Shock-Induced Borehole Waves and Fracture Effects

We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section, the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves.     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

On the theory of seepage waves of pressure in a fracture in a porous permeable medium

Seepage pressure waves in fractures in a porous permeable medium are studied. The effects of the reservoir and fracture porosity and permeability, the fracture width, and the rheological properties of the saturating fluid on the perturbation dynamics in the fracture are analyzed. It is shown that in porous permeable reservoirs, fractures are wave channels through which low-frequency fluctuations of borehole pressure propagate. Accurate solutions are obtained which describe the evolution of pressure fields in a fracture with an instantaneous change in the borehole pressure by a constant value. Based on these solutions, dependences of the fluid flow rate on time and interface pressure are determined.     

Experimental study of toroidal shock wave focusing in a compact vertical annular diaphragmless shock tube

The paper reports results of experiments regarding toroidal shock wave focusing in a vertical shock tube as a part of a series of converging shock wave studies. This compact vertical shock tube was designed to achieve a high degree of reproducibility with minimum shock formation distance by adopting a diaphragmless operating system. The shock tube was manufactured in the Institute of Fluid Science, Tohoku University. An aspheric lens shaped cylindrical test section was connected at the open end of the shock tube to visualize the diffraction and focusing of the toroidal shock wave released from the ring shaped shock tube opening. Pressure transducers were flush mounted on the shock tube’s test section to measure pressure histories at the converging test section. Double exposure holographic interferometry was employed to quantitatively visualize the shock waves. The whole sequence of toroidal shock wave diffraction, focusing, and its reflection from the symmetrical axis were successfully studied. The transition of reflected shock waves was observed.     

气相爆轰波绕射流场显示研究

采用基于红宝石激光器（波长694.3 nm）的纹影系统,对气相爆轰波绕射进行了初步的流场显示研究。采用单色激光和合适半带宽（15 nm）的滤光片,有效地消除了爆轰波自发光对流场显示的影响。合理设置激光器同步控制系统的触发延时,得到了序列的爆轰波阵面纹影照片。结果表明:图像清晰地显示了爆轰波阵面的诱导激波、横波及化学反应区。当爆轰波在左尖点处绕射,受稀疏波作用,诱导激波与化学反应区明显分离,导致爆轰波衰减为爆燃。分离的诱导激波和折皱的化学反应区在纹影图上清晰可见。诱导激波在垂直支管右壁面反射,诱导二次起爆。畸变爆轰波在水平和垂直支管中均发生马赫反射。提高初压,爆轰波受分叉口几何属性的影响减小,畸变爆轰波在水平和垂直支管下游较易恢复为自持爆轰波。     

Reflection and Transmission of Elastic Waves at the Interface Between Water and a Double Porosity Solid

The reflection and transmission of an incident plane wave at an interface between water and a fluid-saturated double porosity solid are investigated. The properties of the three compressional waves and one shear wave in double porosity media are discussed in detail. The effect of the viscosity, permeability, and porosity on the phase velocity and attenuation of four bulk waves is presented. Comparison between the double porosity theory and the Biot theory reveals that there exists obvious difference in the phase velocity, attenuation and the reflection and transmission coefficients. Two cases of boundary conditions, i.e., the sealed-pore and the open-pore boundaries, are introduced in the numerical calculation. At last, the effect of the fracture permeability and porosity on the reflection and transmission coefficients considered. It is revealed that the amplitudes of the reflected and transmitted waves strongly depend the boundary condition, fracture permeability, and porosity.     

连续分层流体中垂直薄板的水动力特性

研究了在线性连续分层流体中水波与半潜式刚性垂直薄板相互作用的问题. 在 Boussinesq近似下，基于分离变量法，导出了具有自由面的平面前进波的色散关系，建立 了半潜式刚性垂直薄板的反射与透射能量、水平波浪力的计算方法. 对给定的频率，当它大 于浮力频率时，流场中只有一种模态的平面前进波，当它小于浮力频率时，流场 中有无数多个模态的平面前进波，并证明了对每一种模态的入射波，其它每个模态水波的反射与透射能量是 相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量，以及作用在薄板上的水平波浪力 进行了数值计算分析，表明了流体的线性连续分层效应对这些水动力的影响是不可忽视 的. 特别地，在入射波频率小于浮力频率时，与第1模态入射波的能量转化量及其对薄板产 生的水平波浪力相比，其它模态入射波的能量转化量及其对薄板产生的水平波浪力都要大得 多.     

Fractured water injection wells: Pressure transient analysis

In this paper we study the pressure drop in a hydraulic fracture after shut-in of a water injection well. The pressure transient behavior depends on fracture closure, lateral stress, rock elasticity and fracture fluid leak-off. Under the assumption that horizontal cross-sections of a vertical fracture do not depend on the vertical variable, we formulate a mathematical model which allows for determination of both pore pressure and elastic rock displacements jointly with the fracture aperture and fracture fluid pressure. An analytical consideration is performed for the case of an ideal very long fracture with the same aperture along its full length. In the general case, fracture closure is analyzed numerically.     

Propagation of a pressure wave in two-phase flow with very high void fraction

An experimental and theoretical study of a finite amplitude pressure wave propagating through a two-phase media of about 0.9999–0.99999 void fraction is performed. This two-phase media consists of many parallel liquid films in a gas. The films are perpendicular to the wave propagation direction and result in a two-phase fluid of extremely high void fraction. Experiments are done in a vertical shock tube and show that the shock wave is broken down into an initial sharply rising wave and a second gradually rising wave. The velocity of the first wave agrees well with the theoretical prediction assuming an adiabatic thermal equilibrium change, which approaches the gas sonic velocity in the two-phase flow in the low void fraction region. The second wave is caused by the complex reflection and destruction of the waves.     

