Experimental study of planar shock wave interactions with dense packed sand wall

A dense packed sand wall is impacted by a planar shock wave in a horizontal shock tube to study the shock-sand wall interaction. The incident shock Mach number ranges from 2.18 to 2.38. A novel device for actively rupturing diaphragm is designed for the driver section of the shock tube. An apparatus for loading particles is machined by the electrical discharge cutting technique to create a dense packed particle wall. High-speed schlieren imaging system and synchronized pressure measurement system are used together to capture the wave structures and particle cloud velocity. The dynamic evolution model from dense packed particles to dense gas–solid cloud at the initial driving stage is established. The blockage and permeation effects of the sand wall work together and influence each other. The high pressure gas behind the incident shock wave blocked by the sand wall pushes the upstream front of the wall forward like a piston. Meanwhile, the high speed gas permeating through the sand wall drags the sands of the most downstream layer forward. The incident shock strength, initial sand wall thickness and particle diameter are varied respectively to investigate the shock attenuation and the wall acceleration. Increasing the sands diameter or mixing in small diameter sands can significantly attenuate the incident shock. The smaller particles or the particles in thinner wall can be dispersed into a larger range in the process of transform from dense packed particles to dense gas–solid cloud. Moreover, the stronger incident shock can disperse the particles into a larger region.     

Self-intensification in shock wave and vortex interaction

Computer simulation has been performed for the interaction between a shock wave and a vortex ring moving toward the wave. The computed density contours are compared with the pattern of shadowgraphs. A remarkable property found in the simulation is that, during the passage of the shock wave over the vortex ring, the part of the wave propagating through the inside of the ring-vortex is intensified spontaneously at a localized region. Maximum pressure occurs inside the vortex and attains a high value, about several times that of the impinging shock for incident Mach numbers of around 1.2 with the vortex translation Mach number 0.60. This is due to a double-step mechanism of intensification within the flow field by the shock-vortex interaction.     

Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

Particle image velocimetry is used to investigate the interaction between an incident shock wave and a turbulent boundary layer at Mach 2.1. A particle response assessment establishes the fidelity of the tracer particles. The undisturbed boundary layer is characterized in detail. The mean velocity field of the interaction shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. Significant reversed flow is measured instantaneously, although, on average no reversed flow is observed. The interaction instantaneously exhibits a multi-layered structure, namely, a high-velocity outer region and a low-velocity inner region. Flow turbulence shows the highest intensity in the region beneath the impingement of the incident shock wave. The turbulent fluctuations are found to be highly anisotropic, with the streamwise component dominating. A distinct streamwise-oriented region of relatively large kinematic Reynolds shear stress magnitude appears within the lower half of the redeveloping boundary layer. Boundary layer recovery towards initial equilibrium conditions appears to be a gradual process.     

用环形激波聚焦实现爆轰波直接起爆的数值模拟

利用基元反应模型和有限体积法对环形激波在可燃气体中聚焦实现爆轰波直接起爆进行了数值模拟。研究结果表明，标准状态下的氢气-空气混合气体在马赫数为3.1以上的环形激波聚焦产生的高温高压区作用下会诱发可燃气体的直接起爆形成爆轰波，爆轰波与激波和接触间断相互作用产生了复杂的波系结构；爆轰波爆点位置在对称轴上并不是固定的点，而是随着初始激波马赫数的变化而发生移动；可燃气体初始温度和压力对起爆临界马赫数都有影响，但是初始温度的影响大得多。     

The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.      

Numerical investigation of toroidal shock wave focusing in a cylindrical chamber

In this paper, focusing of a toroidal shock wave propagating from an annular shock tube into a cylindrical chamber was investigated numerically with the dispersion controlled dissipation (DCD) scheme. The first case for an incident Mach number of 1.5 was conducted and compared with experiments for validation. Then, several cases were calculated for higher incident Mach numbers varying from 2.0 to 5.0, and complicated flow structures were observed. The numerical study was mainly focused on two aspects: focusing process and flow structures. The process, including diffraction, focusing, and reflection, is displayed to reveal the focusing mechanism, and the flow structures at different incident. Mach numbers are used to demonstrate shock reflection styles and focusing characteristics. PACS 47.40.Ki; 47.40.Nm; 52.35.Tc     

