Experimental determination of the drag coefficient in a swarm of bubbles

Abstract Simultaneous measurements of liquid velocity by laser Doppler velocimetry and bubble velocity, diameter, and void fraction by a double optical probe are performed in a bubble column to study the influence of the void fraction on the relative velocity of a swarm of gas bubbles. Bubble diameters d b vary from 2 to 10 mm and local void fractions α loc can reach 35%. It is found that, for α loc 15 % , the relative bubble velocity is determined by the hindrance effect and consequently decreases with the void fraction. Beyond this critical value, the aspiration of bubbles in the wake of the leading ones dominates the hindrance effect and the relative velocity thus increases suddenly. The contribution of the bubble diameters to this evolution is also determined. Finally, a drag correlation, valid for the whole range of void fraction and for pure water–air systems, is proposed.

[1]  Gabriel Wild,et al.  Numerical simulation of multiphase flow in bubble column reactors. Influence of bubble coalescence and break-up , 2001 .

[2]  D. Marchisio,et al.  Momentum transfer in a swarm of bubbles: estimates from fluid-dynamic simulations , 2004 .

[3]  Jyeshtharaj B. Joshi,et al.  CFD simulation of sparger design and height to diameter ratio on gas hold-up profiles in bubble column reactors , 2004 .

[4]  Jyeshtharaj B. Joshi,et al.  Stability analysis of bubble columns: Predictions for regime transition , 2005 .

[5]  Roberto Zenit,et al.  Measurements of the average properties of a suspension of bubbles rising in a vertical channel , 2001, Journal of Fluid Mechanics.

[6]  L. Timkin,et al.  Slip velocity measurements in an upward bubbly flow by combined LDA and electrodiffusional techniques , 1999 .

[7]  Xiaojin Tang,et al.  Optical Probe Technique for Two-Phase Flow Measurements in an Extraction Column (R&D Note) , 2005 .

[8]  Andrea Prosperetti,et al.  Dynamics of bubble growth and detachment from a needle , 1993, Journal of Fluid Mechanics.

[9]  G. Marrucci.  Communication. Rising Velocity of Swarm of Spherical Bubbles , 1965 .

[10]  Hanns Hofmann,et al.  Investigations and modelling of bubble columns , 1992 .

[11]  Hugo A. Jakobsen,et al.  Phase distribution phenomena in two-phase bubble column reactors , 2001 .

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

[13]  Leon Lapidus,et al.  The mechanics of vertical gas‐liquid fluidized system I: Countercurrent flow , 1964 .

[14]  R. I. Issa,et al.  Modelling of dispersed bubble and droplet flow at high phase fractions , 2004 .

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

[16]  John R. Chaplin,et al.  Optical fibre probe measurements of bubbly flow in hydraulic jumps , 2005 .

[17]  J. F. Richardson,et al.  Sedimentation and fluidisation: Part I , 1997 .

[18]  M. Fialová,et al.  Duality of the gas-liquid flow regimes in bubble column reactors , 1997 .

[19]  Gabriel Wild,et al.  Experimental study of bubble column hydrodynamics , 2001 .

[20]  J. Marié,et al.  Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction , 2002 .

[21]  A. Biesheuvel,et al.  Experiments on the motion of gas bubbles in turbulence generated by an active grid , 2002, Journal of Fluid Mechanics.

[22]  P. Spelt,et al.  On the motion of gas bubbles in homogeneous isotropic turbulence , 1997, Journal of Fluid Mechanics.

[23]  Ranganathan Kumar,et al.  Liquid and gas velocity measurements using LDV in air–water duct flow , 1999 .

[24]  Mohammad Jamialahmadi,et al.  Terminal bubble rise velocity in liquids , 1994 .

[25]  R. F. Mudde,et al.  Application of LDA to bubbly flows , 1998 .

[26]  H. Müller-Steinhagen,et al.  Effect of alcohol, organic acid and potassium chloride concentration on bubble size, bubble rise velocity and gas hold-up in bubble columns , 1992 .

[27]  J. Davidson,et al.  The behaviour of a continuously bubbling fluidised bed , 1966 .

[28]  H. Delmas,et al.  Measurements of Bubble Characteristics: Comparison Between Double Optical Probe and Imaging , 2008 .

[29]  Jyeshtharaj B. Joshi,et al.  Regime transition in bubble columns: experimental and predictions , 2004 .

[30]  Rajamani Krishna,et al.  Rise velocity of a swarm of large gas bubbles in liquids , 1999 .

[31]  Graham B. Wallis,et al.  Two-Phase Slug Flow , 1961 .

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