Dual-element directional shock wave attenuators

This study explores the interaction between shock waves and dual-element porous plates used to ameliorate the hazardous effects of these waves. Tests were performed in a shock tube to determine the effects that a pair of porous plates with directional resistance properties had on the initial peak pressure and impulse amelioration experienced by an end wall. Mild steel test specimens, ranging in porosity values from 6.6% to 41.1%, were mounted two at a time at different spacings in the test section. Each plate had directional properties, i.e. resistance to flow was different for flow coming from either side. Four plates were used, and 48 plate configurations were tested. Side wall and end wall pressure measurements and schlieren photographs were taken of the interactions. Tests were run at Mach numbers of 1.23, 1.35 and 1.42. The separation distances between the plate specimens were varied between 30 mm and 60 mm; however, the distance between the downstream plate and the end wall was kept constant at 140 mm for all tests.Both the initial peak pressure and impulse amelioration values were found to be dependant on the plate combination porosity. As the porosity of the combination increased, the amelioration values decreased. Complementary plate combinations produced differing results as different wave interactions occur when plate positions were interchanged. The porosity of the combined plates was found to have an overriding influence on the end wall peak pressure and impulse amelioration values when compared to the effect that plate arrangement (i.e. geometrical influences) had. Impulse amelioration values were found to increase as the separation distance between plates were increased. The amplitude of the end wall pressure trace was found to increase as the incident Mach number was increased. The significant attenuation of the incident shock wave obtained during this study is attributed to the system of multiple reflected and transmitted waves that are produced by the presence of the plate specimens in series. This increases the frequency of shock wave and barrier interactions, when compared to just using a single barrier.     

爆炸冲击波作用于墙体及对墙体绕射的实验研究

采用试验的方法,对爆炸冲击波作用于防爆墙及绕过墙体的规律进行了研究.采用压力传感器测压,获得了防爆墙前后不同距离的压力波形.试验结果表明:作用于前墙迎爆面反射超压一般要比墙后最大绕射超压大一个数量级,马赫反射一般发生在距离墙后1.5~2.0倍墙高处,药量与爆心距离对墙体反射超压及墙后绕射超压的变化规律有重要影响.通过综合分析和试验结果,得到了爆炸波绕射的内在机理,为防爆墙的设计与加固提供依据和参考.     

EXPERIMENTAL 3-D SIMULATION OF THE COMPRESSION WAVE,DUE TO TRAIN–TUNNEL ENTRY

The work presented in this paper concerns the first compression wave generated in a tunnel when a high-speed train enters it. This wave is the first of successive compression and expansion waves which propagate back and forth in the tunnel. Once generated at the tunnel entrance, its amplitude and gradient vary according to the train and tunnel characteristics. These waves provoke: (a) an aural discomfort for train passengers, (b) mechanical stresses on train and tunnel structures, and (c) emission of impulsive noises outside the tunnel. A reduced-scale test method, using low-sound-speed gas mixtures, has been developed and validated by using newly available European full-scale test-results. It can reproduce quite well the three-dimensional effects due to the train geometry and its position in the tunnel. The study also clearly points out that three-dimensional effects on the front of the first compression wave are attenuated with distance from the tunnel entrance and that the wave front can be considered well established and planar for distances larger than four times the tunnel diameter. Characteristics of the planar wave are in good agreement with Japanese results. The reduced-scale train Mach number has been extended up to 0.34 to determine its test domain. Our study clearly shows that, as far as the characteristics of the wave front of well-established planar first compression wave are concerned, axially symmetrical models can advantageously replace three-dimensional models, provided that the longitudinal cross-sectional area profile is the same for both configurations. This feature yields the following train nose design procedure: first determine the cross-sectional profile of a train nose against train–tunnel interactions by means of axially symmetrical configuration, then give a three-dimensional shape for drag and stability optimisation.     

Shock wave attenuation by grids and orifice plates

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.     

