Effect of the initial pressure of multicomponent bubble media on the characteristics of detonation waves

The effect of the initial pressure of multicomponent bubble media on the conditions of initiation, the structure, the velocity, and the pressure of detonation waves is experimentally studied. The variation of the initial pressure of a bubble medium is found to be an effective method to control the parameters of bubble detonation waves.     

Calculation of shock wave propagation in water containing reactive gas bubbles

The entry of a shock wave from air into water containing reactive gas (stoichiometric acetylene–oxygen mixture) bubbles uniformly distributed over the volume of the liquid has been numerically investigated using equations describing two-phase compressible viscous reactive flow. It has been demonstrated that a steady-state supersonic self-sustaining reaction front with rapid and complete fuel burnout in the leading shock wave can propagate in this bubbly medium. This reaction front can be treated as a detonation-like front or “bubble detonation.” The calculated and measured velocities of the bubble detonation wave have been compared at initial gas volume fraction of 2 to 6%. The observed and calculated data are in satisfactory qualitative and quantitative agreement. The structure of the bubble detonation wave has been numerically studied. In this wave, the gas volume fraction behind the leading front is approximately 3–4 times higher than in the pressure wave that propagates in water with air bubbles when the other initial conditions are the same. The bubble detonation wave can form after the penetration of the shock wave to a small depth (~300 mm) into the column of the bubbly medium. The model suggested here can be used to find optimum conditions for maximizing the efficiency of momentum transfer from the pressure wave to the bubbly medium in promising hydrojet pulse detonation engines.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

Features of the dynamics of postdetonation waves

We present the results of numerical investigations of the parameters of postdetonation waves forming at a passage from the zone occupied with a bubbly liquid formed by the detonation wave to a zone filled with a liquid without bubbles. The dependence of the pressure amplitude of detonation waves and postdetonation waves on the gas volumetric content of bubbles has been studied. A possibility of the detonation transfer through the layer of a bubble-free liquid separating the regions of the bubbly liquid has been shown, the map of possible situations at the detonation transfer through the layer of this liquid has been presented.     

Influence of the initial pressure of polydisperse bubble media on characteristics of detonation waves

The influence of the initial pressure of polydisperse bubble media on the initiation conditions, structure, propagation velocity, and the pressure of detonation waves has been experimentally studied. It has been established that variations in the initial pressure of the bubble medium is an effective method of controlling the parameters of bubble detonation waves.     

Influence of the surrounding pressure on acoustic properties of slightly compressible porous media permeated with air-filled bubbles

The effective wave velocity, attenuation, and nonlinear properties of slightly compressible porous media permeated with air-filled bubbles are studied numerically by employing the nonlinear Hooke’s law for different surrounding pressures. Numerical simulations show that the acoustic properties of porous media are greatly affected by the surrounding pressure if the shear modulus of the elastic medium is very small due to the fact that the acoustic wave propagation in porous media are strongly influenced by the nonlinear oscillation of bubbles; moreover, the oscillation of a bubble depends on the equilibrium bubble radius, which is affected by the surrounding pressures. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 490–496. The text was submitted by the authors in English.     

Shock waves and formation of carbon dioxide hydrate at an increased pressure in the gas-liquid medium

The processes of breaking, solution, and formation of hydrates behind a shock wave of moderate amplitude were studied experimentally in water with carbon dioxide bubbles under different initial static pressures. It is shown that an increase in the static pressure in a gas-liquid medium leads to reduction of critical relative amplitude of the shock wave, corresponding to starting development of Kelvin — Helmholtz instability and bubble splitting into small gas inclusions behind the shock wave front. It is shown that the rates of carbon dioxide solution and hydrate formation behind the shock wave front are close by the value; their dependences on medium and wave parameters are determined. Calculations by the model of gas hydration behind the shock wave are presented. The work was financially supported by the Russian Foundation for Basic Research (grants Nos. 06-01-00142 and 06-08-00657).     

Influence of the Fluid on the Parameters and Limits of Bubble Detonation

The compression and inflammation of reactive gas bubbles in bubble detonation waves have been studied, and the considerable influence of the fluid (liquid or vapor) on the detonation parameters has been found. It has been shown numerically that the final values of the pressure and temperature significantly decrease if the temperature dependence of the adiabatic index is taken into account at the compression stage. The parameters of reactive gas combustion products in the bubble have been calculated in terms of an equilibrium model, and the influence of the fluid that remains in the bubble in the form of microdroplets and vapor on these parameters has been investigated.

     

Transformation of detonation waves at the interface between bubble media

The passage of detonation waves through the interface between bubble media is studied experimentally. Data are obtained for the structure, velocity, and pressure of an incident detonation wave and a wave transmitted through the interface.     

A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation

The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.     

