Energy Transport during Growth and Collapse of a Cavitation Bubble

Abstract

Cavitation bubbles are widely observed in a variety of applications, from naval engineering to biomedical science. One of the major outcomes of cavitation is structural damage produced by the repeated collapse of bubbles, which is undesirable in naval applications. Due to limited optical access and the destructive nature of bubbles, damage induced by cavitation bubbles is not well understood.

As cavitation bubbles undergo a rapid compression that concentrates energy into a small volume, some of this energy is released through a shock wave that has the potential to induce damage to the nearby rigid surface. To develop strategies to mitigate the damage induced by bubbles, it is essential to understand the relationship between the shock properties and the initial conditions (e.g., bubble size, and the liquid and bubble pressures). For this purpose, we consider the canonical problem of the collapse of a single bubble in a liquid, both in a free field and near a solid surface. In particular, we investigate energy transport in the system comprising the bubble and surrounding liquid, with a focus on the role of compressibility.

We first examine the role of liquid compressibility in energy concentration and release during the inertial collapse of a spherical gas bubble. We develop an improved approach for calculating energy transport during bubble collapse, which enables more accurate predictions of energy transport. We also provide closed-form expressions for the energy and size of the bubble at collapse in terms of the parameters governing the problem, which can account for the effects of liquid compressibility. We further provide an analytical model relating the shock pressure to the parameters governing the problem. Our framework and scaling relations could be used in conjunction with single-phase simulations as a means to estimate the cavitation activity and to help devise strategies to mitigate cavitation.

We identify the dependence of the bubble response and key shock properties on waveform parameters in ultrasound-driven bubble growth and collapse. We develop a framework to understand how energy is transferred from the wave to the system, and to determine the effect of viscosity and surface tension on energy transport in the system. This framework enables us to identify relationships describing bubble expansion during growth and energy concentration at collapse based on the waveform properties.

When the bubble is adjacent to a neighboring boundary, the boundary breaks the symmetry, such that the bubble collapses in a non-spherical fashion, thereby producing a re-entrant jet that penetrates the bubble, impacts the distal side, and thus generates a water-hammer shock. We investigate the role of compressibility in the dynamics of a gas bubble collapsing near a rigid surface. By comparing direct simulations with potential flow simulations, we assess the effects of compressibility on the dynamics of the bubble and the re-entrant jet. We observe a delay between the two approaches, attributed to differences in the pressure fields at an early stage due to compressibility effects. Nevertheless, the bubble morphologies are similar for most of the collapse, with discrepancies visible only in the final stages of collapse. We discuss the effects of compressibility on the dynamics of the bubble and the jet at jet impact. This knowledge will improve the understanding of the importance of waves generated during collapse and will inform efforts to develop a better model to predict shock properties.