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.     

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.      

Three-dimensional supersonic internal flows

In order to examine the transition between regular and Mach reflection in a three-dimensional flow, a range of special geometry test pieces, and inlets, were designed. The concept is to have a geometry consisting of two plane wedges which results in regular reflection between the incident waves off the top and bottom of the inlet capped by two curved end sections causing Mach reflection. The merging of these two reflection patterns and the resulting downstream flow are studied using laser vapor screen and shadowgraph imaging supported by numerical simulation. An angled Mach disc is formed which merges with the line of regular reflection. A complex wave pattern results with the generation of a bridging shock connecting the reflected wave from the Mach reflection with the reflected waves from the regular reflection. In order to experimentally access the flow within the duct, a number of tests were conducted with one end cap removed. This resulted in a modified flow due to the expansive flow at the open end the influence of which was also studied in more detail.     

Numerical investigation of shock wave reflections near the head ends of rotating detonation engines

The influence of various chamber geometries on shock wave reflections near the head end of rotating detonation engines was investigated. A hydrogen/air one-step chemical reaction model was used. The results demonstrated that the variation in flow field along the radial direction was not obvious when the chamber width was small, but became progressively more obvious as the chamber width increased. The thrust increased linearly, and the detonation height and the fuel-based gross specific impulse were almost constant as the chamber width increased. Near the head end, shock waves reflected repeatedly between the inner and outer walls. Both regular and Mach reflections were found near the head end. The length of the Mach stem increased as the chamber length increased. When the chamber width, chamber length and injection parameters were the same, the larger inner radius resulted in more shock wave reflections between the inner and outer walls. The greater the ratio of the chamber width to the inner radius, the weaker the shock wave reflection near the head end. The detonation height on the outer wall and the thrust, both increased correspondingly, while the specific impulse was almost constant as the inner radius of the chamber increased. The numerical shock wave reflection phenomena coincided qualitatively with the experimental results.     

The reflection of a shock wave over a cone

An investigation was made of the reflection of planar shock waves from cones. 86 cones, the half apex angle of which varied from 10° to 52° at every 0.5°, were installed in a 60 mm×150 mm diaphragmless shock tube equipped with holographic interferometry. The diaphragmless shock tube had a high degree of reproducibility with which the scatter of shock wave Mach number was within ±0.25% for shock wave Mach number ranging from 1.16 to approximately 2.0. The reflection of shock waves over cones was visualized using double exposure holographic interferometry. Whitham's geometrical shock wave dynamics was used to analyse the motion of Mach stems over cones. It is found that for relatively smaller apex angles of cones trajectory angles of resulting irregular reflections coincide with the so-called glancing incidence angles and their Mach stems appear to be continuously curved from its intersection point with the incident shock wave, which shows the chractericstic of von Neumann reflection. The domain of the existence of the von Neumann reflection was analytically obtained and was found to be broadened much more widely than that of two-dimensional reflections of shock waves over wedges.     

Effects of a Single-pulse Energy Deposition on Steady Shock Wave Reflection

The effects of energy deposition in the free stream on steady regular and Mach shock wave reflections are studied numerically. A short-duration laser pulse is focused upstream of the incident shock waves. It causes formation of the expanding blast wave and the residual hot-spot interacting in a complex way with the steady shock wave reflection. It was found that the laser energy addition in the free stream may force the transition from regular to Mach reflection in the dual solution domain. In contrast to previously reported numerical results, the transition from Mach to regular reflection has not been reproduced in our refined computations since the Mach reflection is restored after the flow perturbation.     

Oblique reflection of shock waves from rigid porous materials

A study to determine the general gas dynamic behaviour associated with the impact of a shock wave on a porous wedge has been undertaken. A number of interesting features are noted. The pattern of wave reflection is shown to be significantly affected by the inflow of gas into the wedge. This has the effect of reducing the triple point trajectory angle for cases of Mach reflection and for strongly reducing the reflection angle in regular reflection. The permeability of the wedge has a significant effect on the strength of the reflected wave and in some cases this wave can be attenuated to the extent that it is almost eradicated. Pressure measurements taken under the wedge are characterized by oscillations which are of similar shape, for a given wedge, over a range of shock wave Mach numbers. It is shown that the wave transmitted into the wedge is attenuated to varying degrees depending on the material properties, and that for weak incident waves the mean propagation velocity can be less than the sound speed in the pore fluid. Photographs taken using a specially constructed wedge which allows the transmitted wave to be visualised, show that the transmitted wave is nearly plane.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.     

非定常激波三维双楔面反射的数值研究

采用基于MUSCL-Hancock插值的有限体积方法, 在非结构自适应网格上求解三维Euler方程, 研究了非定常激波在三维垂直双楔面上的反射现象. 研究结果表明, 由于三维效应的影响, 通过二维非定常激波反射理论预测的三维马赫反射区域范围存在着一定的局限, 在该区域范围内出现了一种非典型的三维突起结构, 即第二类三维马赫干. 另外, 对于不同的激波马赫数和楔面倾角组合, 非定常激波在三维双楔面上会形成具有四波结构的三维马赫反射或具有三波结构的三维规则反射.      

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.      

