Prediction of shock heating during ultrasound-induced bubble collapse using real-fluid equations of state

Abstract

Numerical simulations of collapsing air bubbles considering complex and more accurate equations of state (EoS) for estimating the properties of both the liquid and gas are presented. The necessity for utilising such EoSs in bubble collapse simulations is illustrated by the unphysical (spurious) liquid temperature jump formed in the vicinity of the bubble-air interface when simplified EoSs are used. The solved fluid flow equations follow the mechanical equilibrium multiphase method of Kapila. The solver is coded in the AMReX platform, enabling high-performance computation with parallel processing and Adaptive Mesh Refinement for speeding up simulations. It is initially demonstrated that the frequently used Stiffened Gas (SG) EoS overpredicts the liquid temperature at high compression. More sophisticated EoS models, such as the International Association for the Properties of Water and Steam (IAPWS), the Modified Noble Abel Stiffened Gas (MNASG) and a modified Tait EoS introduced here, are also implemented into the flow solver and their differences are highlighted for bubble collapse cases for the first time. Subsequently, application of the developed model to cases of practical interest is showcased. More specifically, simulations of bubble collapse near a solid wall are presented for conditions simulating shock wave lithotripsy (SWL). It is concluded that for such cases, a maximum increase of 25 K of the liquid temperature in contact along the solid wall is caused during the collapse of the air bubble due to shock wave focusing effects. It is also highlighted that the maximum liquid heating varies depending on the initial bubble-wall stand-off distance.

Keywords: Bubble collapse dynamics; IAPWS data; MNASG; Real-liquid EoS; Shock wave lithotripsy (SWL); Tait EoS.