Abstract
The wobbling motions of single and two inline bubbles rising in quiescent liquid are investigated via three-dimensional simulations using the volume of fluid method. First, we simulate an 8 mm air bubble rising in quiescent water, yielding the wobbling motion. The bubble wobbling has two roles: (1) the excessive curvature speeds up the separation of the boundary layer and (2) the velocity peaks (high Reynolds number) result in the formation of asymmetrical vortices. The oscillation frequencies (6 Hz, St = 0.22) of the bubble movement, the vorticity accumulated on the bubble surface, the lift force and viscous force are the same while the oscillation frequency of the aspect ratio is twice that of the bubble movement. The volume-averaged liquid velocity presents a linear increase with the bubble rise while the kinetic energy displays a quadratic increase. Finally, two bubbles rising inline are investigated with different initial distances. The central breakup of the trailing bubble is observed at a short distance of 2d (d is the bubble diameter). For a longer distance of 6d, the wake of the leading bubble results in the lateral motion of the trailing bubble, depending on the position of the trailing bubble in the wake and the intensity of the vortices it encounters.
Highlights
Bubbles rising in liquids are encountered in many engineering applications, including the chemical engineering, nuclear industry, enhanced oil recovery, and so on.1,2 The rising bubbles in liquid can yield different shapes, paths, and wakes3 due to the coupled effect of gravity, surface tension, and liquid inertia.4 Among others, the wobbling motion with path instability has motivated numerous investigations5 due to its complexity
The oscillation frequencies (6 Hz, Strouhal number (St) 1⁄4 0.22) of the bubble movement, the vorticity accumulated on the bubble surface, the lift force and viscous force are the same while the oscillation frequency of the aspect ratio is twice that of the bubble movement
Weber number (We) calculate the bubble movement, the vorticity accumulated on the bubble surface, the lift force and viscous force exerted on the bubble, which is shown in scitation.org/journal/phf accumulated on the bubble surface, the lift force, and viscous force are the same
Summary
Bubbles rising in liquids are encountered in many engineering applications, including the chemical engineering, nuclear industry, enhanced oil recovery, and so on. The rising bubbles in liquid can yield different shapes, paths, and wakes due to the coupled effect of gravity, surface tension, and liquid inertia. Among others, the wobbling motion with path instability has motivated numerous investigations due to its complexity. There are still open questions about the path instability, the velocity oscillation, and the interaction of the bubble with the wakes. The path instability of single bubble rising in liquid is studied in numerous research studies.. Few research studies focus on the study of two inline bubbles rising in liquid with path instability. Hallez and Legendre studied the flow around a pair of bubbles with various relative angles numerically They showed that a strong shear-induced lift force in the wake of LB acts on TB. The numerical research on two inline bubbles with path instability at high Re is still missing. Another objective of the present research is about the numerical investigation of two inline bubbles with path instability For this purpose, we carry out high-resolution three-dimensional time-dependent simulations on single and two inline bubbles rising in quiescent liquid.
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