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.     

Near-wall imaging using toluene-based planar laser-induced fluorescence in shock tube flow

A quantitative thermometry technique, based on planar laser-induced fluorescence (PLIF), was applied to image temperature fields immediately next to walls in shock tube flows. Two types of near-wall flows were considered: the side wall thermal boundary layer behind an incident shock wave, and the end wall thermal layer behind a reflected shock wave. These thin layers are imaged with high spatial resolution (15μm/pixel) in conjunction with fused silica walls and near-UV bandpass filters to accurately measure fluorescence signal levels with minimal interferences from scatter and reflection at the wall surface. Nitrogen, hydrogen or argon gas were premixed with 1–12% toluene, the LIF tracer, and tested under various shock flow conditions. The measured pressures and temperatures ranged between 0.01 and 0.8 bar and 293 and 600 K, respectively. Temperature field measurements were found to be in good agreement with theoretical values calculated using 2-D laminar boundary layer and 1-D heat diffusion equations, respectively. In addition, PLIF images were taken at various time delays behind incident and reflected shock waves to observe the development of the side wall and end wall layers, respectively. The demonstrated diagnostic strategy can be used to accurately measure temperature to about 60 μm from the wall.     

On flows behind shock waves reflected from a solid wall

The flow fields associated with the interaction of a normal shock wave with a plane wall kept at a constant temperature were studied based on kinetic theory which can describe appropriately the shock structure and its reflection process. With the use of a difference scheme, the time developments of the distributions of the fluid dynamic quantities (velocity, temperature, pressure and number density of the gas) were obtained numerically from the BGK model of the Boltzmann equation subject to the condition of diffusive-reflection at the wall for several cases of incident Mach number:M ₁=1.2, 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0. The reflection process of the shocks is shown explicitly together with the resulting formation of the flow fields as time goes on. The nonzero uniform velocity toward the wall occurring between the viscous boundary layer and the reflected shock wave is found to be fairly large, the magnitude of which is of the order of several percent of the velocity induced behind the incident shock, decreasing as the incident Mach number increases. It is also seen that a region of positive velocity (away from the wall) within the viscous boundary layer manifests itself in the immediate vicinity of the wall, which is distinct for larger incident Mach numbers. Some of the calculated density profiles are compared with available experimental data and also with numerical results based on the Navier-Stokes equations. The agreement between the three results is fairly good except in the region close to the wall, where the difference in the conditions of these studies and the inappropriateness of the Navier-Stokes equations manifest themselves greatly in the gas behavior.This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.     

Application of unsteady mixing equations to some aerodynamic problems

Tangential discontinuities [1] are introduced in solving several transient and steady-state problems of gas dynamics. These discontinuities are unstable [2] as a result of the effects of viscosity and thermal conductivity. Therefore it is advisable to replace the tangential discontinuity by a mixing region and account for its interaction with the inviscid flows, establishing on the boundaries of this region the conditions of vanishing friction stress and equality of the velocity and temperature components to the corresponding velocity and temperature components of the inviscid flows. This formulation improves the accuracy of the solution of such problems by posing them as problems with irregular reflection and intersection of shock waves [1].The consideration of the interaction of unsteady turbulent mixing regions with the inviscid flow also permits the formulation of several problems in which the effects of viscosity lead to complete rearrangement of the flow pattern (the lambda-configuration) with the interaction of the reflected shock wave with the boundary layer in the shock tube [3,4], the formation of zones of developed separation ahead of obstacles, etc.).In this connection, §1 presents an analysis of the self-similar solutions of the unsteady turbulent mixing equations (a corresponding analysis of the laminar mixing equations which coincide with the boundary layer equations is presented in [1]). It is shown that these self-similar solutions describe, along with the several problems noted above, the problems of the formation of steady jets and mixing zones in the base wake.As an example, §2 presents, within the framework of the proposed schematization, an approximate solution of the problem of the interaction of a shock wave reflected from a semi-infinite wall with the boundary layer on a horizontal plate behind the incident shock wave. The results obtained are applied to the analysis of reflection in a shock tube. Computational results are presented which are in qualitative agreement with experiment [3, 4].     

STUDY ON THE FUEL AIR MIXING INDUCED BY A SHOCK WAVE PROPAGATING INTO A H_2-AIR INTERFACE

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｕｅｌａｉｒｍｉｘｉｎｇｉｎａｓｈｅａｒｌａｙｅｒｆｌｏｗｉｓａｎｉｍｐｏｒｔａｎｔｐｒｏｂｌｅｍｉｎｓｔｕｄｙｉｎｇｃｏｍｐｒｅｓｓｉｂｌｅｆｌｏｗａｎｄｓｕｐｅｒｓｏｎｉｃｃｏｍｂｕｓｔｉｏｎ ,ｓｕｃｈａｓｆｕｅｌｄｉｆｆｕｓｉｏｎａｎｄｍｉｘｉｎｇｉｎａＳｃｒａｍｊｅｔ[1].Ｒｏｓｈｋｏ[2 ]ｓｔｕｄｉｅｄｅｘｐｅｒｉｍｅｎｔａｌｌｙｔｈｅｐｈｅｎｏｍｅｎｏｎｏｆｆｕｅｌａｉｒｍｉｘｉｎｇｉｎａｓｕｂｓｏｎｉｃｓｈｅａｒｆｌｏｗａｎｄｆｏｕｎｄｌａｒｇｅ ,ｃｏｈ…     

