Centered simple waves for the two-dimensional pseudo-steady isothermal ?ow around a convex corner

The two-dimensional(2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state.     

Simple stationary waves in an inclined magnetic field

One component of the solution to the problem of flow around a corner within the scope of magnetohydrodynamics, with the interception or stationary reflection of magnetohydrodynamic shock waves, and also steady-state problems comprising an ionizing shock wave, is the steady-state solution of the equations of magnetohydrodynamics, independent of length but depending on a combination of space variables, for example, on the angle. The flows described by these solutions are called stationary simple waves; they were considered for the first time in [1], where the behavior of the flow was investigated in stationary rotary simple waves, in which no change of density occurs. For a magnetic wave, of parallel velocity, the first integrals were found and the solution was reduced to a quadrature. The investigations and the applications of the solutions obtained for a qualitative construction of the problems of streamline flow were continued in [2–8]. In particular, problems were solved concerning flow around thin bodies of a conducting ideal gas. The general solution of the problem of streamline flow or the intersection of shock waves was not found because stationary simple waves with the magnetic field not parallel to the flow velocity were not investigated. The necessity for the calculation of such a flow may arise during the interpretation of the experimental results [9] in relation to the flow of an ionized gas. In the present paper, we consider stationary simple waves with the magnetic field not parallel to the flow velocity. A system of three nonlinear differential equations, describing fast and slow simple waves, is investigated qualitatively. On the basis of the pattern constructed of the behavior of the integral curves, the change of density, magnetic field, and velocity are found and a classification of the waves is undertaken, according to the nature of the change in their physical quantities. The relation between waves with outgoing and incoming characteristics is explained. A qualitative difference is discovered for the flow investigated from the flow in a magnetic field parallel to the flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 130–138, September–October, 1976.The author thanks A. A. Barmin and A. G. Kulikovskii for constant interest in the work and for valuable advice.     

基于势流理论的内孤立波与立管作用数值研究

内孤立波是一种发生在水面以下的在世界各个海域广泛存在的大幅波浪, 其剧烈的波面起伏所携带的巨大能量对以海洋立管为代表的海洋结构物产生严重威胁, 分析其传播演化过程的流场特征及立管在内孤立波作用下的动力响应规律对于海洋立管的设计具有重要意义. 本文基于分层流体的非线性势流理论, 采用高效率的多域边界单元法, 建立了内孤立波流场分析计算的数值模型, 可以实时获得内孤立波的流场特征. 根据获得的流场信息, 采用莫里森方程计算内孤立波对海洋立管作用的载荷分布. 将内孤立波流场非线性势流计算模型与动力学有限元模型结合来求解内孤立波作用下海洋立管的动力响应特征, 讨论了内孤立波参数、顶张力大小以及内部流体密度对立管动力响应的影响. 发现随着内孤立波波幅的增大, 海洋立管的流向位移和应力明显增大. 由于上层流体速度明显大于下层, 且在所研究问题中拖曳力远大于惯性力, 因此管道顺流向的最大位移发生在上层区域. 顶张力通过改变几何刚度阵的值进而对立管的响应产生明显影响. 对于弱约束立管, 内部流体的密度对管道的流向位移影响较小.      

The interaction of oblique blast waves with buildings

Assessment of the net load imparted to a building that is oriented at some angle to an incident blast wave is complicated by the difficulty of establishing the impulse delivered to each part of the building’s surfaces. Expansion waves originating from the edges and top of the building—where regions of different pressures meet—tend to reduce the (oblique) reflected impulses that would develop on an infinitely large surface. This process is referred to as oblique clearing. An investigation which considered a single, tall building aligned obliquely to an effectively uniform blast wave has been undertaken with the aim of demonstrating and describing the path of these expansion waves as the blast wave passes over the building. The investigation comprised a series of small-scale experiments supported by numerical simulations using the code ftt_air3d. The loads arising at two scaled stand-off distances were considered. It is shown that depending on the angle of the building to the blast and the length of the blast wave with respect to the size of the building, the effect of the expansion waves may vary considerably, hence altering the load experienced by the building.     

