Richtmyer-Meshkov不稳定性扰动增长率冲击模型的微尺度效应

本文通过考虑流体介质输运性质对激波理论的影响,针对微型激波管中的RichtmyerMeshkov(RM)不稳定性,分析了微尺度效应对三种冲击模型扰动增长率的影响。一维气体动力学计算结果表明:流动尺度对于Richtmyer模型、Meyer-Blewett(M-B)模型和Vandenboomgaerde-Mügler-Gauthier(V-M-G)模型中的线性扰动增长率有显著影响。当流动尺度由宏观状态逐渐减小至微尺度时,三种模型的扰动增长率均会经历从少量增长到明显下降,然后迅速上升的过程。微尺度条件下,V-M-G模型的扰动增长率相比宏观尺度有显著提高。与其他两种模型相比,修正后的V-M-G模型更合理地描述了微尺度效应对于线性扰动增长率的影响。此外,对于修正后的V-M-G模型,当入射激波马赫数较低时,扰动增长率受微尺度效应的影响更为明显。     

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.     

关于星系激波——一类扰动气体引力场的影响

如果假设物质的扰动引力场与星际气体的扰动密度成正比,以此来摸拟星系激波压缩气体所造成的扰动引力场,可以分析这类非线性气体流动解在速度平面上的性质。只有在超声速基本流动时,包含光滑跨声速流动所对应的那一根积分曲线,才可能存在周期的局部激波解;所有其他积分曲线都不存在有物理意义的周期解。而且,即使存在光滑的跨声速流动,若扰动引力场超过某一临界值,也就不再存在局部激波解。具体计算结果表明,这类情况可以存在星系激波宏图,激波可使星际气体的密度压缩,并增大3～4倍。当这类扰动引力场的强度非常弱时,其线性化波动解即为林家翘和徐遐生的线性密度波的结果。     

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.      

柱形汇聚激波冲击球形重气体界面的实验研究

采用高速纹影法实验研究了柱形汇聚激波与球形重气体界面相互作用的 Richtmyer-Meshkov不稳定性问题. 激波管实验段基于激波动力学理论设计, 将马赫数为1.2 的平面激波转化为柱形汇聚激波, 气体界面由肥皂膜分隔六氟化硫(内)和空气(外)得到. 采用高速摄影机在单次实验中拍摄激波运动的全过程, 对柱形激波的形成进行了实验验证, 并进一步观测了汇聚激波与球形气体界面相互作用过程中的波系发展和气体界面变形以及反射激波同已变形界面二次作用的流场演化. 结果表明: 当柱形汇聚激波穿过气泡界面以后, 气泡左侧界面极点沿激波传播方向保持匀速运动, 气泡右侧界面发展成为射流结构, 气泡主体发展成为涡环结构; 在反射激波的二次作用下, 流场中无序运动显著增强并很快进入湍流混合阶段.     

绕射激波和反射激波作用下N_2/SF_6界面R-M不稳定性实验研究

利用高速纹影测试实验研究低马赫数入射激波绕圆柱体后冲击N2/SF6平面界面,以及来自固壁的反射激波再冲击过程的(Richmyer--Meshkov,R--M)不稳定性特征.与平面激波作用不同的是,绕射后的激波会在界面处生成局部扰动.实验结果显示,入射激波作用下界面宽度增长缓慢,而反射激波再冲击后,局部扰动会产生大的"尖钉"和"气泡"结构;以及反射激波与边界层相互作用产生壁面涡,它们会加剧湍流混合区的增长;实验中反射激波过后混合区增长率不十分依赖于波前状态,增长规律同Mikaelian模型较吻合;来自尾部固壁的反射稀疏波会再次加剧湍流混合区的增长.     

EXPERIMENTALLY STUDY OF THE RICHTMYER-MESHKOV INSTABILITY AT N2/SF6 FLAT INTERFACES BY DIFFRACTED INCIDENT SHOCK WAVES AND RESHOCK

利用高速纹影测试实验研究低马赫数入射激波绕圆柱体后冲击N₂/SF₆平面界面,以及来自固壁的反射激波再冲击过程的（Richmyer-Meshkov,R-M）不稳定性特征.与平面激波作用不同的是,绕射后的激波会在界面处生成局部扰动.实验结果显示,入射激波作用下界面宽度增长缓慢,而反射激波再冲击后,局部扰动会产生大的“尖钉”和“气泡”结构;以及反射激波与边界层相互作用产生壁面涡,它们会加剧湍流混合区的增长;实验中反射激波过后混合区增长率不十分依赖于波前状态,增长规律同Mikaelian模型较吻合;来自尾部固壁的反射稀疏波会再次加剧湍流混合区的增长.     

