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

When a viscous fluid filling the voids in a porous medium is driven forwards by the pressure of another driving fluid, the interface between them is liable to be unstable if the driving fluid is the less viscous of the two. This condition occurs in oil fields. To describe the normal modes of small disturbances from a plane interface and their rate of growth, it is necessary to know, or to assume one knows, the conditions which must be satisfied at the interface. The simplest assumption, that the fluids remain completely separated along a definite interface, leads to formulae which are analogous to known expressions developed by scientists working in the oil industry, and also analogous to expressions representing the instability of accelerated interfaces between fluids of different densities. In the latter case the instability develops into round-ended fingers of less dense fluid penetrating into the more dense one. Experiments in which a viscous fluid confined between closely spaced parallel sheets of glass, a Hele-Shaw cell, is driven out by a less viscous one reveal a similar state. The motion in a Hele-Shaw cell is mathematically analogous to two-dimensional flow in a porous medium.
Analysis which assumes continuity of pressure through the interface shows that a flow is possible in which equally spaced fingers advance steadily. The ratio λ = (width of finger)/(spacing of fingers) appears as the parameter in a singly infinite set of such motions, all of which appear equally possible. Experiments in which various fluids were forced into a narrow Hele-Shaw cell showed that single fingers can be produced, and that unless the flow is very slow λ = (width of finger)/(width of channel) is close to , so that behind the tips of the advancing fingers the widths of the two columns of fluid are equal. When λ = 1/2 the calculated form of the fingers is very close to that which is registered photographically in the Hele-Shaw cell, but at very slow speeds where the measured value of λ increased from 1/2 to the limit 1.0 as the speed decreased to zero, there were considerable differences. Assuming that these might be due to surface tension, experiments were made in which a fluid of small viscosity, air or water, displaced a much more viscous oil. It is to be expected in that case that λ would be a function of μU/T only, where μ is the viscosity, U the speed of advance and T the interfacial tension. This was verified using air as the less viscous fluid penetrating two oils of viscosities 0.30 and 4.5 poises.

The Penetration of a Fluid into a Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid

The 1990 National Academy of Science final report of its review of the Inertial Confinement Fusion Program recommended completion of a series of target physics objectives on the 10-beam Nova laser at the Lawrence Livermore National Laboratory as the highest-priority prerequisite for proceeding with construction of an ignition-scale laser facility, now called the National Ignition Facility (NIF). These objectives were chosen to demonstrate that there was sufficient understanding of the physics of ignition targets that the laser requirements for laboratory ignition could be accurately specified. This research on Nova, as well as additional research on the Omega laser at the University of Rochester, is the subject of this review. The objectives of the U.S. indirect-drive target physics program have been to experimentally demonstrate and predictively model hohlraum characteristics, as well as capsule performance in targets that have been scaled in key physics variables from NIF targets. To address the hohlrau...

The physics basis for ignition using indirect-drive targets on the National Ignition Facility

Models for predicting flow pattern transitions during steady gas-liquid flow in vertical tubes are developed, based on physical mechanisms suggested for each transition. These models incorporate the effect of fluid properties and pipe size and thus are largely free of the limitations of empirically based transition maps or correlations.

Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes

The shapes and terminal velocities of bubbles rising in viscous liquids have been determined. For Morton numbers (M) greater than 4 × 10−3 the drag coefficient and dimensionless bubble shape are functions only of Reynolds number (R). Shape regimes and terminal rise velocities have been correlated. The flow field around a rising bubble was visualized through the hydrogen bubble tracer technique. For M > 4 × 10−3 and R 110 the wake was open and unsteady. Streamlines for the flow were obtained by raising a cine camera at the same speed as the bubble and filming the H2 tracer bubbles. Results are presented for R < 150 and 7·4 × 10−4 < M < 850.

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Bubbles in viscous liquids: shapes, wakes and velocities

Part I describes measurements of the shape and rate of rise of air bubbles varying in volume from 1·5 to 200 cm. 3 when they rise through nitrobenzene or water. Measurements of photographs of bubbles formed in nitrobenzene show that the greater part of the upper surface is always spherical. A theoretical discussion, based on the assumption that the pressure over the front of the bubble is the same as that in ideal hydrodynamic flow round a sphere, shows that the velocity of rise, U , should be related to the radius of curvature, R , in the region of the vertex, by the equation U = 2/3√( gR ); the agreement between this relationship and the experimental results is excellent. For geometrically similar bubbles of such large diameter that the drag coefficient would be independent of Reynolds’s number, it would be expected that U would be proportional to the sixth root of the volume, V ; measurements of eighty-eight bubbles show considerable scatter in the values of U/V 1/6 , although there is no systematic variation in the value of this ratio with the volume. Part II. Though the characteristics of a large bubble are associated with the observed fact that the hydrodynamic pressure on the front of a spherical cap moving through a fluid is nearly the same as that on a complete sphere, the mechanics of a rising bubble cannot be completely understood till the observed pressure distribution on a spherical cap is understood. Failing this, the case of a large bubble running up a circular tube filled with water and emptying at the bottom is capable of being analyzed completely because the bubble is not then followed by a wake. An approxim ate calculation shows that the velocity U of rise is U = 0·46 √( ga ), where a is the radius of the tube. Experiments with a tube 7·9 cm. diameter gave values of U from 29·1 to 30·6 cm./sec., corresponding with values of U /√( ga ) from 0·466 to 0·490.

F. R. S. Sir Geoffrey Taylor

Papers

The mechanics of large bubbles rising through extended liquids and through liquids in tubes