Direct numerical simulations of the drag force of bi-disperse bubble swarms

Numerical simulations of bubbly flows in industrial process equipment rely for an important part on accurate modeling of the drag force. The drag acting on bubbles determines the rise velocity to a very large extent and hence the inter-phase mass transfer characteristics. Recently, we have proposed a correlation (Roghair et al., 2011a) to describe the drag on bubbles in a mono-disperse bubble swarm up to high gas fractions, and in this work we have extended this work to simulations of dense bi-disperse bubble swarms. The influence of the gas hold-up is determined by simulating a bi-disperse swarm of 8 relatively small bubbles (3.5 mm) and 8 relatively large bubbles (4.4 mm) in a periodic domain. The resulting drag coefficient acting on the bubbles agrees very well with the earlier proposed correlation. The composition of the swarm has first been varied in different ways; first, the ratio of the number of large to small bubbles was varied. In this case, the resulting drag coefficient remained constant indicating that no influence of the number of large and small bubbles is expected, with a typical deviation from the mono-disperse correlation up to 15%. Second, the composition of the bi-disperse swarm has been changed by altering the diameter ratio. These simulations showed a good agreement with the mentioned correlation as well. In general, it can be said that the mono-disperse correlation describes the drag coefficient of the bubbles in a bi-disperse swarm well if an error margin in the order of 15% is allowed for.