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 boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

A front-tracking method for the computations of multiphase flow

Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves

This review discusses the use of the combination of surface roughness and hydrophobicity for engineering large slip at the fluid-solid interface. These superhydrophobic surfaces were initially inspired by the unique water-repellent properties of the lotus leaf and can be employed to produce drag reduction in both laminar and turbulent flows, enhance mixing in laminar flows, and amplify diffusion-osmotic flows. We review the current state of experiments, simulations, and theory of flow past superhydrophobic surfaces. In addition, the designs and limitations of these surfaces are discussed, with an eye toward implementing these surfaces in a wide range of applications.

Slip on Superhydrophobic Surfaces

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

Partial cavitation in the separated region forming from the apex of a wedge is examined to reveal the flow mechanism responsible for the transition from stable sheet cavity to periodically shedding cloud cavitation. High-speed visualization and time-resolved X-ray densitometry measurements are used to examine the cavity dynamics, including the time-resolved void-fraction fields within the cavity. The experimentally observed time-averaged void-fraction profiles are compared to an analytical model employing free-streamline theory. From the instantaneous void-fraction flow fields, two distinct shedding mechanisms are identified. The classically described re-entrant flow in the cavity closure is confirmed as a mechanism for vapour entrainment and detachment that leads to intermittent shedding of smaller-scale cavities. But, with a sufficient reduction in cavitation number, large-scale periodic cloud shedding is associated with the formation and propagation of a bubbly shock within the high void-fraction bubbly mixture in the separated cavity flow. When the shock front impinges on flow at the wedge apex, a large cloud is pinched off. For periodic shedding, the speed of the front in the laboratory frame is of the order of half the free-stream speed. The features of the observed condensation shocks are related to the average and dynamic pressure and void fraction using classical one-dimensional jump conditions. The sound speed of the bubbly mixture is estimated to determine the Mach number of the cavity flow. The transition from intermittent to transitional to strongly periodic shedding occurs when the average Mach number of the cavity flow exceeds that required for the generation of strong shocks.

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Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities

Turbulent boundary layer skin friction in liquid flows may be reduced when bubbles are present near the surface on which the boundary layer forms. Prior experimental studies of this phenomenon reached downstream-distance-based Reynolds numbers (m. At the lowest test speed and highest air injection rate, buoyancy pushed the air bubbles to the plate surface where they coalesced to form a nearly continuous gas film that persisted to the end of the plate with near-100% skin-friction drag reduction. At the higher two flow speeds, the bubbles generally remained distinct and skin-friction drag reduction was observed when the bubbly mixture was closer to the plate surface than 300 wall units of the boundary-layer flow without air injection, even when the bubble diameter was more than 100 of these wall units. Skin-friction drag reduction was lost when the near-wall shear induced the bubbles to migrate from the plate surface. This bubble-migration phenomenon limited the persistence of bubble-induced skin-friction drag reduction to the first few metres downstream of the air injector in the current experiments.

Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer

Partial cavities that formed on the vertices of wedges and on the leading edge of stationary hydrofoils were examined experimentally. The geometry of these test objects did not vary in the spanwise direction (i.e. two-dimensional). Open partial cavities formed on a series of two-dimensional wedges and on a plano-convex hydrofoil. These cavities terminated near the point of maximum cavity thickness, and small vapour-filled vortices were shed in the turbulent cavity wake. The turbulent flow in the wake of the open cavity was similar to the turbulent shear flow downstream of a rearward-facing step. Re-entrant flow was not observed in the cavity closure of open cavities, although recirculating flow associated with a region of flow separation was detected for some cases. Predictions of a two-dimensional free-streamline model of the cavitating wedge flows were compared to the experimentally observed cavities. The model predicted the profile of the open cavity only to the point of maximum cavity thickness. Examination of the flow field near the closure of the open cavities revealed adverse pressure gradients near the cavity closure. The pressure gradients around the open cavities were sufficient to cause large-scale condensation of the cavity. Unsteady re-entrant partial cavities formed on a two-dimensional NACA0009 hydrofoil. The interface of the unsteady closed cavities smoothly curved to form a re-entrant jet at the cavity terminus, and the re-entrant flow was directed upstream. The re-entrant flow impinged on the cavity interface and led to the periodic production of cloud cavitation. These cavities exhibited a laminar flow reattachment. The flow around the closed cavity was largely irrotational, while vorticity was created when the cloud cavitation collapsed downstream of the cavity. Examination of the flow field near closure of these cavities also revealed adverse pressure gradients near the partial cavity closure, but the rise in pressure did not lead to the premature condensation of the cavity.

Partial cavity flows. Part 1. Cavities forming on models without spanwise variation

To investigate the phenomena of skin-friction drag reduction in a turbulent boundary layer (TBL) at large scales and high Reynolds numbers, a set of experiments has been conducted at the US Navy's William B. Morgan Large Cavitation Channel (LCC). Drag reduction was achieved by injecting gas (air) from a line source through the wall of a nearly zero-pressure-gradient TBL that formed on a flat-plate test model that was either hydraulically smooth or fully rough. Two distinct drag-reduction phenomena were investigated; bubble drag reduction (BDR) and air-layer drag reduction (ALDR). The streamwise distribution of skin-friction drag reduction was monitored with six skin-friction balances at downstream-distance-based Reynolds numbers to 220 million and at test speeds to 20.0 m s -1 . Near-wall bulk void fraction was measured at twelve streamwise locations with impedance probes, and near-wall (0 25 %) is limited to the first few metres downstream of injection; marginal improvement was possible with a porous-plate versus an open-slot injector design; BDR has negligible sensitivity to surface tension; bubble size is independent of surface tension downstream of injection; BDR is insensitive to boundary-layer thickness at the injection location; and no synergetic effect is observed with compound injection. Using these data, previous BDR scaling methods are investigated, but data collapse is observed only with the 'initial zone' scaling, which provides little information on downstream persistence of BDR. ALDR was investigated with a series of experiments that included a slow increase in the volumetric flux of air injected at free-stream speeds to 15.3 m s -1 . These results indicated that there are three distinct regions associated with drag reduction with air injection: Region I, BDR; Region II, transition between BDR and ALDR; and Region III, ALDR. In addition, once ALDR was established: friction drag reduction in excess of 80 % was observed over the entire smooth model for speeds to 15.3 m s -1 ; the critical volumetric flux of air required to achieve ALDR was observed to be approximately proportional to the square of the free-stream speed; slightly higher injection rates were required for ALDR if the surface tension was decreased; stable air layers were formed at free-stream speeds to 12.5 m s -1 with the surface fully roughened (though approximately 50 % greater volumetric air flux was required); and ALDR was sensitive to the inflow conditions. The sensitivity to the inflow conditions can be mitigated by employing a small faired step (10 mm height in the experiment) that helps to create a fixed separation line.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112008003029

Steven L. Ceccio

Papers

Friction Drag Reduction of External Flows with Bubble and Gas Injection

Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities

Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer

Partial cavity flows. Part 1. Cavities forming on models without spanwise variation

Bubble-induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction