Numerical study of liquid jet and shock wave induced by two-bubble collapse in open field

Abstract

The shock waves and high-speed jets induced by the violent collapse of bubbles can cause serious damage to nearby structures. To fully understand the shock wave and jet characteristics induced by bubble-bubble interaction, we developed a diffuse-interface method for the simulation of compressible two-phase flow, which combined interface compression technique with interface sharpening technique to keep the sharpness of the shock wave and phase interface. The thermodynamically consistent five-equation model was improved using interface compression technique to maintain a constant thickness of the phase interface. To further suppress numerical dissipation, the high-order scheme WENO (Weighted Essentially Non-Oscillatory) and interface sharpening function THINC (Tangent of Hyperbola for INterface Capturing) were used for the flux reconstruction at the grid boundary to ensure that the total variation at the cell boundary was minimized (Boundary Variation Diminishing, BVD), thus the spatial reconstruction scheme, named WENO-THINC-BVD, was developed. Moreover, we extended the present method to a block-structured adaptive mesh refinement framework to improve grid resolution and save computing resources. Numerical results of several benchmark tests fully demonstrated the advantages of the present method in simulating complex compressible flows containing shock-shock and shock-interface interactions. Based on the present high-fidelity numerical methods, we investigated the shock wave and liquid jet induced by the two-bubble interaction in an open space. A phase diagram of the liquid jet propagation direction as a function of the initial bubble pressure and the inter-bubble distance was summarized. Finally, according to the bubble-bubble interaction process, an empirical formula for the collapse strength and another for the attenuation of shock waves were developed.