Reflection of a plane shock wave from a rigid concave wall

We present the results of an experimental study of the reflection of a plane stationary shock wave with Mach number in the range 1.21–1.35 from a rigid cylindrical concave wall. The experiments were carried out in a shock tube. In experimental shock tube technology the reflection of a shock wave from a rigid wall is often used for obtaining high temperatures [1]. This circumstance is associated with the fact that the temperature behind the reflected wave is significantly higher than that behind the incident wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 33–39, July–August, 1970.     

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.     

Shock wave diffraction on multi-facetted and curved walls

The two-dimensional diffraction of a shock wave over a wall made up of a series of plane and/or curved sections is considered. The analysis is based on the theory presented by, for the interaction of an originally plane shock wave with a corner. A method is presented by which the shock profile may be determined for a wall of any shape and for any incident Mach number, in regions where the characteristics form a simple wave. Comparisons are made between experimental measurements and theoretical predictions for convex walls consisting of a number of facets, and for circular arcs, for a range of incident shock wave Mach numbers. It is shown that the theory gives a satisfactory prediction of the wave shape, which improves as the Mach number increases. Modifications in the flow field behind the shock, compared to that for a simple corner made up of two plane walls is discussed, particularly relating to flow separation. For circular arc concave walls a inverse Mach reflection results experimentally, leading to regular reflection, for which the theory is of no use. PACS 47.40.Nm     

Radiative cooling of plasma behind a reflected shock front

Calculation of gas flow in a shock tube on the basis of ideal theory [1] leads to results that differ from the real picture. In particular, the calculated velocity of the reflected shock wave exceeds the experimentally measured velocity [2] by about 20%. The calculated parameters of shock-heated gas agree well with the experimental results only directly behind the shock front [3]. The present paper reports a theoretical and experimental investigation of the variation of the plasma parameters behind the front of a reflected shock wave in argon. A picture of the gas-dynamic processes taking place after reflection of the incident shock wave by the end of the shock tube is determined. A method is developed for approximate analytic calculation, this making it possible to determine not only the parameters of the gas directly behind the front of the reflected shock wave for different positions of the wave relative to the end of the shock tube but also the variation of these parameters in other regions behind the reflected shock wave. The calculation takes into account the influence of the boundary layer and radiative cooling in the approximation of a low degree of ionization of the plasma and persistence of equilibrium conditions in the entire region behind the reflected shock wave. The experimental and theoretical profiles of the radiation behind the reflected shock wave are compared.     

Study on the Fuel Air Mixing Induced by a Shock Wave Propagating into a H2-Air Interface

2nd-order upwind TVD scheme was used to solve the laminar, fully Navier-Stokes equations. The numerical simulations were done on the propagation of a shock wave with Ma _S = 2 and 4 into a hydrogen and air mixture in a duct and a duct with a rearward step. The results indicate that a swirling vortex may be generated in the lopsided interface behind the moving shock. Meanwhile, the complex shock system is also formed in this shear flow region. A large swirling vortex is produced and the fuel mixing can be enhanced by a shock wave at low Mach number. But in a duct with a rearward step, the shock almost disappears in hydrogen for Ma _S = 2. The shock in hydrogen will become strong if Ma _S is large. Similar to the condition of a shock moving in a duct full of hydrogen and air, a large vortex can be formed in the shear flow region. The large swirling vortex even gets through the reflected shock and impacts on the lower wall. Then, the distribution of hydrogen behind the rearward step is divided into two regions. The transition from regular reflection to Mach reflection was observed as well in case Ma _S = 4.     

Three dimensional shock wave/boundary layer interactions

An investigation into a three-dimensional, curved shock wave interacting with a three-dimensional, curved boundary layer on a slender body is presented. Three different nose profiles mounted on a cylindrical body were tested in a supersonic wind tunnel and numerically simulated by solving the Navier–Stokes equations. The conical and hemispherical nose profiles tested were found to generate shock waves of sufficient strength to separate the boundary layer on the cylinder, while the shock wave generated by the ogival profile did not separate the boundary layer. For the separated flow, separation was found to occur predominantly on the windward side of the cylinder with the lee-side remaining shielded from the direct impact of the incident shock wave. A thickening of the boundary layer on the lee-side of all the profiles was observed, and in the conical and hemispherical cases this leads to the re-formation of the incident shock wave some distance away from the surface of the cylinder. A complex reflection pattern off the shock wave/boundary layer interaction (SWBLI) was also identified for the separated flow cases. For comparative purposes, an inviscid simulation was performed using the hemispherical profile. Significant differences between the viscous and inviscid results were noted including the absence of a boundary layer leading to a simplified shock wave reflection pattern forming. The behaviour of the incident shock wave on the lee-side of the cylinder was also affected with the shock wave amalgamating on the surface of the cylinder instead of away from the surface as per the viscous case. Test data from the wind tunnel identified two separation lines present on the cylindrical surface of the hemispherical SWBLI generator. The pair of lines were not explicitly evident in the original CFD simulations run, but were later identified in a high-resolution simulation.     

