Numerical derivation of the drag force coefficient in bubble swarms using a Front Tracking model


Dijkhuizen, Wouter and Roghair, Ivo and Sint Annaland, Martin van and Kuipers, Hans (2008) Numerical derivation of the drag force coefficient in bubble swarms using a Front Tracking model. In: 6th International Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries, CFD 2008, 10-12 June 2008, Trondheim, Norway.

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Abstract:Dispersed gas-liquid flows are often encountered in the
chemical process industry. Large scale models which describe
the overall behavior of these flows use closure relations to
account for the interactions between the phases, such as the
drag, lift and virtual mass forces. The closure relations for the
drag force on a single rising bubble in an infinite quiescent
liquid has been studied in great detail, both by dedicated
experiments and detailed numerical simulations. However, the
effect of neighboring bubbles on the drag coefficient
experienced by a bubble in a bubble swarm is much less
studied, despite its strong influence on the hydrodynamics and
mass and heat transfer. It is very difficult to measure the drag
coefficient on a bubble in a bubble swarm, especially at high
gas hold-ups, a.o. because of lack of visual accessibility.
Detailed information on the drag force in bubble swarms can
however be obtained using Direct Numerical Simulations
(DNS). In this work, a fully resolved 3D Front Tracking
model (Van Sint Annaland et al., 2006) is used to derive
closures for the drag coefficient in mono-disperse bubble
swarms, extending the work by Dijkhuizen et al. (2005) on the
drag coefficient on a bubble rising in an initially quiescent
First, it was found that for bubble swarms in relatively viscous
liquids, a single bubble in a domain with periodic boundary
conditions in all three directions can accurately mimic an
infinite swarm of equally sized bubbles. The time averaged
drag force coefficient on a single bubble in a periodic domain
(mimicking a structured array of bubbles) was equal to the
time and number averaged drag force coefficient in case
several bubbles were positioned in a periodic domain
(mimicking a random array of bubbles). For less viscous
liquids, such as water, simulations with several bubbles in a
periodic domain are required to accurately determine the drag
force coefficient.
Front Tracking simulations have been performed for air
bubble swarms in two different liquids: a water/glycerol
mixture with a viscosity of 0.10 Pa·s, and water, where the
bubble size and void fraction (up to 15%) were varied. In all
cases studied, hindered rise was found (i.e. a higher drag force
coefficient of a bubble in a bubble swarm in comparison with
the drag force on a single bubble), explained by the increased
liquid flow in between the bubbles (see Fig. 1). For bubbles
with a larger diameter, the relative increase in experienced
drag was lower, which is caused by bubble shape deformation:
larger bubbles become more spherical, when they rise in a
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