During the collapse of an initially spherical cavitation bubble near a rigid wall, a reentrant jet forms from the side of the bubble farthest from the wall. This re-entrant jet impacts and penetrates the bubble surface closest to the wall during the final stage of the collapse. In the present paper, this phenomenon is modelled with potential flow theory, and a numerical approach based on conventional and hypersingular boundary integral equations is presented. The method allows for the continuous simulation of the bubble motion from growth to collapse and the impact and penetration of the reentrant jet. The numerical investigations show that during penetration the bubble surface is transformed to a ring bubble that is smoothly attached to a vortex sheet. The velocity of the tip of the re-entrant jet is always directed toward the wall during penetration with a speed less than its speed before impact. A high-pressure region is created around the penetration interface. Theoretical analysis and numerical results show that the liquid-liquid impact causes a loss in the kinetic energy of the flow field. Variations in the initial distance from the bubble centre to the wall are found to cause large changes in the details of the flow field. No existing experimental data are available to make a direct comparison with the numerical predictions. However, the results obtained in this study agree qualitatively with experimental observations.

We present a numerical study of the impact of a two-dimensional plunging wave on a rigid vertical wall in the context of potential flow. The plunging wave impinging the wall is generated using a mixed-Eulerian-Lagrangian (MEL) boundary-integral scheme. The initial stage of the impact is characterized by an oblique impact of a liquid wedge on the wall and is solved using a similarity solution. Following the initial impact, the MEL simulation is continued to capture the transient impact process. The effect of an air cushion trapped between the plunger and the wall is considered. In addition to details such as temporal evolutions and surface profiles, the main interests are the maximum impact pressure on the wall and its rise time. To arrive at appropriate scaling laws for these, simulations are performed and correlations are explored for a broad range of local plunging wave kinematic and geometric parameters. To assess the present results, direct comparisons are made with the experiment of Chan & Melville (1988). Reasonable quantitative agreement is obtained and likely sources for discrepancies are identified and discussed.

The behavior of a cavitation bubble adjacent to a rigid wall is studied numerically with the boundary integral method described in Zhang, Duncan, and Chahine [J. Fluid Mech. 257, 147 (1993)]. In the previous work, the pressure inside the bubble was held constant (this is referred to herein as the empty bubble case). In the present calculations, an internal gas pressure, which is a function of the bubble volume, is included in the model. The present results are qualitatively similar to those in the empty bubble case in several ways: a wall-directed reentrant jet is formed in the later phase of the collapse; this jet impacts with the side of the bubble closest to the wall creating a toroidal-shaped bubble; and a shear layer develops along the impact interface. However, unlike the empty bubble, whose volume decreases monotonically to zero at the end of the collapse, the present gas-filled bubble reaches a minimum volume and then, due to its high internal gas pressure, begins to grow again (rebound). In the empty bubble case, the hydrodynamic pressure on the wall rises rapidly at the end of the calculation making it impossible to compute the maximum value of the pressure. In the present calculations, the pressure on the wall is found to reach a maximum value when the bubble starts to rebound. This timing of the pressure peak is in agreement with the experimental data of Tomita and Shima [J. Fluid Mech. 169, 535 (1986)] and Kimoto [International Symposium on Cavitation Research Facilities and Techniques (American Society of Mechanical Engineers, New York, 1987), Vol. 57, pp. 535–564], as are the orders of magnitude of the maximum pressures. Direct comparison with the numerical results of Best [J. Fluid Mech. 251, 79 (1993)] are also presented. Large differences in bubble shapes and flow fields are found.

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