Explorations on the multi-scale flow structure and stability condition in bubble columns

Abstract Physical understanding of heterogeneous flow structure is of crucial importance for modelling and simulation of gas–liquid systems. This article presents a review and report of recent progress in our group on exploratory application of the variational (analytical) multi-scale approach to gas–liquid systems. The work features the closure of a hydrodynamic model with the incorporation of a stability condition reflecting the compromise between the dominant mechanisms in the system. A dual-bubble-size (DBS) model is proposed to approximate the heterogeneous structure of gas–liquid systems based on a single-bubble-size (SBS) model previously established. Reasonable variation of the gas holdup and the composition of the two bubble species with operating conditions have been calculated and the regime transition can therefore be reasonably predicted for air-water system, suggesting that stability condition may provide an insightful concept to explain the general tendencies in gas–liquid systems out of their hydrodynamic complexity, and to give simple models of their overall behaviors. Of course, the diversity of the correlations for drag force and minimum bubble size and the sensitivity of the model predictions to these correlations may suggest the necessity to clarify further the essential and robust results in the current model and to reduce the uncertainties involved.

[1]  Gabriel Wild,et al.  Influence of coalescence behaviour of the liquid and of gas sparging on hydrodynamics and bubble characteristics in a bubble column , 1999 .

[2]  M. Simonnet,et al.  Experimental determination of the drag coefficient in a swarm of bubbles , 2007 .

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

[4]  Snehal A. Patel,et al.  Holdup and interfacial area measurements using dynamic gas disengagement , 1989 .

[5]  Jyeshtharaj B. Joshi,et al.  Bubble Formation and Bubble Rise Velocity in Gas−Liquid Systems: A Review , 2005 .

[6]  Margaritis Kostoglou,et al.  Toward a unified framework for the derivation of breakage functions based on the statistical theory of turbulence , 2005 .

[7]  H. Blanch,et al.  Bubble coalescence and break‐up in air‐sparged bubble columns , 1990 .

[8]  N. Midoux,et al.  Description of flow regime transitions in bubble columns via laser Doppler anemometry signals processing , 2003 .

[9]  Jinghai Li,et al.  The EMMS model - its application, development and updated concepts , 1999 .

[10]  Rajamani Krishna,et al.  A unified approach to the scale-up of gas—solid fluidized bed and gas—liquid bubble column reactors , 1994 .

[11]  Liang-Shih Fan,et al.  Gas-Liquid-Solid Fluidization Engineering , 1989 .

[12]  D. Scott,et al.  The role of gas phase momentum in determining gas holdup and hydrodynamic flow regimes in bubble column operations , 1994 .

[13]  Wei Ge,et al.  Analytical multi-scale method for multi-phase complex systems in process engineering—Bridging reductionism and holism , 2007 .

[14]  H. Kumazawa,et al.  Gas-liquid interfacial area and liquid-side mass-transfer coefficient in a slurry bubble column , 1987 .

[15]  Jinghai Li,et al.  Exploring complex systems in chemical engineering - the multi-scale methodology , 2003 .

[16]  Jinfu Wang,et al.  A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow , 2003 .

[17]  S. Asai,et al.  Gas hold-up in bubble columns , 1980 .

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

[19]  Rajamani Krishna,et al.  Gas holdup in bubble column reactors operating in the churn‐turbulent flow regime , 1996 .

[20]  Liang-Shih Fan,et al.  Bubble formation and dynamics in gas–liquid–solid fluidization—A review , 2007 .

[21]  Liang-Shih Fan,et al.  Flow structure in a three‐dimensional bubble column and three‐phase fluidized bed , 1994 .

[22]  I. Eames,et al.  The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows , 2000 .

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

[24]  G. A. Hughmark,et al.  Holdup and Mass Transfer in Bubble Columns , 1967 .

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

[26]  H. Svendsen,et al.  Theoretical model for drop and bubble breakup in turbulent dispersions , 1996 .

[27]  Robert F. Mudde,et al.  Gravity-driven bubbly flows , 2005 .

[28]  Wei Ge,et al.  Multi-scale compromise and multi-level correlation in complex systems , 2005 .

[29]  Rajamani Krishna,et al.  Size, structure and dynamics of “large” bubbles in a two-dimensional slurry bubble column , 1996 .

[30]  J. Zahradnı́k,et al.  The effect of bubbling regime on gas and liquid phase mixing in bubble column reactors , 1996 .

[31]  Jinghai Li,et al.  Physical mapping of fluidization regimes—the EMMS approach , 2002 .

[32]  Rajamani Krishna,et al.  Three-phase Eulerian simulations of bubble column reactors operating in the churn-turbulent flow regime: A scale up strategy , 2000 .

[33]  Rajamani Krishna,et al.  Influence of scale on the hydrodynamics of bubble columns operating in the churn-turbulent regime: experiments vs. Eulerian simulations , 1999 .

[34]  Robert W. Field,et al.  Bubble Column Reactors , 1991 .

[35]  C. P. Ribeiro,et al.  Direct-contact evaporation in the homogeneous and heterogeneous bubbling regimes. Part I: experimental analysis , 2004 .

[36]  N. Cheremisinoff,et al.  Shapes and velocities of single drops and bubbles moving freely through immiscible liquids. , 1976 .

[37]  Fahir Borak,et al.  Bubble column reactors , 2005 .

[38]  Liang-Shih Fan,et al.  Bubble wake dynamics in liquids and liquid-solid suspensions , 1990 .

[39]  Jyeshtharaj B. Joshi,et al.  Coherent flow structures in bubble column reactors , 2002 .