Vertically neutral collapse of a pulsating bubble at the corner of a free surface and a rigid wall

Abstract

Vertically neutral collapse of a pulsating bubble occurs when the boundaries above or below the bubble balance the buoyancy effect over a pulsation. In this study, the vertically neutral collapse of a bubble near a vertical rigid wall below the free surface is investigated. The boundary integral method (BIM) is employed to model the bubble dynamics with an open-domain free surface. Moreover, this method is validated against several buoyant bubble experiments. Bubble dynamics in such conditions are associated with three dimensionless parameters: the bubble-free surface distance $\gamma _{{f}}$ , bubble–wall distance $\gamma _{{w}}$ and buoyancy parameter $\delta$ . We derive the Kelvin impulse of a spherical bubble and the algebraic relationship for vertically neutral collapse, which proves to be accurate for predicting vertically neutral collapse when the bubble is relatively far from the boundaries. Four patterns of the vertically neutral collapse of the bubble for different $\gamma _{{w}}$ and $\gamma _{{f}}$ are identified: (i) formally downward jet; (ii) annular collapse; (iii) horizontal jet; and (iv) weak jet. Despite the downward jet shape, the ‘formally downward jet’ is in the vertically neutral collapse state in terms of the profile of toroidal bubbles and the orientation of local high-pressure zones around the bubble at jet impact. A bulge with a high curvature above the bubble in the ‘annular collapse’ pattern is formed during bubble collapse under two local high-pressure zones at the left and right extremities of the bubble. The ‘horizontal jet’ pattern has the greatest potential to attack the wall, and the power laws of the moment of the jet impact, jet velocity and bubble displacement with respect to the theoretical Kelvin impulse are discussed. In particular, we quantitatively illustrate the role of the free surface on bubble migration towards the wall through the variational power-law exponents of the bubble displacement with respect to $\gamma _{{w}}$ .

Dynamic Response of a Warship’s Metal-Jet-Damaged Double-Layer Plates Subjected to the Subsequent Underwater Explosion

“…Currently, scholars have initiated studies on the interaction between bubbles and boundaries with breaches [6][7][8][9]. For instance, Cui et al [10] studied the mechanism of interaction between a single bubble generated by electric sparks and a perforated wall, identifying the critical distance at which the bubble moves away from the incomplete boundary.…”

Numerical and experimental investigations on the jet and shock wave dynamics during the cavitation bubble collapsing near spherical particles based on OpenFOAM

“…Sun et al [24] found that a rigid wall with a gas entrapping hole can change the direction of motion of the bubble and the jet morphology, thus effectively reducing cavitation on the wall surface. Li et al [25] , [26] found that cavitation bubble near the free surface and vertically rigid wall has four jet behaviors, namely, 'formally downward jet', 'annular collapse', 'horizontal jet' and 'weak jet'. For jet dynamics near a single particle, with the increase of the distance between the cavitation bubble and the particle, Zevnik and Dular [27] observed the transition of the jet from a fast, thin, annular shape to a spherical shape.…”

Theoretical study on bubble dynamics under hybrid-boundary and multi-bubble conditions using the unified equation

“…Furthermore, when the bubble buoyancy effect is considered, the jet may turn from downward to upward upon improving the buoyancy effect [60]. When both a free surface and a sidewall are present at similar distances to the bubble, the bubble is more affected by the free surface, producing a downward but slightly inclined jet [61][62][63][64]. Li et al [65] investigated three boundaries, including the free surface, sidewall, and bottom wall, and linked the various bubble collapse patterns (e.g., jetting and quasi-spherical collapsing) to distance parameters and the buoyancy effect.…”