Lift force in bubbly flow systems

Abstract From the significance of three-dimensional simulation of dispersed flow systems in many engineering fields, extensive study was conducted for lift force in a single particle system as well as a multiparticle system. In this study, the lift force in a single particle system was modeled by considering the effect of bubble deformation on the lift force. The model was finalized based on existing data obtained in the range of particle Reynolds number from 3.68 to 78.8, viscous number from 0.0435 to 0.203 and Eotvos number from 1.40 to 5.83. The viscous number is defined by μ f / [ ρ f σ σ / ( g Δ ρ ) ] 1 / 2 where μ f , ρ f , σ , g and Δ ρ are, respectively, fluid viscosity, fluid density, surface tension, gravitational acceleration and density difference between phases. The applicability of the model to higher particle Reynolds number system such as an air–water system was qualitatively examined. The lift force model developed in a single particle system was extended to a multiparticle system. The applicability of the extended lift force model was qualitatively examined. The similarity between drag and lift forces were also discussed.

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

[2]  R. Kurose,et al.  Drag and lift forces acting on a spherical bubble in a linear shear flow , 2001 .

[3]  M. Ishii,et al.  Thermo-Fluid Dynamics of Two-Phase Flow , 2007 .

[4]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[5]  M. Ishii,et al.  Local Flow Measurements of Vertical Upward Bubbly Flow in an Annulus , 2003 .

[6]  P. Cherukat,et al.  The inertial lift on a rigid sphere in a linear shear flow field near a flat wall , 1994, Journal of Fluid Mechanics.

[7]  Dominique Legendre,et al.  Forces on a high-Reynolds-number spherical bubble in a turbulent flow , 2005, Journal of Fluid Mechanics.

[8]  Dominique Legendre,et al.  Drag, deformation and lateral migration of a buoyant drop moving near a wall , 2003, Journal of Fluid Mechanics.

[9]  T. R. Auton,et al.  The lift force on a spherical body in a rotational flow , 1987, Journal of Fluid Mechanics.

[10]  D. Hall Measurements of the mean force on a particle near a boundary in turbulent flow , 1988, Journal of Fluid Mechanics.

[11]  John B. McLaughlin,et al.  Wall-induced lift on a sphere , 1990 .

[12]  G. Tryggvason,et al.  Deformable bubbles in a free shear layer , 1997 .

[13]  Hidesada Tamai,et al.  Transverse migration of single bubbles in simple shear flows , 2002 .

[14]  Mamoru Ishii,et al.  Local drag laws in dispersed two-phase flow , 1979 .

[15]  Renwei Mei,et al.  Shear lift force on spherical bubbles , 1994 .

[16]  D. Drew The lift force on a small sphere in the presence of a wall , 1988 .

[17]  R. G. Cox,et al.  The lateral migration of spherical particles sedimenting in a stagnant bounded fluid , 1977, Journal of Fluid Mechanics.

[18]  Donald A. Drew,et al.  The virtual mass and lift force on a sphere in rotating and straining inviscid flow , 1987 .

[19]  S. Balachandar,et al.  Shear versus vortex-induced lift force on a rigid sphere at moderate Re , 2002, Journal of Fluid Mechanics.

[20]  Dominique Legendre,et al.  Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid , 2003, Journal of Fluid Mechanics.

[21]  J. McLaughlin,et al.  The inertial lift on an oscillating sphere in a linear shear flow , 1999 .

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

[23]  I. Zun,et al.  Effects of Eötvös Number and Dimensionless Liquid Volumetric Flux on Lateral Motion of a Bubble in a Laminar Duct Flow , 1995 .

[24]  N. Zuber ON THE DISPERSED TWO-PHASE FLOW IN THE LAMINAR FLOW REGIME. , 1964 .

[25]  T. J. Liu Bubble size and entrance length effects on void development in a vertical channel , 1993 .

[26]  I. Zun,et al.  The transverse migration of bubbles influenced by walls in vertical bubbly flow , 1980 .

