Numerical simulation of two-phase flow with bubble break-up and coalescence coupled with population balance modeling

Abstract A computational fluid dynamic (CFD) model was developed with an improved source term based on previous work by Hagesaether et al. [1] for bubble break up and bubble coalescence to carry out numerical prediction of number density of different bubble class in turbulent dispersed flow. The numerical prediction was based on two fluid models, using the Eulerian–Eulerian approach where the liquid phase was treated as a continuum and the gas phase (bubbles) was considered as a dispersed phase. Bubble–bubble interactions, such as breakage due to turbulence and coalescence due to the combined effect of turbulence and laminar shear were considered. The result shows that the radial distributions of number densities of lower bubble classes are more than its higher counterpart. The result also shows that the Sauter mean diameter increases with the increase of height up to 1 m and then become steady. Simulated results are found to be in good agreement with the experimental data.

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

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

[3]  Alexei Lapin,et al.  Numerical simulation of the dynamics of two-phase gasliquid flows in bubble columns , 1994 .

[4]  Geoffrey Brooks,et al.  A computational fluid dynamics model of shrouded supersonic jet impingement on a water surface , 2012 .

[5]  Geoffrey Ingram Taylor,et al.  The formation of emulsions in definable fields of flow , 1934 .

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

[7]  Mamoru Ishii,et al.  One-group interfacial area transport in vertical bubbly flow , 1998 .

[8]  Anders Rasmuson,et al.  High shear wet granulation modelling—a mechanistic approach using population balances , 2005 .

[9]  John B. McLaughlin,et al.  SIMULATION OF BUBBLE BREAKUP DYNAMICS IN HOMOGENEOUS TURBULENCE , 2006 .

[10]  Yong Jin,et al.  Theoretical prediction of flow regime transition in bubble columns by the population balance model , 2005 .

[11]  Kangtaek Lee,et al.  Solution of the population balance equation using constant-number Monte Carlo , 2002 .

[12]  M. A. Sattar,et al.  Numerical simulation of creaming and foam formation in aerated liquid with population balance modeling , 2013 .

[13]  S. Iveson,et al.  Limitations of one-dimensional population balance models of wet granulation processes☆ , 2002 .

[14]  C. Chung,et al.  Mechanistic study for the interfacial area transport phenomena in an air/water flow condition by using fine-size bubble group model , 2006 .

[15]  M. Reuter,et al.  Computational Fluid Dynamics (CFD) Investigation of Submerged Combustion Behavior in a Tuyere Blown Slag-fuming Furnace , 2012, Metallurgical and Materials Transactions B.

[16]  Ilkka Turunen,et al.  Multi-phase-multi-size-group model for the inclusion of population balances into the CFD simulation of gas-liquid bubbly flows , 2006 .

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

[18]  H. Schlichting Boundary Layer Theory , 1955 .

[19]  Milorad P. Dudukovic,et al.  Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures , 2005 .

[20]  I. Turunen,et al.  Experimental Determination of Bubble Coalescence and Break‐up Rates in a Bubble Column Reactor , 2008 .

[21]  P. I. Barton,et al.  Effective parameter estimation within a multi-dimensional population balance model framework , 2010 .

[22]  Brian Scarlett,et al.  Population balances for particulate processes - a volume approach. , 2002 .

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

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

[25]  E. Windhab,et al.  Single bubble deformation and breakup in simple shear flow , 2008 .

[26]  Geoffrey Brooks,et al.  Inclined jetting and splashing in electric arc furnace steelmaking , 2011 .

[27]  Markus A. Reuter,et al.  CFD Modeling of Swirl and Nonswirl Gas Injections into Liquid Baths Using Top Submerged Lances , 2010 .

[28]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[29]  Geoffrey Brooks,et al.  Computational Fluid Dynamics Modeling of Supersonic Coherent Jets for Electric Arc Furnace Steelmaking Process , 2010 .

[30]  Gerhart Eigenberger,et al.  Dynamic Numerical Simulation of Gas-Liquid Two Phase Flows, Euler-Euler versus Euler-Lagrange , 1997 .

[31]  Markus A. Reuter,et al.  Computational Fluid Dynamic Modeling of Zinc Slag Fuming Process in Top-Submerged Lance Smelting Furnace , 2012, Metallurgical and Materials Transactions B.

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

[33]  Geoffrey Brooks,et al.  Computational Fluid Dynamics Simulation of Supersonic Oxygen Jet Behavior at Steelmaking Temperature , 2010 .

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

[35]  Doraiswami Ramkrishna,et al.  CFD simulation of bubble columns incorporating population balance modeling , 2008 .

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

[37]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization—II. A moving pivot technique , 1996 .

[38]  J. Kuipers,et al.  Dynamic simulation of dispersed gas-liquid two phase flow using a discrete bubble model. , 1996 .

[39]  Pierre Proulx,et al.  Three-dimensional mathematical modeling of dispersed two-phase flow using class method of population balance in bubble columns , 2008, Comput. Chem. Eng..

[40]  Said Elghobashi,et al.  DIRECT NUMERICAL SIMULATIONS OF BUBBLE-LADEN TURBULENT FLOWS USING THE TWO-FLUID FORMULATION , 1998 .