Guderley reflection for higher Mach numbers in a standard shock tube

An experimental study shows that the Guderley reflection (GR) of shock waves can be produced in a standard shock tube. A new technique was utilised which comprises triple point of a developed weak Mach reflection undergoing a number of reflections off the ceiling and floor of the shock tube before arriving at the test section. Both simple perturbation sources and diverging ramps were used to generate a transverse wave in the tube which then becomes the weak reflected wave of the reflection pattern. Tests were conducted for three ramp angles (10°, 15°, and 20°) and two perturbation sources for a range of Mach numbers (1.10–1.40) and two shock tube expansion chamber lengths (2.0 and 4.0 m). It was found that the length of the Mach stem of the reflection pattern is the overall vertical distance traveled by the triple point. Images with equivalent Mach stem lengths in the order of 2.0 m were produced. All tests showed evidence of the fourth wave of the GR, namely the expansion wave behind the reflected shock wave. A shocklet terminating the expansion wave was also identified in a few cases mainly for incident wave Mach numbers of approximately 1.20.     

Numerical investigation of axisymmetric shock wave focusing over paraboloidal reflectors

The problem of a plane shock wave incident to a paraboloidal reflector is numerically investigated. The numerical solver used is developed by an improved, implicit, upwind total variation diminishing scheme in a finite-volume approach. The real-gas effect is taken into account if high temperature occurs. The solver is validated on four test problems. The complicated flow fields of axisymmetric shock wave focusing for different-depth reflectors at various incident shock Mach numbers are studied. An interesting result of a maximum pressure happening at the reflector center is found. This is due to the occurrence of an implosion phenomenon. A maximum temperature might occur at the reflector center or at other locations, depending on the incident shock Mach number and the reflector depth. Moreover, vortical flows induced by shock wave focusing and their formation mechanism are explored. It was found that the vortices near the reflector are caused by a ring-shaped shock/slipline interaction. Owing to the slipline on the symmetry axis, a jet flow is induced, resulting in the formation of vortices near the symmetry axis. Received 13 January 1998 / Accepted 10 November 1998     

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。     

金属铅在斜冲击波对碰加载下动态行为的数值模拟

高强度冲击加载作用下金属材料的动态物理行为是当前冲击波领域基础研究和工程应用最为关注的焦点。采用光滑粒子法(SPH)开展不同位置起爆诱发的斜冲击波对碰加载金属铅的二维数值模拟研究,得到了金属铅内入射斜冲击波的角度和强度,并利用极曲线方法理论上导出发生马赫反射时的临界入射角和入射马赫数关系。根据计算结果可知,金属铅内入射斜波对碰后将发生马赫反射。随着起爆位置与金属铅表面距离的增加,不仅金属铅内入射冲击波强度和入射角增加,而且形成的马赫杆宽度也在增加。由自由面速度剖面给出了马赫杆宽度及张角,结果与理论预测的结果吻合较好。     

Supersonic low-concentration dusty-gas flow past a plane cylinder in the presence of an oblique shock wave interacting with the bow shock

The motion of an inertial dispersed admixture near a plane cylinder immersed in a steady-state hypersonic dusty flow in the presence of an oblique shock wave interacting with the bow shock is considered. It is assumed that the free-stream particle mass concentration is small and the particles do not affect the carrier flow. The III and IV shock wave interaction regimes are considered. The gas flow parameters in the shock layer are calculated from the numerical solution of the full Navier-Stokes equations for the perfect gas. A TVD second-order finite-difference scheme constructed on the basis of a finite volume method is used. For calculating the dispersed-phase parameters, including the concentration, the full Lagrangian method is used. On a wide range of variation of the particle inertia parameters, the patterns of the particle trajectories, velocity, concentration, and temperature in the shock layer are studied. The possibility of aerodynamic focusing of the particles behind the shock wave intersection point and the formation of narrow beams with a high particle concentration is revealed. These beams impinge on the cylinder surface and result in a sharp increase in the local heat fluxes. The maximal possible increase in the heat fluxes caused by the particles colliding with the cylinder surface is estimated for the flows with and without the incident oblique shock wave.     

