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

W. Dijkhuizen, I. Roghair, M. van Sint Annaland, J.A.M. Kuipers

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    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 liquid. 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 swarm.
    Original languageUndefined
    Number of pages9
    Publication statusPublished - 2008
    Event6th International Conference on CFD in the Oil & Gas, Metallurgical and Process Industries 2008 - Trondheim, Norway
    Duration: 10 Jun 200812 Jun 2008


    Conference6th International Conference on CFD in the Oil & Gas, Metallurgical and Process Industries 2008
    Other10-12 June 2008


    • IR-67408

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