Pressure Waves in a Gas–Liquid Medium with a Stratified Liquid–Bubbly Mixture Structure

Evolution and decay of pressure waves of moderate amplitude in a vertical shock tube filled by a gas–liquid medium with a nonuniform (stepwise) distribution of bubbles over the tube cross section are studied experimentally. The gas–liquid layer has the form of a ring located near the tube wall or the form of a gas–liquid column located in the center of the tube. It is shown that the nonuniformity of bubble distribution over the tube cross section increases the attenuation rate of pressure waves.     

Hydrodynamics of a bubble formed at vent pipe exit

In this paper, the hydrodynamics of a bubble formed during transient injection of air through a tube submerged in a pool of water has been studied. The experiments were performed by injecting air through vertical tubes varying in diameter from 0.9 to 9.5 cm and located in the middle of a 45 cm dia. and 120 cm high plexiglas chamber. The plexiglas chamber was partly filled with water and was open at the top to the outside. Data for bubble growth and vent line pressure histories are obtained under different upstream pressure conditions. Effect of presence of an orifice in the vent line on bubble growth has also been investigated.A theoretical model describing the bubble growth at the exit of a vent pipe submerged in a pool of water is developed. Predictions of bubble radius, line static pressure and uplift on the bottom of the test chamber have been made and are found to compare well with the data. Insertion of an orifice in the pipe line between the solenoid valve and the vent exit has been found to inhibit the bubble expansion as well as alter the bubble oscillation characteristics.     

Pressure Wave Evolution in a Fluid with a Bubble Zone

The specific features of pressure wave dynamics in a fluid containing a bubble zone are considered. It is found that for nonlinear waves the shielding effect of the bubble zone, typical of acoustic waves, is less pronounced. In some cases, due to the nonlinear effects and the radial inertia of the bubbly fluid [1], the bubble zone may result in a certain increase in the original-signal amplitude. It is shown that when a bubble screen is located near a solid surface, by choosing an appropriate bubble radius and volume fraction, it is possible to achieve (i) the absence of a reflected signal and (ii) substantial damping of the wave action on the wall.     

Boundary-layer transition on a cylinder with and without separation bubbles

Boundary layer transition with and without transitional separation bubbles was investigated on a cylinder in cross flow. Measurements of the pressure distribution and hot-wire measurements within the boundary layer were carried out at two free-stream velocities and with different flow disturbances. The separation bubble reacts very sensitively to changes in inlet turbulence. Tollmien-Schlichting waves were observed in the separated shear layer just before transition, and their frequencies were in good agreement with stability theory. However, correlations concerning bubble length which were fitted using airfoil data are apparently not suitable for describing separation bubbles on cylinders. Finally, measurements in periodically disturbed flow show how the bubble reacts to this type of disturbance.     

Dynamics of a Gas Bubble during Its Interaction with Compression and Rarefaction Waves

The problem of the passage of acoustic waves in the neighborhood of a gas bubble in a tube is formulated and solved numerically. The main parameters determining the bubble dynamics in a non-stationary field are determined. The mechanism of jet deformation of the bubble followed by jet fragmentation and formation of a secondary small-size bubble fraction is studied. A possible explanation of the nature of local sonoluminiscence is proposed.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 76–85, September–October, 2005.     

高速斜入水和水平入水气炮水箱实验系统

为开展模型高速斜入水和水中高速航行的水流场实验研究,研制了立式和卧式气炮与水箱组合的实验系统。通过快速阀和活塞阀控制气炮激发和驱动状态,一级气炮采用高压空气直接驱动弹托和模型,二级气炮采用高压空气驱动重活塞压缩使集气腔中产生高压气体,再驱动弹托和模型达到预定速度。通过调节水箱和发射管角度,使高速模型斜入水或水平入水。其中,立式可变发射角二级气炮可发射质量1～1000 g的模型至2500 m/s最大速度,卧式一级气炮可发射质量1～100 kg的模型至300 m/s最大速度。和小气室、高燃气压力火药驱动方式相比,新型气炮采用大体积、中低驱动压力气室,高压气体更接近等熵膨胀做功,调节高压气体压力,能较好地满足模型质量和速度的宽范围要求。结合光反射通断法测速、高速摄影和阴影流场显示等测量技术,得到立式气炮压缩管重活塞运动速度、压缩管末端压力时间曲线和模型倾斜与水平入水的流场阴影图像。结果表明:重活塞速度在膜片破裂前和理论计算值符合较好,但破膜后差异较大。立式气炮流场阴影图像反映了模型斜入水产生的空中和水中激波以及在气水界面的反射激波、空泡形成和侧向气水界面的破碎与飞溅等现象。从卧式气炮的模型水平入水阴影图像提取气泡轮廓,清楚地看出尾部气泡气水界面的波动和失稳。和商业计算软件Fluent计算结果相比,空泡上游区域基本重合,但尾流区域强湍流导致两者存在明显差异。和水洞实验相比,气炮水箱实验系统近真实地再现高速入水过程伴随的冲击和动态空化等物理现象和模型尺度效应。     