Diffuse holographic interferometric observation of shock wave reflection from a skewed wedge

The pattern of shock wave reflection over a wedge is, in general, either a regular reflection or a Mach reflection, depending on wedge angles, shock wave Mach numbers, and specific heat ratios of gases. However, regular and Mach reflections can coexist, in particular, over a three-dimensional wedge surface, whose inclination angles locally vary normal to the direction of shock propagation. This paper reports a result of diffuse double exposure holographic interferometric observations of shock wave reflections over a skewed wedge surface placed in a 100 × 180 mm shock tube. The wedge consists of a straight generating line whose local inclination angle varies continuously from 30° to 60°. Painting its surface with fluorescent spray paint and irradiating its surface with a collimated object beam at a time interval of a few microseconds, we succeeded in visualizing three-dimensional shock reflection over the skewed wedge surface. Experiments were performed at shock Mach numbers, 1.55, 2.02, and 2.53 in air. From reconstructed holographic images, we estimated critical transition angles at these shock wave Mach numbers and found that these were very close to those over straight wedges. This is attributable to the flow three-dimensionality.      

Shock wave configurations and flow structures in non-axisymmetric underexpanded sonic jets

An experimental and numerical study of underexpanded free sonic jet flows issuing from rectangular, elliptical and slot nozzles has been undertaken. Aspect ratios (AR) of 1, 2, and 4 are described at pressure ratios (exit plane pressure to ambient pressure), of 2 and 3. There is good qualitative agreement between the experimental observations and the numerical predictions. In the case of rectangular jets, a complex system of shock waves forming the incident shock system is identified. This shock wave system originates at the corners of the nozzle exits, and proceeds downstream. Mach reflections are found to occur on the incident shock wave surface as well as the presence of a Mach disk terminating the first jet cell. This Mach disk has the shape of a square, a hexagon, or an octagon depending on the nozzle shape. For slot and elliptical jets, the formation of the incident shock wave was not observed along the minor axis plane of the nozzle for AR > 2. The incident shock wave was observed to originate downstream of the nozzle exit in the major axis plane. This wave system undergoes a transition to Mach reflection as it propagates downstream of the nozzle exit. In all cases tested, the shape of the jet boundary is significantly distorted. In rectangular jets, the narrowing of the jet boundary along the diagonal axis of the nozzle exit is observed, and in the case of the elliptical and slot jets axis switching is noted.     

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。     

Three-dimensional effects on regular reflection in steady supersonic flows

The reflection of shock waves between two symmetrical wedges is investigated for the case of three-dimensional flows. Oblique shadowgraphs at various optical angles of yaw and pitch were used to examine the nature of fully three-dimensional flows, with wedge aspect ratios as low as 0.25 being considered. These images were used to construct surface models of the overall flow field for various reflection patterns and aspect ratios, which provides a visual indication of the flow field shape. For a Mach number of 3.1, and suitable wedge angles, the flow field with regular reflection on the tunnel centreline and Mach reflection further out is examined. The point of transition from regular reflection to the peripheral Mach surfaces is identified for various wedge angles and aspect ratios. It is shown that the transition points move outwards from the central plane as the aspect ratio decreases. This shows that three-dimensional flows favor regular reflection, because of the increasing curvature of the incident shock as the wedge becomes narrower, causing a decrease in the local angle of incidence. The height of the Mach stem is shown to be highly dependent on the geometry of the test wedge models. The Mach stem height decreases with aspect ratio due to the three-dimensional relieving effect, where the increase in lateral flow relieves the pressure over the surfaces of the wedges. Experimental evidence of the existence of the strong oblique shock solution in steady flows is presented.Received: 7 July 2003, Revised: 20 October 2003, Accepted: 6 November 2003, Published online: 10 February 2004PACS: 47.40.Nm Correspondence to: B.W. Skews     

The interaction between shock waves and solid spheres arrays in a shock tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in the wave propagation process. The wave interactions with vortices behind each sphere‘s wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.     

Double Mach reflection of strong shock waves

The Mach reflection of shock waves in those cases in which the gas ideality condition is satisfied with high accuracy is well-known. The effects associated with the excitation of the internal degrees of freedom for the molecules lead to a qualitative change in the reflection pattern. The present study is an extension of [1, 2], devoted to the study of the Mach reflection of shock waves from a wedge under conditions in which the physical and chemical transformations in the gas heated by the shock wave play a significant role.     

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     

铅飞层中斜冲击波对碰马赫反射行为实验研究

采用线阵多普勒光纤探针测速技术（Doppler pins system，DPS）和高速光电分幅相机照相两种精密诊断技术，对铅飞层中斜冲击波对碰后的反射行为进行了观测。获得了飞层对碰部位速度-时间历史曲线和凸起形貌演化图像，给出了凸起轮廓发展演化过程、压力分布等实验数据和信息。结合冲击波反射理论，对铅飞层对碰区动力学现象进行了分析和解释，证实铅飞层中斜冲击波对碰后发生了马赫反射。     

Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H ₂/O ₂ diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes. The English text was polished by Yumming Chen.     

Numerical simulation of Mach reflection of cellular detonations

The Mach reflection of cellular detonation waves on a wedge is investigated numerically in an attempt to elucidate the effect of cellular instabilities on Mach reflection, the dependence of self-similarity on the thickness of a detonation wave, and the initial development of the Mach stem near the wedge apex. A two-step chain-branching reaction model is used to give a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. A sufficiently large distance of travel of the Mach stem is computed to observe the asymptotic behavior in the far field. Depending on the scale at which the Mach reflection process occurs, it is found that the Mach reflection of a cellular detonation behaves essentially in the same way as a planar ZND detonation wave. The cellular instabilities, however, cause the triple-point trajectory to fluctuate. The fluctuations are due to interactions of the triple point of the Mach stem with the transverse waves of cellular instabilities. In the vicinity of the wedge apex, the Mach reflection is found to be self-similar and corresponds to that of a shock wave of the same strength, since the Mach stem is highly overdriven initially. In the far field, the triple-point trajectory approaches a straight line, indicating that the Mach reflection becomes self-similar asymptotically. The distance of the approach to self-similarity is found to decrease rapidly with decreasing thickness of the detonation front.     

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.