A DNS study of laminar bubbly flows in a vertical channel

Direct numerical simulations are used to examine laminar bubbly flows in vertical channels. For equal size nearly spherical bubbles the results show that at steady state the number density of bubbles in the center of the channel is always such that the fluid mixture there is in hydrostatic equilibrium. For upflow, excess bubbles are pushed to the walls, forming a bubble rich wall-layer, one bubble diameter thick. For downflow, bubbles are drawn into the channel center, leading to a wall-layer devoid of bubbles, of a thickness determined by how much the void fraction in the center of the channel must be increased to reach hydrostatic equilibrium. The void fraction profile can be predicted analytically using a very simple model and the model also gives the velocity profile for the downflow case. For the upflow, however, the velocity increase across the wall-layer must be obtained from the simulations. The slip velocity of the bubbles in the channel core and the velocity fluctuations are predicted reasonably well by results for homogeneous flows.

[1]  D. Juric,et al.  A front-tracking method for the computations of multiphase flow , 2001 .

[2]  O. C. Jones,et al.  3-D turbulence structure and phase distribution measurements in bubbly two-phase flows , 1987 .

[3]  S. G. Bankoff,et al.  Structure of air-water bubbly flow in a vertical pipe—I. liquid mean velocity and turbulence measurements , 1993 .

[4]  Gretar Tryggvason,et al.  The effect of bubbles on the wall drag in a turbulent channel flow , 2005 .

[5]  Peter Smereka,et al.  On the motion of bubbles in a periodic box , 1993, Journal of Fluid Mechanics.

[6]  Gretar Tryggvason,et al.  Comparison of results from DNS of bubbly flows with a two-fluid model for two-dimensional laminar flows , 2005 .

[7]  I. Celik,et al.  A New Approach in Modeling Phase Distribution in Fully Developed Bubbly Pipe Flow , 2002 .

[8]  Isao Kataoka,et al.  Local instant formulation of two-phase flow , 1986 .

[9]  Andrea Prosperetti,et al.  Averaged equations for inviscid disperse two-phase flow , 1994, Journal of Fluid Mechanics.

[10]  Tay-Jian Liu.  Investigation of the wall shear stress in vertical bubbly flow under different bubble size conditions , 1997 .

[11]  Gad Hetsroni,et al.  Handbook of multiphase systems , 1982 .

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

[13]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

[14]  V. Nakoryakov,et al.  Gas-Liquid Bubbly Flow in Vertical Pipes , 1996 .

[15]  Xingtuan Yang,et al.  Laminar light particle and liquid two-phase flows in a vertical pipe , 2003 .

[16]  Yuichi Murai,et al.  Experimental detection of bubble–bubble interactions in a wall-sliding bubble swarm , 2004 .

[17]  I. Kataoka,et al.  Basic equations of turbulence in gas-liquid two-phase flow , 1989 .

[18]  N. Zuber,et al.  Drag coefficient and relative velocity in bubbly, droplet or particulate flows , 1979 .

[19]  J. Flaherty,et al.  Analysis of phase distribution in fully developed laminar bubbly two-phase flow , 1991 .

[20]  Robert F. Mudde,et al.  Bubble size effect on low liquid input drift–flux parameters , 2004 .

[21]  Ching-Chang Chieng,et al.  EULERIAN-LAGRANGIAN COMPUTATIONS ON PHASE DISTRIBUTION OF TWO-PHASE BUBBLY FLOWS , 1997 .

[22]  R. Lahey,et al.  Phase distribution in bubbly two-phase flow in vertical ducts , 1994 .

[23]  Gretar Tryggvason,et al.  A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number , 2005 .

[24]  G. Tryggvason,et al.  Effect of bubble deformation on the properties of bubbly flows , 2003, Journal of Fluid Mechanics.

[25]  Isao Kataoka,et al.  Turbulence structure of air-water bubbly flow—III. transport properties , 1975 .

[26]  Gretar Tryggvason,et al.  Dynamics of homogeneous bubbly flows Part 1. Rise velocity and microstructure of the bubbles , 2002, Journal of Fluid Mechanics.

[27]  Donald A. Drew,et al.  Phase-distribution mechanisms in turbulent low-quality two-phase flow in a circular pipe , 1982, Journal of Fluid Mechanics.

[28]  A. Sangani,et al.  Dynamic simulations of flows of bubbly liquids at large Reynolds numbers , 1993, Journal of Fluid Mechanics.

[29]  W. Sirignano.  Volume averaging for the analysis of turbulent spray flows , 2005 .

[30]  Gretar Tryggvason,et al.  Dynamics of homogeneous bubbly flows Part 2. Velocity fluctuations , 2002, Journal of Fluid Mechanics.

[31]  Roberto Zenit,et al.  Clustering in high Re monodispersed bubbly flows , 2005 .

[32]  G. Buscaglia,et al.  Analytical and numerical evaluation of two-fluid model solutions for laminar fully developed bubbly two-phase flows , 2003 .

[33]  R. V. A. Oliemans,et al.  Simplified two‐fluid model for gas‐lift efficiency predictions , 2005 .

[34]  Eugênio Spanó Rosa,et al.  The phase distribution of upward co-current bubbly flows in a vertical square channel , 2004 .

[35]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[36]  A. P. Burdukov,et al.  Local characteristics of upward gas-liquid flows , 1981 .

[37]  J. Converti,et al.  A model for turbulent polydisperse two-phase flow in vertical channels , 2003 .

[38]  D. Rodrigue,et al.  Generalized correlation for bubble motion , 2001 .

[39]  O. C. Jones,et al.  Development of a k-ε Model for Bubbly Two-Phase Flow , 1994 .

[40]  Yoichiro Matsumoto,et al.  Laser Doppler velocimetry measurement of turbulent bubbly channel flow , 2002 .

[41]  Isao Kataoka,et al.  Turbulence structure of air-water bubbly flow—II. local properties , 1975 .

[42]  O. N. Kashinsky,et al.  Downward bubbly gas–liquid flow in a vertical pipe , 1999 .

[43]  Qiang Song,et al.  Phase distributions for upward laminar dilute bubbly flows with non-uniform bubble sizes in a vertical pipe , 2001 .