The thickness of detonation waves visualised by slight obstacles

The reflection of detonation waves from slight obstacles, which hardly disturb the wave propagation, is observed by time-resolved schlieren photography. The following stoichiometric mixtures are used: pure and argon-diluted hydrogen-oxygen, hydrogen-air, acetylene-oxygen, and acetylene-air. Initial pressures are varied such that cell widths range from 1.4 up to 108 mm, which is twice the side length of the square cross-section of the tube. The trajectories of the incident and the reflected waves in the x,t-plane are used to determine lower limit values for the wave thickness. The considerable influences of the obstacle shape and of the evaluation method on the results are discussed in detail, and error sources are analyzed. The method has been improved since a previous publication by the authors. The ratio of the lower limit values to the cell width spreads from 0.4 to 0.8 in the medium cell size range. It decreases with increasing marginality and seems to increase at small scale. A unique correlation between the lower limit value and the tube diameter, both referred to the cell size, that was proposed earlier in the literature has to be refused. The velocities of the reflected waves are presented as additional information on the post-detonation wave state. The sonic transition is discussed theoretically, enhancing the stream tube model, and practically, based on detailed observations for marginal detonations.Received: 29 April 2003, Accepted: 20 October 2003, Published online: 3 February 2004PACS: 47.40.-xCorrespondence to: M. Weber     

椭球罩作用下的水下爆炸冲击波反射聚焦模型

基于冲击波传播、非线性反射和聚焦理论,建立水下爆炸冲击波在椭球罩作用下的反射聚焦模型。讨论自由传播、壁面反射和定向聚焦阶段的冲击波特性和压力计算方法,利用波前和波法线的近似方程构建压力场的数值计算域,进而模拟聚焦过程,并与现有实验结果进行对比,结果表明:所建模型可为正聚焦压力提供满足工程精度的预测,并能描述水下冲击波及产生的拉伸波聚焦过程中的一些细节;椭球罩能有效地聚焦水下冲击波,在动力学焦点附近获得有效增益区,在近轴方向上明显削弱冲击波压力衰减;理想条件下的动力学焦点一般位于几何焦点之前,但实际的反射罩变形和背向位移将使其发生后迁,甚至能越过几何焦点。     

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.     

Visualisation and modelling studies of churn flow in a vertical pipe

Churn flow is an important flow regime intermediate between slug flow and annular flow. A feature of this regime is the occurrence of very large waves travelling upwards over a liquid film substrate which may intermittently travel downwards. These waves are often formed close to the liquid inlet where their behaviour is usually difficult to observe. This paper describes a series of experiments using a test section with a specially constructed transparent liquid inlet. High-speed video recordings show clearly the process of wave formation and analysis of the recordings gave data on wave frequencies and typical velocities. Also, predictions of velocity and distance travelled by the waves were obtained via the application of a simple mathematical model that takes into account the forces acting on a circumferentially coherent wave.     

Head on collision of a planar shock wave with a dusty gas layer

The head-on collision of a planar shock wave with a dust-air suspension is studied numerically. In this study the suspension is placed inside a conduit adjacent to its rigid end-wall. It is shown that as a result of this collision two different types of transmitted shock waves are possible, depending on the strength of the incident shock wave and the dust loading ratio in the suspension. One possibility is a partially dispersed shock wave, the other is a compression wave. The flow fields resulting in these two options are investigated. It is shown that in both cases, at late times after the head-on reflection of the transmitted shock wave from the conduit end-wall a negative flow (away from the end-wall) is evident. The observed flow behavior may suggest a kind of dust particle lifting mechanism that could shed new light on the complex phenomenon of dust entrainment behind sliding shock waves.      

