Numerical analysis of the jet stage of bubble near a solid wall using a front tracking method

Abstract

The dynamics of a toroidal bubble near a solid wall for a large part of stand-off parameters γ (γ=d/Rmax, d is the distance between the solid wall and the bubble centre at the moment of formation and Rmax is the maximum bubble radius) have been extensively studied, but some mechanics of a toroidal bubble are not completely clear, especially for the small stand-off parameters γ ≤ 0.8. In the present study, on the basis of the finite volume method, the Navier-Stokes equations with inviscid and incompressible assumption are directly solved using a staggered grid on the fixed grid. The dynamics of the toroidal bubble near the solid for different stand-off parameters (γ = 0.4, 0.6, 0.8, and 0.97, respectively) are simulated by a front tracking method. Initial conditions of numerical simulation are estimated through the Rayleigh–Plesset equation, based on the maximum size and collapse time of a spark-generated bubble. One of the numerical results is compared with a spark-generated bubble experiment, showing that the results between them are favorable with regard to both the bubble shape history and translational motion of the bubble. The numerical results for the different stand-off parameters, including the change process of the water layer, the development process of the splash flow and radial flow, the splitting phenomenon of the toroidal bubble, and the trend of pressure on the center of the solid wall, are discussed, where some new phenomena are discovered.