Numerical simulation and PIV study of compressible vortex ring evolution

Formation and evolution of a compressible vortex ring generated at the open end of a short driver section shock tube has been simulated numerically for pressure ratios (PR) of 3 and 7 in the present study. Numerical study of compressible vortex rings is essential to understand the complicated flow structure and acoustic characteristics of many high Mach number impulsive jets where simultaneously velocity, density and pressure fields are needed. The flow development, incident shock formation, shock diffraction, vortex ring formation and its evolution are simulated using the AUSM+ scheme. The main focus of the present study is to evaluate the time resolved vorticity field of the vortex ring and the shock/expansion waves in the starting jet for short driver section shock tubes—a scenario where little data are available in existing literature. An embedded shock and a vortex induced shock are observed for PR =  7. However the vortex ring remains shock free, compact and unaffected by the trailing jet for PR =  3. Numerical shadowgraph shows the evolution of embedded shock and shock/expansion waves along with their interactions. The velocity and vorticity fields obtained from simulation are validated with the particle image velocimetry results and these data match closely. The translational velocity of the vortex ring, velocity across the vortex and the centre line velocity of the jet obtained from simulation also agree well with the experimental results.     

Estimation of shock induced vorticity on irregular gaseous interfaces: a wavelet-based approach

We study the interaction of a shock with a density-stratified gaseous interface (Richtmyer–Meshkov instability) with localized jagged and irregular perturbations, with the aim of developing an analytical model of the vorticity deposition on the interface immediately after the passage of the shock. The jagged perturbations, meant to simulate machining errors on the surface of a laser fusion target, are characterized using Haar wavelets. Numerical solutions of the Euler equations show that the vortex sheet deposited on the jagged interface rolls into multiple mushroom-shaped dipolar structures which begin to merge before the interface evolves into a bubble-spike structure. The peaks in the distribution of x-integrated vorticity (vorticity integrated in the direction of the shock motion) decay in time as their bases widen, corresponding to the growth and merger of the mushrooms. However, these peaks were not seen to move significantly along the interface at early times i.e. t < 10 τ, where τ is the interface traversal time of the shock. We tested our analytical model against inviscid simulations for two test cases – a Mach 1.5 shock interacting with an interface with a density ratio of 3 and a Mach 10 shock interacting with a density ratio of 10. We find that this model captures the early time (t/τ ∼ 1) vorticity deposition (as characterized by the first and second moments of vorticity distributions) to within 5% of the numerical results. PACS 47.40.Nm; 47.20.Ma     

A three-dimensional numerical study on instability of sinusoidal flame induced by multiple shock waves

The instabilities of a three-dimensional sinusoidally premixed flame induced by an incident shock wave with Mach = 1.7 and its reshock waves were studied by using the Navier–Stokes(NS) equations with a single-step chemical reaction and a high resolution, 9th-order weighted essentially non-oscillatory scheme. The computational results were validated by the grid independence test and the experimental results in the literature. The computational results show that after the passage of incident shock wave the flame interface develops in symmetric structure accompanied by large-scale transverse vortex structures. After the interactions by successive reshock waves, the flame interface is gradually destabilized and broken up, and the large-scale vortex structures are gradually transformed into small-scale vortex structures. The small-scale vortices tend to be isotropic later.The results also reveal that the evolution of the flame interface is affected by both mixing process and chemical reaction. In order to identify the relationship between the mixing and the chemical reaction, a dimensionless parameter, η, that is defined as the ratio of mixing time scale to chemical reaction time scale, is introduced. It is found that at each interaction stage the effect of chemical reaction is enhanced with time.The enhanced effect of chemical reaction at the interaction stage by incident shock wave is greater than that at the interaction stages by reshock waves. The result suggests that the parameter η can reasonably character the features of flame interface development induced by the multiple shock waves.     

Nonlinear Strong Shock Interactions: A Shock-Fitted Approach

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M ₁, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM ₁ > 1. Received 28 June 1997 and accepted 25 November 1997     

Experimental investigation of a twice-shocked spherical gas inhomogeneity with particle image velocimetry

Results are presented from an experimental investigation into the interaction of a planar shock wave with a vortex ring. A free-falling spherical soap bubble is traversed by the incident shock wave and develops into a vortex ring as a result of baroclinically deposited vorticity (?r×?p 1 0{\nabla\rho\times\nabla p \neq 0}). The vortex ring translates with a velocity relative to the particle velocity behind the shock wave due to circulation. After the shock wave reflects from the tube end wall, it traverses the vortex ring (this process is called “reshock”) and deposits additional vorticity. Planar Mie scattering is used to visualize the atomized soap film at high frame rates (up to 10,000 fps). Particle image velocimetry (PIV) was performed for an argon bubble in nitrogen accelerated by a M = 1.35 shock wave. Circulation was determined from the PIV velocity field and found to agree well with Kelvin’s vortex ring model.     

