Computational Fluid Dynamics–Population Balance Modeling of Gas–Liquid Two-Phase Flow in Bubble Column Reactors With an Improved Breakup Kernel Accounting for Bubble Shape Variations

Abstract Traditionally, bubble shapes have been assumed to be spherical in breakup models such as the one developed by Luo and Svendsen in 1996. This particular breakup model has been widely accepted and implemented into computational fluid dynamics (CFD) modeling of gas–liquid two-phase flows. However, simulation results from this model usually provide unreliable predictions about the breakage of very small bubbles. The incorporation of bubble shape variation into breakup models has rarely been documented in literature but the bubble shape plays an important role in the interactions with the surrounding eddies, especially when the effects of bubble deformation, distortion, and bubble internal pressure change are considered during the events of eddy-bubble collision. Thus, the assumption of spherical bubbles seems to be no longer appropriate in reflecting this phenomenon. This study proposes and implements a modified bubble breakup model, which accounts for the variation of bubble shapes when solving the population balance equations for CFD simulation of gas–liquid two-phase flows in bubble columns. The key parameters predicted by the modified breakup model have been compared with the ones predicted by the original model. The simulation results of interfacial area and mass transfer coefficient for larger bubbles have been greatly enhanced by the modified breakup model.

[1]  Roberto Zenit,et al.  On the deformation of gas bubbles in liquids , 2012 .

[2]  He’an Luo,et al.  Influence of energy spectrum distribution on drop breakage in turbulent flows , 2014 .

[3]  Sarit K. Das,et al.  Investigation of Bubble Behavior in Subcooled Flow Boiling of Water in a Horizontal Annulus Using High-Speed Flow Visualization , 2013 .

[4]  He’an Luo,et al.  A theoretical model for droplet breakup in turbulent dispersions , 2011 .

[5]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

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

[7]  J. Tsamopoulos,et al.  Steady bubble rise and deformation in Newtonian and viscoplastic fluids and conditions for bubble entrapment , 2008, Journal of Fluid Mechanics.

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

[9]  Jan Dušek,et al.  Marginal stability curve of a deformable bubble , 2017 .

[10]  Masao Watanabe,et al.  Behavior of Single Rising Bubbles in Superpurified Water , 2007 .

[11]  Carlos A. Dorao,et al.  Modeling of Bubble Column Reactors: Progress and Limitations , 2005 .

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

[13]  Bidyut Baran Saha,et al.  Development of High-Speed and Large-Scale Culture Technology of Marine Algae Using Seawater With High Concentrations of Dissolved Carbon Dioxide , 2016 .

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

[15]  Y. Sato,et al.  Liquid velocity distribution in two-phase bubble flow , 1975 .

[16]  Rama Govindarajan,et al.  Dynamics of an initially spherical bubble rising in quiescent liquid , 2015, Nature Communications.

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

[18]  A. Tomiyama,et al.  Shapes of ellipsoidal bubbles in infinite stagnant liquids , 2016 .

[19]  W. Marsden.  I and J , 2012 .

[20]  Colm-cille Caulfield,et al.  Spherical cap bubbles with a toroidal bubbly wake , 2008 .

[21]  Bengt Andersson,et al.  Modeling the breakup of fluid particles in turbulent flows , 2006 .

[22]  Bhaskar D. Kulkarni,et al.  Application of multiresolution analysis for simultaneous measurement of gas and liquid velocities and fractional gas hold-up in bubble column using LDA , 2001 .

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

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

[25]  Sailesh Kumar,et al.  Gas‐holdup measurements in bubble columns using computed tomography , 1997 .

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

[27]  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 .

[28]  Aniruddha B. Pandit,et al.  EFFECT OF SPARGER DESIGN AND HEIGHT TO DIAMETER RATIO ON FRACTIONAL GAS HOLD-UP IN BUBBLE COLUMNS , 1998 .

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

[30]  Giulia Bozzano,et al.  Shape and Terminal Velocity of Single Bubble Motion: a Novel Approach , 2001 .

[31]  Ning Yang,et al.  A kinetic inlet model for CFD simulation of large-scale bubble columns , 2017 .

[32]  H. C. Simpson.  Bubbles, drops and particles , 1980 .

[33]  Jun Li,et al.  Implementation of an improved bubble breakup model for TFM-PBM simulations of gas–liquid flows in bubble columns , 2016 .

[34]  Mamoru Ishii,et al.  Two-group interfacial area transport in vertical air–water flow: I. Mechanistic model , 2003 .

[35]  D. W. Moore.  The velocity of rise of distorted gas bubbles in a liquid of small viscosity , 1965, Journal of Fluid Mechanics.

[36]  Patricio Bohorquez,et al.  Wake instability of a fixed axisymmetric bubble of realistic shape , 2013 .

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

[38]  Carlos A. Dorao,et al.  Numerical Simulation of Evaporation Process of Two-Phase Flow in Small-Diameter Channels , 2014 .