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

The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.

The growth of vapor bubbles in superheated liquids. report no. 26-6

Single-phase Convective Heat Transfer in Microchannels: a Review of Experimental Results

A new cavity model that can explain the interaction between viscous effects including vortices and cavitation bubbles is presented in this study. This model, which is named a bubble two-phase flow (BTF) model, treats the inside and outside of a cavity as one continuum by regarding the cavity as a compressible viscous fluid whose density changes greatly. Navier–Stokes equations including cavitation bubble clusters are solved in finite-difference form by a time-marching scheme, where the growth and collapse of a bubble cluster is given by a modified Rayleigh's equation. Computation was made on a two-dimensional flow field around a hydrofoil NACA0015 at angles of attack of 8° and 20°. The Reynolds number was 3 × 105. The experiments were also performed at the same Reynolds number for comparison. The computed results by the BTF cavity model can express the feature of cloud-type cavitation shed from the trailing edge of the attached cavities when the angle of attack is 8°. It shows the mechanism of cavitation cloud generation and large-scale vortices. The boundary layer separates at the cavity leading edge. Then it rolls up and produces the cavitation cloud. In other words, the instability of the shear layer may produce the cavitation cloud. When the angle of attack is 20°, the flow was fully separated from the leading edge of the hydrofoil and vortex cavitation occurs in the separated region. The BTF cavity model can also express the generation of such vortex cavitation and the effect of cavitation nuclei in the uniform flow.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211209200003X

A new modelling of cavitating flows : a numerical study of unsteady cavitation on a hydrofoil section

The lubrication of external liquid flow with a bubbly mixture or gas layer has been the goal of engineers for many years, and this article presents the underlying principles and recent advances of this technology. It reviews the use of partial and supercavities for drag reduction of axisymmetric objects moving within a liquid. Partial cavity flows can also be used to reduce the friction drag on the nominally two-dimensional portions of a horizontal surface, and the basic flow features of two-dimensional cavities are presented. Injection of gas can lead to the creation of a bubbly mixture near the flow surface that can significantly modify the flow within the turbulent boundary layer, and there have been significant advances in the understanding of the underlying physical process of drag reduction. Moreover, with sufficient gas flux, the bubbles flowing beneath a solid surface can coalesce to form a thin drag-reducing air layer. The current applications of these techniques to underwater vehicles and surface ships are discussed.

Friction Drag Reduction of External Flows with Bubble and Gas Injection

-Foreword Hiroharu Kato. -Preface. Symbols. -1: Introduction - The main features of cavitating flows. 1.1. The physical phenomenon. 1.2. Cavitation in real liquid flows. 1.3. Specific features of cavitating flow. 1.4. Non-dimensional parameters. 1.5. Some historical aspects. -2: Nuclei and cavitation. 2.1. Introduction. 2.2. Equilibrium of a nucleus. 2.3. Heat and mass diffusion. 2.4. Nucleus population. References. -3: The dynamics of spherical bubbles. 3.1. Basic equations. 3.2. The collapse of a vapor bubble. 3.3. The explosion of a nucleus. 3.4. The effect of viscosity. 3.5. Non-linear oscillations of a bubble. 3.6. Scaling considerations. 3.7. Stability of a spherical interface. References. -4: Bubbles in a non-symmetrical environment. 4.1. Introduction. 4.2. Motion of a spherical bubble in a liquid at rest. 4.3. Non-spherical bubble evolution. 4.4. The path of a spherical bubble. References. Appendix to Section 4.3.3. -5: Further insights into bubble physics. 5.1. The effect of compressibility. 5.2. Bubble noise. 5.3. Some thermal aspects. 5.4. A typical numerical solution. References. Appendix to Section 5.1.3. -6: Supercavitation. 6.1. Physical aspects of supercavities. 6.2. Supercavity flow modeling using steady potential flow theory. 6.3. Typical results. 6.4. Axisymmetric cavities. 6.5. Specific problems. References. Appendix: singular behavior at detachment. -7: Partial cavities. 7.1. Partial cavities on two-dimensional foils. 7.2. Partial cavities in internal flows. 7.3. The cloud cavitation instability. 7.4. Wakes of partial cavities. 7.5. Thermal effects in partial cavitation. References. Appendix: sonic velocity in a liquid/vapor mixture with phase change. -8: Bubbles and cavities on two-dimensional foils. 8.1. Attached cavitation. 8.2. Traveling bubble cavitation. 8.3. Interaction between bubbles and cavities. 8.4. Roughness and cavitation inception. References. -9: Ventilated supercavities. 9.1. Two-dimensional ventilated supercavities. 9.2. Axisymmetric ventilated supercavities. 9.3. Analysis of pulsating ventilated supercavities. References. -10: Vortex cavitation. 10.1. Theoretical results. 10.2. The non-cavitating tip vortex. 10.3. Cavitation in a tip vortex. References. -11: Shear cavitation. 11.1. Jet cavitation. 11.2. Wake cavitation. References. -12: Cavitation erosion. 12.1. Empirical methods. 12.2. Some global results. 12.3. Basic hydrodynamic mechanisms of energy concentration. 12.4. Aggressiveness of a cavitating flow. 12.5. Insight into the material response. References. Index.

