Numerical Study of Bubbly Flow Using the Second-Order Moment Turbulence Model and the Population Balance Method

REFERENCES

• D. A. Drew Mathematical Modeling of Two-Phase Flow, Annu. Rev. Fluid Mech., vol. 15, pp. 261–291, 1983.
   Web of Science ®Google Scholar
• A. Biesheuvel and L. V. Wijngaarden Two-Phase Flow Equations for a Dilute Dispersion of Gas Bubbles in Liquid, J. Fluid Mech., vol. 148, pp. 301–318, 1984.
   Web of Science ®Google Scholar
• M. Lopez de Bertodano, S. J. Lee, T. T. Lahey, and D. A. Drew The Prediction of Two-Phase Turbulence and Phase using a Reynolds Stress Model, J. Fluid Eng., vol. 112, pp. 107–113, 1990.
   Web of Science ®Google Scholar
• R. F. Mudde and O. Simonin Two- and Three-Dimensional Simulations of a Bubble Plume using a Two-Fluid Model, Chem. Eng. Sci., vol. 54, pp. 5061–5069, 1999.
   Web of Science ®Google Scholar
• Y. Pan and M. P. Dudukovic Numerical Investigation of Gas-Driven Flow in 2-D Bubble Column, AIChE J., vol. 46, pp. 434–449, 2000.
   Web of Science ®Google Scholar
• J. P. Wen and S. L. Xu Local Hydrodynamics in a Gas–Liquid–Solid Three-Phase Bubble Column Reactor, Chem. Eng. J., vol. 70, pp. 81–84, 1998.
   Web of Science ®Google Scholar
• M. T. Dhotre, B. L. Smith, and B. Niceno CFD Simulation of Bubbly Flows: Random Dispersion Model, Chem. Eng. Sci., vol. 62, pp. 7140–7150, 2007.
   Web of Science ®Google Scholar
• L. X. Zhou, M. Yang, C. Y. Lian, L. S. Fan, and D. J. Lee On the Second-Order Moment Turbulence Model for Simulating a Bubble Column, Chem. Eng. Sci., vol. 57, pp. 3269–3281, 2002.
   Web of Science ®Google Scholar
• H. A. Jakobsen, B. H. Sannaes, S. Grevskott, and H. F. Svendsen Modeling of Vertical Bubble-Driven Flows, Ind. Eng. Chem. Res., vol. 36, pp. 4052–4074, 1997.
   Web of Science ®Google Scholar
• J. B. Joshi Computational Flow Modeling and Design of Bubble Column Reactors, Chem. Eng. Sci., vol. 55, pp. 5893–5933, 2001.
   Google Scholar
• D. Lucas, E. Krepper, and H. M. Prasser Prediction of Radial Gas Profiles in Vertical Pipe Flow on the Basis of Bubble Size Distribution, Int. J. Therm. Sci., vol. 40, pp. 217–25, 2001.
   Web of Science ®Google Scholar
• A. Tomiyama Struggle with Computational Bubble Dynamics. In: Third International Conference on Multiphase Flow, ICMF98, Lyon, France, 1998.
   Google Scholar
• T. F. Wang, J. F. Wang, and Y. Jin A Novel Theoretical Breakup Kernel Function of Bubble/Droplet in a Turbulent Flow, Chem. Eng. Sci., vol. 59, pp. 2593–2595, 2003.
   Web of Science ®Google Scholar
• P. Chen, J. Sanyal, and M. P. Dudukovic Numerical Simulation of Bubble Columns Flows: Effect of Different Breakup and Coalescence Closures, Chem. Eng. Sci., vol. 60, pp. 1085–1101, 2005.
   Web of Science ®Google Scholar
• T. F. Wang, J. F. Wang, and Y. Jin Theoretical Prediction of Flow Regime Transition in Bubble Columns by the Population Balance Model, Chem. Eng. Sci., vol. 60, pp. 6199–6209, 2005.
   Web of Science ®Google Scholar
• F. Lehr, M. Millies, and D. Mewes Bubble-Size Distributions and Flow Fields in Bubble Columns, AIChE J., vol. 48, pp. 2426–2443, 2002.
   Web of Science ®Google Scholar
• H. Luo and H. F. Svendsen Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions, AIChE J., vol. 42, pp. 1225–1233, 1996.
   Web of Science ®Google Scholar
• M. J. Prince and H. W. Blanch Bubble Coalescence and Break-Up in Air-Sparged Bubble Columns, AIChE J., vol. 36, pp. 1485–1499, 1990.
   Web of Science ®Google Scholar
• S. C. P. Cheung, G. H. Yeoh, and J. Y. Tu On The Numerical Study Of Isothermal Vertical Bubbly Flow Using Two Population Balance Approaches, Chem. Eng. Sci., vol. 62, pp. 4659–4674, 2007.
   Web of Science ®Google Scholar
• X. Y. Duan, S. C. P. Cheung, G. H. Yeoh, J. Y. Tu, E. Krepper, and D. Lucas Gas–Liquid Flows in Medium and Large Vertical Pipes, Chem. Eng. Sci., vol. 66, pp. 872–883, 2011.
   Web of Science ®Google Scholar
• S. Degaleesan, M. Dudukovic, and Y. Pan Experimental Study OF Gas Induced Liquid-Flow Structures IN Bubble Columns, AIChE J., vol. 47, pp. 1913–1931, 2001.
   Web of Science ®Google Scholar
• A. Ohnuki and H. Akimoto Experimental Study on Transition of Flow Pattern and Phase Distribution in Upward Air-Water Two-Phase Flow along a Large Vertical Pipe, Int. J. Multiphas. Flow, vol. 26, pp. 367–386, 2000.
   Web of Science ®Google Scholar
• P. Bagchi and S. Balachandar Unsteady Motion and Forces on a Spherical Particle in Non-Uniform Flows, ASME FEDSM 2000–11128, Boston, 2000.
   Google Scholar
• M. F. Goz, M. Sommerfeld, B. Bunner, S. Mortazavi, and G. Tryggvason The Unsteady Dynamics of Two-Dimensional Bubbles in a Regular Array, ASME FEDSM00–11151, Boston, 2000.
   Google Scholar
• H. M. Hulbert and S. Katz Some Problems in Particle Technology: A Statistical Mechanical Formulation, Chem. Eng. Sci., vol. 19, pp. 555–574, 1964.
   Web of Science ®Google Scholar
• S. Kumar and D. Ramkrishna On the Solution of Population Balance Equation by Discretizations I. A Fixed Pivot Technique, Chem. Eng. Sci., vol. 51, pp. 1311–1332, 1996.
   Web of Science ®Google Scholar
• V. G. Levich Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, 1962.
   Google Scholar
• A. K. Chesters and G. Hoffman Bubble Coalescence in Pure Liquids, Flow Turbul. Combust., vol. 38, pp. 353–361, 1982.
   Google Scholar
• S. V. Patankar Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, Taylor & Francis Group, New York, 1980.
   Google Scholar
• V. Alopaeus, M. Laakkonen, and J. Aittamaa Solution of Population Balances with Breakage and Agglomeration by High-Order Moment-Conserving Method of Classes, Chem. Eng. Sci., vol. 61, pp. 6732–6752, 2006.
   Web of Science ®Google Scholar
• S. Borde, R. Mato, and S. Villaverde Modeling of the Evolution with Length of Bubble Size Distributions in Bubble Columns, Chem. Eng. Sci., vol. 61, pp. 3663–3673, 2006.
   Web of Science ®Google Scholar