This book describes and explains the fundamental physical processes involved in bubble dynamics and the phenomenon of cavitation. It is intended as a combination of a reference book for those scientists and engineers who work with cavitation or bubble dynamics and as a monograph for advanced students interested in some of the basic problems associated with this category of multiphase flows. A basic knowledge of fluid flow and heat transfer is assumed but otherwise the analytical methods presented are developed from basic principles.

The book begins with a chapter on nucleation and describes both the theory and observations of nucleation in flowing and non-flowing systems. The following three chapters provide a systematic treatment of the dynamics of the growth, collapse or oscillation of individual bubbles in otherwise quiescent liquids. Chapter 4 summarizes the state of knowledge of the motion of bubbles in liquids. Chapter 5 describes some of the phenomena which occur in homogeneous bubbly flows with particular emphasis on cloud cavitation and this is followed by a chapter summarizing some of the experiemntal observations of cavitating flows. The last chapter provides a review of the free streamline methods used to treat separated cavity flows with large attached cavities.

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Cavitation and Bubble Dynamics

Ultrasonic irradiation of liquids causes acoustic cavitation: the formation, growth, and implosive collapse of bubbles. Bubble collapse during cavitation generates transient hot spots responsible for high-energy chemistry and emission of light. Determination of the temperatures reached in a cavitating bubble has remained a difficult experimental problem. As a spectroscopic probe of the cavitation event, sonoluminescence provides a solution. Sonoluminescence spectra from silicone oil were reported and analyzed. The observed emission came from excited state C2 (Swan band transitions, d3IIg—a3IIµ), which has been modeled with synthetic spectra as a function of rotational and vibrational temperatures. From comparison of synthetic to observed spectra, the effective cavitation temperature was found to be 5075 ± 156 K.

https://science.sciencemag.org/content/sci/253/5026/1397.full.pdf

The temperature of cavitation.

In order to elucidate the mechanism of cavitation erosion, the dynamics of a single laser-generated cavitation bubble in water and the resulting surface damage on a flat metal specimen are investigated in detail. The characteristic effects of bubble dynamics, in particular the formation of a high-speed liquid jet and the emission of shock waves at the moment of collapse are recorded with high-speed photography with framing rates of up to one million frames/s. Damage is observed when the bubble is generated at a distance less than twice its maximum radius from a solid boundary (γ=2, where γ=s/Rmax, s is the distance between the boundary and the bubble centre at the moment of formation and Rmax is the maximum bubble radius). The impact of the jet contributes to the damage only at small initial distances (γ[les ]0.7). In this region, the impact velocity rises to 83 m s−1, corresponding to a water hammer pressure of about 0.1 GPa, whereas at γ>1, the impact velocity is smaller than 25 m s−1. The largest erosive force is caused by the collapse of a bubble in direct contact with the boundary, where pressures of up to several GPa act on the material surface. Therefore, it is essential for the damaging effect that bubbles are accelerated towards the boundary during the collapse phases due to Bjerknes forces. The bubble touches the boundary at the moment of second collapse when γ<2 and at the moment of first collapse when γ<1. Indentations on an aluminium specimen are found at the contact locations of the collapsing bubble. In the range γ=1.7 to 2, where the bubble collapses mainly down to a single point, one pit below the bubble centre is observed. At γ[les ]1.7, the bubble shape has become toroidal, induced by the jet flow through the bubble centre. Corresponding to the decay of this bubble torus into multiple tiny bubbles each collapsing separately along the circumference of the torus, the observed damage is circular as well. Bubbles in the ranges γ[les ]0.3 and γ=1.2 to 1.4 caused the greatest damage. The overall diameter of the damaged area is found to scale with the maximum bubble radius. Owing to the possibility of generating thousands of nearly identical bubbles, the cavitation resistance of even hard steel specimens can be tested.

Cavitation erosion by single laser-produced bubbles

The dynamics of laser-produced cavitation bubbles near a solid boundary and its dependence on the distance between bubble and wall are investigated experimentally. It is shown by means of high-speed photography with up to 1 million frames/s that jet and counterjet formation and the development of a ring vortex resulting from the jet flow are general features of the bubble dynamics near solid boundaries. The fluid velocity field in the vicinity of the cavitation bubble is determined with time-resolved particle image velocimetry. A comparison of path lines deduced from successive measurements shows good agreement with the results of numerical calculations by Kucera & Blake (1988). The pressure amplitude, the profile and the energy of the acoustic transients emitted during spherical bubble collapse and the collapse near a rigid boundary are measured with a hydrophone and an optical detection technique. Sound emission is the main damping mechanism in spherical bubble collapse, whereas it plays a minor part in the damping of aspherical collapse. The duration of the acoustic transients is 20-30 ns. The highest pressure amplitudes at the solid boundary have been found for bubbles attached to the boundary. The pressure inside the bubble and at the boundary reaches about 2.5 kbar when the maximum bubble radius is 3.5 mm. The results are discussed with respect to the mechanism of cavitation erosion.

Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary

Bubbles in liquids, soft and squeezy objects made of gas and vapour, yet so strong as to destroy any material and so mysterious as at times turning into tiny light bulbs, are the topic of the present report. Bubbles respond to pressure forces and reveal their full potential when periodically driven by sound waves. The basic equations for nonlinear bubble oscillation in sound fields are given, together with a survey of typical solutions. A bubble in a liquid can be considered as a representative example from nonlinear dynamical systems theory with its resonances, multiple attractors with their basins, bifurcations to chaos and not yet fully describable behaviour due to infinite complexity. Three stability conditions are treated for stable trapping of bubbles in standing sound fields: positional, spherical and diffusional stability. Chemical reactions may become important in that respect, when reacting gases fill the bubble, but the chemistry of bubbles is just touched upon and is beyond the scope of the present report. Bubble collapse, the runaway shrinking of a bubble, is presented in its current state of knowledge. Pressures and temperatures that are reached at this occasion are discussed, as well as the light emission in the form of short flashes. Aspherical bubble collapse, as for instance enforced by boundaries nearby, mitigates most of the phenomena encountered in spherical collapse, but introduces a new effect: jet formation, the self-piercing of a bubble with a high velocity liquid jet. Examples of this phenomenon are given from light induced bubbles. Two oscillating bubbles attract or repel each other, depending on their oscillations and their distance. Upon approaching, attraction may change to repulsion and vice versa. When being close, they also shoot self-piercing jets at each other. Systems of bubbles are treated as they appear after shock wave passage through a liquid and with their branched filaments that they attain in standing sound fields. The N-bubble problem is formulated in the spirit of the n-body problem of astrophysics, but with more complicated interaction forces. Simulations are compared with three-dimensional bubble dynamics obtained by stereoscopic high speed digital videography.

Physics of bubble oscillations

Analytical and numerical analyses have been made of the physical behaviour of a collapsing bubble in a liquid. The mathematical formulation takes into account the effects of compressibility of the liquid, non-equilibrium condensation of the vapour, heat conduction and the temperature discontinuity at the phase interface. Numerical solutions for the collapse of the bubble are obtained beyond the time when the bubble reaches its minimum radius up to the stage when a pressure wave forms and propagates outward into the liquid. The numerical results indicate that evaporation and condensation strongly influence the dynamical behaviour of the bubble.In addition, the propagation of the stress wave, both in a solid and a liquid, due to the collapse of the bubble has been observed by means of the dynamic photoelasticity. It is clearly demonstrated that the stress wave in a photoelastic specimen is caused by impact of the pressure wave radiated from the bubble.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112080002662

Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid

This paper deals experimentally with the mechanism of an impulsive pressure generated by a collapsing bubble. In a water filled shock tube, an expansion wave and a subsequent compression wave are applied to single, twin and triadic bubbles. The growth, collapse and rebound of bubbles situated at various distances from a solid boundary are observed by means of high-speed photography and in-line Fraunhofer holography using a pulsed dye laser. The results indicate that the impulsive pressure is caused by a shock wave radiated at the instant of the rebound of a collapsing bubble, and that the subsequent jet impingement does not produce any detectable effects. The pressure pulse is found to be of the order 104 ∼ 105 atm, and its duration 2 ∼ 3 μsec.

Experimental Investigations of Cavitation Bubble Collapse by a Water Shock Tube

This paper deals theoretically with a filmwise condensation of a vapour on the endwall of a shock tube behind a reflected shock wave. The gas dynamics, accompanied by heat and mass transfer at the vapour-liquid interface, is treated by the method of matched asymptotic expansions. The first and second approximate solutions are obtained and evaluated numerically. It is clarified that there exists a transition process on the growth of a liquid film, that is, the liquid film grows approximately in proportion to the time t in the early stages after the reflection of the shock wave, and after some time, it grows in proportion to the square root of the time. This transition process from the t-dependent growth to the t½-dependent one is mainly controlled by the intensity of condensation. In the t-dependent growth region, the growth rate of the liquid film is proportional to the condensation parameter, depending both upon an initial condition and upon thermal properties of the vapour and the liquid film, while in the t½-dependent growth region it becomes independent of the condensation parameter and is controlled only by thermal properties of the vapour, liquid film and shock-tube endwall. This result suggests that the measurement of the condensation parameter by shock tubes should be made in the t-dependent growth region immediately after the reflection of the shock wave.

Non-equilibrium vapour condensation on a shock-tube endwall behind a reflected shock wave

http://eportfolio.lib.ksu.edu.tw/user/T/0/T097000001/repository/Fujikawa_Takahira-1998.pdf

Dynamics of two nonspherical cavitation bubbles in liquids

This paper deals with a theoretical investigation of the effects of heat and mass transfer on the impulsive pressure due to the collapse of a bubble in a compressible liquid. It is found that the dynamical behaviour of the bubble strongly depends on heat and mass transfer through the wall of the bubble. The smaller is the initial radius of the bubble, the more violently contracts the bubble, while the higher becomes an impulsive pressure, on the other hand, the shorter becomes the time duration of it. The higher is the temperature of the surrounding liquid, the more slowly contracts the bubble, and consequently it merely radiates a weak pressure wave.

Shigeo Fujikawa

Papers

Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid

Experimental Investigations of Cavitation Bubble Collapse by a Water Shock Tube

Non-equilibrium vapour condensation on a shock-tube endwall behind a reflected shock wave

Dynamics of two nonspherical cavitation bubbles in liquids

Effects of Heat and Mass Transfer on the Impulsive Pressure Developed by the Bubble Collapse