Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water

Abstract

A free-Lagrange numerical method is implemented to simulate the axisymmetric jetting collapse of air bubbles in water. This is performed for both lithotripter shock-induced collapses of initially stable bubbles, and for free-running cases where the bubble initially contains an overpressure. The code is validated using two test problems (shock-induced bubble collapse using a step shock, and shock–water column interaction) and the results are compared to numerical and experimental results. For the free-running cases, simulations are conducted for a bubble of initial radius 0.3 mm located near a rigid boundary and near an aluminium layer (planar and notched surfaces). The simulations suggest that the boundary and its distance from the bubble influence the flow dynamics, inducing bubble elongation and jetting. They also indicate stress concentration in the aluminium and the likelihood of aluminium deformation associated with bubble collapse events. For the shock-induced collapse, a lithotripter shock, consisting of 56 MPa compressive and −10 MPa tensile waves, interacts with a bubble of initial radius 0.04 mm located in a free field (case 1) and near a rigid boundary (case 2). The interaction of the shock with the bubble causes it to involute and a liquid jet is formed that achieves a velocity exceeding 1.2 km s−1 for case 1 and 2.6 km s−1 for case 2. The impact of the jet on the downstream wall of the bubble generates a blast wave with peak overpressure exceeding 1 GPa and 1.75 GPa for cases 1 and 2, respectively. The results show that the simulation technique retains sharply resolved gas/liquid interfaces regardless of the degree of geometric deformation, and reveal details of the dynamics of bubble collapse. The effects of compressibility are included for both liquid and gas phases, whereas stress distributions can be predicted within elastic–plastic solid surfaces (both planar and notched) in proximity to cavitation events. There is a movie with the online version of the paper.

Prediction of far-field acoustic emissions from cavitation clouds during shock wave lithotripsy for development of a clinical device

“…The interaction between the lithotripter shock and expansion waves originating at the bubble surface results in weakening and curvature of the shock. The dynamic behaviour of the collapse of bubble 1 is nearly identical to the problem for a single air bubble in the free field [14]. Bubble 1 is collapsed by the shock wave, and a strong air shock propagates in bubble 1, whereas a weak pressure wave is transmitted in the air of bubble 2.…”

“…In the years since its discovery, several laboratories around the world have found ways to exploit this interpretation of the two peak structure by the Gilmore model to characterize responses as a result of lithotripsy [61][62][63][64][65][66]. Indeed, application of the technique to in vivo data [46] identified the initial bubble size to be used in the CFD simulations in this and earlier papers in the series [14,15,21].…”

“…In introducing figure 9b, it was noted that the only source of asymmetry in the radiated field came from the finite time for the passage of the lithotripter shock wave across a spatially distributed bubble cloud (and even then it lacks bubble-bubble interactions that can affect emissions in clouds; [13,68]). In the free-Lagrange simulations, the ability to introduce a nearby boundary with real material properties was demonstrated [14], but even this cannot mimic the acoustical effects of the stone because the far-field pressures will also include emissions generated by the finite size of the stone (internal reflections-including resonances-and surface waves [17,69]). The passive sensor was designed to detect these in m 1 so that they could be included in the diagnosis.…”

“…The far-field acoustic wave of the bubble cloud predicted here is for the interaction of these stable bubbles with the subsequent incident lithotripter shock wave. These assumptions are not inherent in the process, and the scheme could readily be used to include a range of initial bubble conditions (initial bubble sizes and wall speeds, collapse by bubble-generated pressure fields, inter-bubble effects) because these can all be included in the separate computational fluid dynamics (CFD) simulations of the type Although bubble fragmentation is included in the free-Lagrange bubble wall simulations, these blast wave emissions occur prior to significant fragmentation [14], and so while fragmentation can, in principle, affect cavitation noise [56], it does not do so here because the initial number and size of bubbles are stated within the initial conditions. shown in figure 4.…”

“…This study forms the third part in a series of simulation studies [14,15] that complement a series of laboratory and clinical studies [16][17][18], which together form a coherent research programme aimed at the development of a passive acoustic device for monitoring the effectiveness of SWL. Following successful clinical trials where its automated response proved to have 94.7 per cent sensitivity in predicting a successful patient outcome, compared with 36.8 per cent achieved by the clinician performing the treatment [18], this device is currently being used for real-time assessment of treatment in the clinic (a typical lithotripsy treatment lasts about an hour).…”