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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.

Recent clinical trials have shown the efficacy of a passive acoustic device used during shock wave lithotripsy (SWL) treatment. The device uses the far-field acoustic emissions resulting from the interaction of the therapeutic shock waves with the tissue and kidney stone to diagnose the effectiveness of each shock in contributing to stone fragmentation. This paper details simulations that supported the development of that device by extending computational fluid dynamics (CFD) simulations of the flow and near-field pressures associated with shock-induced bubble collapse to allow estimation of those far-field acoustic emissions. This is a required stage in the development of the device, because current computational resources are not sufficient to simulate the far-field emissions to ranges of O(10 cm) using CFD. Similarly, they are insufficient to cover the duration of the entire cavitation event, and here simulate only the first part of the interaction of the bubble with the lithotripter shock wave in order to demonstrate the methods by which the far-field acoustic emissions resulting from the interaction can be estimated. A free-Lagrange method (FLM) is used to simulate the collapse of initially stable air bubbles in water as a result of their interaction with a planar lithotripter shock. To estimate the far-field acoustic emissions from the interaction, this paper developed two numerical codes using the Kirchhoff and Ffowcs William-Hawkings (FW-H) formulations. When coupled to the FLM code, they can be used to estimate the far-field acoustic emissions of cavitation events. The limitation of the technique is that it assumes that no significant nonlinear acoustic propagation occurs outside the control surface. Methods are outlined for ameliorating this problem if, as here, computational resources cannot compute the flow field to sufficient distance, although for the clinical situation discussed, this limitation is tempered by the effect of tissue absorption, which here is incorporated through the standard derating procedure. This approach allowed identification of the sources of, and explanation of trends seen in, the characteristics of the far-field emissions observed in clinic, to an extent that was sufficient for the development of this clinical device.

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