Instability theory of shock wave in a shock tube

The instability theory of shock wave in a shock tube including the effects of tube wall and contact surface is studied. The experimental data of unstable shock wave coincide with one of instability criteria derived in the present paper.     

Instability theory of shock wave in a channel

The instability theory of shock wave was extended from the case with an infinitefront to the case of a channel with a rectangular cross section.First,themathematical formulation of the problem was given which included a system ofdisturbed equations and three kinds of boundary conditions.Then,the general solutionsof the equations upstream and downstream were given and each contained fiveconstants to be determined.Thirdly,under one boundary condition and oneassumption,it was proved that all of the disturbances in front of the shock front andone of the two acoustic disturbances behind the shock front should be zero.Theboundary condition was that all of the disturbed physical quantities should approach tozero at infinity.The assumption was that only the unstable shock wave was concernedhere.So it was reasonable to assumeω=iγ,γwas the instability growth rate andwas a positive real number.Another kind of boundary conditions was that the normaldisturbed velocities should be zero at the solid wall of the cha     

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     

外爆条件下冲击波与组合壳结构的相互作用

为研究冲击波与组合壳结构的相互作用,针对带防护墙的地面直立钢筋混凝土组合壳结构,考虑结构安置于地面和周边围土2种工况,开展结构爆炸实验,分析了结构外表面冲击波荷载分布及振动特性。实验结果表明:冲击波作用下,结构外表面爆炸荷载主要产生在冲击波绕射过程,确定荷载时应考虑冲击波压力在绕射传播过程中的自然衰减;整个结构中与冲击波最早接触的构件先产生振动,而后由于结构整体参与使得振动频率降低,振动幅值减小;结构周边围土可降低防护墙迎爆部分构件的振动频率,减小防护墙和组合壳的振动幅值。     

Large-amplitude long wave interaction with a vertical wall

The rigorous solution of the nonlinear shallow-water equations for the wave field near a vertical wall is derived; it is used to calculate the height of the water oscillations near the wall versus the height of the incident wave. This solution is used to find the exceedance probability of characteristics of the wave motion near the vertical wall. It is shown that the wave height and trough distributions of water oscillations near vertical structures are less than the Rayleigh distribution. Beside of this, the distribution of the crest heights exceeds the Rayleigh distribution (using normalization of the amplification factor for such geometry within the framework of the linear theory), and this explains the high frequency of freak wave events on breakwaters and coasts.     

FLAT-PLATE BOUNDARY-LAYER FLOWS INDUCED BY DUSTY SHOCK WAVE

ＦＬＡＴ－ＰＬＡＴＥＢＯＵＮＤＡＲＹ－ＬＡＹＥＲＦＬＯＷＳＩＮＤＵＣＥＤＢＹＤＵＳＴＹＳＨＯＣＫＷＡＶＥ（王柏懿）（陶锋）ＦＬＡＴ－ＰＬＡＴＥＢＯＵＮＤＡＲＹ－ＬＡＹＥＲＦＬＯＷＳＩＮＤＵＣＥＤＢＹＤＵＳＴＹＳＨＯＣＫＷＡＶＥ￥ＷａｎｇＢｏｙｉ；Ｔａ...     

Shock unsteadiness in a thrust optimized parabolic nozzle

This paper discusses the nature of shock unsteadiness, in an overexpanded thrust optimized parabolic nozzle, prevalent in various flow separation modes experienced during start up and shut down sequences. The results are based on simultaneously acquired data from real-time wall pressure measurements using Kulite pressure transducers, high-speed schlieren (2 kHz) of the exhaust flow-field and from strain-gauges installed on the nozzle bending tube. Shock unsteadiness in the separation region is seen to increase significantly just before the onset of each flow transition, even during steady nozzle operation. The intensity of this measure (rms level) is seen to be strongly influenced by relative locations of normal and overexpansion shock, the decrease in radial size of re-circulation zone in the back-flow region, and finally, the local nozzle wall contour. During restricted shock separation, the pressure fluctuations in separation region exhibit periodic characteristics rather than the usually observed characteristics of intermittent separation. The possible physical mechanisms responsible for the generation of flow unsteadiness in various separation modes are discussed. The results are from an experimental study conducted in P6.2 cold-gas subscale test facility using a thrust optimized parabolic nozzle of area-ratio 30.