Experimental and numerical study on the growth and collapse of a bubble in a narrow tube

The growth, expansion and collapse of a bubble in a narrow tube are studied using both experiments and numerical simulations. In experiment, the bubble is generated by an electric spark in a water tank and recorded by a high-speed camera system. In numerical simulation, the evolution of the bubble is solved by adopting axisymmetric boundary integral equation, considering the surface tension effect. The results of experiments and numerical simulations are compared and good agreements are achieved. Both of them show that a counter-jet forms and penetrates the bubble at the end of the collapse stage, before a ring type bubble forms. Under the attraction of the tube wall due to Bjerknes force, a ring jet is generated, pointing towards the tube. On the basis of this, some physical quantities like the pressure on the tube wall and kinetic energy are calculated in a case study. The effects of tube diameters and tube lengths on the bubble’s behaviors are also investigated.     

Non-linear wave modulation in a prestressed viscoelastic thin tube filled with an inviscid fluid

In the present work, the propagation of weakly non-linear waves in a prestressed thin viscoelastic tube filled with an incompressible inviscid fluid is studied. Considering that the arteries are initially subjected to a large static transmural pressure P₀ and an axial stretch λ_z and, in the course of blood flow, a finite time-dependent displacement is added to this initial field, the governing non-linear equation of motion in the radial direction is obtained. Using the reductive perturbation technique, the propagation of weakly non-linear, dispersive and dissipative waves is examined and the evolution equations are obtained. Utilizing the same set of governing equations the amplitude modulation of weakly non-linear and dissipative but strongly dispersive waves is examined. The localized travelling wave solution to these field equations are also given.     

爆燃波在含内构件管道中传播现象的实验研究

为了评估高温气冷核反应堆热交换器H2泄漏、爆炸的安全性,研究含内构件管道的H2/空气爆燃传播现象,建造了几何相似、尺寸相同的实验管道（真空筒）。分别充入不同初压和当量比H2/空气混合物,在真空筒顶部点火并引发爆燃,利用多通道瞬态压力测量和数据采集系统,记录各测点压力时间曲线。结果表明:对化学计量比H2/空气混合物,在慢化剂室和真空筒顶部空间产生爆燃,邻近测点的压力时间曲线显示了冲击波特征。该冲击波通过慢化剂室和真空筒侧壁的狭缝（2.5 mm）,进入含内构件的扩张管道并形成爆燃。冲击波在真空筒端部反射、向后传播并与火焰相互作用,爆炸流场波系复杂。对富油和低初压化学计量比混合物,在慢化剂室和真空筒顶部空间产生燃烧,高温富油燃气的压力上升速率较慢。当燃气通过上述狭缝时,在真空筒突扩空间内再次点火并形成较强爆燃,压力时间曲线显示了冲击波特征及其在端面的反射。     

Propagation characteristics of pressure disturbances originated by gas jets in fluidized beds

An experimental investigation has been carried out on velocities and amplitudes of pressure disturbances in fluidized beds made of 100–200 μm glass ballotini. Disturbances were originated by gas jetting in a 0.35 m i.d. fluidized bed. A fluidization tube 0.10 m i.d. has also been used. Different types of disturbances have been induced in the bed contained in this tube: injection of a freely rising bubble and of a captive bubble; injection of a bubble chain; and compression of the bed free surface. The dynamic wave character of the disturbances has been shown. Velocities and amplitudes of waves moving through the beds have been measured. In particular, wave velocities have been compared with theoretical results obtained by the application of “pseudo-homogeneous” and “separated phase flow” models.     

