定性的发展规律; 激波冲击下多种形状及大振幅界面的演化机理; 三
维界面的RM 不稳定性发展规律; 可压缩湍流的形成与混合机理.      

A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids

In order to examine the influence of initial bubble conditions on bubble rise motion, two-dimensional direct numerical simulations of the motion of a gas bubble rising in viscous liquids were carried out by a coupled level set/volume-of-fluid (CLSVOF) method. For dimensionless groups predicting a “spherical-cap bubble shape” (high Eötvös and low Morton numbers), we have found computationally that solutions depend on initial bubble conditions. Specifically, for spherical-cap bubble areas, we could obtain computational results of toroidal bubbles or spherical-cap bubbles depending on initial bubble conditions. On the other hand, we showed for low Eo and high M conditions that initial bubble conditions did not affect the final state of bubble rise motion.     

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller(HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257–311(2004)). By analyzing the distribution of the finite-time Lyapunov exponent(FTLE) along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE.This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.     

柱形汇聚几何中内爆驱动金属界面不稳定性

采用自研的高保真度爆轰与冲击动力学程序,对柱形汇聚几何中内爆驱动金属材料界面不稳定性的动力学行为,进行了数值模拟研究。结果表明,首次冲击后至约12 μs,界面发展以RM（Richtmyer-Meshkov）不稳定性为主;12 μs后至冲击波聚心反弹加载前,界面聚心运动处于加速减速状态,界面发展由RT (Rayleigh-Taylor)不稳定性主导;冲击波聚心反弹加载后,界面发展又由RM不稳定性主导。另外,还研究了初始条件（初始振幅、初始波长、钢壳初始厚度和几何构型）对柱形内爆驱动金属材料界面不稳定性的影响。结果显示:初始振幅较大时振幅增长也较大;初始波长较小（模数较大）时振幅增长较小,而且存在一个截止波长;钢壳厚度会抑制扰动增长,也存在一个截止厚度;几何汇聚效应会使扰动增长速度更快。     

二维会聚波在气体内传播不稳定性的数值模拟

利用CE/SE(conservation element and solution element )格式研究了柱面会聚波在气体中传播时间断面的不稳定问题和波阵面的演变问题,并利用level set函数追踪了驱动气体与低压气体间断面的发展过程。得到了间断面的Rayleigh-Taylor(R-T)和Richtmyer-Meshkov(R-M)不稳定性发展成典型的尖钉和气泡结构的图像,初始正弦扰动下的会聚波产生尖角和尖瓣结构。结果表明,CE/SE格式在涉及会聚波的数值计算中是可行的。     

小扰动界面形态对RM不稳定性影响的数值分析

采用Navier-Stokes 方程对入射激波及其反射激波连续诱导小振幅扰动界面的Richtmyer-Meshkov 不稳定性增长过程进行了二维数值模拟,分析了单模和随机多模两种不同初始形态的界面上钉结构和泡结构在反射激波作用前后的发展特性. 研究结果发现:单模扰动的初始界面形态对反射激波前、后界面的扰动增长都有影响,反射激波前的界面形态信息可以通过钉和泡结构之间的反转传递到反射激波过后. 扰动界面上钉结构的发展速度控制了界面混合区总体的发展速度,反射激波前界面上发展成具有完整冠部形态的钉,在反射激波后会反转成复杂的泡结构,此泡结构对反射激波后钉的发展不利. 随机多模界面显示了与单模界面类似的发展规律,但随机多模界面上的复杂泡结构分布的不对称性使得其对钉结构增长的拖曳效应相对要弱,这导致了相似扰动波长下多模随机界面的扰动发展相对单模界面扰动发展要快.      

多次激波诱导正弦扰动预混火焰界面失稳的数值研究

激波诱导火焰失稳是实际中常见的现象,为深入研究火焰失稳特性,采用三维单步化学反应的Navier-Stokes方程和9阶weighted essentially non-oscillatory (WENO)的高精度格式,对不同马赫数的入射激波及其反射激波多次诱导正弦型预混火焰界面失稳的现象进行了三维数值模拟,并对计算结果的可靠性进行了验证。研究结果显示,在激波的多次作用下,火焰界面的演变过程主要受Richtmyer-Meshkov (RM)不稳定特性和化学反应特性的双重影响,且随着入射激波强度的增强,上述2种特性均得到进一步强化。为构造体现反应性RM不稳定特性的参数,根据火焰界面混合区平均涡量和化学反应速率,提出了表征界面受不稳定性和化学反应影响的量纲一参数。通过分析发现,在同一入射激波强度下,该参数的对数形式随入射激波和反射激波的多次作用呈基本相同的线性增长趋势;对不同马赫数的入射激波,该参数对数形式的线性增长率也基本一致。这样的变化表明该量纲一参数能够反映反应性RM不稳定过程中火焰界面发展的内在规律。     

