Underwater Gas Bubble Research Articles

Generation of underwater discharges inside gas bubbles using a 30-needles-to-plate electrode

Underwater discharges inside helium (He) gas bubbles were generated using a 30-needles-to-plate electrode system with the gas flowing through the needles. The set-up allows continuous treatment of flowing water. The plasma electron temperature and density determined from spectral line intensities and profiles of the Hα and Hβ hydrogen lines were found to be 1.1 ± 0.6 eV and ∼5 × 1016 cm−3, respectively. These parameters are comparable with those of plasmas generated by other underwater gas bubble discharges for the production of OH radicals. The two main long-lived species, hydrogen peroxide (H2O2) and nitrate ions (NO3−), produced in plasma treated water were measured. It was found that without a continuous water flow, the energy yield of H2O2 was comparable with other underwater discharges, while with a continuous flow, the production of H2O2 appeared to be somewhat reduced by nitrites from dissolved air.

Modeling the Effect of Underwater Explosion on a Submerged Plate Structure

Abstract The experiments have determined that, even close to the detonating underwater charge, the gas bubble and shock wave are sufficiently separated to produce individual effects on plane structures. These results allow evaluating the shock wave parameters and the effects of these two phenomena to be studied separately. This paper focuses on the numerical modeling of the underwater gas bubble effect on submerged plate. We consider a plane structure made from ideal rigid-plastic material. An interaction between underwater explosion and plate will be analytically studied to obtain the equation governing the fluid force per unit length of the structure and the fluid – plane structure interaction equation. The time variation of the gas bubble radius and the explosion magnitude is graphically shown. The interaction between underwater explosion and a submerged flat structure will be simulated.

Propagation of Underwater Shock Wave and Gas Bubble Behavior Induced by Electrical Discharge in Water

The basic behavior during underwater electrical discharge up to 10 kJ stored energy is investigated through both numerical analysis and optical-observation experiments. Since the authors have been investigating the use of underwater exploding phenomena for food processing and other applications, it is necessary to know the whole process which may affect the quality of the samples recovered. In the present investigation, the propagation of underwater shock wave was measured using a high-speed camera and compared with the numerically simulated results using LS-DYNA. Also, the motion of gas bubble, which is induced quite after the propagation of the shock wave, was measured and compared with the numerical simulation using the same code. The pressure of the bubble is not such high as the shock wave, but it is known that the impulse is not possible to be ignored due to its relatively long duration of the pressurization. Through a series of optical-observation experiments, it is confirmed that the numerical simulation is potentially possible to predict the whole phenomena for processing foods and other materials.

Plasma formation in underwater gas bubbles

The generation of plasma in underwater gas bubbles offers the potential to produce large volume plasma in water while minimizing electrode erosion. Such attributes are desirable for the design of plasma-based water purification systems. In this work, gas bubbles of diameter 0.4–0.7 mm were trapped in the node of a 26.4 kHz underwater acoustic standing wave and pulsed with voltages in the range 10–14 kV. Plasma formation in trapped, isolated bubbles was observed to occur through two separate pathways: (1) plasma generated in the bubble through impact by a liquid streamer and (2) plasma generated in the bubble due solely to the applied electric field. The former case demonstrates the mechanism of so-called streamer hopping in which the discharge transitions from a water streamer to a gaseous surface streamer. Perturbations of the bubble's fluid boundary due to the streamer are also discussed.

Growth of a gas bubble in a supersaturated and slightly compressible liquid at low Mach number

In this paper, the growth of a gas bubble in a supersaturated and slightly compressible liquid is discussed. The mathematical model is solved analytically by using the modified Plesset and Zwick method. The growth process is affected by: sonic speed in the liquid, polytropic exponent, diffusion coefficient, initial concentration difference, surface tension, viscosity, adjustment factor and void fraction. The famous formula of Plesset and Zwick is produced as a special case of the result at some values of the adjustment factor. Moreover, the resultant formula is implemented to the case of the growth of underwater gas bubble.

Dynamic plastic response of a submerged free-free beam to an underwater gas bubble

The dynamic plastic response of a submerged free-free beam to an underwater explosion bubble is studied in this paper. A fluid-structure analysis is given to find the fluid force acting on the beam. Assuming that the beam is made from rigid, perfectly plastic material, we obtain the hydroplastic equation governing the dynamic plastic deflection of such a beam. The equation is analytically solved. Examples are given to discuss the features of the dynamic plastic response. It is observed that longer beams sustain larger plastic deformations than shorter beams, but shorter beams undergo larger rigid body motion than longer beams. Most of energy is consumed on plastic deformation rather than on rigid body motion. It is impossible, however, for more than three hinges to form on the beam.

