Bubble ring

Abstract: Bubble dynamics near a rigid boundary are associated with wide and important applications in cavitation erosion in many industrial systems and medical ultrasonics. This classical problem is revisited with the following two developments. Firstly, computational studies on the problem have commonly been based on an incompressible fluid model, but the compressible effects are essential in this phenomenon. Consequently, a bubble usually undergoes significantly damped oscillation in practice. In this paper this phenomenon will be modelled using weakly compressible theory and a modified boundary integral method for an axisymmetric configuration, which predicts the damped oscillation. Secondly, the computational studies so far have largely been concerned with the first cycle of oscillation. However, a bubble usually oscillates for a few cycles before it breaks into much smaller ones. Cavitation erosion may be associated with the recollapse phase when the bubble is initiated more than the maximum bubble radius away from the boundary. Both the first and second cycles of oscillation will be modelled. The toroidal bubble formed towards the end of the collapse phase is modelled using a vortex ring model. The repeated topological changes of the bubble are traced from a singly connected to a doubly connected form, and vice versa. This model considers the energy loss due to shock waves emitted at minimum bubble volumes during the beginning of the expansion phase and around the end of the collapse phase. It predicts damped oscillations, where both the maximum bubble radius and the oscillation period reduce significantly from the first to second cycles of oscillation. The damping of the bubble oscillation is alleviated by the existence of the rigid boundary and reduces with the standoff distance between them. Our computations correlate well with the experimental data (Philipp & Lauterborn, J. Fluid Mech., vol. 361, 1998, pp. 75‐116) for both the first and second cycles of oscillation. We have successively reproduced the bubble ring in direct contact with the rigid boundary at the end of the second collapse phase, a phenomenon that was suggested to be one of the major causes of cavitation erosion by experimental studies.

Abstract: Material deformation and pitting from cavitation bubble collapse is investigated using fluid and material dynamics and their interaction. In the fluid, a novel hybrid approach, which links a boundary element method and a compressible finite difference method, is used to capture non-spherical bubble dynamics and resulting liquid pressures efficiently and accurately. The bubble dynamics is intimately coupled with a finite-element structure model to enable fluid/structure interaction simulations. Bubble collapse loads the material with high impulsive pressures, which result from shock waves and bubble re-entrant jet direct impact on the material surface. The shock wave loading can be from the re-entrant jet impact on the opposite side of the bubble, the fast primary collapse of the bubble, and/or the collapse of the remaining bubble ring. This produces high stress waves, which propagate inside the material, cause deformation, and eventually failure. A permanent deformation or pit is formed when the local equivalent stresses exceed the material yield stress. The pressure loading depends on bubble dynamics parameters such as the size of the bubble at its maximum volume, the bubble standoff distance from the material wall and the pressure driving the bubble collapse. The effects of standoff and material type on the pressure loading and resulting pit formation are highlighted and the effects of bubble interaction on pressure loading and material deformation are preliminarily discussed.

Abstract: Waterjet nozzles (STRATOJETS) have been developed which achieve passive structuring of cavitating submerged jets into discrete ring vortices, and which possess cavitation incipient numbers six times higher than obtained with conventional cavitating jet nozzles. In this study we developed analytical and numerical techniques and conducted experimental work to gain an understanding of the basic phenomena involved. The achievements are: (1) a thorough analysis of the acoustic dynamics of the feed pipe to the nozzle; (2) a theory for bubble ring growth and collapse; (3) a numerical model for jet simulation; (4) an experimental observation and analysis of candidate second-generation low-sigma STRATOJETS. From this study we can conclude that intensification of bubble ring collapse and design of highly resonant feed tubes can lead to improved drilling rates. The models here described are excellent tools to analyze the various parameters needed for STRATOJET optimizations. Further analysis is needed to introduce such important factors as viscosity, nozzle-jet interaction, and ring-target interaction, and to develop the jet simulation model to describe the important fine details of the flow field at the nozzle exit.