NUMERICAL STUDY ON THE EFFECTS OF SMALL-AMPLITUDE INITIAL PERTURBATIONS ON RM INSTABILITY

采用Navier-Stokes 方程对入射激波及其反射激波连续诱导小振幅扰动界面的Richtmyer-Meshkov 不稳定性增长过程进行了二维数值模拟,分析了单模和随机多模两种不同初始形态的界面上钉结构和泡结构在反射激波作用前后的发展特性. 研究结果发现：单模扰动的初始界面形态对反射激波前、后界面的扰动增长都有影响,反射激波前的界面形态信息可以通过钉和泡结构之间的反转传递到反射激波过后. 扰动界面上钉结构的发展速度控制了界面混合区总体的发展速度,反射激波前界面上发展成具有完整冠部形态的钉,在反射激波后会反转成复杂的泡结构,此泡结构对反射激波后钉的发展不利. 随机多模界面显示了与单模界面类似的发展规律,但随机多模界面上的复杂泡结构分布的不对称性使得其对钉结构增长的拖曳效应相对要弱,这导致了相似扰动波长下多模随机界面的扰动发展相对单模界面扰动发展要快.     

Measurements of turbulent mixing due to Kelvin–Helmholtz instability in high-energy-density plasmas

Kelvin–Helmholtz (KH) turbulent mixing measurements were performed in experiments on the OMEGA Laser Facility [T.R. Boehly et al., Opt. Commun. 133 (1997) 495]. In these experiments, laser-driven shock waves propagated through low-density plastic foam placed on top of a higher-density plastic foil. Behind the shock front, lower-density foam plasma flowed over the higher-density plastic plasma. The interface between the foam and plastic was KH unstable. The experiments were performed with pre-imposed, sinusoidal 2D perturbations, and broadband 3D perturbations due to surface roughness at the interface between the plastic and foam. KH instability growth was measured using X-ray, point-projection radiography. The mixing layer caused by the KH instability with layer width up to ～100 μm was observed at a location ～1 mm behind the shock front. The measured mixing layer width was in good agreement with simulations using a K–L turbulent mixing model in the two-dimensional ARES hydrodynamics code. In the definition of the K–L model K stands for the specific turbulent kinetic (K) energy, and L for the scale length (L) of the turbulence.     

Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations

Ultimately, numerical simulation of viscoelastic flows will prove most useful if the calculations can predict the details of steady-state processing conditions as well as the linear stability and non-linear dynamics of these states. We use finite element spatial discretization coupled with a semi-implicit θ-method for time integration to explore the linear and non-linear dynamics of two, two-dimensional viscoelastic flows: plane Couette flow and pressure-driven flow past a linear, periodic array of cylinders in a channel. For the upper convected Maxwell (UCM) fluid, the linear stability analysis for the plane Couette flow can be performed in closed form and the two most dangerous, although always stable, eigenvalues and eigenfunctions are known in closed form. The eigenfunctions are non-orthogonal in the usual inner product and hence, the linear dynamics are expected to exhibit non-normal (non-exponential) behavior at intermediate times. This is demonstrated by numerical integration and by the definition of a suitable growth function based on the eigenvalues and the eigenvectors. Transient growth of the disturbances at intermediate times is predicted by the analysis for the UCM fluid and is demonstrated in linear dynamical simulations for the Oldroyd-B model. Simulations for the fully non-linear equations show the amplification of this transient growth that is caused by non-linear coupling between the non-orthogonal eigenvectors. The finite element analysis of linear stability to two-dimensional disturbances is extended to the two-dimensional flow past a linear, periodic array of cylinders in a channel, where the steady-state motion itself is known only from numerical calculations. For a single cylinder or widely separated cylinders, the flow is stable for the range of Deborah number (De) accessible in the calculations. Moreover, the dependence of the most dangerous eigenvalue on De≡λV/R resembles its behavior in simple shear flow, as does the spatial structure of the associated eigenfunction. However, for closely spaced cylinders, an instability is predicted with the critical Deborah number De_c scaling linearly with the dimensionless separation distance L between the cylinders, that is, the critical Deborah number De_Lc≡λV/L is shown to be an O(1) constant. The unstable eigenfunction appears as a family of two-dimensional vortices close to the channel wall which travel downstream. This instability is possibly caused by the interaction between a shear mode which approaches neutral stability for De ≫ 1 and the periodic modulation caused by the presence of the cylinders. Nonlinear time-dependent simulations show that this secondary flow eventually evolves into a stable limit cycle, indicative of a supercritical Hopf bifurcation from the steady base state.     