An analytical model for shock wave impact on compressible open-cell foam

A simple model is proposed to describe the main features of the complex phenomena that occur when a plane shock wave strikes a open-cell foam block. The complex two-phase interactions can be simplified using the experimental evidence that the foam face may be treated as a contact surface, that the length of the collapsed foam plug grows linearly in time, and that the gas pressure profile in the region between the head of the plug and the undisturbed material may be treated as being pseudo-stationary. These simplifications enable the prominent features of the compression process to be predicted for a variety of foam types. Analytical results for the reflected shock strength, foam front face velocity, transmitted wave velocity and strength, and maximum peak back wall pressures are presented.      

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m³ were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Behavior of shock trains in a diverging duct

A shock train inside a diverging duct is analyzed at different pressure levels and Mach numbers. Nonreactive pressurized cold gas is used as fluid. The structure and pressure recovery inside the shock train is analyzed by means of wall pressure measurements, Schlieren images and total pressure probes. During the course of the experiments, the total pressure of the flow, the back pressure level and the Mach number upstream of the compression region have been varied. It is shown that the Reynolds number has some small effect on the shock position and length of the shock train. However, more dominant is the effect of the confinement level and Mach number. The results are compared with analytical and empirical models from the literature. It was found that the empirical pseudo-shock model from Billig and the analytical mass averaging model from Matsuo are suitable to compute the pressure gradient along the shock train and total pressure loss, respectively.     

Three-dimensional propagation of the transmitted shock wave in a square cross-sectional chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.PACS: 43.40.Nm     

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.     

Particle image velocimetry investigation of a finite amplitude pressure wave

Particle image velocimetry is used to study the motion of gas within a duct subject to the passage of a finite amplitude pressure wave. The wave is representative of the pressure waves found in the exhaust systems of internal combustion engines. Gas particles are accelerated from stationary to 150 m/s and then back to stationary in 8 ms. It is demonstrated that gas particles at the head of the wave travel at the same velocity across the duct cross section at a given point in time. Towards the tail of the wave viscous effects are plainly evident causing the flow profile to tend towards parabolic. However, the instantaneous mean particle velocity across the section is shown to match well with the velocity calculated from a corresponding measured pressure history using 1D gas dynamic theory. The measured pressure history at a point in the duct was acquired using a high speed pressure transducer of the type typically used for engine research in intake and exhaust systems. It is demonstrated that these are unable to follow the rapid changes in pressure accurately and that they are prone to resonate under certain circumstances.     

Stability analysis and transition prediction of hypersonic boundary layer over a blunt cone with small nose bluntness at zero angle of attack

Stability and transition prediction of hypersonic boundary layer on a blunt cone with small nose bluntness at zero angle of attack was investigated. The nose radius of the cone is 0.5 mm; the cone half-angle is 5°, and the Mach number of the oncoming flow is 6. The base flow of the blunt cone was obtained by direct numerical simulation. The linear stability theory was applied for the analysis of the first mode and the second mode unstable waves under both isothermal and adiabatic wall condition, and eN method was used for the prediction of transition location. The N factor was tentatively taken as 10, as no experimentally confirmed value was available. It is found that the wall temperature condition has a great effect on the transition location. For adiabatic wall, transition would take place more rearward than those for isothermal wall. And despite that for high Mach number flows, the maximum amplification rate of the second mode wave is far bigger than the maximum amplification rate of the first mode wave, the transition location of the boundary layer with adiabatic wall is controlled by the growth of first mode unstable waves. The methods employed in this paper are expected to be also applicable to the transition prediction for the three dimensional boundary layers on cones with angle of attack.     

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.     

Normal incidence of a plane acoustic wave on a rigid wall covered with a thin compressible layer

The one-dimensional unsteady problem of the variation of the pressure on a rigid wall covered with a thin compressible layer upon which a plane acoustic wave impinges is investigated. The investigation is carried out from two standpoints: without allowance for wave processes in the layer (in this case the layer is modeled by means of a special boundary condition [1] and the pressure on the wall is a continuous function of time) and with allowance for the waves transporting the pressure perturbation from the outer edge of the layer to the wall and back (in this case the pressure on the wall is a piecewise-continuous function of time). A criterion of the proximity of the results of the two approaches is the smallness of the acoustic impedance ratio before interaction begins. This holds true even when the high intensities of the incident waves lead to considerable compression of the layer and an increase in its acoustic impedance.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 139–148, July–August, 1988.     