不同初始磁场对激波冲击R22重气柱过程影响的数值模拟

基于磁流体动力(magneto-hydrodynamic,MHD)方程,采用CTU+CT方法,对在不同初始磁场作用下的平面入射激波与磁化R22重质气柱作用过程进行了数值研究。数值结果清晰地描述了不同初始磁场条件时激波诱导R22气柱界面不稳定性的过程,揭示了磁场控制界面不稳定性的机理。另外,还分析了磁感应强度对界面不稳定性的影响,发现在磁场较小时,涡层附着于界面,但随着磁感应强度的增大,平均涡量随之增大,涡层与界面逐渐分离,最终更好地抑制了界面不稳定性。同时,还发现平均涡度拟能随着磁感应强度的增大而减小,而垂直磁场比平行磁场更能降低平均涡度拟能,因而平均涡度拟能可较好地反映磁场对不稳定性的影响效果。     

激波冲击SF6重气泡引发射流的数值模拟

为深入研究重气泡内激波聚焦和射流生成的机理,采用高精度计算格式和高网格分辨率对马赫数为1.23的平面入射激波与SF₆重气泡的作用过程进行数值模拟,计算结果与文献中实验吻合较好。结果显示:入射激波在重气泡内首先在流向上汇聚形成上、下对称的高压区,随后,这对高压区在SF₆重气泡中心对称轴处再次碰撞,完成激波聚焦过程,并在气泡下游界面附近形成远大于初始压力和密度的局部高压高密度区,体现出SF₆重气泡极强的聚能效应;激波聚焦还引起气泡下游界面附近的涡量变化,涡对的旋转能够加速射流形成与发展。因此,SF₆重气泡下游界面附近的高压区和涡量分布对形成射流结构均有促进作用。     

Interaction Between a Slow Magnetohydrodynamic Shock Wave and a Tangential Discontinuity

The self-similar problem of the oblique interaction between a slow MHD shock wave and a tangential discontinuity is solved within the framework of the ideal magnetohydrodynamic model. The constraints on the initial parameters necessary for the existence of a regular solution are found. Various feasible wave flow patterns are found in the steady-state coordinate system moving with the line of intersection of the discontinuities. As distinct from the problems of interaction between fast shock waves and other discontinuities, when the incident shock wave is slow the state ahead of it cannot be given and must to be determined in the process of solving the problem. As an example, a flow in which the slow shock wave incident on the tangential discontinuity is generated by an ideally conducting wedge located in the flow is considered. The basic features of the developing flows are determined.     

A hybrid vortex method for the simulation of three‐dimensional flows

This paper presents an integral vorticity method for solving three‐dimensional Navier–Stokes equations. A finite volume scheme is implemented to solve the vorticity transport equation, which is discretized on a structured hexahedral mesh. A vortex sheet algorithm is used to enforce the no‐slip boundary condition through a vorticity flux at the boundary. The Biot–Savart integral is evaluated to compute the velocity field, in conjunction with a fast algorithm based on multipole expansion. This method is applied to the simulation of uniform flow past a sphere. Copyright © 2007 John Wiley & Sons, Ltd.     

脉冲激光等离子体与正激波相互作用的PIV实验研究

脉冲激光等离子体与超声速流场相互作用在飞行器减阻隔热、点火助燃等方面具有重要的应用价值.纹影实验方法只能定性或半定量地反映流动状态.为定量研究速度分布和旋涡结构,针对激光等离子体及其与正激波相互作用过程开展粒子图像测速PIV实验研究.在激波管实验平台上建立了纳秒脉冲激光能量沉积系统和PIV测量系统,通过定量测量,探明了激光等离子体引致的激光空气泡以及热核的流动特性,揭示了激光等离子体在正激波冲击下的流动特性与演化规律,并给出了激光能量大小和位置对相互作用过程的影响.结果表明:激光空气泡内的速度分布在激光入射方向上并不关于击穿点对称,而是在靠近激光入射方向一侧的流速略大于远离激光入射方向一侧;斜压导致热核在演化初期产生涡环,后期则由剪切主导;正激波与激光空气泡界面、热核界面相互作用时,产生斜压涡量,当激光能量为87.8 mJ、正激波马赫数1.4时,热核在正激波作用下产生的涡量比在静止空气中演化时大1个数量级;激光与正激波相互作用的关键过程是热核在正激波冲击下演化成涡环,在激波波前注入激光能量能够获得更加显著的涡环.     

