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.

Experiments are carried out on the interaction and coalescence of two, three, and four bubbles with approximately the same sizes, distributed evenly and symmetrically. The bubbles are generated simultaneously by electric discharges, using an in-house designed series circuit, and their interaction is captured using a high-speed camera. Particular attentions are paid to if/when coalescence of bubbles happens and the motion of the joined bubbles. Some new features are observed, which depend mainly on the dimensionless distance γbb = dbb/Rmax, where dbb is the inter-bubble distance and Rmax is the maximum bubble radius. For γbb > 2, a jet forms and penetrates each side bubble, directed to the center of the configuration, resulting in a protrusion. Towards the end of collapse, a large portion of bubble gases is compressed into the protrusion from the main part of the toroidal bubble. For γbb < 2, the bubbles coalesce during expansion, and the part of the joined bubble’s surface distal from the center of the configuration collapses faster than elsewhere. The experiments show that the oscillation period of multi-bubbles does not change appreciably without coalescence but increases significantly with coalescence. For three bubbles initiated at collinear positions with γbb > 2, the jets that form from the side bubbles are towards the middle, and the middle bubble splits into two parts, moving towards the two side bubbles. For γbb < 2, the side bubbles merge with the middle bubble during expansion, forming an ellipsoid bubble; the joined bubble collapses predominantly from two sides, where two inward jets form towards the end of collapse.

The interaction between an underwater explosion bubble and an elastic-plastic structure is a complex transient process, accompanying violent bubble collapsing, jet impact, penetration through the bubble, and large structural deformation. In the present study, the bubble dynamics are modeled using the boundary element method and the nonlinear transient structural response is modeled using the explicit finite element method. A new fully coupled 3D model is established through coupling the equations for the state variables of the fluid and structure and solving them as a set of coupled linear algebra equations. Based on the acceleration potential theory, the mutual dependence between the hydrodynamic load and the structural motion is decoupled. The pressure distribution in the flow field is calculated with the Bernoulli equation, where the partial derivative of the velocity potential in time is calculated using the boundary integral method to avoid numerical instabilities. To validate the present fully coupled model, the experiments of small-scale underwater explosion near a stiffened plate are carried out. High-speed imaging is used to capture the bubble behaviors and strain gauges are used to measure the strain response. The numerical results correspond well with the experimental data, in terms of bubble shapes and structural strain response. By both the loosely coupled model and the fully coupled model, the interaction between a bubble and a hollow spherical shell is studied. The bubble patterns vary with different parameters. When the fully coupled model and the loosely coupled model are advanced with the same time step, the error caused by the loosely coupled model becomes larger with the coupling effect becoming stronger. The fully coupled model is more stable than the loosely coupled model. Besides, the influences of the internal fluid on the dynamic response of the spherical shell are studied. At last, the case that the bubble interacts with an air-backed stiffened plate is simulated. The associated interesting physical phenomenon is obtained and expounded.

This paper is concerned with bubble dynamics at a corner formed by two flat rigid boundaries associated with applications in ultrasonic cleaning and cavitation damage. This phenomenon is modeled using the potential flow theory and the boundary integral method. The Green’s function is obtained to satisfy the impenetrable conditions at the rigid boundaries using the method of images with the corner angle α = π/k, where k is a natural number. To evaluate the numerical model, experiments were carried out with a spark-generated bubble in water and recorded using a high-speed camera. The predicted bubble shapes are in excellent agreement with those from the experiments. A jet forms toward the end of the collapse, pointing to the corner when initiated at the bisector of the two walls but pointing to the near wall and inclined to the corner when initiated near one of the two walls. The Kelvin impulse theory predicts the jet direction well. As compared to a bubble near a flat wall, the oscillation period and the jet width increase but the jet velocity decreases. The bubble migrates away from the near wall and the corner during its expansion and moves back toward them during its collapse, but at a much larger speed and amplitude. A velocity stagnation point forms at the start of the collapse, and a high-pressure zone is generated at the base of the jet during the late stages of the collapse, which drives the jet and the bubble toward the near wall and the corner.

Energy concentration and loss due to a violent collapsing bubble are essential phenomena to many applications such as cavitation erosion, biomedical ultrasonics, sonochemistry, cavitation cleaning and underwater explosions. It has been generally known that the energy of a bubble system is radiated away as an acoustic wave and dissipated by viscosity. However, there is no study in the scientific literature on the time history of the energy of a bubble system in a compressible flow. Here we have introduced the local energy of a non-spherical bubble system, consisting of the energy of the interior gas, the interface and the exterior liquid in the inner asymptotic region. The local energy determines the local bubble and flow dynamics, including the concentration of energy, stress and momentum. We obtain a simple formula for the radiated energy associated with acoustic radiation in terms of the bubble volume history. We perform calculations of the energy history for a transient bubble in a compressible liquid in an infinite domain, subject to buoyancy and near a rigid boundary, respectively. Our calculations show that the local energy of a transient bubble follows a step function in time, being nearly conserved for most of each cycle of oscillation but decreasing rapidly and significantly at bubble inception and at the end of collapse, due to the emission of steep pressure waves or shock waves. The loss of the local energy of the bubble system due to the emission of steep pressure waves and the associated damping of the bubble oscillation are diminished by buoyancy effects and decrease with the buoyancy parameter. Similarly, the loss of the local energy of a bubble system is diminished by the presence of a rigid boundary and decreases with the proximity of the bubble to the boundary. We also analyse the energy concentration of single bubble sonoluminescence in a standing acoustic wave.

The jet characteristics of bubbles near mixed boundaries have been the focus of research in many fields. As the associated parameters are complicated, relatively few reports have been published. In this paper, a numerical model is established by considering the influence of the free surface and a mutual vertical wall using the boundary element method. To determine the jet characteristics of collapsing bubbles in different areas, two nondimensional parameters must be investigated: the distance γ_v from the bubble to the vertical wall and the distance γ_h from the bubble to the horizontal wall. At the same time, the buoyancy parameter δ cannot be ignored. First, the jet characteristics under an infinite vertical solid wall are discussed; furthermore, the jet direction in the stage of collapsing bubble under combined boundaries without buoyancy is studied, and we find that the variation amplitude of the jet angle changes with the free surface. Considering the buoyancy, we then divide the total area into six regions with different ranges of jet angle under small buoyancy values, allowing the significant effect of buoyancy to be studied as δ increases. In addition, we study the jet velocity qualitatively under the condition of negligible buoyancy and find that a peak jet velocity may exist at mid water depths.