流体/准饱和多孔介质中伪Scholte波的传播特性

研究流体/多孔介质界面Scholte波的传播特性对于水下勘探、地震工程等领域具有重要意义.本文基于Biot理论和等效流体模型,采用势函数方法,推导了描述有限厚度流体/准饱和多孔半空间远场界面波的特征方程和位移、孔压计算公式.在此基础上,分别以砂岩和松散沉积土为例,研究了流体/硬多孔介质和流体/软多孔介质两种情况下,可压缩流体层厚度和多孔介质饱和度对伪Scholte波传播特性的影响.结果表明：多孔介质软硬程度显著影响界面波的种类、相速度、位移和水压力分布;有限厚度流体/饱和多孔半空间界面处伪Scholte波相速度与界面波波长和流体厚度的比值有关;孔隙水中溶解的少量气体对剪切波的相速度的影响不大,对压缩波相速度、伪Scholte波相速度和孔隙水压力分布影响显著.     

Solution and hydrate formation behind a shock wave in liquid with nitrogen — carbon dioxide bubbles in a presence of surfactant

The processes of solution and hydrate formation behind a shock wave of moderate amplitude were studied experimentally in water with bubbles of nitrogen — carbon dioxide mixture at different initial static pressures in the medium and surfactant concentrations. It is shown that these bubbles do not affect significantly the processes of solution and hydrate formation behind a shock wave during the considered periods. The hypothesis about partial hydration of nitrogen from the gas mixture at intense formation of carbon dioxide hydrate was suggested for the conditions, when the pressure behind the wave is less than the equilibrium pressure of nitrogen hydrate formation at a given temperature. The work was financially supported by the President of RF (NSh-3417.2008.8) and Russian Foundation for Basic Research (Grant No. 06-08-00657).     

Radial oscillation and translational motion of a gas bubble in a micro-cavity

According to classical nucleation theory, a gas nucleus can grow into a cavitation bubble when the ambient pressure is negative. Here, the growth process of a gas nucleus in a micro-cavity was simplified to two “events”, and the full confinement effect of the surrounding medium of the cavity was considered by including the bulk modulus in the equation of state. The Rayleigh–Plesset-like equation of the cavitation bubble in the cavity was derived to model the radial oscillation and translational motion of the cavitation bubble in the local acoustic field. The numerical results show that the nucleation time of the cavitation bubble is sensitive to the initial position of the gas nucleus. The cavity size affects the duration of the radial oscillation of the cavitation bubble, where the duration is shorter for smaller cavities. The equilibrium radius of a cavitation bubble grown from a gas nucleus increases with increasing size of the cavity. There are two possible types of translational motion: reciprocal motion around the center of the cavity and motion toward the cavity wall. The growth process of gas nuclei into cavitation bubbles is also dependent on the compressibility of the surrounding medium and the magnitude of the negative pressure. Therefore, gas nuclei in a liquid cavity can be excited by acoustic waves to form cavitation bubbles, and the translational motion of the cavitation bubbles can be easily observed owing to the confining influence of the medium outside the cavity.     

Cavitation under spherical focusing of acoustic pulses

The early stage of the dynamics of interacting cavitation bubbles in a transmitted spherically focused pulsed wave consisting of compression and rarefaction phases is studied. The cavitation is investigated away from the liquid boundaries for negative pressures up to −42 MPa with a decrease rate of −40 MPa/μs by high-speed microscopic filming (100 million frames per second and a spatial resolution of 5–50μm/pixel) and pressure measurements. It is demonstrated that, according to the kinematics of size variation, the bubbles are separated into two fractions: expanding and collapsing ones. Experimental data provide grounds to assume that the formation of a two-fraction bubble cluster occurs on account of different threshold values of pressure in the rarefaction wave for two characteristic sizes of nuclei, namely, micronuclei (d _I < 10μm) and nanonuclei (“bubstons,” d _II ∼ 1 nm), which become detectable only when the rarefaction wave amplitude exceeds the critical one. Pulsed compression of small bubbles in the process of transformation of a rarefaction wave into a compression wave occurs under the effect of a cluster’s internal pressure up to 20 MPa and proceeds with the conservation of the spherical shape of the second-fraction bubbles. It is demonstrated that the velocity of the center of mass of a bubble reaches its peak value close to the moment of bubble collapse. The translational and radial dynamics of a bubble are studied in a numerical experiment using the Rayleigh-Plesset equation and taking into account the viscous force and the pressure gradient. The results of measuring the translational shift may be useful for estimating the minimum bubble radius by comparing the numerical results with the experiment.     

Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles

To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theoretically derived and numerically solved. The Zener viscoelastic model and Keller–Miksis bubble equation, which have been used for analyses of single or few bubbles in viscoelastic liquid, are used to model the liquid containing multiple bubbles. From the theoretical analysis based on the perturbation expansion with the multiple-scales method, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which has been used as a mathematical model of weakly nonlinear propagation in single phase liquid, is extended to viscoelastic liquid containing multiple bubbles. The results show that liquid elasticity decreases the magnitudes of the nonlinearity, dissipation, and dispersion of ultrasound and increases the phase velocity of the ultrasound and linear natural frequency of the bubble oscillation. From the numerical calculation of resultant KZK equation, the spatial distribution of the liquid pressure fluctuation for the focused ultrasound is obtained for cases in which the liquid is water or liver tissue. In addition, frequency analysis is carried out using the fast Fourier transform, and the generation of higher harmonic components is compared for water and liver tissue. The elasticity suppresses the generation of higher harmonic components and promotes the remnant of the fundamental frequency components. This indicates that the elasticity of liquid suppresses shock wave formation in practical applications.     

Propagation of pressure waves in a three-phase medium of cluster structure

The propagation of a step-shaped shock wave in a liquid is investigated experimentally. The liquid contains spherical three-phase clusters (liquid, solid balls, gas bubbles). A comparison of the experimental data on the velocity and wave structure with calculations with the use of the Boussinesq equation for a three-phase cluster medium is made. It is shown that the sound speed in a three-phase medium of cluster structure is higher than in a homogeneous three-phase medium.     

Generation of microbubbles from hollow cylindrical ultrasonic horn

In this study, we found that microbubbles with diameters of less than 100 μm can be easily generated by using a hollow cylindrical ultrasonic horn. Consecutive images of bubbles obtained by using high-speed and high-resolution cameras reveal that a capillary wave is formed on the gas–liquid interface under weak ultrasonic irradiation and that the wave head is detached in the form of bubbles by the fragmentation of the interface as the power of ultrasonic irradiation increases. Moreover, consecutive images of the bubble interface obtained by an ultra-high-speed camera indicate that the breakup of bubbles oscillating harmonically with the ultrasonic irradiation generates many microbubbles that are less than 100 μm in diameter. With regard to the orifice diameter of the horn end, we found that its optimum value varies with the ultrasonic power input. When the orifice diameter is small, the capillary wave generated from the horn end easily propagates all over the gas–liquid interface, thereby starting the generation of microbubbles at a lower ultrasonic power input. When the orifice diameter is large, the capillary wave is attenuated because of viscosity and surface tension. Hence, in this case, microbubble generation from the horn requires a higher ultrasonic power input. Furthermore, the maximum yield of microbubbles via primary and secondary bubble generation can be increased by increasing the gas flow rate.     

Cumulation processes in gravitational and inertial force fields and in zero gravity

The effect of gravitational and inertial forces on precision cumulation of fast flows of matter, bubbles, and detonation and shock waves is studied. Possible effects on the motion of masses and waves, whose velocity, direction, and structure change, and on the change in the properties of the medium in front of waves, causing the parameters of the waves to change and giving rise to refraction, are noted. The advantages of doing experiments with precision cumulation in zero gravity are indicated. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 748–751 (10 May 1996)     

Excitation of the acoustic and leaky waves in the atmosphere by a sub-surface seismic source

We study excitation of acoustic, leaky, and surface waves by a time-harmonic force source located in a homogeneous isotropic elastic half-space contacting a homogeneous gas. The force acts in the normal direction to the interface between the media. We consider the case where the sound velocity in the gas is less than the velocity of the Rayleigh wave propagating along the surface of the solid. An expression is derived for the period-averaged radiation power of the surface Stoneley wave. The total radiation power is calculated for the acoustic wave in the gas and for the leaky pseudo-Rayleigh wave. Variations in the radiation powers of the surface and leaky waves are analyzed as functions of the source depth. If the velocities of compressional and shear waves in the elastic medium significantly exceed the sound velocity in the gas, then the radiation power of the Stoneley wave turns out to be a factor of 10⁶–10⁸ smaller than the radiation powers of other waves. The radiation power of the Stoneley wave decreases monotonically with increasing source depth, and the decrease becomes more pronounced with the increase in the difference between the acoustic impedances of the contacting media. If the shear-wave velocity in the solid is close to the sound velocity in the gas, then the radiation power of the Stoneley wave is comparable with the radiation powers of other waves and exhibits maximum at a certain source depth. For some parameters of the gas and the solid, and for certain source depths, the Stoneley wave carries away more than a half of the total radiation power. It is shown that, for certain relations between the parameters of the media, the radiation power of the Stoneley wave increases due to redistribution of the radiated power from the pseudo-Rayleigh leaky wave. The total power of these waves remains approximatly constant and, with accuracy of the order of 10⁻³, is equal to the radiation power of the Rayleigh wave at the vacuum-solid interface. It is shown that the acoustic-wave power which can be transmitted to the upper layers of the atmosphere during an earthquake does not exceed 0.01% of the total power radiated at a given frequency. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 577–592, July 2006.