柱状汇聚激波冲击单模气体界面的实验研究

在自行设计和加工的半环形汇聚激波管中,开展了柱状汇聚激波冲击单模Air/SF6气体界面的Richtmyer-Meshkov(RM)不稳定性实验研究。不同于以往的环形激波管,该激波管具有半圆形结构的实验段,使半环形管道和实验段都向外敞开,能够参考传统水平激波管的方式设置初始扰动界面和观测系统。采用线约束肥皂膜的方法形成单模初始扰动界面。利用高速纹影成像技术得到了柱形汇聚激波作用下界面演化的完整过程。为了研究初始振幅对界面演化形态的影响,实验中生成了三种不同初始振幅的单模界面,并获得了三种工况下界面位移和扰动振幅随时间的变化。结果表明,汇聚激波作用下的RM不稳定性与平面激波有很大差别,主要原因在于汇聚效应,包括结构汇聚、流动压缩以及界面反相等。     

反射激波作用重气柱的Richtmyer-Meshkov不稳定性的实验研究

采用高速摄影结合激光片光源技术,研究了反射激波冲击空气环境中重气体(SF₆)气柱的Richtmyer-Meshkov不稳定性。通过在横式激波管试验段采用可移动反射端壁获得不同反射距离,实现了反射激波在不同时刻二次冲击处于演化中后期的气柱界面,得到了不同的界面演化规律。反射距离较小时,斜压机制对气柱界面形态演化的影响显著,界面衍生出二次涡对结构;反射距离较大时,压力扰动机制的影响显著,界面在流向上被明显地压缩,没有形成明显的涡结构。由气柱界面形态的时间演化图像得到了界面位置和整体尺度随时间的变化,对反射激波作用后气柱界面的演化进行了量化分析。     

反射激波冲击重气柱的RM不稳定性数值研究

数值研究了二维气柱在入射激波以及反射激波作用下的Richtmyer-Meshkov(RM)不稳定性发展规律, 采用有限体积法结合网格自 适应技术的VAS2D程序, 精确刻画激波和界面的演化. 入射平面激波的马赫数为1.2, 气柱界面内气体为六氟化硫(SF₆), 环境气体为空气, 激波管的尾端为固壁. 通过改变气柱与尾端之间的距离调节反射激波再次作用已经变形的气柱的时间, 获得不同时刻下已经变形的气柱形态、界面尺寸以及环量演化受到反射激波的影响. 结果表明, 反射激波再次作用气柱时, 气柱所处发展阶段不同, 界面演化规律以及环量随时间的变化也不相同, 反射激波与气柱相互作用过程中的涡量产生和分布与无反射情况差异较大, 揭示了不同情况下界面演化的物理机理.     

An experimental study of the regimes of motion of spheres falling or ascending freely in a Newtonian fluid

This paper presents the results of an experimental investigation aimed at verifying some of the interesting conclusions of the numerical study by Jenny et al. concerning the instability and the transition of the motion of solid spheres falling or ascending freely in a Newtonian fluid. The phenomenon is governed by two dimensionsless parameters: the Galileo number G, and the ratio of the density of the spheres to that of the surrounding fluid ρ_s/ρ. Jenny et al. showed that the (G, ρ_s/ρ) parameter space may be divided into regions with distinct features of the trajectories followed eventually by the spheres after their release from rest. The characteristics of these ‘regimes of motion’ as described by Jenny et al., agree well with what was observed in our experiments. However, flow visualizations of the wakes of the spheres using a Schlieren optics technique raise doubts about another conclusion of Jenny et al., namely the absence of a bifid wake structure.     

Particle image velocimetry study of the shock-induced single mode Richtmyer–Meshkov instability

Full field particle image velocimetry (PIV) measurements are obtained for the first time in Richtmyer–Meshkov instability shock tube experiments. The experiments are carried out in a vertical shock tube in which the light gas (air) and the heavy gas (SF₆) flow from opposite ends of the shock tube driven section and exit through narrow slots at the interface location. A sinusoidal perturbation is given to the interface by oscillating the shock tube in the horizontal direction. Richtmyer–Meshkov instability is then produced by the interaction with a weak shock wave (M _s  = 1.21). PIV measurements are obtained by seeding the flow with 0.30 μm polystyrene Latex spheres which are illuminated using a double-pulsed Nd:YAG laser. PIV measurements indicate the vorticity to be distributed in a sheet-like distribution on the interface immediately after shock interaction and that this distribution quickly rolls up into compact vortices. The integration of the vorticity distribution over one half wave length shows the circulation to increase with time in qualitative agreement with the numerical study of Peng et al. (Phys. Fluids, 15, 3730–3744, 2003).     