Imploding conical shock waves

The behaviour of conical shock waves imploding axisymmetrically was first studied numerically by Hornung (J Fluid Mech 409:1–12, 2000) and this prompted a limited experimental investigation into these complex flow patterns by Skews et al. (Shock Waves 11:323–326, 2002). Modification of the simulation boundary conditions, resulting in the loss of self-similarity, was necessary to image the flow experimentally. The current tests examine the temporal evolution of these flows utilising a converging conical gap of fixed width fed by a shock wave impinging at its entrance, supported by CFD simulations. The effects of gap thickness, angle and incident shock strength were investigated. The wave initially diffracts around the outer lip of the gap shedding a vortex which, for strong incident shock cases, can contain embedded shocks. The converging shock at exit reflects on the axis of symmetry with the reflected wave propagating outwards resulting in a triple point developing on the incident wave together with the associated shear layer. This axisymmetric shear layer rolls up into a mushroom-shaped toroidal vortex ring and forward-facing jet. For strong shocks, this deforms the Mach disk to the extent of forming a second triple point with the primary shock exhibiting a double bulge. Separate features resembling the Richtmeyer–Meshkov and Kelvin–Helmholtz instabilities were noted in some tests. Aside from the incident wave curvature, the reflection patterns demonstrated correspond well with the V- and DV-types identified by Hornung although type S was not clearly seen, possibly due to the occlusion of the reflection region by the outer diffraction vortex at these early times. Some additional computational work explicitly exploring the limits of the parameter space for such systems has demonstrated the existence of a possible further reflection type, called vN-type, which is similar to the von Neumann reflection for plane waves. It is recommended that the parameter space be more thoroughly explored experimentally.     

斜激波和可压缩流向涡相互作用的实验观察

激波和可压缩流向涡相互作用现象近年来成为流体力学研究中的一个热点。本文在激波风洞中研究了可压缩流向涡与斜激波相互作用的现象。实验发现,相互作用后激波和旋涡均发生不同程度变形,但旋涡未发生明显破碎。并且发现在干扰点附近,从涡核发出一束膨胀波,这些膨胀波与斜激波作用,使得激波干扰后发生弯曲。     

平面激波冲击并排液滴的三维数值模拟研究

采用三维守恒清晰界面数值方法, 研究平面激波冲击并排液滴的动力学过程. 研究的焦点在于激波接触液滴后的复杂波系结构生成, 以及并排液滴相互耦合作用诱导的单个液滴非对称界面演化. 首先, 分析并排液滴之间界面通道内的波系结构发展, 发现在冲击初期由于反射激波相交而形成新的反射激波以及马赫杆; 这些流动现象与液滴另外一侧 (非通道侧) 由激波反射所形成的弯曲波阵面截然不同, 而且所导致的液滴横向两侧流场差异是中后期冲击过程液滴两侧界面非对称演化的主要原因. 其次, 研究冲击中期时, 特别是入射激波已运动至液滴下游并远离并排液滴, 界面形态的演化过程和规律, 揭示通道下游出口处由于气流膨胀导致的界面闭合、以及随后气流阻塞导致的界面破碎等新的流动现象. 最后, 研究液滴间距对并排液滴相互作用的影响规律, 发现液滴间距大小与通道内压力峰值具有明显的关联关系. 研究表明, 更小的液滴间距不仅带来更大的压力峰值, 而且使得峰值出现的时间更早.      

Regular reflection of a magnetohydrodynamic shock wave from a conducting wall

In two-dimensional supersonic gasdynamics, one of the classical steady-state problems, which include shock waves and other discontinuities, is the problem concerning the oblique reflection of a shock wave from a plane wall. It is well known [1–3] that two types of reflection are possible: regular and Mach. The problem concerning the regular reflection of a magnetohydrodynamic shock wave from an infinitely conducting plane wall is considered here within the scope of ideal magnetohydrodynamics [4]. It is supposed that the magnetic field, normal to the wall, is not equal to zero. The solution of the problem is constructed for incident waves of different types (fast and slow). It is found that, depending on the initial data, the solution can have a qualitatively different nature. In contrast from gasdynamics, the incident wave is reflected in the form of two waves, which can be centered rarefaction waves. A similar problem for the special case of the magnetic field parallel to the flow was considered earlier in [5, 6]. The normal component of the magnetic field at the wall was equated to zero, the solution was constructed only for the case of incidence of a fast shock wave, and the flow pattern is similar in form to that of gasdynamics. The solution of the problem concerning the reflection of a shock wave constructed in this paper is necessary for the interpretation of experiments in shock tubes [7–10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 102–109, May–June, 1977.The author thanks A. A. Barmin, A. G. Kulikovskii, and G. A. Lyubimov for useful discussion of the results obtained.     