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Fundamentals of Cavitation

The instability of a partial cavity induced by the development of a re-entrant jet is investigated on the basis of experiments conducted on a diverging step. Detailed visualizations of the cavity behaviour allowed us to identify the domain of the re-entrant jet instability which leads to classical cloud cavitation. The surrounding regimes are also investigated, in particular the special case of thin cavities which do not oscillate in length but surprisingly exhibit a re-entrant jet of periodical behaviour. The velocity of the re-entrant jet is measured from visualizations, in the case of both cloud cavitation and thin cavities. The limits of the domain of the re-entrant jet instability are corroborated by velocity fluctuation measurements. By varying the divergence and the confinement of the channel, it is shown that the extent of the auto-oscillation domain primarily depends upon the average adverse pressure gradient in the channel. This conclusion is corroborated by the determination of the pressure gradient on the basis of LDV measurements which shows a good correlation between the domain of the cloud cavitation instability and the region of high adverse pressure gradient. A simple phenomenological model of the development of the re-entrant jet in an adverse pressure gradient confirms the strong influence of the pressure gradient on the development of the re-entrant jet and particularly on its thickness. An ultrasonic technique is developed to measure the re-entrant jet thickness, which allowed us to compare it with the cavity thickness. By considering an estimate of the characteristic height of the perturbations developing on the interface of the cavity and of the re-entrant jet, it is shown that cloud cavitation requires negligible interaction between both interfaces, i.e. a thick enough cavity. In the case of thin cavities, this interaction becomes predominant; the cavity interface breaks at many points, giving birth to small-scale vapour structures unlike the large-scale clouds which are periodically shed in the case of cloud cavitation. The low-frequency content of the cloud cavitation instability is investigated using spectral analysis of wall pressure signals. It is shown that the characteristic frequency of cloud cavitation corresponds to a Strouhal number of about 0.2 whatever the operating conditions and the cavity length may be, provided the Strouhal number is computed on the basis of the maximum cavity length. For long enough cavities, another peak is observed in the spectra, at lower frequency, which is interpreted as a surge-type instability. The present investigations give insight into the instabilities that a partial cavity may undergo, and particularly the re-entrant jet instability. Two parameters are shown to be of most importance in the analysis of the re-entrant jet instability: the adverse pressure gradient and the cavity thickness compared to the re-entrant jet thickness. The present results allowed us to conduct a qualitative phenomenological analysis of the stability of partial cavities on cavitating hydrofoils. It is conjectured that cloud cavitation should occur for short enough cavities, of the order of half the chordlength, whereas the instability often observed at the limit between partial cavitation and super-cavitation is here interpreted as a cavitation surge-type instability.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2819429B69AFDF15C7C3ECFEAEB3A69D/S0022112001005420a.pdf/div-class-title-the-cavitation-instability-induced-by-the-development-of-a-re-entrant-jet-div.pdf

The cavitation instability induced by the development of a re-entrant jet

This book provides a comprehensive treatment of the cavitation erosion phenomenon and state-of-the-art research in the field It is divided into two parts Part 1 consists of seven chapters, offering a wide range of computational and experimental approaches to cavitation erosion It includes a general introduction to cavitation and cavitation erosion, a detailed description of facilities and measurement techniques commonly used in cavitation erosion studies, an extensive presentation of various stages of cavitation damage (including incubation and mass loss), and insights into the contribution of computational methods to the analysis of both fluid and material behavior The proposed approach is based on a detailed description of impact loads generated by collapsing cavitation bubbles and a physical analysis of the material response to these loads Part 2 is devoted to a selection of nine papers presented at the International Workshop on Advanced Experimental and Numerical Techniques for Cavitation Erosion (Grenoble, France, 1-2 March 2011), representing the forefront of research on cavitation erosion Innovative numerical and experimental investigations illustrate the most advanced breakthroughs in cavitation erosion research

Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction

The results of an experimental work concerning the behavior of flows with partial cavities are presented. The tests were carried out using a plano-convex foil placed in the free surface channel of the I.M.G. Hydrodynamic Tunnel. The experimental conditions concerning ambient pressure, water velocity, and body size were such that various and realistic kinds of flows could be realized. The main flow regimes are described and correlated to the values of foil incidence and cavitation parameter. Attention is paid to the shedding of large vapor pockets into the cavity wake and its possible periodic character. Aside from classical consideration to the cavity length and shedding frequency in the periodic regime, results concerning the wall pressure distribution in the rear part of the cavity are given. They lead to distinguish thin, stable, and closed cavities from the thick ones in which the reentrant jet plays a dominant role for the shedding of vortical structures and the flow unsteadiness.

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Partial Cavities: Global Behavior and Mean Pressure Distribution

Attached cavitation on a wall with continuous curvature is investigated on the basis of experiments carried out on various bodies (circular and elliptic cylinders, NACA 16 012 foil). Visualization of the boundary layer by dye injection at the leading edge shows that a strong interaction exists between attached cavitation and the boundary layer. In particular, it is shown that the cavity does not detach from the body at the minimum pressure point, but behind a laminar separation, even in largely developed cavitating flow. A detachment criterion which takes into account this link between attached cavitation and boundary layer is proposed. It consists of connecting a cavitating potential-flow calculation and a boundary-layer calculation. Among all the theoretically possible detachment points, the actual detachment point is chosen to be the one for which the complete calculation predicts a laminar separation just upstream. This criterion, applied to the NACA foil, leads to a prediction which is in good agreement with experimental results.

Jean-Pierre Franc

Papers

Fundamentals of Cavitation

The cavitation instability induced by the development of a re-entrant jet

Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction

Partial Cavities: Global Behavior and Mean Pressure Distribution

Attached cavitation and the boundary layer: experimental investigation and numerical treatment