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Computation of shock wave/turbulent boundary layer interactions using a two-equation model with compressibility corrections

In this paper computational results for two different types of shock wave / turbulent boundary layer interaction flows are presented. It is shown that upstream effects of the shock induced separation cannot be reproduced by Wilcox's (1991) k--model, whereas downstream of the interaction, predictions of pressure distribution and skin friction are acceptable. The inclusion of the compressible part of the dissipation rate and the pressure dilatation in the model has noticeable, but not dramatic effects on wall pressure and skin friction in the selected flow cases.     

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     

On the interference of a weak and a strong shock wave in a dissociating nitrogen flow

The influence of the nitrogen dissociation on the interactions due to the interference of two planar shock waves in a hypersonic high enthalpy flow is theoretically investigated for infinite reaction rates. The two limiting cases of infinitely slow and infinitely fast reactions are modelled as a perfect gas and an ideal dissociating gas in chemical equilibrium.To investigate the influence of finite reaction rates on the interactions of shock waves, experiments are performed in the high enthalpy shock tunnel Göttingen (HEG) with a wind tunnel model consisting of a wedge type shock generator and a transversally mounted cylinder. The pressure and heat transfer loads resulting from the shock wave interferences are measured and the flow field is visualized by means of interferograms. The experimental results are compared with the results of a numerical simulation for a dissociating nitrogen flow and with the experimental results for a perfect gas flow.     

环形浅液池内热流体波的本质特征

为了了解环形浅液池内热毛细对流的特征,利用有限容积法对外壁受热、内壁冷却、厚度为1 mm的环形浅液池内硅油的热毛细对流进行了三维数值模拟.结果表明,当Marangoni(Ma)数小于临界值时,随着Ma数的增加,内、外壁附近的温度梯庹上升,稳定的二维轴对称流动的径向速率增加;超过临界Ma数后,漉动转化为三维振荡对流,形成热流体波.沿径向运动的同时,伴随着热流体波的传播流体质点成对地绕顺时针和逆时针方向旋转.热流体波的周向传播速度较快,而流体质点的周向速度很小.分析发现,热流体波为对数螺线形波纹,其传播角为常数;随着Ma数的增大,传播角增大.     

Particle and drop dynamics in the flow behind a shock wave

The results of an investigation of the dynamics of hard particles and liquid drops in the flow behind a transmitted shock wave are presented. From the equation of motion of a particle in the shock wave, relations for the displacement, velocity and acceleration as functions of time and certain velocity-relaxation parameters taking into account the properties of the gas and the aerodynamic drag of the particles are obtained for unsteady flow around the particles at an acceleration of 10³–10⁴ m/s². It is shown that the velocity-relaxation parameters are universal. Approaches to finding the aerodynamic drag of freely-accelerating bodies from the dynamics of their acceleration after being suddenly exposed to the flow are considered. It is established that under these conditions the drop dynamics observed can be well described in terms of the same velocity-relaxation parameters with account for linear growth of the transverse drop size. All the kinematic functions obtained are confirmed experimentally.     

Diffraction of a solitary wave by a thin wedge

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when the incident solitary wave is directed along the wedge axis. The method of multiple scales is extended to this problem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary and initial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithm in which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paper are found to corroborate the Melville's experiments not only qualitatively but also quantitatively. The maximum run-up of our results agrees well with Funakoshi's numerical one but it is considerably larger than that in Melville's experiment. An important reason for this discrepancy is believed to be the effect of viscous boundary layer on the vertical side wall.     

Interaction of isotropic turbulence with a normal shock wave

The evolution of incompressible and compressible isotropic 2-d turbulent fields interacting with a normal shock wave up to Mach numbers of 2.4 was investigated by means of direct numerical simulation using an ENO scheme. A comparison of statistics with linear analysis results is presented. Vorticity amplification in the DNS agrees well with the linear theory. Energy spectra are enhanced more in the small scales than in the large scales for incoming incompressible turbulence. The amplification rate for initially compressible turbulence is comparatively small.     

Peristaltic flow and heat transfer in a vertical porous annulus, with long wave approximation

In this paper, we study the interaction of peristalsis with heat transfer for the flow of a viscous fluid in a vertical porous annular region between two concentric tubes. Long wavelength approximation (that is, the wavelength of the peristaltic wave is large in comparison with the radius of the tube) is used to linearise the governing equations. Using the perturbation method, the solutions are obtained for the velocity and the temperature fields. Also, the closed form expressions are derived for the pressure-flow relationship and the heat transfer at the wall. The effect of pressure drop on flux is observed to be almost negligible for peristaltic waves of large amplitude; however, the mean flux is found to increase by 10-12% as the free convection parameter increases from 1 to 2. Also, the heat transfer at the wall is affected significantly by the amplitude of the peristaltic wave. This warrants further study on the effects of peristalsis on the flow and heat transfer characteristics.     