Growth rate predictions of single- and multi-mode Richtmyer�CMeshkov instability with reshock

The single- and multi-mode Richtmyer–Meshkov instabilities (RMI) with reshock are numerically analyzed in two- and three-dimensional domains. Four different types of air/SF ₆ interface shapes are investigated in a shock tube configuration, and the predicted post-reshock growth rates are compared with available empirical models of Mikaelian’s (Physica D 36(3):343–347, 1989) and Charakhch’an’s (J Appl Mech Tech Phys 41(1):23–31, 2000). The simulation of 3D multi-mode RMI shows good agreement with a past experimental study, but other interface types (2D single-mode, 2D multi-mode and 3D single-mode) result in different growth rates after reshock. Parametric studies are therefore performed to investigate the sensitivities of the post-reshock growth rates to model the empirical parameters. For single-mode RMI configurations, the interface shape is found to be only a weak function of the post-reshock growth rate, as also predicted by previous reshock models. The post-reshock growth rate shows a linear correlation to the velocity jump due to reshock; however, it is only about a half of the prediction of Charakhch’an’s model even though the growth before reshock compares well with pre-reshock models. The 3D single-mode post-reshock RMI growth rate is nearly 1.6 times larger than the 2D single-mode RMI. The parametric studies of multi-mode RMI show two distinctly different growth rates depending on the mixing conditions at reshock. If the interface remains sharp at the time of reshock, the post-reshock growth rate is as large as the single-mode cases. However, if the interface is mixed due to non-linear interactions of bubbles and spikes, the growth rates becomes slow and independent of the interface shapes. Overall, this study provides new insights into the flow features of reshocked RMI for different initial perturbation types.     

Numerical Study of Smoothly Perturbed Shocks in the Newtonian Limit

Previous weakly nonlinear analyses of strong shocks in the Newtonian limit have shown that the main characteristics of the cellular pattern of detonations, namely the network of triple points propagating in the transverse direction, are associated with nonlinear mechanisms which are inherent to the leading shock (Clavin and Denet, Phys. Rev. Lett. 88(4), 044,502, 2002; Clavin, J. Fluid Mech. 721, 324–339, 2013). Motivated by this theoretical analysis, experimental and numerical studies have been conducted on a smoothly perturbed Mach 1.5 shock in air, reflected from a sinusoidal wall of small amplitude (Jourdan et al., Shock Waves 13(6), 501–504, 2004; Denet et al., Combust Sci. Technol. 187, 296–323, 2015; Lodato et al., J. Fluid Mech. 789, 221–258, 2016). Under such flow conditions, the reflected shock is relatively weak and the Newtonian limit, used in the above mentioned analysis, is rather far from being met. Despite of this, the theoretical results concerning the nonlinear dynamics of the shock front were, for the most part, confirmed. In an effort to get closer to the conditions of the theoretical analysis, namely strong shocks in the Newtonian limit, a similar numerical analysis is performed in the present study where the incident Mach number is increased up to 5 and the specific heat ratio is decreased down to 1.15, leading to reflected shocks Mach numbers of about 3.2. This provides additional evidence about the main driving mechanism behind the structure of cellular detonations. Theoretical predictions regarding the spontaneous formation and transverse velocity of the triple points are further confirmed. In particular, significant improvements are observed in reproducing the theoretically predicted trajectories of the triple points. As a result of the increased Mach number of the reflected shock, stronger vortex sheets are formed within the shocked gases. This enables to better assess the impact of the molecular viscosity—a previously left open question—but also to highlight similarities with cellular detonations on a wider range of heat releases.     

Interaction of a gasdynamic shock with small disturbances

The stability of shock wave based on the definition of Landau and Lifschitz^[1] is treated in this paper. This is tantamount to solving the problem of interaction of small disturbances with a shock wave. Small disturbances are introduced on both sides of a steady, non-dissipative, plane shock wave. Landau et al.^[1] obtained the stability criterionM ₁>1,M ₂<1 for small disturbances which are travelling in the direction perpendicular to the shock wave. In the present paper, we assume that the small disturbances may be two dimensional, i.e. they may be propagating in the direction inclined to the shock wave. The conclusions obtained are: regardless of whether the incident wave and diverging wave are defined according to the direction of the phase velocity or the group velocity, the shock wave is unstable for some frequencies and longitudinal wave lengths of the disturbances, even if the conditionsM ₁>1,M ₂<1 are fulfilled. Then several experiments are proposed, and the problem of ways to define the incident wave and diverging wave is discussed. The meaning of this problem is illustrated. The same results can be obtained for the steady shock wave in a tube.     