Wave dispersion of a gas in a liquid

A novel method of dispersing a gas in a liquid by pressure pulses generated by waves propagating from a hydrodynamic oscillation generator is proposed. Devices that realize this method, wave dispersers, are created and investigated experimentally. The amplitude-frequency characteristics of the wave processes in the dispersers and the size distribution density functions of the gas bubbles are obtained. It is shown that there are optimal pressure values at the disperser inlet at which a minimum bubble size is achieved. The average diameter of the gas bubbles produced by water wave dispersers in the optimal operation regimes varied on the range from 0.3 to 0.6 mm, depending on the gas flow-rate.     

Potential flow around a deforming bubble in a Venturi

The differential pressure between the entrance and throat of a Venturi will fluctuate if the liquid flowing through the Venturi contains bubbles. This paper reports computations of the pressure fluctuation due to the passage of a single bubble. The liquid is assumed inviscid and its velocity, assumed irrotational, is computed by means of a boundary integral technique. The liquid velocity at the entrance to the Venturi is assumed constant and uniform across the pipe, as is the pressure at the outlet. The bubble is initially far upstream of the Venturi and moves with velocity equal to that of the liquid. Buoyancy is neglected. If the bubble is sufficiently small that interactions with the Venturi walls may be neglected, a simple one-dimensional model for the bubble velocity is in good agreement with the full boundary integral computations. The differential pressure (taken to be positive) decreases when the bubble enters the converging section of the Venturi, and then increases to a value higher than for liquid alone as the bubble passes the pressure measurement position within the throat. The changes can be estimated using the one-dimensional model, if the bubble is small. The bubble is initially spherical (due to surface tension) but is perturbed by the low pressure within the Venturi throat. In the absence of viscosity, the bubble oscillates after leaving the Venturi. The quadrupole oscillations of the bubble are similar in frequency to those of a bubble in unbounded fluid; the frequency of the monopole oscillations is modified by the presence of the pipe walls. Numerical results for the frequency of monopole oscillations of a bubble in a uniform tube of finite length are in good agreement with analytic predictions, as is the computed drift of the oscillating bubble.     

Waves in thin-walled elastic tubes containing an incompressible inviscid fluid

The effect of the non-linearity of the governing equations on the propagation of waves in fluid filled elastic tubes is investigated. Results are obtained by the method of characteristics for a particular form of pressure pulse applied at the end of a semi-infinite initially uniform tube. An expression is obtained for the distance along the tube at which shock formation is predicted. Two different hyperelastic materials whose elastic properties model those of biological tissue are considered for the tube walls. Numerical results are presented in graphical form.     

Interactions between a central bubble and a surrounding bubble cluster

The interaction of multiple bubbles is a complex physical problem. A simplified case of multiple bubbles is studied theoretically with a bubble located at the center of a circular bubble cluster. All bubbles in the cluster are equally spaced and own the same initial conditions as the central bubble. The unified theory for bubble dynamics [35] is applied to model the interaction between the central bubble and the circular bubble cluster. To account for the effect of the propagation time of pressure waves, the emission source of the wave is obtained by interpolating the physical information on the time axis. An underwater explosion experiment with two bubbles of different scales is used to validate the theoretical model. The effect of the bubble cluster with a variation in scale on the pulsation characteristics of the central bubble is studied.     