Propagation of surface waves in a half-space with vertical,inclined or curved interfaces

The paper reviews the author's theoretical studies on reflection and transmission of surface waves at vertical and near-vertical boundaries. For estimation of reflection and transmission coefficients a new approximate method based on the Green function technique is proposed. The method is valid if a body waves field arised at the boundary is approximately orthogonal to the fields of reflected and transmitted normal modes. It may be used for normal as well as for oblique incidence. A Green function in each quarterspace is assumed to be the same as in a halfspace with the same vertical distribution of elastic parameters. For large angles of incidence when the reflected wave field is strong enough, the Green function may be corrected for the reflected wave. The results of calculation for some models by means of this method are discussed.     

The interaction of surface waves with fixed semi immersed cylinders having symmetric cross sections

The reflection of water waves by a semi immersed cylinder having a symmetric cross section is studied for both Dirichlet and Neumann boundary conditions on the cylinder. The method of conformal transformations as utilized by Ursell and by Tasai for the radiation problem is adapted to the present diffraction problem. The problem is solved by expansions of the reflected wave potential using nonorthogonal functions (wave free potentials). These functions are not complete, and an additional source and a dipole are required. Infinite systems of linear equations are obtained for the unknown expansion coefficients and the unknown strengths of the source and the dipole terms. Numerical results are obtained for the reflection coefficient, transmission coefficient, horizontal force on cylinder, vertical force on cylinder. In the long wave region analytical approximations are obtained for these functions when the cross section is circular. The reflection and transmission coefficients are very different for the two boundary conditions in the long wave region, the Dirichlet reflection coefficient being much larger than the corresponding Neumann coefficient. This behavior is similar to acoustic and electromagnetic diffraction problems in two dimensions. On leave of absence from Itek Corporation, Lexington (Mass.), U.S.A.     

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.     

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     

两层流体中水波在垂直薄板上的反射与透射

研究在两层流体中表面波模态和内波模态的波浪与半潜式刚性垂直薄板 相互作用的问题. 基于特征函数展开理论，建立了两种模态入射波作用下，半潜式刚性垂直 薄板的反射与透射能量的计算方法，证明了对每一种模态的入射波，另一种模态波浪的反射 与透射能量是相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量，以及作用在其上的 水平波浪力进行了数值计算分析，表明在某个频率范围内，流体的分层效应对这些水动力 量的影响是不可忽视的. 特别地，当薄板的一端位于两层流体的内界面上时，两种模态波浪 的能量转化是最大的.     

波在双孔隙与单孔隙介质界面上的反射与透射

基于Biot理论和双重孔隙介质理论研究了弹性波在双重孔隙介质与流体饱和单一孔隙介质 界面的反射和透射问题，在界面上假定裂缝孔隙流体相对于固体骨架的位移为零，推导了反 射系数和透射系数的计算公式，数值讨论了反射系数和透射系数随入射角和频率的变化关 系. 同时，讨论了双重孔隙介质中3种压缩波(P-1, P-2和P-3波)和一种剪切波(S波) 的频散和衰减特性.     

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.     

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.     

A model for the scattering of long waves by slotted breakwaters in the presence of currents

Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwaters are investigated by using a simple model. The model is based on a long wave approximation. The effects of wave height, barrier geometry and current strength on the reflection and transmission coefficients are examined by the model. The model results are compared with recent experimental data. It is found that both the wave-following and wave-opposing currents can increase the reflection coefficient and reduce the transmission coefficient. The model can be used to study the interaction between long waves and slotted breakwaters in coastal waters. The project partially supported by the Hong Kong Research Grant Council under Grant No. HKUST-DAG03/04.EG39 and HKUST6227/04E.     

金属材料SHPB实验数据处理的三波校核法

通过自编程序调整入射波、透射波和反射波的相对位置。当移动波相对位置时,程序界面显示2 幅图:一幅显示入射波、透射波、反射波以及透射波与反射波之差;另一幅显示试样的3条应力应变。这3条 曲线分别由第1幅图中的入射波与透射波、入射波与反射波以及三波法求得。根据SHPB实验的基本假定, 这3条应力应变曲线的塑性段应该一致,同时透射波与入射波之差应等于反射波,把这2个等价的特点作为 正确处理SHPB实验数据标准的方法称为三波校核法。     

小不耦合系数装药爆破孔壁压力峰值计算方法

基于轮廓爆破孔壁压力峰值计算方法的相关研究,充分考虑空气冲击波的传播与爆轰产物膨胀的过程,理论分析了小不耦合系数装药爆破过程中空气冲击波与炮孔壁的相互作用,建立了三维空气介质径向不耦合装药单孔爆破有限元模型,研究了工程爆破中常用的多种小不耦合系数装药组合工况下,炸药单点起爆后的炮孔壁压力峰值,并获得了相应工况下的孔壁压力峰值较爆生气体准静态等熵膨胀压力的压力增大倍数。结果表明:小不耦合系数装药爆破过程中,爆轰产物参数会对空气冲击波波后物质参数产生显著影响,揭示了小不耦合系数装药爆破与轮廓爆破在孔壁压力峰值计算方法上的本质差异;柱状装药结构爆轰波沿轴向传播使得空气冲击波撞击炮孔壁时存在叠加效应,孔壁压力峰值也相应增大,通过统计分析不同炸药类型、不同岩石类型工况下压力增大倍数与不耦合系数的关系,发现压力增大倍数随不耦合系数的增大近似呈线性增长;基于理论推导结果及常用爆破孔壁压力峰值计算形式,综合考虑炸药性能、孔壁岩石介质条件、不耦合装药系数对空气冲击波撞击炮孔壁后压力增大倍数的影响,提出了不耦合系数较小时爆破孔壁压力峰值计算方法。