二维激波与剪切层相互作用的直接数值模拟研究

采用五阶weighed esseritially non-oscillatory (WENO) 格式和三阶total variation diminishing (TVD) Runge-Kutta 格式, 通过求解二维非定常Navier-Stokes 方程, 直接数值模拟了激波与剪切层相互作用, 目的在于揭示激波与剪切层相互作用过程中噪声产生的机理. 研究发现:(1) 当入射激波穿过剪切层时, 剪切层中心位置向下层区域偏移;(2) 入射激波穿过剪切层产生小激波, 在小激波与剪切层接触点处产生声波并向外辐射;(3) 反射激波穿过剪切层后形成了分段弧状激波;(4) 当反射激波穿过剪切层时, 激波在鞍点处泄漏并向外辐射声波, 这是一种激波泄漏机制.     

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     

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.     

Reflection of shock waves from a solid boundary in a mixture of condensed materials. 1. Equilibrium approximation

The process of reflection of shock waves (SW) from a solid wall in a two-component mixture of condensed materials is studied within the framework of mechanics of heterogeneous media. The velocity of a reflected SW and the values of the parameters behind its front are analytically determined as functions of the velocity of the incident wave and the initial parameters of the mixture. It is shown that the absolute value of the velocity of the reflected SW can be greater than the velocity of the incident SW in mixtures with a small content of the light component and at low velocities of the incident shock wave. The nonmonotonic character of the dependence of pressure in the final equilibrium state behind the incident SW on the initial volume concentration of particles is demonstrated. The velocity of the incident SW is estimated for the case where a similar effect is also observed behind a reflected SW. It is established that, for weak shock waves, the dependence of the amplification factor of the reflected SW on the initial volume concentration of the light component is nonmonotonic and has a local maximum. It is noted that, as the velocity of the incident SW increases, the effect of compacting of the mixture (increase in concentration of the heavy component) behind the reflected SW becomes much less pronounced than in a passing SW. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 73–78, September–October, 1999.     

竖直平面激波与水平热层作用后流场的理论计算方法研究

围绕竖直平面激波与固壁附近水平热层作用问题,提出了流动进入准自相似阶段后固壁附近流场参量的理论计算方法。与已有的Mirels方法相比,本文的方法在下列三个方面进行了改进:（1）舍弃“热层内激波速度与入射激波速度相等”的假定,分析了热层内激波的传播过程,并基于几何激波动力学理论计算热层内激波强度;（2）假定在与入射激波后流体而非入射激波阵面固连的坐标系中,波后流体在定常等熵波作用下,形成沿固壁运动的“活塞”,驱动其前方的热层气体运动;（3）“活塞”内流体与其毗邻的热层气体满足压力和速度连续,不再引入速度比例系数。利用改进后的方法,对于马赫数为2.00的竖直平面激波,在不同热层密度条件下进行计算。本文方法得到的热层内激波强度以及物质界面处的压力、速度和密度等参量,与数值模拟结果偏差均小于10%,优于Shreffler和Mirels计算方法。对于马赫数为1.36的竖直平面激波,当其传播速度小于热层内气体声速时,Shreffler和Mirels计算方法不再适用,而本文中提出的方法得到的计算结果与数值模拟结果和已有实验数据基本吻合,最大偏差约20%。上述结果表明,本文中提出的理论计算方法提高了现有方法的合理性,扩大了适用范围。     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

Shock waves in water with Freon-12 bubbles and formation of gas hydrates

The evolution of a shock wave and its reflection from a wall in a gas-liquid medium with dissolution and hydration are experimentally investigated. Dissolution and hydration behind the front of a moderate-amplitude shock wave are demonstrated to be caused by fragmentation of gas bubbles, resulting in a drastic increase in the area of the interphase surface and in a decrease in size of gas inclusions. The mechanisms of hydration behind the wave front are examined. Hydration behind the front of a shock wave with a stepwise profile is theoretically analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 58–75, May–June, 2007.     

可燃气体中激波聚焦的点火特性

数值模拟了二维平面激波从抛物面上反射在可燃气体中聚焦的过程,研究了形 成爆轰波的点火特性. 对理想化学当量比氢气/空气混合气体,在初始压强20kPa的条件下, 马赫数2.6-2.8的激波聚焦能产生两个点火区：第1个点火区是反射激波会聚引起的,第 2个点火区是由入射激波在抛物面上发生马赫反射引起的. 这种条件下流场中会出现爆燃转 爆轰,起爆点分别分布在管道壁面、抛物反射面和第2点火区附近. 起爆机理分别为激波管 道壁面反射、点火诱导激波的抛物面反射和点火诱导的激波与第2点火区产生的爆燃波的相 互作用. 不同的点火和起爆过程导致了不同的流场波系结构,同时影响了爆轰波传播的波动 力学过程.     

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.