On the propagation of acoustic energy in the vicinity of a bubble chain

Abstract

In this paper, experimental data on the propagation of acoustic energy in the vicinity of a vertical chain of discrete air bubbles are presented. The acoustic energy was created naturally during the formation of each bubble at the bottom of the chain. Previous work has reported that the root-mean-squared pressure distribution is highly anisotropic in the vicinity of a bubble chain. A new experimental set-up has been developed to obtain ‘snapshots’ of the instantaneous acoustic pressure field using a triggering technique with two hydrophones. This methodology allowed coordinated measurement of the acoustic signal in the near and far field and the data were used to construct the instantaneous spatial distribution of acoustic energy around the bubble chains. The results show that the phase speed in the direction of the bubble chain has values substantially lower than the speed of sound in pure water. Bubble chains of different configurations were investigated and it was found that this speed of propagation is reduced for chains consisting of larger and more closely spaced bubbles.

Introduction

Acoustic energy is capable of being transmitted through the sea to distances that are significant to oceanographic and marine exploration [1], [2], [3]. Because of this, sound is used for underwater communications, antisubmarine warfare, and underwater navigation. The large difference in characteristic impedance between the air and the water make bubbles very efficient as reflectors of acoustic energy in water. Very little sound will penetrate a curtain of air bubbles, making them very effective as camouflage for noise sources. A single bubble has little impact on the transmission of sound, but an assembly of bubbles introduces significant changes to the acoustic properties of the host medium [4], [5]. When sound traverses a cluster of bubbles, every bubble produces a secondary scattered wave and these waves reinforce in some directions and interfere in others [6], [7]; this gives rise to coherent, incoherent, and multiple scattering.

The size and distribution of bubbles in the medium has a strong influence on physical properties of the system, such as the rate of gas–liquid mass transfer [8], [9], [10] or the energy dissipation of ocean breakers [11]. In active bubble acoustics, sound is sent into the system and the propagation of the resulting signals is interpreted to infer the bubble-size distribution or other properties of the system. The ‘continuum’ (averaged) acoustic properties of bubbly flows [12] have been the basis of several instruments for oceanographic and industrial applications [13], [14], [15], [16], [17] although none are in widespread use. An obvious limitation of these theories is the assumption that the bubbles are uniformly distributed. In reality, the distribution of bubbles in a liquid is rarely isotropic or homogeneous and thus the propagation of sound is rarely isotropic. Even in passive or ‘listening’ systems, sound could be more efficiently channelled along chains of bubbles [18], impairing interpretation of the data when there is a non-isotropic distribution of bubbles. Hence, a better understanding of the variation of sound speed in a complex bubbly flow could lead to better instruments for industrial and oceanographic applications. For completeness, it must be mentioned here that the bubble chain also exhibits many interesting hydrodynamic properties and the hydrodynamic stability of bubble chains has been investigated by Ruzicka [19].

The choice of the appropriate theoretical model for the acoustic field of a bubble chain system is a topic that has been investigated by many researchers, focussing primarily on coupled-oscillator approximations. Important works include those of Zabolotskaya [20], Ogũz and Prosperetti [21], Doinikov and Zavtrak [22], Tolstoy [23], [24], Feuillade [6], [25] and Ida [26]. From a theoretical point of view there have been a number of earlier works on the behaviour of different configurations of bubble systems [27], [28]. In 1966, Weston [29] first considered the frequency response of a line of air bubbles. He derived approximate formulas for sound scattered by an air-bubble as a cell of an array and predicted that the line array of bubbles displays properties like a cylindrical bubble; this work was continued by Tolstoy [23]. Later, bubbles embedded in a line array were also numerically studied by Feuillade [30] and Tolstoy [24]. The emergence of super- and quasi-resonances was a new phenomenon associated with the line and plane structures [23], [25] predicting that enhanced resonances can be observed in these bubble systems. The models have been validated for the two and three bubble case by comparing the predicted natural frequencies with experimental data [31], [32].

Few cases of more than two bubbles (distributed in an anisotropic fashion) have been studied. Manasseh et al. [18] reported an anisotropic sound field around a bubble chain by simply comparing rms pressures along horizontal and vertical lines, and suggested that a coupled-oscillator model could qualitatively explain the anisotropy. Doinikov et al. [33] subsequently improved the comparison with experiment by introducing time delays to the model.

It is well known that the speed of sound in a bubbly medium can be dramatically reduced from the speed in pure water [34], based simply on the averaged compressibility and density of an air–water mixture. Much work (e.g. Ref. [12]) has been done to predict sound speeds in homogenous bubbly media where bubble resonances are also taken into account. Even though there has been many theoretical models predicting the frequency response of discrete bubbly systems, the authors are unaware of any experimental studies on the channelling of acoustic energy and the propagation speed of this energy near discrete anisotropic bubbly structures. In the system investigated here, the bubbles are arranged in an almost vertical line and they originate from a nozzle at the bottom of the bubble chain. Acoustic energy is generated when a bubble detaches at the nozzle and this energy is guided along the chain of discrete bubbles. The energy is in the form of a discrete pulse of sound that typically dies off in 10–20 ms, and depending on the bubble production rate (BPR), these pulses are typically separated by 30–100 ms, so that the pulses never overlap. This paper provides high-resolution experimental data showing instantaneous snapshots of the spatial distribution of the acoustic energy around the bubble chain. The data were obtained by a new experimental system using a coordinated robotic traverse and acoustically triggered data acquisition system.

In summary, the phenomenon of anisotropic sound propagation along a bubble chain is a special case of a more general situation in which sound propagates through a medium in which bubbles are distributed inhomogeneously. It is possible to model the acoustics of arrays of finite numbers of bubbles by reducing the equations of motion to a set of coupled oscillators [6], [20], [25], [26]. Furthermore, Manasseh et al. [18] and Doinikov et al. [33] showed that a bubble chain transmits sound anisotropically because the coupled oscillators effectively behave like a set of masses hanging on springs. If the oscillators are arranged in a line and all connected together, a point vibration initiated at one end travels to the other end without the reduction in amplitude that spherical propagation from a point source normally entails. Each bubble re-radiates sound as the disturbance passes and the result is an anisotropic sound field with the sound very efficiently ‘channelled’ along the chain. In the present experiments, as in Refs. [17], [18], [33], [36], [37], the exciting signal is provided naturally by the formation sound of each bubble at the base of the chain.

The first part of this paper will describe in detail the characteristics of the measurement system designed for this purpose. The second part will concentrate on the acoustic variables measured for several different bubble chain configurations generated by two different sized nozzles and at different airflow rates. Finally, data on the propagation of acoustic energy and sound attenuation along the bubble chain will be summarized.