Buoyancy-driven bubbly flows: ordered and free rise at small and intermediate volume fraction

Abstract

Various expressions have been proposed previously for the rise velocity of gas bubbles in homogeneous steady bubbly flows, generally a monotonically decreasing function of the bubble volume fraction. For suspensions of freely moving bubbles, some of these are of the form expected for ordered arrays of bubbles, and vice versa, as they do not reduce to the behaviour expected theoretically in the dilute limit. The microstructure of weakly inhomogeneous bubbly flows not being known generally, the effect of microstructure is an important consideration. We revisit this problem here for bubbly flows at small to moderate Reynolds number values for deformable bubbles, using direct numerical simulation and analysis. For ordered suspensions, the rise velocity is demonstrated not to be monotonically decreasing with volume fraction due to cooperative wake interactions. The fore-and-aft asymmetry of an isolated ellipsoidal bubble is reversed upon increasing the volume fraction, and the bubble aspect ratio approaches unity. Recent work on rising bubble pairs is used to explain most of these results; the present work therefore forms a platform of extending the former to suspensions of many bubbles. We adopt this new strategy also to support the existence of the oblique rise of ordered suspensions, the possibility of which is also demonstrated analytically. Finally, we demonstrate that most of the trends observed in ordered systems also appear in freely evolving suspensions. These similarities are supported by prior experimental measurements and attributed to the fact that free bubbles keep the same neighbours for extended periods of time.

Interaction between a large buoyant bubble and turbulence

“…We have checked that the magnitude of this correction is negligible (max | ψ|/ x 10 −6 in the present simulations). A more detailed description of the numerical method and the results of benchmark tests in laminar flows can be found in [33]. The governing equations (1) and (2) are solved by a projection method [27].…”

“…In our simulations the grid spacing was set to x = 0.64η = d b /16, a resolution found to be sufficient at the Reynolds number considered, and the Courant number based on the instantaneous maximal velocity was always less than 0.1. A more detailed description of the code as well as the results of some benchmark tests is provided in [33].…”

“…This configuration effectively corresponds to a cubic array of bubbles with volume fraction of 0.03%. It was shown in [33] that even at very low volume fraction a bubble rising in quiescent liquid may be affected by the wakes of its preceding neighbors. The situation is however very different here.…”

Phase boundary dynamics of bubble flow in a thick liquid metal layer under an applied magnetic field

“…To optimize these processes, the underlying physics must be well established. Aside from the fact that many aspects of single gas bubble hydrodynamics, let alone bubble collective dynamics and interactions with MF (i.e., coalescence, splitting, collisions, agglomeration, phase boundary/wake dynamics), are not fully understood [1,3,[10][11][12][13][14][15][16], liquid metal systems are notoriously difficult to probe noninvasively, due to their opacity, high temperatures and additional complications due to strong MF [1]. Consequently, visual data regarding how applied MF alters bubble shape and bubble collective dynamics are scarce.…”

Hydrodynamic interaction of bubbles rising side-by-side in viscous liquids

“…Studies of Roghair et al (2011aRoghair et al ( , b, 2013a have resulted in several correlations quantifying the swarm effect on the effective drag coefficient. Recently, Loisy et al (2017) studied bubbles rising in configurations of ordered and freely rising bubble arrays. In addition, the velocity fluctuation of rising bubbles due to the swarm effect was studied experimentally in spite of the experimental limitation at high gas volume fraction (Martínez-Mercado et al 2007;Riboux et al 2010;Colombet et al 2015).…”