Numerical simulation of the interaction between a vortex ring and a bubble plume

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.

On the dynamics of vortex–droplet co-axial interaction: insights into droplet and vortex dynamics

“…A similar type of secondary ring was also observed in the interaction of the vortex ring with a wall (Walker et al. 1987; Hu & Peterson 2018) or its co-axial collision with a solid sphere (Allen, Joanne & Shashikanth 2007; de Sousa 2011; Yu, Huang & Lu 2014; Nguyen, Degawa & Uchiyama 2019). In the above studies, the interaction of primary and secondary vortex rings has shown significant influence on the primary vortex ring characteristics.…”

Numerical simulation of bubbly flow around a cylinder by semi-Lagrangian–Lagrangian method

“…Based on these assumptions, the mass and momentum conservation equations for the liquid phase are explained as (Nguyen et al , 2019a; Nguyen et al , 2019b; Soolichin and Eienberger, 1997; Sokolichin and Eigenberger, 1999; Uchiyama and Yoshii, 2015): Where: and α l is the liquid volume fraction, which correlates with the gas volume fraction α g by: …”

“…The momentum equation for the motion of an individual spherical bubble, proposed by Auton et al (1988), reviewed by Sridhar and Katz (1995) and used in the semi-L–L model (Nguyen et al , 2019a; Nguyen et al , 2019b; Uchiyama and Yoshii, 2015), is expressed as: where F B , F D, F L , F VM and F P are forces acting upon a spherical bubble and have been expressed by Sridhar and Katz (1995), as shown in Table I. Equation (5) can then be rewritten as follows: where β is the density ratio between the gas and liquid phases and the virtual-mass and the lift coefficients on a spherical bubble, C V and C L , respectively, moving at low Reynolds numbers, are equal to 0.5.…”

“…This classification is based on a mathematical description of each phase, with which its governing equations are solved using either a mesh-free method or mesh-based method. Here, a semi-Lagrangian–Lagrangian (semi-L–L) method composed of a vortex-in-cell (VIC) method for the liquid phase and a Lagrangian description of the gas phase is developed, based on previous works (Nguyen et al , 2016; Nguyen et al , 2019b; Uchiyama and Yoshii, 2015; Uchiyama et al , 2014), for the simulation of a bubbly flow around an obstacle.…”

“…The VIC method has also been used to simulate a variety of two-phase flows such as bubbly flows by Uchiyama and Yoshii (2015) and solid particle–gas flows by Uchiyama and Shimada (2014). In this study, the VIC method used to simulate bubbly flow (Nguyen et al , 2019a; Nguyen et al , 2019b; Uchiyama and Yoshii, 2015) is combined with an IB method (Nguyen et al , 2016) to investigate the characteristics of a bubbly flow around a circular cylinder. The remainder of this chapter is organized as follows: the numerical method is explained in Section 2, the results are discussed in Section 3 and conclusions are given in Section 4.…”