Purpose This study aims to provide discussions of the numerical method and the bubbly flow characteristics of an annular bubble plume. Design/methodology/approach The bubbles, released from the annulus located at the bottom of the domain, rise owing to buoyant force. These released bubbles have diameters of 0.15–0.25 mm and satisfy the bubble flow rate of 4.1 mm3/s. The evolution of the three-dimensional annular bubble plume is numerically simulated using the semi-Lagrangian–Lagrangian (semi-L–L) approach. The approach is composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Findings First, a new phenomenon of fluid dynamics was discovered. The bubbly flow enters a transition state with the meandering motion of the bubble plume after the early stable stage. A vortex structure in the form of vortex rings is formed because of the inhomogeneous bubble distribution and the fluid-surface effects. The vortex structure of the flow deforms as three-dimensionality appears in the flow before the flow fully develops. Second, the superior abilities of the semi-L–L approach to analyze the vortex structure of the flow and supply physical details of bubble dynamics were demonstrated in this investigation. Originality/value The semi-L–L approach is applied to the simulation of the gas–liquid two-phase flows.

This study is dealing with the two-dimensional numerical simulation of a plane bubble plume experimentally investigated by Alam and Arakeri. A vortex method for gas-liquid twophase flow, proposed by the authors in a prior paper, is applied for the simulation. The method simulates the bubble motion and the induced liquid flow by the two-way coupling approach. In a tank containing water, small hydrogen bubbles are released from an electrode placed on the base of the tank. The bubbles, rising due to the buoyant force, cause the vortical flow of water. The existing numerical methods, such as the finite-difference method and the finitevolume method, compute the bubble plume with regard to the velocity field. But the vortex method calculates directly the vorticity field. Therefore, it promises to simulate successfully the vortical structure predominating the bubble plume. The present simulation makes clear that the meandering behaviour of bubble plume is caused by the large-scale eddies induced by the rising bubbles. The effect of bubble flowrate on the meandering behaviour in the simulation is confirmed to agree well with the experiment. It is also demonstrated that the time-averaged water velocity on the horizontal sections satisfies the similarity distribution when the bubble flowrate is low. These indicate that the authors' vortex method is indeed applicable to the analysis of plane bubble plume.

No abstract

Purpose This paper aims to provide discussions of a numerical method for bubbly flows and the interaction between a vortex ring and a bubble plume. Design/methodology/approach Small bubbles are released into quiescent water from a cylinder tip. They rise under the buoyant force, forming a plume. A vortex ring is launched vertically upward into the bubble plume. The interactions between the vortex ring and the bubble plume are numerically simulated using a semi-Lagrangian–Lagrangian approach composed of a vortex-in-cell method for the fluid phase and a Lagrangian description of the gas phase. Findings A vortex ring can transport the bubbles surrounding it over a distance significantly depending on the correlative initial position between the bubbles and the core center. The motion of some bubbles is nearly periodic and gradually extinguishes with time. These bubble trajectories are similar to two-dimensional-helix shapes. The vortex is fragmented into multiple regions with high values of Q, the second invariant of velocity gradient tensor, settling at these regional centers. The entrained bubbles excite a growth rate of the vortex ring's azimuthal instability with a formation of the second- and third-harmonic oscillations of modes of 16 and 24, respectively. Originality/value A semi-Lagrangian–Lagrangian approach is applied to simulate the interactions between a vortex ring and a bubble plume. The simulations provide the detail features of the interactions.

No abstract