平面激波加载下砂墙结构的冲击响应特性

砂墙结构在爆炸安全防护领域具有广泛应用,为了研究激波加载下砂墙结构的冲击响应特性,基于水平激波管实验装置,开展平面激波冲击砂墙结构系列实验,采用高速纹影摄像系统捕捉流场中激波波系的演化过程和砂墙结构的运动过程。入射激波马赫数为1.827~2.413,相应入射激波载荷强度为0.378~0.724 MPa。砂墙结构利用铁砂、矾土、石英砂3种实验用砂制备,所制备砂墙结构孔隙度分别为56.6%、69.3%、56.6%。高速纹影照片显示:平面激波冲击砂墙结构发生反射和透射,伴随入射激波和透射激波的传播,在百微秒内,砂墙未产生显著运动,表现出显著的类固体动力学响应特性。基于冲击理论,确定了铁砂墙、矾土砂墙、石英砂墙的线性冲击关系,冲击关系中线性常数λ值量级为100,根据凝聚介质实用状态方程推断:较低强度载荷冲击作用下,砂墙主要产生体积变形,而由冲击引起的热能效应则可以忽略。     

激波驱动的气固两相流的动态压力测量

利用水平圆柱形激波管对激波驱动的可压缩性气固两相流进行了试验研究.利用压电式压力传感器、电荷放大器、示波器及计算机组成的压力信号测试系统, 对激波与颗粒作用前后的气相参数进行测量及分析. 试验中测得了激波在管中的传播速度, 波后气流的压力, 反射激波、透射激波的压力和速度等. 分别考察颗粒、装载比、驱动气源以及入射激波马赫数等因素的差异对气相参数的影响.试验结果表明: 激波与颗粒群相互作用时, 会产生反射激波和透射激波,其强度与驱动气源、颗粒大小、颗粒装载比等参数有关;激波衰减率随着装载比、马赫数的增大而减小. 研究指出,在颗粒群被激波加速的初始阶段, 颗粒间的弹性碰撞起着重要的作用.      

Two-phase reactive particle flow through normal shock waves

An analysis is presented for the steady one-dimensional flow behind a normal shock wave of a compressible gas containing small spherical particles of solid propellant. The solids mass fraction is assumed large enough to require that the void volume fraction be retained as a variable in the governing conservation equations. The particles are ignited by the shocked air and by viscous interaction. Propellant gases are then generated which depend on the instantaneous size of the particles and on the linear burning rate. The latter is assumed dependent upon the local pressure and the particle temperature. These calculations are of interest because of the potential hazards of such particle flows, in that extreme pressures are predicted within the relaxation zone, pressures even greater than those calculated for the final equilibrium conditions. The results stress the importance of the Mach number of the normal (strong shock) and the energy content of the propellant (J/kg).     

Dense particle cloud dispersion by a shock wave

A dense particle flow is generated by the interaction of a shock wave with an initially stationary packed granular bed. High-speed particle dispersion research is motivated by the energy release enhancement of explosives containing solid particles. The initial packed granular bed is produced by compressing loose powder into a wafer with a particle volume fraction of $\phi _\mathrm{p} = 0.48$ . The wafer is positioned inside the shock tube, uniformly filling the entire cross-section. This results in a clean experiment where no flow obstructing support structures are present. Through high-speed shadowgraph imaging and pressure measurements along the length of the channel, detailed information about the particle shock interaction was obtained. Due to the limited strength of the incident shock wave, no transmitted shock wave is produced. The initial solid-like response of the particle wafer acceleration forms a series of compression waves that eventually coalesce to form a shock wave. Breakup is initiated along the periphery of the wafer as the result of shear that forms due to the fixed boundary condition. Particle breakup is initiated by local failure sites that result in the formation of particle jets that extend ahead of the accelerating, largely intact, wafer core. In a circular tube, the failure sites are uniformly distributed along the wafer circumference. In a square channel, the failure sites, and the subsequent particle jets, initially form at the corners due to the enhanced shear. The wafer breakup subsequently spreads to the edges forming a highly non-uniform particle cloud.     

