Computational modelling of the interaction of shock waves with multiple gas-filled bubbles in a liquid

Abstract

This study presents a computational investigation of the interactions of a single shock wave with multiple gas-filled bubbles in a liquid medium. This work illustrates how multiple bubbles may be used in shock-bubble interactions to intensify the process on a local level. A high resolution front-tracking approach is used, which enables explicit tracking of the gas-liquid interface. The collapse of two identical bubbles, one placed behind the other is investigated in detail, demonstrating that peak pressures in a two bubble arrangement can exceed those seen in single bubble collapse. Additionally, a parametric investigation into the effect of bubble separation is presented. It is found that the separation distance has a significant effect on both the shape and velocity of the main transverse jet of the second bubble. Extending this analysis to effects of relative bubble size, we show that if the first bubble is sufficiently small relative to the second, it may become entirely entrained in the second bubble main transverse jet. In contrast, if the first bubble is substantially larger than the second, it may offer it significant protection from the incident shock. This protection is utilised in the study of a triangular array of three bubbles, with the central bubble being significantly smaller than the outer bubbles. It is demonstrated that, through shielding of bubbles until later in the collapse process, pressures over five times higher than the maximum pressure observed in the single bubble case may be achieved. This corresponds to a peak pressure that is approximately 40 times more intense than the incident shock wave. This work has applications in a number of different fields, including cavitation erosion, explosives, targeted drug delivery/intensification, and shock wave lithotripsy.

Bubbles with shock waves and ultrasound: a review

“…In a follow-up work, multiple bubbles in an array were simulated [49]. The mechanics of bubble-shockwave interaction can be more complicated when there are multiple bubbles involved.…”

The evolution of the temperature field during cavity collapse in liquid nitromethane. Part I: inert case

“…This wave then combines with S 12 , as seen in Fig. 7f, and is thus labelled as S 12,14,16 . Meanwhile, several reflection/transmission processes take place at the lobe-nitromethane interface, which lead to the lobe closing up due to its rapid compression.…”

“…Bourne and Milne [6,7] modelled the temperature within the collapsing cavity, for circular, triangular and hemispherical isolated cavities and cavities in arrays. Ball et al [8] and Hawker and Ventikos [9] simulated a single cavity collapse in water and computed the water temperature field, while Lauer et al [10], Michael et al [11], and Betney et al [12] simulated the collapse of arrays in water and focused on the effect of the collapse on the pressure field and subsequent pressure amplification. Similarly, the collapse of circular and ellipsoidal cavities collapsing in an inert, hydrodynamically modelled solid material was studied by Ozlem et al [13] who also focused on the pressure fields recovery and Kapila et al [14] who presented temperature fields in an exemplary explosive.…”

Characterizing shock waves in hydrogel using high speed imaging and a fiber-optic probe hydrophone

“…Moreover, such configurations will help validate computational studies of shock-induced cavity collapse. 26,27 FOPH measurements and high-speed images were captured for varying projectile velocities, and these are summarized in Figure 9. As expected, both U s and ρ max increase steadily with projectile velocity.…”