激波的传播与干扰

激波的传播特性既取决于激波的产生条件,也与所处的传播环境密切相关。驱动条件、几何边界、介质的物理化学属性等发生变化时,都会引起激波传播特性的改变,而激波的变化反过来又会对其波及的流场产生影响。尽管激波传播及其干扰现象广泛存在于自然界和人类科技活动之中,其复杂机理的认识、规律的描述乃至应用潜力的挖掘仍有漫长的路要走。本文根据气体中激波传播和干扰现象以及与之相关的理论描述特征,在对激波传播以及反射、折射等基本现象进行简要阐述的基础上,重点围绕目前的热点问题,包括激波/激波干扰、激波/边界层干扰、激波与湍流作用、激波的聚焦与点火以及激波作用下气体界面不稳定性等研究进行了介绍和讨论,旨在对近年来该领域的进展及获得的成果做一个概述和归纳,期望对将来的深入研究有一个鉴借意义。     

Magnetosonic wave propagation in a weakly diffusive plasma

The evolution of fast magnetosonic waves in a Hartmann type magnetohydrodynamic equilibrium is studied with geometric optics methods. Rays are shown either to oscillate a round a fixed line parallel to the wall, go to infinity or hit the wall at a finite time. Perturbations of the equilibrium whose frequency has the same order as the inverse of the kinetic and magnetic diffusivities of the plasma are shown to satisfy a transport equation along the rays which may be converted into a viscous Burgers one. This allows us to describe the later evolution of these perturbations, which for periodic rays decay exponentially.     

Pressure wave propagation in liquid-filled tubes of viscoelastic material

The propagation of small-amplitude waves in a thick-walled long viscoelastic tube of variable cross-section, filled with a viscous incompressible fluid, is considered with account for wave reflection at the tube end in application to arterial pulse wave propagation. A solution is obtained in the form of expansions in a small parameter. The effect of the coefficient of wave reflection at the tube end and the wall material parameters on the fluid volume flow-rate and the tube wall displacement is investigated. It is shown that the volume flow-rate phase spectrum characteristics depend only slightly on the wall properties and can be used in clinical diagnostics for finding the reflection coefficient from pressure and flow-rate records.     

Shock wave propagation and interactions

激波的传播特性既取决于激波的产生条件,也与所处的传播环境密切相关.驱动条件、几何边界、介质的物理化学属性等发生变化时,都会引起激波传播特性的改变,而激波的变化反过来又会对其波及的流场产生影响.尽管激波传播及其干扰现象广泛存在于自然界和人类科技活动之中,其复杂机理的认识、规律的描述乃至应用潜力的挖掘仍有漫长的路要走.本文根据气体中激波传播和干扰现象以及与之相关的理论描述特征,在对激波传播以及反射、折射等基本现象进行简要阐述的基础上,重点围绕目前的热点问题,包括激波/激波干扰、激波/边界层干扰、激波与湍流作用、激波的聚焦与点火以及激波作用下气体界面不稳定性等研究进行了介绍和讨论,旨在对近年来该领域的进展及获得的成果做一个概述和归纳,期望对将来的深入研究有一个鉴借意义.     

On reflection of a planar solitary wave at a vertical wall

The reflection of a planar solitary wave at a vertical wall is investigated by solving the Boussinesq equations analytically as well as numerically. The analytical solution is obtained by means of the inner-outer expansions technique, while the numerical solution is based on a finite-difference scheme. The maximum wave amplitude at the wall and the time at which this maximum amplitude is reached are presented. It is also found that the incident wave does not reflect immediately at the wall as predicted by the linear wave theory. Rather, the wave suffers a time delay, called the phase lag, during the reflection process. This phase lag is found to be inversely proportional to the square root of the initial wave amplitude. As the reflected wave eventually propagates away from the wall, it has a phase shift in comparison with that obtained by the linear wave theory. The analytical results obtained in this paper are in good agreement with the numerical results, and they also agree fairly well with the existing experimental data.