Stability of converging cylindrical shock waves

An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Characteristics of an annular vertical diaphragmless shock tube

Abstract. This paper reports on the characteristics of a compact vertical diaphragmless shock tube, which was constructed and tested in the Shock Wave Research Center to study experimentally the behavior of toroidal shock waves. It is 1.15 m in height and has a self-sustained co-axial vertical structure consisting of a 100 mm i.d. outer tube and an 80 mm o.d. inner tube. To create a ring shaped shock wave between the inner and outer tubes, a rubber sheet is inserted to separate a high pressure driver gas from a test gas, which is bulged with auxiliary high pressure helium from the behind. When the rubber membrane is contracted by the sudden release of the auxiliary gas so as to break the seal, shock waves are formed. Special design features of the shock tube are described and their role in producing repeatable shock waves is discussed. Its special opening characteristics make possible the production of annular shaped shock waves that are unlikely met with a conventional tube that uses rupturing diaphragms. Performance of the shock tube is evaluated in terms of the shock wave Mach numbers and the measured flow properties. It eventually showed a higher degree of repeatability and the scatter in the shock wave Mach numbers Ms was found to be 0.2% for Ms ranging from 1.1 to 1.8. The shock wave Mach number so far measured agreed very well with the simple shock tube theory. Received 3 February 1999 / Accepted 6 April 2000     

环形激波绕射, 反射和聚焦的数值模拟研究

应用频散可控耗散格式对环形激波在圆柱形激波管内绕射、反射和聚焦的问题进行了数值模拟研究，研究结果表明环形激波形成强烈聚焦的关键因素是环形激波在圆柱形管道中向对称轴运动时，绕射激波就不断加速而不作通常情况下的衰减；不同马赫数的环形激波绕射也产生不同马赫数及形状的准柱形激波，导致聚焦效果和位置的差异；另外，环形激波聚焦于一个点而圆柱形激波聚焦于一条线，两者有本质不同。     

环形激波聚焦流场特性的数值研究

针对环形激波聚焦过程产生的高温、高压特性,采用间断有限元方法模拟了环形激波在同轴圆柱 形激波管内的聚焦流场特性。计算结果表明,采用间断有限元方法能够有效地捕捉激波聚焦过程形成的二次 激波、涡环、三波交点和球面双马赫反射等主要流动特征。此外,通过改变环形管道内外半径对聚焦流场进行 模拟发现,环形管道外径对中心轴线上聚焦峰值压力的大小和位置影响较小,环形管道内径对中心轴线上聚 焦峰值压力的大小和位置影响较大。计算结果可以为工程应用提供一定的理论指导。     

Regular versus Mach reflection for converging polygonal shocks

The onset of Mach reflection or regular reflection at the vertices of a converging polygonal shock wave was investigated experimentally in a horizontal annular shock tube. The converging shock waves were visualized by schlieren optics. Two different types of polygonal shock convergence patterns were observed. We compared the behavior during the focusing process for triangular and square-shaped shocks. It is shown that once a triangular shaped shock is formed, the corners in the converging shock will undergo regular reflection and consequently the shape will remain unaltered during the focusing process. A square-shaped shock suffers Mach reflections at the corners and hence a reconfiguring process takes place; the converging shock wave alternates between a square and an octagon formation during the focusing process.      

A holographic interferometric study of shock wave focusing in a circular reflector

A holographic interferometric study was made of the focusing of reflected shock waves from a circular reflector. A diaphragmless shock tube was used for incident shock Mach numbers ranging from 1.03 to 1.74. Hence, the process of reflected shock wave focusing was quantitatively observed. It is found that a converging shock wave along the curved wall undergoes an unsteady evolution of mach reflection and its focusing is, therefore, subject to the evolution of the process of shock wave reflections. The collision of triple points terminates the focusing process at the geometrical focus. In order to interprete quantitatively these interferograms, a numerical simulation using an Eulerian solver combined with adaptive unstructured grids was carried out. It is found numerically that the highest density appears immediately after the triple point collision. This implies that the final stage of focusing is mainly determined by the interaction between shock waves and vortices. The interaction of finite strength shock waves, hence, prevents a curved shock wave from creating the infinite increase of density or pressure at a focal point which is otherwise predicted by the linear acoustic theory.     