Appearance of Nucleation Shocks in a Boiling Liquid

Depressurization of high-pressure vessels filled with a liquid coming to the boil with a decrease in pressure is investigated. After depressurization, which takes less than 1 ms, a rarefaction wave propagates into the vessel. Experiments [1–5] demonstrated that the pressure behind the wave goes over to a constant value, which is independent of the vessel diameter and lies between the saturation point and atmospheric pressure.The correspondence between the experiments and different bubble formation theories (bubble formation on the vessel walls, due to rupture of the bonds between the water molecules or boiling on foreign particles) is analyzed. A “ mechanical nucleation” theory is proposed, in which it is assumed that the liquid comes to the boil on a limited number of foreign particles, and the bubbles formed on the nucleation centers undergo multiple fragmentation due to the instability developing under the action of centrifugal accelerations of the bubble surface in the course of bubble growth.The calculations demonstrated that, after depressurization, bubble fragmentation occurs at the vessel outlet. Due to the growth of the phase interface in the course of fragmentation, the boiling intensity increases, the pressure grows, and a shock wave propagates into the vessel, following the rarefaction wave. Multiple fragmentation of the bubbles occurs on the shock front. This wave is followed by a series of waves with smaller amplitudes. The pressure in the vessel attains a stable level, without any shocks. This level is characterized by the metastability or superheating of the liquid, i.e. the difference between the liquid temperature and the saturation point. It is demonstrated that the resultant pressure in the vessel is independent of the number of initial boiling centers or the initial pressure in the vessel and is determined only by the initial temperature. For water, the dependence of the superheating of the liquid on the initial temperature is found and compared with experimental data.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 103–117.Original Russian Text Copyright © 2005 by Ivashnev and Smirnov.     

Measurements with a flow direction boundary-layer probe in a two-dimensional laminar separation bubble

 Measurements with a directional sensitive hot-wire probe have been carried out in a two-dimensional laminar separation bubble caused by an adverse pressure gradient. The probe has three parallel, in plane wires and can be traversed in the boundary layer in all spatial directions. The central wire, operated as a conventional hot-wire in CTA mode, and two surrounding resistance wires measure the instantaneous magnitude and direction of the flow, respectively. The probe is calibrated and operated in a similar way as a single hot-wire probe for boundary layer measurements. The frequency response is high enough for measurements of naturally occurring instability waves in the bubble. The flow direction intermittency was measured inside the bubble and regions with reversed flow were mapped out. Prior to reattachment periodical oscillations of the flow direction are found associated with shedding of vortical structures from the bubble. Received: 13 March 1998/Accepted: 22 April 1998     

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.     

Forced nonlinear oscillations of a gas bubble in a large spherical flask (resonator) filled with a fluid

Radial oscillations of a gas bubble in a large spherical flask filled with a fluid are considered. We derive an equation of the change of the bubble radius by the known law of pressure variation at the boundary of the liquid volume (the law of motion of the piston) for a period of time during which, repeatedly reflected from the piston, the leading front of the reflected-from-the bubble perturbations reaches the bubble. For further calculations of the change of the bubble radius, recurrent relations which include the wave reflected from the bubble in the previous cycle and its subsequent reflection from the piston are obtained. Under harmonic action of the piston on the fluid-bubble system, a certain periodic regime with a package of bubble oscillations is established. Institute of Mechanics, Ural Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 77–87, September–October, 1998.     

Forced oscillations of a gas bubble in a spherical volume of a compressible liquid

A spherically symmetric problem of oscillations of a single gas bubble at the center of a spherical flask filled with a compressible liquid under the action of pressure oscillations on the flask wall is considered. A system of differential-difference equations is obtained that extends the Rayleigh-Plesset equation to the case of a compressible liquid and takes into account the pressure-wave reflection from the bubble and the flask wall. A linear analysis of solutions of this system of equations is performed for the case of harmonic oscillations of the bubble. Nonlinear resonance oscillations and nearly resonance nonharmonic oscillations of the bubble caused by harmonic pressure oscillations on the flask wall are analyzed. Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 111–118, March–April, 1999.     

Void fraction and pressure waves in a transient horizontal slug flow

The void fraction and the pressure waves in an air–water mixture flowing in the slug regime are experimentally investigated in a horizontal line. The test section is made of a transparent Plexiglas pipe with 26 mm ID and 26.24 m long, operating at ambient temperature and pressure. The flow induced transients are made by quickly changing the air or the water inlet velocity. The test grid has four operational points. This choice allows one to create expansion and compression waves due to the changes to the gas or to the liquid. Each experimental run is repeated 100 times to extract an ensemble average capable of filtering out the intrinsic flow intermittence and disclosing the void fraction and pressure waves’ features. The slug flow properties such as the bubble nose translational velocity, the lengths of liquid film underneath the bubble and the liquid slug are also measured. The objective of the work is two-fold: access the main characteristics of the void fraction and pressure waves and disclose the mechanics of the transient slug flow as described through the changes of the slug flow properties.