Implicit and explicit secular equations for Rayleigh waves in two-dimensional anisotropic media

This paper is concerned with the derivation of implicit and explicit secular equations for Rayleigh waves polarized in a plane of symmetry of an anisotropic linear elastic medium. It has been confirmed, in accord with Ting’s paper [2], that the Rayleigh waves propagate with no geometric dispersion. Numerical evaluations of both the implicit and explicit equations give the same values of Rayleigh wave velocities. In the case of orthotropic material (thin composites) it has been found that Rayleigh wave velocity depends significantly (as with bulk waves) on the directions of principal material axes. For the same material model the analytical solutions, based on implicit and explicit secular equations, were compared against the finite element and experimental data that had been published by Cerv et al. [4] in 2010. It emerged that the theory was in accordance with the experiment.     

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     

Numerical and experimental investigation of wave dynamic processes in high-speed train/tunnels

Numerical and experimental investigation on wave dynamic processes induced by high-speed trains entering railway tunnels are presented. Experiments were conducted by using a 1:250 scaled train-tunnel simulator. Numerical simulations were carried out by solving the axisymmetric Euler equations with the dispersion-controlled scheme implemented with moving boundary conditions. Pressure histories at various positions inside the train-tunnel simulator at different distance measured from the entrance of the simulator are recorded both numerically and experimentally, and then compared with each other for two train speeds. After the validation of nonlinear wave phenomena, detailed numerical simulations were then conducted to account for the generation of compression waves near the entrance, the propagation of these waves along the train tunnel, and their gradual development into a weak shock wave. Four wave dynamic processes observed are interpreted by combining numerical results with experiments. They are: high-speed trains moving over a free terrain before entering railway tunnels; the abrupt-entering of high-speed trains into railway tunnels; the abrupt-entering of the tail of high-speed trains into railway tunnels; and the interaction of compression and expansion waves ahead of high-speed trains. The effects of train-tunnel configuration, such as the train length and the train-tunnel blockage ratio, on these wave processes have been investigated as well.     

Transition of plane overdriven detonation wave to the Chapman-Jouguet regime

The asymptotic laws of behavior for plane, cylindrical, and spherical infinitely thin detonation waves were found in [1, 2] for increasing distance from an igniting source in those cases in which the waves changed into Chapman-Jouguet waves as they decayed. It was shown that the plane overdriven detonation wave approaches the Chapman-Jouguet regime asymptotically, while the transition of the cylindrical or spherical strong detonation wave into the Chapman-Jouguet wave may occur at a finite distance from the initiation source.Similar conclusions are valid for the propagation of stationary steadystate detonation waves which arise with flow of combustible gas mixtures past bodies.However, numerous experiments [3, 4] on firing bodies in a detonating gas show that the overdriven detonation wave which forms ahead of the body decays and decomposes into an ordinary compression shock and a slow combustion front. To establish why the wave does not make the transition to the Chapman-Jouguet regime, in the following we consider the propagation of a plane detonation wave and account for finite chemical reaction rates. We use the very simple two-front model (ordinary shock wave and following flame front). Conditions are found for which transition to the Chapman-Jouguet regime does not occur. We first consider the propagation of an unsteady plane wave and then the steady plane wave. It is found that for all the mixtures used in these experiments transition to the Chapman-Jouguet regime is not possible within the framework of the assumed model.     

Waves on the surface of a falling power-law fluid film

Waves that occur at the surface of a falling film of thin power-law fluid on a vertical plane are investigated. Using the method of integral relations an evolution equation is derived for two types of waves equation which are possible under long wave approximation. This equation reveals the presence of both kinematic and dynamic wave processes which may either act together or singularly dominate the wave field depending on the order of different parameters. It is shown that, at a small flow rate, kinematic waves dominate the flow field and the energy is acquired from the mean flow during the interaction of the waves, while, for high flow rate, inertial waves dominate and the energy comes from the kinematic waves. It is also found that this exchange of energy between kinematic and inertial waves strongly depends on the power-law index n. Linear stability analysis predicts the contribution of different terms in the wave mechanism. Further, it is found that the surface tension plays a double role: for a kinematic wave process, it exerts dissipative effects so that a finite amplitude case may be established, but for a dynamic wave process it yields dispersion. Further, it is shown that the non-Newtonian character n plays a vital role in controlling the role of the term that contains surface tension in the above processes.     

