Dynamic interaction of a bubble and discontinuous boundaries: A three-dimensional study with the fast multipole boundary element method

Abstract

A high-pressure oscillating bubble near discontinuous boundaries (composed of a vertical air-backed plate with a circular opening and a free surface) may generate a high-speed water spike through the opening. This phenomenon is relevant to the survivability of the warship and marine structures subject to underwater explosions, needle-free injection, and inkjet printing. The complicated interactions among the oscillating bubble, the water spike through the opening, and the free surface wave are modelled using the dual fast multipole boundary element method. A moving five-point least-squares smoothing scheme is adopted to maintain smoothness of the surface of the opening. Multiple water jets form during the late compression stage of the bubble owing to the influence of the complex boundaries and gravity, and are directed away from the discontinuous boundaries, with the result that the jet may not impact on the broken boundary. The compression of the bubble induces the necking of the water spike passing through the opening and the formation of a cavity in the area near the opening, reducing the amount of water flooding through the opening. Nevertheless, the depth and speed of the flooding water spike due the oscillating bubble can be much larger than those in the natural flooding case (i.e., in the absence of an oscillating bubble). Both the late expansion and the compression stages of the bubble can accelerate the speed of the water spike. In the case of an opening caused by damage to the cabin wall of a marine vessel, such high-speed spikes may have significant effects on structures and facilities inside the cabin, especially for small opening sizes and short distances between bubble and opening. The results also reveal that at large depths, the dynamic behaviour of the water spike is dominated by hydrostatic pressure, and the interaction between bubble and inrushing water becomes weaker.