A comprehensive method for evaluating the design of air guns and air gun arrays

Since the early days of marine seismic exploration, geophysicists have had to contend with the seismic effects of underwater gas bubbles generated by their energy sources. To hope to control the pressure waves emanating from the oscillating bubbles, geophysicists need to understand the physics of the bubbles, including not only the motions themselves but also the mechanisms that can create them. This need has persisted for all types of underwater sources, particularly so for the air gun array — the source most widely used today. Even though air guns have been in use for many years, the physics of their behavior is still undergoing research.

Effect of a dense gas equation of state on the expansion and contraction of an underwater gas bubble

At the high pressure believed to occur in underwater explosion gases, and in cavitation gas bubble collapse, deviations from an ideal gas must be considered. A theoretical investigation into the effect of a simplified dense gas equation of state on underwater gas bubble dynamics is presented. Our approach is to make a direct comparison between ideal and dense gas results. First, the lossless, incompressible liquid case is analyzed. The requirement of a realistic equation of state yields some startling results, placing severe bounds on some of the key parameters: the peak bubble pressure, the maximum bubble wall velocity, and the minimum bubble radius. Next, nonviscous energy losses are discussed. A generalization of the Herring method is used for approximate evaluation of the radiation‐loss integral derived from the Kirkwood–Bethe equation. These calculations appear to give physically reasonable loss estimates under both the ideal and dense gas assumptions. Also, an often‐quoted formula for the acoustic radiation loss has been found to be in error and has been corrected. For ease in calculation of some of the important quantities of interest, useful graphs and formulas have been presented.Subject Classification: 30.60, 30.75; 25.60.

Effect of a dense gas equation of state on the expansion and contraction of an underwater gas bubble

At the high pressure believed to occur in underwater explosion gases, and in cavitation bubble collapse, deviations from an ideal gas much be considered. A theoretical investigation into the effect of a simplified dense gas equation of state on underwater gas bubble dynamics is presented. Our approach is to make a direct comparison between ideal and dense gas results. First, the lossless, incompressible liquid case is analyzed. The requirement of a realistic equation of state yields some startling results, placing severe bounds on some of the key parametrs: the peak bubble pressure, the maximum bubble wall velocity, and the minimum bubble radius. Next, nonviscous energy losses are discussed. A generalization of the Herring technique is used for approximate evaluation of the radiation loss integral derived from the Kirkwood-Bethe equation. These calculations appear to give physically reasonable loss estimates under both the ideal and dense gas assumptions. Also, an oft-quoted formula for the acoustic radiation loss has been found to be in error and has been corrected.

Energy Losses from Large- and Small-Amplitude Underwater Gas Bubble Oscillations Compared

It is an experimental fact that the period of oscillation of successive bubbles from an underwater explosion decreases. In a typical sequence, the bubble starts out as a large-amplitude nonlinear pulsation and ends up as a small-amplitude linear oscillation about the equilibrium radius. This effect is attributed to the bubble energy losses since in the incompressible no-loss treatment, successive pulsations have the same period. Thus losses cause a decrease in the period of large-amplitude pulsations; but, conversely, analysis reveals that when losses are taken into account, the small-amplitude oscillation period shows an increase relative to the lossless case. Hence it appears that the loss mechanism has an opposite effect on the bubble pulse period in the cases of nonlinear and linear bubble pulse oscillations, respectively.

Expansion and Contraction of Planar, Cylindrical, and Spherical Underwater Gas Bubbles

The one-dimensional motion of a planar gas bubble, the axially symmetric motion of a cylindrical bubble, and the spherically symmetric motion of a spherical bubble in a liquid are considered. Following J. B. Keller and I. I. Kolodner [J. Appl. Phys. 27, 1152–1161 (1956)], the velocity potential in the liquid is assumed to satisfy the wave equation, while the pressure is assumed to be uniform throughout the bubble. In each case there is an equilibrium bubble radius ā. First the small-amplitude motions about equilibrium are found. In the planar case the bubble radius a (t) tends monotonically to ā; in the cylindrical case a (t) performs a finite number of damped oscillations and then tends monotonically to ā; and in the spherical case a (t) tends in an oscillatory way to ā. Next, large-amplitude motions are treated. In the planar case they are determined analytically and it is found that a (t) still tends monotonically to ā. In the spherical case an ordinary differential equation is derived for a (t) which has been solved numerically by Keller and Kolodner (op. cit.), and which yields damped oscillations. In the cylindrical case a pair of nonlinear integrodifferential equations is derived for a (t) and for the velocity potential. These equations are solved numerically and yield a finite number of oscillations followed by a monotonic approach to equilibrium, in agreement with the small-amplitude theory.