Attenuation of shock waves propagating over arrayed baffle plates

The paper reports results of shock tube experiments of the attenuation of shock waves propagating over arrayed baffle plates, which is motivated to simulate shock wave attenuation created accidentally at the acoustic delay line in synchrotron radiation factory upon the rupture of a metal membrane separating the acceleration ring at high vacuum and atmospheric test chambers. Experiments were carried out, by using double exposure holographic interferometry with double path arrangement, in a 100 mm×180 mm shock tube equipped with a test section of 180 mm×1100 mm view field. Two baffle plate arrangements were tested: Oblique and staggered baffle plates; and vertical symmetric ones. Pressures were measured along the shock tube sidewall at individual compartments for shock Mach numbers ranging from 1.2 to 3.0 in air. The results were compared with a numerical simulation. The rate of shock attenuation over these baffle plates was compared for vertical and oblique baffle plates. Shock wave attenuation is more pronounced in the oblique baffle plate arrangements than in the vertical ones. PACS 47.40.Nm; 42.40.Kw Communicated by C. Needham     

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     

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.     

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.     

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。     

环形激波绕射、反射和聚焦流场的间断有限元模拟

采用间断有限元方法对环形激波在圆柱形激波管内绕射、反射和聚焦流场进行了数值模拟。将二维守恒方程的间断有限元方法发展到轴对称Euler方程,并对环形激波绕后台阶流动进行了数值计算。计算结果表明,采用间断有限元方法能够有效地捕捉运动激波在圆柱形激波管内传播的复杂流场结构;在聚焦点附近,数值解具有较大的梯度变化,表明该方法对间断解具有较强的捕捉能力,在聚焦点附近不会产生振荡或抹平间断现象。     

流动肥皂膜气体界面及其在柱状汇聚激波作用下演化的实验研究

在Richtmyer-Meshkov(RM)不稳定性实验研究中,形成两种不同密度流体的初始扰动界面是前提和关健.本文提出了一种流动肥皂膜气体界面生成方法,其工作原理是由细丝构成的导流框从激波管实验段穿过,肥皂液从导流框的上端注入并在重力作用下在导流框中形成流动肥皂膜,膜的两测可以分别充入不同密度的气体从而形成稳定的气体...     

An experimental investigation of the stability of converging cylindrical shock waves in air

An experimental study was made of the stability of converging cylindrical shock waves. The experiments were conducted on annular shock tubes equipped with a double exposure holographic interferometer in the Stoßwellenlabor, RWTH Aachen, and in the Institute of High Speed Mechanics, Tohoku University, Sendai, for shock Mach numbers of 1.1 to 2.1 in air. By comparing these two different shock tube experiments, it is found that in the former facility the mode-three instability is predominant at the center of convergence, whereas the mode-four instability appears in the latter setup. The instabilities are denoted in this way because the shock and the flow field behind it reveal a remarkable triangular and quadrangular symmetry, respectively. It is concluded that the converging cylindrical shock wave is always unstable and sensitive to the structure of the annular shock tube. Usefulness of holographic interferometry to this kind of shock wave research is also demonstrated.To Prof. Dr. sq. techn. Dr.-Ing. e.h. Fritz Schultz-Grunow on the occasion of his 80th birthday     