Shock wave deformation in shock-vortex interactions

An initially planar shock wave can undergo significant distortion to its shape along with changes in its strength during the period of its interaction with a compressible vortex. This phenomenon is studied by numerically simulating the shock wave-vortex interaction with a high resolution shock-capturing scheme. Incident shock waves of various Mach numbers are made to interact with a compressible vortex and the dependence of the shock wave distortion on the strength of the incident shock wave is studied in detail. It is known that the type of complex shock structure formed in the later stages of a compressible vortex-shock wave interaction is dependent on the Mach number of the incident shock wave. A simple physical model based on the principle of shock wave reflection is proposed to explain this complex shock structure formation and its dependence on the relative strengths of the interacting vortex and shock wave. Received July 28, 1997 / Accepted November 17, 1997     

Shock wave refraction patterns at interfaces

Interactions of shock waves with gas–gas and gas–liquid interfaces (under both slow–fast and fast–slow configurations) are studied using the recently developed Adaptive Characteristics-based Matching (aCBM) method for capturing interfaces in compressible multi-fluid media. First, we verify our approach for the gas–gas case; a class of problems for which a substantial body of knowledge already exists. Then, we consider slow–fast, gas–liquid interfaces under weak shocks, and fast–slow, liquid–gas interfaces under strong shocks. The very high acoustic impedance mismatch situation here creates significant numerical (simulation) and experimental (visualization) difficulties, and the literature for it is meager and sporadic. Compared to gas–gas interfaces we note both similarities and differences. We discuss the sources for these differences, as well as potential implications of generalizing and embedding such results in multi-dimensional simulation schemes towards improving their front-capturing performance.     

Generalized ray expansion for pulse propagation and attenuation in fluid-saturated porous media

A theory suitable for studying pulses propagating through a layered fluid-saturated porous medium is presented. Biot's theory is used to describe the constitutive equation of a fluid-saturated porous solid. Since fast and slow compressional waves exist in a Biot solid even at normal incidence, there is mode conversion at the interface and, therefore, the transmission and reflection coefficients are 2x2 matrices. We use matrix methods in developing the solution of the wave propagation problem. A generalized ray expansion algorithm is obtained by using the Gauss-Seidel matrix iterative method. The arrivals of the fast and the slow waves are easily identified. A compact computational algorithm is developed using combinatorial analysis and the Cayley-Hamilton theorem.     

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.     

Vortex structure generation on the frontal surface of a cylinder set transversely in a hypersonic flow

The problem of formation of spatially periodic structures on the frontal surface of a cylindrically blunted body set transversely in a hypersonic flow is studied. Within the framework of the model adopted, a possible mechanism of vortex structure generation on the frontal surface of the blunt body is proposed and confirmed by calculations; in this mechanism, the curved bow shock produces a vortex flow, while in its turn the vortex, which persists under weak dissipation, acts on the shock thus maintaining its curved shape. It is shown that the spatially periodic mode of hypersonic flow past a cylinder can exist in the case of a uniform incident flow and under homogeneous boundary conditions on the body surface.     

Superposition of two incident shocks in R718 vapor flows

Although the positive values of the fundamental gas-dynamic derivative of R718 near vapor-liquid equilibrium line ensures no occurrence of the non-classical behavior like rarefaction shock waves, the occurrence of the homogenous condensations due to rarefaction waves must be taken into account when using the moving shocks and rarefaction waves in wave devices. In this article, the superposition behaviors such as shockwave refraction and reflection of two moving incident shocks for R718 vapor flows near this the vapor-liquid equilibrium zone, have been intensively studied. And the supercharging characteristic of two superposition moving incident shocks for R718 vapor flows achieves remarkable high boosting pressure ratios of about square of those of one primary equal-intensity shock. This inspiring result could be fully used for vapor recompression in multi-effect distillation technology (MED) for brine water treatment.