Skip to main content Accessibility help
×
Home

A lattice Boltzmann study on the drag force in bubble swarms

  • J. J. J. GILLISSEN (a1), S. SUNDARESAN (a2) and H. E. A. VAN DEN AKKER (a1)

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 = 2RUslipeff 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 νeffRUslipφ, 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).

Copyright

Corresponding author

Email address for correspondence: j.j.j.gillissen@tudelft.nl

References

Hide All
Barnea, E. & Mizrahi, J. 1973 A generalized approach to the fluid dynamics of particulate systems: Part 1. general correlation for fluidization and sedimentation in solid multiparticle systems. Chem. Engng J. 5, 171189.
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. Phys. Rev. 94, 511.
Blanco, A. & Magnaudet, J. 1995 The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Phys. Fluids 7, 1265.
Bunner, B. & Tryggvason, G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77118.
Cercignani, C. 1988 The Boltzmann Equation and its Applications. Springer.
Chen, M., Kontomaris, K. & McLaughlin, J. B. 1998 Direct numerical simulation of droplet collisions in a turbulent channel flow. Part I: collision algorithm. Intl J. Multiphase Flow 24, 10791103.
Colosqui, C. E. 2010 High-order hydrodynamics via lattice Boltzmann methods. Phys. Rev. E 81, 026702.
Duineveld, P. C. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325332.
Esmaeeli, A. & Tryggvason, G. 2005 A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number. Phys. Fluids 17, 093303.
Garnier, C., Lance, M. & Marié, J. L. 2002 Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction. Exp. Therm. Fluid Sci. 26, 811815.
Harteveld, W. K., Mudde, R. F. & Van Den Akker, H. E. A. 2003 Dynamics of a bubble column: Influence of gas distribution on coherent structures. Can. J. Chem. Engng 81, 389394.
He, X. & Luo, L.-S. 1997 A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55 (6/A), 63336336.
Ishii, M. & Zuber, N. 1979 Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J. 25, 843855.
Kim, J., Kim, D. & Choi, H. 2001 An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput Phys. 171, 132150.
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 555.
Martínez-Mercado, J., Palacios-Morales, C. A. & Zenit, R. 2007 Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for 10 < Re < 500. Phys. Fluids 19, 103302.
Maxworthy, T., Gnann, C., Kurten, M. & Durst, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421441.
Mei, R. & Klausner, J. F. 1992 Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free-stream velocity. Phys. Fluids 4, 6370.
Moore, W. D. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749766.
Philippi, P. C., Hegele, L. A. Jr., dos Santos, L. O. E. & Surmas, R. 2006 From the continuous to the lattice Boltzmann equation: The discretization problem and thermal models. Phys. Rev. E 73, 056702.
Riboux, G., Risso, F. & Legendre, D. 2010 Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J. Fluid Mech. 643, 509539.
Roma, A. M., Peskin, C. S. & Berger, M. J. 1999 An adaptive version of the immersed boundary method. J. Comput Phys. 153, 509534.
Sangani, A. S. & Acrivos, A. 1983 Creeping flow through cubic arrays of spherical bubbles. Intl J. Multiphase Flow 9, 181185.
Sangani, A. S. & Didwania, A. K. 1993 Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech. 250, 307337.
Shan, X., Yuan, X.-F. & Chen, H. 2006 Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation. J. Fluid Mech. 550, 413441.
Somers, J. A. 1993 Direct simulation of fluid flow with cellular automata and the lattice-Boltzmann equation. Appl. Sci. Res. 51 (1/2), 127.
Ten Cate, A., Deksen, J. J., Portela, L. M. & Van Den Akker, H. E. A. 2004 Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233.
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448476.
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20, 053305.
Van Sint Annaland, M., Dijkhuizen, W., Deen, N. G. & Kuipers, J. A. M. 2006 Numerical simulation of behavior of gas bubbles using a 3-D front-tracking method. AIChE J. 52, 99110.
Yin, X. & Koch, D. L. 2008 Lattice-Boltzmann simulation of finite Reynolds number buoyancy-driven bubbly flows in periodic and wall-bounded domains. Phys. Fluids 20, 103304.
Zenit, R., Koch, D. L. & Sangani, A. S. 2001 Measurements of the average properties of a suspension of bubbles rising in a vertical channel. J. Fluid Mech. 429, 307342.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

A lattice Boltzmann study on the drag force in bubble swarms

  • J. J. J. GILLISSEN (a1), S. SUNDARESAN (a2) and H. E. A. VAN DEN AKKER (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.