Chemical Engineering Science 54 (1999) 171—183 Rise velocity of a swarm of large gas bubbles in liquids R. Krishna*, M.I. Urseanu, J.M. van Baten, J. Ellenberger Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, Netherlands Received 19 January 1998; accepted 2 September 1998 Abstract This paper develops a procedure for estimation of the rise velocity of a swarm of large gas bubbles in a bubble column operating in the churn-turbulent flow regime. The large bubble swarm velocity is estimated by introducing two correction factors into the classical Davies—Taylor (1950) relation for rise of a single spherical cap bubble in a liquid »  "0.71 gd  (SF) (AF) . The scale correction factor (SF) accounts for the influence of the column diameter. This correction is given by the Collins relation (J. Fluid Mech., 28, 97—112, 1967) and is a function of the ratio of the bubble diameter d  to the column diameter D  . Volume-of-fluid simulations confirm the validity of the Davies—Taylor—Collins relations for a variety of liquid properties. The acceleration factor (AF) accounts for the increase in the rise velocity of a bubble because of its interaction with the wake of a bubble preceding it. By analysis of video recordings of the interactions between two bubbles, both in-line and off-line, it is found that the acceleration factor AF increases linearly as the vertical distance of separation between the two bubbles decreases. Increasing liquid viscosity reduces this wake acceleration effect. With the aid of an extensive data set on the large bubble swarm velocity in columns of 0.051, 0.1, 0.174, 0.19, 0.38 and 0.63 m in diameter a correlation is developed for the acceleration factor. The large bubble swarm velocity is found to be three to six times higher than that of a single isolated bubble.  1998 Elsevier Science Ltd. All rights reserved. Keywords: Bubble columns; Large bubbles; Churn-turbulent flow regime; Bubble rise velocity; Wall effect; Wake acceleration effects; Column diameter influence; Volume-of-fluid simulations 1. Introduction Bubble column reactors are often operated in the het- erogeneous flow regime at high gas throughputs (typi- cally higher than 0.1 m/s), high pressures (gas densities approaching 20 kg/m), and in columns of large dia- meters (approaching 6 m). A simplified picture of the hydrodynamics in the churn-turbulent regime is por- trayed in Fig. 1, which shows that the bubble swarm consists of both ‘small’ and ‘large’ bubbles. The small bubbles are in the size range of 3 to 6 mm and are either spherical or ellipsoidal in shape depending the physical properties of the liquid (Clift et al., 1978). The large bubbles are typically in the range of 20—80 mm range (De Swart et al., 1996) and these bubbles undergo frequent *Corresponding author. Tel.: #31 20 527 7007; fax: #31 20 5255604; e-mail: krishna@chemeng.chem.uva.nl. coalescence and breakup. The large bubbles can have rise velocities approaching 2 m/s (Krishna and Ellenberger, 1996; Wezorke, 1986) and because of the severe bypass- ing effect, these bubbles largely determine the gas phase conversion. It is therefore important to be able to predict the large bubble velocity. While the estimation of the rise velocity of a swarm of small bubbles is reasonably well established (Clift et al., 1978; Fan and Tsuchiya, 1990), the estimation of the large bubble rise velocity is much more uncertain. There are two empirical correlations for estimating the rise velocity of swarms of large bubbles. The first one due to Wilkinson et al. (1992) is »     "2.25    g           #2.4  (º!º  )         g           (1) 0009-2509/99/$ — see front matter  1998 Elsevier Science Ltd. All rights reserved PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 2 4 5 - 0