Traveling Waves in Porous Media Combustion: Uniqueness of Waves for Small Thermal Diffusivity

We study traveling wave solutions arising in Sivashinsky’s model of subsonic detonation which describes combustion processes in inert porous media. Subsonic (shockless) detonation waves tend to assume the form of a reaction front propagating with a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity [5]. Moreover, it has been shown that, when the thermal diffusivity is neglected, the traveling wave is unique. The question of whether the wave is unique in the presence of thermal diffusivity has remained open. For the subsonic regime, the underlying physics might suggest that the effect of small thermal diffusivity is insignificant. We analytically prove the uniqueness of the wave in the presence of non-zero diffusivity through applying geometric singular perturbation theory. Dedicated to Mr. Brunovsky in honor of his 70th birthday.     

Generation of Nonlinear Waves on a Viscoelastic Coating in a Turbulent Boundary Layer

Self–induced excitation of periodic nonlinear waves on a viscoelastic coating interacting with a turbulent boundary layer of an incompressible flow is studied. The response of the flow to multiwave excitation of the coating surface is determined in the approximation of small slopes. A system of equations is obtained for complex amplitudes of multiple harmonics of a slow (divergent) wave resulting from the development of hydroelastic instability on a coating with large losses. It is shown that three–wave resonant relations between the harmonics lead to the development of explosive instability, which is stabilized due to the deformation of the mean (Sover the wave period) shear flow in the boundary layer. Conditions of soft and hard excitation of divergent waves are determined. Based on the calculations performed, qualitative features of excitation of divergent waves in known experiments are explained.     

Phase and signal velocities of waves in dissipative media. Special relativistic theory

The signal and phase velocities (and their frequency dependence) for all possible plane waves in a relativistic gas (of molecules or photons) with dissipation have been determined from the linearized relativistic 13-moment theory. For each direction in 3-space, and for each frequency, one transverse and two longitudinal waves were found. (In addition, some waves are associated with the mass flow and have the mass flow speed.) Of the longitudinal waves, the fast one is a pressure (sound) wave. It is accompanied by a slow longitudinal thermal dissipation wave and a transverse viscous dissipation wave. The pressure wave has a velocity larger than the Laplace adiabatic speed of sound, while the two dissipation waves have a velocity less than the Laplace speed. All the speeds have been expressed explicitly in terms of quantities associated with the state of equilibrium which existed before passage of the wave. It has also been shown that in the ultrarelativistic limit (extremely high temperatures) all signal speeds remain less than the speed of light in vacuo.The major part of this article was presented at the Seminar on Natural Philosophy at The Johns Hopkins University, Baltimore, on November 24, 1971.     

Two-dimensional stress wave analysis in incompressible elastic solids

Two-dimensional stress waves in a general incompressible elastic solid are investigated. First, basic equations for simple waves and shock waves are presented for a general strain energy function. Then the characteristic wave speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock waves. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation the oblique reflection problem of a plane shock is not solvable in general.     

Simple waves in general elastic materials

The general theory of simple waves in Green-elastic and Cauchy-elastic materials is given. Such waves generate three-dimensional unsteady deformations. Boundary conditions producing such waves are derived together with conditions under which shocks occur. The theory is used to illustrate conditions behind acceleration fronts moving into homogeneously deformed regions and also the modes of propagation of fronts moving into a simple wave. The steady flow of an elastic material past a rigid developable surface is discussed. Simple waves which are principal waves are also discussed.     

粘弹性Hopkinson压杆中波的衰减和弥散

研究了线性粘弹性Hopkinson压杆中由于粘性效应和横向惯性效应引起的就力波衰减和弥散。导出计及横向惯性效应的线性粘弹性杆中纵波控制方程和应力解应变解，进而导出表征波衰竭和弥散性质的纵波传播系数的修正公式。这一修正公式计入粘性效应和几何效应，与Bacon公式相比，其形式简单，更便于在实验数据处理中应用。最后利用实验方法测定了有机玻璃杆的传播系数。