A Numerical Investigation of Bubbles Rising at Intermediate Reynolds and Large Weber Numbers

A Numerical Model of the Flow Past a Spherical-Cap Bubble Rising in a Fluidized Bed

“…Previous work (Hoffmann and Van den Boogaard, 1995) on bubbles in liquids and also the results shown in Figure 7 of this paper show that the simulations result in rise velocities approaching the Davies-Taylor velocities at higher bubble Reynolds numbers, in spite of the a priori assumption of a spherical-cap bubble shape. It therefore seems likely that this assumption does not, in itself, lead to very large errors in the rise velocity.…”

“…As explained by Hoffmann and Van den Boogaard (1995), this requirement follows from the continuity of σ n across the bubble surface combined with the fact that on the gas side of this surface the viscous contribution to σ n is negligible whereas the pressure contribution is approximately constant on that side.…”

Recirculation within a fluid sphere at moderate Reynolds numbers

“…So far only the Hill's vortex solutions have been discussed. It is interesting that in the application of the theoretical results neither Bhaga & Weber (1981) nor Hoffmann & van den Bogaard (1995) attempted to consider the effect of boundary layer corrections on the theoretical predictions. Such corrections are crucial to the analysis of the experimental data, the details of which follow.…”

“…Based on those crucial experiments, the theory of Harper & Moore (1968) is currently preferred to that of Parlange (1970) (e.g. Dandy & Leal 1989;Fan & Tsuchiya 1990;Hoffmann & van den Bogaard 1995;Hoogstraten et al 1998).…”

Simulation of Rising Bubbles Dynamics Using the Lattice Boltzmann Method

“…The wake velocity and the bubble shapes of single and a chain of bubbles were studied by Miyahara et al [23] for various Tadaki numbers (Re×M 0.23 ). Hoffmann et al [24] investigated bubbles rising at intermediate…”