Oscillatory Marangoni convection around the air bubble in a vertical surfactant stratificationConvection de Marangoni oscillante autour d'une bulle d'air dans une stratification verticale surfactante

The solutocapillary Marangoni convection around a gas bubble in the inhomogeneous binary mixture of miscible fluids with a vertical surfactant concentration gradient was studied experimentally. A new phenomenon, the oscillatory instability of the surfactant mass transfer, near the bubble boundary, was detected and investigated. The interpretation of this effect as an interaction between the surfactant adsorption at the bubble free surface and solutocapillary and buoyancy convective mechanisms is proposed. The experimental data on oscillation period in relation to bubble dimensions, time, liquid layer thickness, physico-chemical fluid parameters and concentration gradients are presented and discussed. To cite this article: K. Kostarev et al., C. R. Mecanique 332 (2004).     

Numerical study of adverse pressure gradient generation over a flat plate using a rotating cylinder

Generating an adverse pressure gradient (APG), using a rotating cylinder in the proximity of a plane wall under a laminar freestream flow, is studied numerically in this work. The magnitude of the generated APG is a function of the gap, G, between the cylinder and the wall, and the rotational speed of the cylinder, Ω. The flow in such a configuration is characterized by periodic transient vortex shedding at high Reynolds number. A numerical model for the computation of the transient flow for this configuration is developed using the ANSYS CFD simulation tool. The model is validated against published experimental and numerical data for similar flow configurations and excellent agreement is observed. A parametric study is carried out for different combinations of G and Ω for two different Reynolds numbers of 200 and 1000 to examine the development of the resulting separation bubble due to the generated APG. The mechanism of the boundary layer separation over the plane wall and the corresponding wake dynamics is investigated. Results are presented in terms of the distribution of the pressure coefficient as well as skin friction coefficient along the wall and flow patterns around and downstream of the cylinder in the proximity of the wall. The results of these computations confirm that using a rotating cylinder over a plane wall in a freestream flow is an effective technique to generate a controlled range of adverse pressure gradients.     

Bubble dynamics in a two-dimensional gas-solid fluidized bed

Related referential studies on gas-solid two-phase flows were briefly reviewed. Bubble ascending in a two-dimensional （2D） gas-solid fluidized bed was studied both experimentally and numerically. A modified continuum model expressed in the conservation form was used in numerical simulation. Solid-phase pressure was modeled via local sound speed; gas-phase turbulence was described by the K-ε two-equation model. The modified implicit multiphase formulation （IMF） scheme was used to solve the model equations in 2D Cartesian/cylindrical coordinates. The bubble ascending velocity and particle motion in the 2D fluidized bed were measured using the photochromic dye activation （PDA） technique, which was based on UV light activation of particles impregnated with the dye. Effects of bed height and superficial gas velocity on bubble formation and ascent were investigated numerically. The numerically obtained bubble ascending velocities were compared with experimental measurements. Gas bubble in jetting gas-solids fluidized bed was also simulated numerically.     

Evolution of material voids for highly anisotropic surface energy

In this paper we consider the evolution by surface diffusion of material voids in a linearly elastic solid, focusing on the evolution of voids with large surface energy anisotropy. It is well known that models for the time evolution of similar material surfaces can become mathematically ill-posed when the surface energy is highly anisotropic. In some cases, this ill-posedness has been associated with the formation of corners along the interface. Here the ill-posedness is removed through a regularization which incorporates higher order terms in the surface energy. Spectrally accurate numerical simulations are performed to calculate the steady-state solution branches and time-dependent evolution of voids, with a particular emphasis on inferring trends in the zero regularization (c→0) limit. For steady voids with large anisotropy we find that apparent corners form as c→0. In the presence of elastic stresses σ the limiting corner angles are most often found to differ from angles found on the (σ=0) Wulff shape. For large elastic stresses we find that steady solutions no longer exist; instead the void steadily lengthens via a filamenting instability referred to as tip streaming.     

Injection de bulles en paroi d'un écoulement cisaillé visqueuxBubble injection at the wall of a viscous shear flow

Air bubble injection at the wall of a viscous shear flow is filmed using a high speed video camera. The temporal evolution of the bubbles equivalent radius and the position of their centre of mass throughout their growth are determined from image processing. The experimental results are then used to validate a model of forces acting on the bubbles during their growth and after their detachment within the limit of small bubble Reynolds numbers. To cite this article: G. Duhar, C. Colin, C. R. Mecanique 331 (2003).