激波点燃粉尘的数值模拟研究

建立了用于模拟入射激波后可燃粉尘颗粒点火的一维非定常两相化学反应流模型，该模型考虑了气固两相间的相互作用、粉尘颗粒的加速、加热和化学反应。粉尘颗粒着火前的化学反应用发生在颗粒外表面和内孔表面的非均相反应描述，颗粒内部的温度变化用一含有化学反应源项的非稳态热传导方程来描述，以颗粒外表面温度的突跃上升作为可燃粉尘颗粒点燃的着火条件。我们用该模型和ＰＳＩＣ方法，对由中等强度激波从纯气相传入煤粉－氧气混合物而引起的非定常两相流动现象，包括气固两相间的相互作用、粉尘颗粒的加速、加热以及点火过程进行了数值研究，计算了对应于不同载荷比、马赫数为４～５的入射激波后煤尘颗粒的点火延迟时间，分析了由于可燃粉尘颗粒的存在，入射激波及波后气固两相流动参数的变化规律。数值计算结果与实验数据符合较好。文中建立的模型和所用的基于ＰＳＩＣ算法的数值方法，用最自然的方式描述气固两相流动，即用连续流模型（欧拉方程）描述输运相（气相）的流动，用轨道颗粒模型（拉格朗日方程）描述分散相（颗粒相）的运动。用这种方法模拟含尘介质中激波后颗粒的点火是很有效的，它可以清楚地确定哪一个颗粒群最先着火，它的初始位置以及在整个点火延迟时间内     

Stability and analogy of shock wave reflection in steady flow

Numerical simulations have been performed to investigate the stability of shock wave reflection in supersonic steady flow. Wall deflection control has been applied just downstream of the reflection point in the regular reflection configuration. The results provide the magnitude of the disturbance required to cause transition from one configuration to the other throughout the range of incident shock angle. An argument focusing on the subsonic region generated behind the Mach stem in the Mach reflection configuration explains the mechanism of the transition. Numerical results show that both regular and Mach reflections are possible in the dual-solution domain, and also indicate the presence of the hysteresis effect. The transition processes and the stability of the possible states are shown to be described consistently by an analogy based on the potential energy of a particle on a surface. The necessity of more sophisticated experimental investigations is emphasized to verify the argument about the stability of shock reflections and proposed analogy. Received 17 March 1997 / Accepted 26 February 1998     

Experimental and computational studies focusing processes of shock waves reflected from parabolic reflectors

This paper describes experimental and numerical studies of the focusing process of shock waves reflected from various shapes of a parabolic reflector. The effect of incident shock strength on the focusing process was also investigated. Experiments were carried out in a conventional shock tube and a test gas was air for incident shock Mach numbers ranging from 1.1 to 2.0. In the experiments, the process of shock focusing was visualized by schlieren method. Numerical simulations were conducted for incident shock Mach numbers up to 3.0 by solving the two-dimensional unsteady Euler equations. The numerical results were compared with experiment for various parabolic reflector shapes and for various incident shock Mach numbers. Based on the experimental and computational results, the pattern of shock focusing and shock focusing mechanism are discussed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave

The effect of incident shock wave strength on the decay of interface introduced perturbations in the refracted shock wave was studied by performing 20 different simulations with varying incident shock wave Mach numbers (M ~ 1.1? 3.5). The analysis showed that the amplitude decay can be represented as a power law model shown in Eq.7, where A is the average amplitude of perturbations (cm), B is the base constant (cm^?(E?1), S is the distance travelled by the refracted shockwave (cm), and E is the power constant. The proposed model fits the data well for low incident Mach numbers, while at higher mach numbers the presence of large and irregular late time oscillations of the perturbation amplitude makes it hard for the power law to fit as effectively. When the coefficients from the power law decay model are plotted versus Mach number, a distinct transition region can be seen. This region is likely to result from the transition of the post-shock heavy gas velocity from subsonic to supersonic range in the lab frame. This region separates the data into a high and low Mach number region. Correlations for the power law coefficients to the incident shock Mach number are reported for the high and low Mach number regions. It is shown that perturbations in the refracted shock wave persist even at late times for high incident Mach numbers.