Stability of a hypersonic shock layer on a flat plateStabilité d'une couche de choc hypersonique sur une plaque plane.

Stability of a hypersonic shock layer on a flat plate is examined with allowance for disturbances conditions on the shock wave within the framework of the linear stability theory. The characteristics of the main flow are calculated on the basis of the Full Viscous Shock Layer model. Conditions for velocity, pressure, and temperature perturbations are derived from steady Rankine–Hugoniot relation on the shock wave. These conditions are used as boundary conditions on the shock wave for linear stability equations. The growth rates of disturbances and density fluctuations are compared with experimental data obtained at ITAM by the method of electron-beam fluorescence and with theoretical data of other authors. To cite this article: A.A. Maslov et al., C. R. Mecanique 332 (2004).     

Passage of shock waves through an interface of two-phase gas-liquid media

Among the problems connected with the motion of shock waves in two-phase media consisting of a mixture of a liquid and bubbles of gas, investigations of the passage of shock waves through an interface inside of a two-phase system, or at its surface are of special interest. Inside a two-phase system, interfaces between two two-phase media with different volumetric concentrations of the gas Β₁, Β₂ are possible. One of the values of Β, for example, Β₁, can revert to zero. There is then a passage of the wave from a two-phase system into an incompressible liquid, or vice versa. The investigation of both of the above cases, as well as of the transition two-phase medium (Β₁)—two-phase medium (Β₂) with Β₁≠Β₂ is not only of scientific, but also of practical importance. As is well known [1], the density of a two-phase mixture ρ with a small volumetric concentration of gas is calculated using the relationship ρ=(1?β)ρ_l+αρ₁.     

Special case of the density distribution behind a nonstationary shock wave

The density distribution behind a nonstationary shock wave for a definite value of the Mach number M_*, which depends on = c_p/c_v, is considered. Use is made of the previously established fact [1] that for M = M_*() there exists a connection between the first and second derivatives of the density along the normal behind the wave. An investigation is made into the density profile in dimensionless variables behind plane, cylindrical, and spherical shock waves in the neighborhood of the shock front. In the first case, if the gas in front of the wave is homogeneous, only two types of density profile are possible (up to small quantities of third order in the coordinate). In the second and third cases, the form of the density distribution also depends on a parameter, the ratio of the first derivative along the normal of the density behind the wave to the radius of curvature of the wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 163–167, November–December, 1979.     

用二阶矩模型研究Richtmyer-Meshkov不稳定性诱导湍流混合

发展了考虑密度脉动和各向异性湍流的二阶矩模型,强调了涉及湍流能量产生项的关联。采用该模型对Poggi等的激波管实验进行了模拟。通过与实验结果的比较分析,验证了采用的模型封闭、模型常数、数值算法和程序实现是合适的。在此基础上,进一步探讨了冲击马赫数和Atwood数对混合的影响。     

Vorticity and its rate of change just downstream of a curved shock

A theory is developed for the vorticity and its substantial derivative just downstream of a curved shock wave, the resulting formulas are exact, algebraic, and explicit. Analysis is for a cylinder-wedge or sphere-cone body, at zero incidence, whose downstream half-angle is θ_b. Derived formulas directly depend only on the ratio of specific heats, γ, the freestream Mach number, M ₁, the local slope and curvature of the shock, and the dimensionality parameter, σ, which is zero for a two-dimensional shock and unity for an axisymmetric shock. In turn, the slope and curvature depend on γ, M ₁, and θ_b. Numerical results are provided for a bow shock in which θ_b is 5°, 10°, or 15°, M ₁ is 2, 4, or 6, and γ = 1.4. There is little dependence on the half angle but a strong dependence on the freestream Mach number and on dimensionality. For vorticity and its substantial derivative, the dimensionality dependence gradually decreases with increasing Mach number. In comparison to the two-dimensional case, an axisymmetric shock generates considerable vorticity in a region relatively close to the symmetry axis. Moreover, the magnitude of the vorticity, in this region, is further enhanced in the flow downstream of the shock. This dimensionality difference in vorticity and its substantial derivative is attributed to the three-dimensional relief effect in an axisymmetric flow.

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