Finite- and Small-Amplitude Underwater Gas Bubble Oscillations Compared

Underwater gas bubble expansion as a function of the ambient-pressure to bubble-pressure ratio p′, in the interval 0⩽p′⩽1, is investigated. At the endpoints, a simple analytic solution to the nonlinear equations of motion in closed form may be found; but, for intermediate values of p′, an approximation is required. In the noncompressive case, representations suitable for large bubble radii, near p′=0, and small-amplitude motion, near p′=1, are derived. A result of this analysis is that the Willis bubble pulse formula, correct in the limit p′ → 0, in agreement with experiment, appears to be valid over much of the interval, but it starts to break down as p′ → 1. The power law governing finite- and small-amplitude periods is different; the actual period has no simple power law dependence, but may be deduced for all p′ by fitting a curve to the asymptotically correct values at p′=0 and p′=1, respectively. Owing to radiation and other loss mechanisms, bubble starting out as finite-amplitude pulsation, with a cusplike shape at the minimum, is gradually transformed into a small-amplitude damped sine wave; concurrently T1 → T̄. (Analysis in this paper refers to case γ = 43.)

Finite and Small Amplitude Underwater Gas Bubble Oscillations Compared

Bubble oscillation is well described by the nonlinear Keller-Kolodner equation. Although compressibility effects, which strongly influence the motion, are considered, analysis starts with incompressible approximation. The key parameter is p1/p0, the ambient/bubble pressure ratio. This ranges from zero to unity; near the lower limit finite amplitude pulsations occur; near the upper, simple harmonic motion ensues. The equation determining the maximum and minimum bubble radii, with p1/p0 as parameter, is graphed; these endpoints coalesce at a level where p1/p0 = 1. Further, taking compressibility into account, at each depth the end-points also converge to an equilibrium radius. T̄ has a simple power law dependence on p1/p0; this is generally not true for the finite amplitude period T1. The curves for T̄ and T1, as calculated from the Willis formula, cross; hence the actual T1 vs depth may be inferred. The shape of the bubble radius vs time curve changes from pulsation to simple oscillation with depth; this is asymptotically correct at any level, since T1 → T̄.

Expansion of an Underwater Cylinderical Gas Bubble

The theory of the expansion of an underwater spherical gas bubble is rather well known; in this paper the theory for cylindrical gas bubbles is developed. It is customary to treat the motion of the fluid in the incompressible approximation, but this procedure leads to difficulties in the cylindrical case owing to the potential's becoming infinite as r approaches infinity. Therefore, the fluid is treated as compressible, and equations for the bubble radius and the radiated pressure as functions of time are derived. Then these equations are examined in the limit of large speed of sound. Approximate equations obtained by employing simplifying assumptions are analyzed, and the properties of the motion discussed.

A theoretical treatment of combustion in a spherical underwater gas bubble

The combustion equations and the equation of motion of the surface of the bubble are formulated on the assumptions that the gases are ignited at their centre and that the flame front travels outward in the form of a sphere. The equations are integrated to yield gas pressure and bubble radius as functions of time. Provided that radial displacements are small, the flame speed can be assumed constant. The formulation is then simple and the equations can be integrated in closed form to give general non-dimensional solutions. These show that pressure and radius increase at an increasing rate until combustion is complete. Radial oscillations ensue whose amplitude in proportion to the initial radius decreases with increase in the ratio of combustion time to oscillation period. For large radial displacements, the formulation is less simple as finite expansion of the burnt gases at the expense of the unburnt gases is involved, which enhances the flame speed. The effect has already been considered for com­bustion in a closed spherical vessel (Flamm & Mache 1917), and an important approximate relation between the fraction of gas burned and the pressure rise has been derived: n = (p — P 0 )/(P — P 0 ), where n is the fraction of gas burned, p is the corresponding pressure an d P an d P 0 are respectively the final and initial pressures. The analysis of Flamm & Mache, which is in any case not entirely satisfactory, cannot be used if the total gas volume varies, as in the present instance. An energy method has, however, been found to give the required relation (and incidentally to afford a simpler, more rigorous proof of the closed vessel relation and am easure of its accuracy). The equations require numerical integration and some typical results are given in graphical and tabular form . These show two features which are absent when displacements are small: as in closed vessels the combustion time is shorter than that for constant flame speed (typically, by a factor of 3); and, during combustion, pressure fluctuations develop which arise from the interaction of combustion and expansion each of which leads to an acceleration of the other.