Lattice Boltzmann simulation to study multiple bubble dynamics

Lattice Boltzmann method (LBM) has been used in this study to understand the behavior of bubble motion and bubble coalescence in liquids. Highly isotropic gradient vectors have been obtained on a lattice for two-phase simulations using LBM. For a fully periodic domain, bubble dynamics and shape for a single bubble and multiple bubbles are dependent on Eotvos number, Reynolds number and Morton number. For single bubble simulations, computations were done for high Eotvos and low to moderate Reynolds numbers, and the results are matched with the experimentally quantified flow visualization chart. The drag coefficient for single bubble motion under buoyancy for both two- and three-dimensional simulations compares well with existing correlations. For multiple bubbles, the bubble dynamics is dictated by the vortex pattern of the leading bubble, which allows the bubbles to coalesce. Coalescence can be described as a three stage process: collision; drainage of the liquid film between adjacent bubbles to a critical thickness; and rupture of this thin film of liquid. Such simulations have also been run for different configurations of the initial bubble distribution for both in-line and staggered bubble configuration to show the effect of vortex shedding on the oscillatory motion of the bubbles and subsequent coalescence.

[1]  D. Martínez,et al.  On boundary conditions in lattice Boltzmann methods , 1996 .

[2]  Ching-Long Lin,et al.  A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio , 2005 .

[3]  Ching-Long Lin,et al.  Lattice Boltzmann Study of Bubble Dynamics , 2006 .

[4]  T. Inamuro,et al.  Lattice Boltzmann simulation of droplet collision dynamics , 2004 .

[5]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[6]  Hongwei Zheng,et al.  A lattice Boltzmann model for multiphase flows with large density ratio , 2006, J. Comput. Phys..

[7]  Owen C. Jones,et al.  The interrelation between void fraction fluctuations and flow patterns in two-phase flow , 1975 .

[8]  Gretar Tryggvason,et al.  Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays , 1998, Journal of Fluid Mechanics.

[9]  Zanetti,et al.  Use of the Boltzmann equation to simulate lattice gas automata. , 1988, Physical review letters.

[10]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[11]  Kaichiro Mishima,et al.  Flow regime transition criteria for upward two-phase flow in vertical narrow rectangular channels , 2001 .

[12]  Qisu Zou,et al.  Evaluation of Two Lattice Boltzmann Models for Multiphase Flows , 1997 .

[13]  Takaji Inamuro,et al.  Numerical simulation of bubble flows by the lattice Boltzmann method , 2004, Future Gener. Comput. Syst..

[14]  L. G. Leal,et al.  Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid , 1984, Journal of Fluid Mechanics.

[15]  Daniel H. Rothman,et al.  Immiscible cellular-automaton fluids , 1988 .

[16]  David R. Noble,et al.  A consistent hydrodynamic boundary condition for the lattice Boltzmann method , 1995 .

[17]  P. Fischer,et al.  Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[19]  Daniel D. Joseph,et al.  Rise velocity of a spherical cap bubble , 2002, Journal of Fluid Mechanics.

[20]  Akio Tomiyama,et al.  Simulation of Bubble Motion under Gravity by Lattice Boltzmann Method , 2001 .

[21]  B. R. Sehgal,et al.  Numerical investigation of bubble growth and detachment by the lattice-Boltzmann method , 2001 .

[22]  J. Buick,et al.  Gravity in a lattice Boltzmann model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Ioannis G. Kevrekidis,et al.  Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method , 2002, Journal of Fluid Mechanics.

[24]  Shiyi Chen,et al.  A lattice Boltzmann model for multiphase fluid flows , 1993, comp-gas/9303001.

[25]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  X. Shan.  Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Laura Schaefer,et al.  Equations of state in a lattice Boltzmann model , 2006 .

[28]  Sankaran Sundaresan,et al.  Lift force in bubbly suspensions , 2002 .

[29]  Yeomans,et al.  Lattice Boltzmann simulation of nonideal fluids. , 1995, Physical review letters.

[30]  Martin E. Weber,et al.  Bubbles in viscous liquids: shapes, wakes and velocities , 1981, Journal of Fluid Mechanics.

[31]  Massimo Tessarotto,et al.  On boundary conditions in the Lattice-Boltzmann method , 2004 .