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A lattice Boltzmann study on the drag force in bubble swarms

Published online by Cambridge University Press:  09 May 2011

J. J. J. GILLISSEN ,
S. SUNDARESAN  and
H. E. A. VAN DEN AKKER
J. J. J. GILLISSEN*
Affiliation:
Department of Multi-Scale Physics, J. M. Burgers Centre for Fluid Mechanics, Delft University of Technology, Prins Bernhardlaan 6, 2628 BW Delft, The Netherlands
S. SUNDARESAN
Affiliation:
Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA
H. E. A. VAN DEN AKKER
Affiliation:
Department of Multi-Scale Physics, J. M. Burgers Centre for Fluid Mechanics, Delft University of Technology, Prins Bernhardlaan 6, 2628 BW Delft, The Netherlands
*
†Email address for correspondence: j.j.j.gillissen@tudelft.nl
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Abstract

Lattice Boltzmann and immersed boundary methods are used to conduct direct numerical simulations of suspensions of massless, spherical gas bubbles driven by buoyancy in a three-dimensional periodic domain. The drag coefficient CD is computed as a function of the gas volume fraction φ and the Reynolds number Re = 2RUslip/ν for 0.03 φ 0.5 and 5 Re 2000. Here R, Uslip and ν denote the bubble radius, the slip velocity between the liquid and the gas phases and the kinematic viscosity of the liquid phase, respectively. The results are rationalized by assuming a similarity between the CD(Reeff)-relation of the suspension and the CD(Re)-relation of an individual bubble, where the effective Reynolds number Reeff = 2RUslip/νeff is based on the effective viscosity νeff which depends on the properties of the suspension. For Re ≲ 100, we find νeff ≈ ν/(1−0.6φ1/3), which is in qualitative agreement with previous proposed correlations for CD in bubble suspensions. For Re ≳ 100, on the other hand, we find νeff ≈ RUslipφ, which is explained by considering the turbulent kinetic energy levels in the liquid phase. Based on these findings, a correlation is constructed for CD(Re, φ). A modification of the drag correlation is proposed to account for effects of bubble deformation, by the inclusion of a correction factor based on the theory of Moore (J. Fluid Mech., vol. 23, 1995, p. 749).

JFM classification

Drops and Bubbles: Bubble dynamics Turbulent Flows: Turbulence simulation

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 101 - 121
Copyright
Copyright © Cambridge University Press 2011

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