Implementation of an improved bubble breakup model for TFM-PBM simulations of gas–liquid flows in bubble columns

Abstract An improved bubble coalescence and breakup model was implemented in the inhomogeneous TFM-PBM model for buoyancy-driven gas–liquid bubbly flows. The bubble coalescence was modeled by considering bubble collisions induced by turbulent fluctuations, buoyancy driven, wake entrainment, and viscous shear, and the liquid film drainage model was used for the description of the coalescence efficiency of collisions. The bubble breakup was analyzed in terms of bubble interactions with turbulent eddies which coupled the restriction of surface energy with the capillary pressure. A generic TFM-PBM model was developed and applied for the simulations of bubble columns operated in different flow regimes. The evolutions of the bubble size distributions were simulated and validated for literature data of a D =0.14 m cylindrical bubble column at gas superficial velocities 0.03 and 0.45 m/s, respectively. Furthermore, a well documented D =0.44 m bubble column was simulated, and the predicted distributions of the gas holdup and liquid velocity were compared with the experimental measurements of Chen et al. (1998) . The model showed the capacity of describing the gas–liquid fluid dynamics of bubble columns operated in both bubbly and churn-turbulent flow regimes.

[1]  Kiyomi Akita,et al.  Bubble Size, Interfacial Area, and Liquid-Phase Mass Transfer Coefficient in Bubble Columns , 1974 .

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

[3]  M. Duduković,et al.  Gas holdup distributions in large-diameter bubble columns measured by computed tomography , 1998 .

[4]  A. K. Agrawal,et al.  Shape of liquid drops moving in liquid media , 1966 .

[5]  Milorad P. Dudukovic,et al.  CFD modeling of bubble columns flows: implementation of population balance , 2004 .

[6]  Eckhard Krepper,et al.  The inhomogeneous MUSIG model for the simulation of polydispersed flows , 2008 .

[7]  M. Al-Dahhan,et al.  Predictions of radial gas holdup profiles in bubble column reactors , 2001 .

[8]  Rajamani Krishna,et al.  Design and scale up of a bubble column slurry reactor for Fischer–Tropsch synthesis , 2001 .

[9]  Liang-Shih Fan,et al.  Discrete simulation of gas‐liquid bubble columns and gas‐liquid‐solid fluidized beds , 2004 .

[10]  Juan C. Lasheras,et al.  On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency , 1999, Journal of Fluid Mechanics.

[11]  Dieter Mewes,et al.  A transport equation for the interfacial area density applied to bubble columns , 2001 .

[12]  Jam Hans Kuipers,et al.  Numerical simulation of the dynamic flow behavior in a bubble column : A study of closures for turbulence and interface forces , 2006 .

[13]  Jiyuan Tu,et al.  On the numerical study of isothermal vertical bubbly flow using two population balance approaches , 2007 .

[14]  Hallvard F. Svendsen,et al.  A model for turbulent binary breakup of dispersed fluid particles , 2002 .

[15]  Shantanu Roy,et al.  Numerical simulation of gas}liquid dynamics in cylindrical bubble column reactors , 1999 .

[16]  Caixia Chen,et al.  Application of Population Balance Model in the Simulation of Slurry Bubble Column , 2014 .

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

[18]  Faïçal Larachi,et al.  CFD simulation of bubble column flows: Investigations on turbulence models in RANS approach , 2009 .

[19]  Y. Liao,et al.  A literature review of theoretical models for drop and bubble breakup in turbulent dispersions , 2009 .

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

[21]  Eckhard Krepper,et al.  Evolution of flow patterns, gas fraction profiles and bubble size distributions in gas-liquid flows in vertical tubes , 2003 .

[22]  J. Solsvik,et al.  On the population balance equation , 2012 .

[23]  Yong Jin,et al.  A CFD–PBM coupled model for gas–liquid flows , 2006 .

[24]  M. Al-Dahhan,et al.  Prediction of axial liquid velocity profile in bubble columns , 2001 .

[25]  Ak Allen Chesters The modelling of coalescence processes in fluid-liquid dispersions : a review of current understanding , 1991 .

[26]  H.E.A. van den Akker,et al.  Sensitivity study on interfacial closure laws in two‐fluid bubbly flow simulations , 2003 .

[27]  J. Lasheras,et al.  Considerations on bubble fragmentation models , 2010, Journal of Fluid Mechanics.

[28]  Jyeshtharaj B. Joshi,et al.  CFD Simulation of Bubble Column Reactor Using Population Balance , 2008 .

[29]  Mandar Tabib,et al.  CFD simulation of bubble column—An analysis of interphase forces and turbulence models , 2008 .

[30]  James M. Church,et al.  Statistical Theories of Turbulence in Predicting Particle Size in Agitated Dispersions , 1960 .

[31]  M. Al-Dahhan,et al.  Impact of Internals Size and Configuration on Bubble Dynamics in Bubble Columns for Alternative Clean Fuels Production , 2015 .

[32]  Caixia Chen,et al.  Numerical Simulation of Bubble Column Flows in Churn-Turbulent Regime: Comparison of Bubble Size Models , 2013 .

[33]  J. Solsvik,et al.  Single Air Bubble Breakup Experiments in Stirred Water Tank , 2015 .

[34]  Wei Ge,et al.  A theoretical bubble breakup model for slurry beds or three-phase fluidized beds under high pressure , 2007 .

[35]  W. Howarth Coalescence of drops in a turbulent flow field , 1964 .

[36]  Eckhard Krepper,et al.  CFD modeling of bubble-induced turbulence , 2013 .

[37]  Lawrence L. Tavlarides,et al.  Description of interaction processes in agitated liquid-liquid dispersions , 1977 .

[38]  Y. Liao,et al.  A literature review on mechanisms and models for the coalescence process of fluid particles , 2010 .

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

[40]  Eckhard Krepper,et al.  Baseline closure model for dispersed bubbly flow: Bubble coalescence and breakup , 2015 .

[41]  F. Boysan,et al.  Renormalization Group Modeling and Turbulence Simulations. , 1993 .

[42]  D. Mewes,et al.  Bubble‐Size distributions and flow fields in bubble columns , 2002 .

[43]  S. Friedlander,et al.  Smoke, dust, and haze , 2000 .

[44]  Milorad P. Dudukovic,et al.  Three‐dimensional simulation of bubble column flows with bubble coalescence and breakup , 2005 .

[45]  J. Thibault,et al.  Modeling a New Rotational Reciprocating Plate Impeller Using Computational Fluid Dynamics , 2012 .

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