Transient cavities near boundaries. Part 1. Rigid boundary

TLDR

Transient vapor cavities near rigid boundaries in buoyancy and stagnation‑point flows are modeled using a boundary‑integral method. The study employs this method to compute bubble shapes, particle pathlines, pressure contours, and uses Kelvin impulse criteria to predict migration direction and jet formation. Simulations show that collapsing bubbles can migrate toward or away from the boundary depending on parameters, can form hour‑glass shapes, and may ultimately split into two toroidal bubbles or ring vortices of opposite circulation.

Abstract

The growth and collapse of transient vapour cavities near a rigid boundary in the presence of buoyancy forces and an incident stagnation-point flow are modelled via a boundary-integral method. Bubble shapes, particle pathlines and pressure contours are used to illustrate the results of the numerical solutions. Migration of the collapsing bubble, and subsequent jet formation, may be directed either towards or away from the rigid boundary, depending on the relative magnitude of the physical parameters. For appropriate parameter ranges in stagnation-point flow, unusual ‘hour-glass’ shaped bubbles are formed towards the end of the collapse of the bubble. It is postulated that the final collapsed state of the bubble may be two toroidal bubbles/ring vortices of opposite circulation. For buoyant vapour cavities the Kelvin impulse is used to obtain criteria which determine the direction of migration and subsequent jet formation in the collapsing bubble.