Attenuation of weak shock waves along pseudo-perforated walls

In order to attenuate weak shock waves in ducts, effects of pseudo-perforated walls were investigated. Pseudo-perforated walls are defined as wall perforations having a closed cavity behind it. Shock wave diffraction and reflection created by these perforations were visualized in a shock tube by using holographic interferometer, and also by numerical simulation. Along the pseudo-perforated wall, an incident shock wave attenuates and eventually turns into a sound wave. Due to complex interactions of the incident shock wave with the perforations, the overpressure behind it becomes non-uniform and its peak value can locally exceed that behind the undisturbed incident shock wave. However, its pressure gradient monotonically decreases with the shock wave propagation. Effects of these pseudo-perforated walls on the attenuation of weak shock waves generated in high speed train tunnels were studied in a 1/250-scaled train tunnel simulator. It is concluded that in order to achieve a practically effective suppression of the tunnel sonic boom the length of the pseudo-perforation section should be sufficiently long. Received 23 June 1997 / Accepted 16 September 1997     

Application of digital phase-shift holographic interferometry to weak shock waves propagating at Mach 1.007

Digital phase-shift holographic interferometry was applied to visualize weak shock waves and related phenomena quantitatively. This method of interferometry is an improved version of double-exposure holographic interferometry using digital image processing and a phase shift method. The obtained interferograms were analyzed using the Carré method. To evaluate the applicability of the interferometry to quantitatively visualize the phenomena, density profiles behind weak spherical shock waves generated with 500 μg of silver azide were examined. The results of the numerical analysis performed with the hydrocode AUTODYN were compared with those of the experiment. The Mach number of visualized shock waves was estimated to be 1.007 ± 0.001 at the pressure transducer near the test section. At the shock fronts, the density difference between the experimental and numerical results was within 0.3%.     

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.     

The effects that changes in the diaphragm aperture have on the resulting shock tube flow

In a conventional shock tube, the driver and the driven sections have similar (if not identical) cross-sectional area and the diaphragm opened area, upon rupturing, is practically equal to the tube cross-sectional area. Such geometry results in generating a well-formed shock wave in the tube’s driven section. The present experimental work checks the effects that changes in the diaphragm ruptured area have on the generated shock and rarefaction waves. Experiments were conducted in an 80?mm by 80?mm cross section shock tube generating incident shock waves having Mach numbers within the range from 1.06 to 1.25. In each run, pressure histories were recorded along the driven and the driver sections of the shock tube. The recorded pressures reveal that progressive reduction in the diaphragm open space resulted in a weaker shock and both longer time and distance until the compression waves generated close to the diaphragm coalesces into a shock wave. In addition, reducing the open space of the diaphragm resulted in a significant slow down in the high pressure reduction prevailing in the driver section.     

Focusing shock waves generated by an accelerating projectile

Unsteady flow fields past a projectile either in parabolic motion or in accelerated motion are investigated numerically, with special attention to shock wave focusing phenomena induced by the motions. The two-dimensional Euler equations are solved by a moving-cell, MUSCL TVD finite-volume method with Steger-Warming flux-vector splitting. The pattern of shock wave focusing induced by the projectile is found to be similar to that of shock waves reflected from a concave wall observed in a laboratory experiment using a shock tube. Effects of projectile shapes and trajectories on focusing are also examined.     

Interaction of a reflected shock from a concave wall with a flame distorted by an incident shock

Observations are presented from calculations where a laminar spherical CH₄/air flame was perturbed successively by incident and reflected shock waves reflected from a planar or concave wall. The two-dimensional axi-symmetric Navier–Stokes equations with detailed chemistry were used. The computational results were qualitatively validated with experiments which were performed in a standard shock tube arrangement. Under the influence of the incident shock wave, a Richtmyer–Meshkov instability is induced in the flame, and the distorted flame finally takes the form of two separated elliptical burning bubbles in the symmetric cross plane. Then, under subsequent interactions with the shock wave reflected from the planar or the concave wall, the flame takes a mushroom-like shape. Transverse waves produced by the shock reflection from the concave wall can compress the flame towards the axis, and the focusing shock generated on the concave wall will lead to a larger mushroom-like flame than that induced by the planar reflection.