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。     

A multiphase shock tube for shock wave interactions with dense particle fields

Currently there is a substantial lack of data for interactions of shock waves with particle fields having volume fractions residing between the dilute and granular regimes. To close this gap, a novel multiphase shock tube has been constructed to drive a planar shock wave into a dense gas–solid field of particles. A nearly spatially isotropic field of particles is generated in the test section by a gravity-fed method that results in a spanwise curtain of spherical 100-micron particles having a volume fraction of about 20%. Interactions with incident shock Mach numbers of 1.66, 1.92, and 2.02 are reported. High-speed schlieren imaging simultaneous with high-frequency wall pressure measurements are used to reveal the complex wave structure associated with the interaction. Following incident shock impingement, transmitted and reflected shocks are observed, which lead to differences in particle drag across the streamwise dimension of the curtain. Shortly thereafter, the particle field begins to propagate downstream and spread. For all three Mach numbers tested, the energy and momentum fluxes in the induced flow far downstream are reduced about 30–40% by the presence of the particle field.     

On the influence of low initial pressure and detonation stochastic nature on Mach reflection of gaseous detonation waves

The two-dimensional, time-dependent and reactive Navier–Stokes equations were solved to obtain an insight into Mach reflection of gaseous detonation in a stoichiometric hydrogen-oxygen mixture diluted by 25 % argon. This mixture generates a mode-7 detonation wave under an initial pressure of 8.00 kPa. Chemical kinetics was simulated by an eight-species, forty-eight-reaction mechanism. It was found that a Mach reflection mode always occurs for a planar detonation wave or planar air shock wave sweeping over wedges with apex angles ranging from \(5^\circ \) to \(50^\circ \) . However, for cellular detonation waves, regular reflection always occurs first, which then transforms into Mach reflection. This phenomenon is more evident for detonations ignited under low initial pressure. Low initial pressure may lead to a curved wave front, that determines the reflection mode. The stochastic nature of boundary shape and transition distance, during deflagration-to-detonation transition, leads to relative disorder of detonation cell location and cell shape. Consequently, when a detonation wave hits the wedge apex, there appears a stochastic variation of triple point origin and variation of the angle between the triple point trajectory and the wedge surface. As the wedge apex angle increases, the distance between the triple point trajectory origin and the wedge apex increases, and the angle between the triple point trajectory and the wedge surface decreases exponentially.     

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     

STUDY OF MECHANISM OF BREAKDOWN IN LAMINARTURBULENT TRANSITION OF SUPERSONIC BOUNDARY LAYER ON FLAT PLATE

Spatial mode direct numerical simulation has been applied to study the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that, during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbance, when they became larger, leads to remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.     

超音速来流中爆轰波衍射和二次起爆过程研究

预爆管技术被广泛地应用在爆轰波发动机的起爆过程中,但是在超音速来流中基于预爆管技术起始爆轰波的研究并未被广泛地开展。基于此,本文中数值研究了横向超音速来流对半自由空间内爆轰波的衍射和自发二次起爆、及管道内的衍射和壁面反射二次起爆两种现象的影响。数值模拟的控制方程为二维欧拉方程,空间上使用五阶WENO格式进行数值离散,采用带有诱导步的两步链分支化学反应模型。所模拟的爆轰波具有规则的胞格结构,对应于用惰性气体高度稀释过的可爆混合物中形成的爆轰波。结果表明:在半自由空间内,在本文所模拟的几何尺寸下,爆轰波并未成功发生二次起爆现象,但是爆轰波的自持传播距离随着横向超音速来流强度的增强而增加。在核心的三角形流动区域外,波面诱导产生了更多的横波结构;在管道内,横向的超音速来流在逆流侧对出口气流产生了压缩作用,能有效提高波面压力,因此反射后的激波压力也比较高。在同样的几何尺寸下,爆轰波在静止和超音速(Ma=2.0)气流中分别出现了二次起爆失败和成功两种现象,这是由于在超音速来流中化学反应面的褶皱诱导产生了横波结构,横波与管壁以及其他横波之间的碰撞提高了前导激波的强度,并最终促进了爆轰波在超声速流主管道内的成功起始。     

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.