[27]  J. McLaughlin Inertial migration of a small sphere in linear shear flows , 1991, Journal of Fluid Mechanics.

[28]  C. Sleicher Maximum stable drop size in turbulent flow , 1962 .

[29]  H. Dwyer,et al.  A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer , 1990, Journal of Fluid Mechanics.

[30]  Mamoru Ishii,et al.  Two-fluid model and hydrodynamic constitutive relations , 1984 .

[31]  J. Katz,et al.  Drag and lift forces on microscopic bubbles entrained by a vortex , 1995 .

[32]  David T. Leighton,et al.  INERTIAL LIFT ON A MOVING SPHERE IN CONTACT WITH A PLANE WALL IN A SHEAR FLOW , 1995 .

[33]  M. Ishii Thermo-fluid dynamic theory of two-phase flow , 1975 .

[34]  M. Ishii,et al.  Axial interfacial area transport of vertical bubbly flows , 2001 .

[35]  J. McLaughlin The lift on a small sphere in wall-bounded linear shear flows , 1993, Journal of Fluid Mechanics.

[36]  Fumio Takemura,et al.  The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number , 2003, Journal of Fluid Mechanics.

[37]  Mamoru Ishii,et al.  Experimental study on interfacial area transport in bubbly two-phase flows , 1999 .

[38]  F. Nieuwstadt,et al.  Measurement of the lift force on a particle fixed to the wall in the viscous sublayer of a fully developed turbulent boundary layer , 1996, Journal of Fluid Mechanics.

[39]  Gretar Tryggvason,et al.  The rise of bubbles in a vertical shear flow , 1997 .

[40]  R. Lahey,et al.  Phase distribution in complex geometry conduits , 1993 .

[41]  I. Zun,et al.  Numerical analysis of bubble motion with the VOF method , 1993 .

[42]  言彦 世古口,et al.  気ほう流の研究 : 第1報, 垂直上昇流における疎な気ほう群について , 1974 .

[43]  Mamoru Ishii,et al.  Interfacial area concentration of bubbly flow systems , 2002 .

[44]  M. T. Lawler,et al.  THE ROLE OF LIFT IN THE RADIAL MIGRATION OF PARTICLES IN A PIPE FLOW , 1971 .

[45]  A. B. Basset,et al.  Treatise on Hydrodynamics , 1889, Nature.

[46]  P. Cherukat,et al.  A computational study of the inertial lift on a sphere in a linear shear flow field , 1999 .

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

[48]  M. Ishii,et al.  One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes , 2003 .

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

[50]  A. Acrivos,et al.  The lift on a small sphere touching a plane in the presence of a simple shear flow , 1985 .

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

[52]  Dominique Legendre,et al.  The lift force on a spherical bubble in a viscous linear shear flow , 1998, Journal of Fluid Mechanics.

[53]  Mamoru Ishii,et al.  Study of two-fluid model and interfacial area , 1980 .

[54]  Ryoichi Kurose,et al.  Drag and lift forces on a rotating sphere in a linear shear flow , 1999, Journal of Fluid Mechanics.

[55]  D. Legendre,et al.  A note on the lift force on a spherical bubble or drop in a low-Reynolds-number shear flow , 1997 .

[56]  M. Lance,et al.  Two-fluid modeling versus mechanistic approach and lift effects in bubbly sheared flows , 1993 .

[57]  P. Saffman The lift on a small sphere in a slow shear flow , 1965, Journal of Fluid Mechanics.

[58]  Michel Lance,et al.  PHASE DISTRIBUTION PHENOMENA AND WALL EFFECTS IN BUBBLY TWO-PHASE FLOWS , 1994 .

[59]  R. Mei An approximate expression for the shear lift force on a spherical particle at finite reynolds number , 1992 .

[60]  D. Drew,et al.  THE ANALYSIS OF VIRTUAL MASS EFFECTS IN TWO-PHASE FLOW , 1979 .