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Investigation of Sphericity Assumption for Bubbles in the Numerical Simulation of Bubbly flow in a Vertical Cylinder

Author Affiliations

  • 1 Deputy Director of Research, Institute for International Energy Studies (IIES), IRAN
  • 2 Department of Engineering, Islamic Azad University, Marivan Branch, IRAN
  • 3 Director of Research, Institute for International Energy Studies (IIES), TEHRAN, IRAN

Res. J. Recent Sci., Volume 4, Issue (1), Pages 9-16, January,2 (2015)


To investigate the sensitivity of the numerical results to the sphericity of the bubbles, numerical simulation of bubbly flow caused by the axial gas injection into a vertical cylinder is studied. The mathematical model solves transport equations for the variables of each phase including the interphase mass and momentum exchange. Both spherical and non-spherical bubbles are investigated. Therefore, two methods are used to calculate the drag coefficient. The first is the empirical correlation obtained from the standard drag curve. This method is suitable when the bubbles remain spherical in shape and the surface-tension effects are negligible. Another approach is the "dirty water" model. This model covers the complete range of Reynolds numbers, Weber numbers, and is suitable for the various shapes of bubbles. The predicted results are in good agreement with experimental data available in the literature. It is found that the numerical results computed by the "dirty water" model are closer to those of the experimental data.


  1. Sherman C.P. Cheung, Yeoh G.H. and Tu J.Y., On the modeling of population balance in isothermal vertical bubbly flows-Average bubble number density approach, International journal of Chemical Engineering and Processing, 46, 742756, (2007)
  2. Durst F., Taylor A.M.K.P. and Whitelaw J.H., Experimental and numerical investigation of bubble-driven laminar flow in an axisymmetric vessel, Journal of Multiphase Flow,10, 557-569 (1984)
  3. Durst F., Schonung B., Selanger K. and Winter M., Bubble-driven liquid flows, International Journal of Fluid Mechanics,170, 53-82 (1986)
  4. Celik I. and Wang Y.Z., Numerical simulation of circulation in gas-liquid column reactor : Isothermal, bubbly, laminar flow, International Journal of Multiphase Flow,20, 1053-1070 (1994)
  5. Johansen S.T., Robertson D.G.C., Woje K. and Engh T.A., Fluid dynamics in bubble stirred ladles : Part I. Experiments, Metallurgical Transactions,19B, 745-754 (1988)
  6. Johansen S.T. and Boysan F., Fluid dynamics in bubble stirred ladles : Part II, Mathematical modeling, Metallurgical Transactions,19B, 755-764 (1988)
  7. Castillejos A.H. and Brimacombe J.K., Measurements of physical characteristics of bubbles in gas-liquid plumes : Part II., Local properties of turbulent air-water plumes in vertically injected jets, Metallurgical Transactions,18B,659-671 (1987)
  8. Jinsong Hua and Chi-Hwa Wang, Numerical Simulation of bubble-driven liquid flows, International Journal of Chemical Engineering Scince,55, 4159-4173 (2000)
  9. Mahmut D. Mat, Kemal Aldas and Olusegun J. Ilegbusi, A two-phase flow model for hydrogen evolution in a electrochemical cell, International Journal of Hydrogen energy,29, 1015-1023 (2004)
  10. Mahmut D. Mat and Kemal Aldas, Application of a two phase flow model for natural convection in an electrochemical cell, International Journal of Hydrogen energy,30, 411-420 (2005)
  11. Kemal Aldas, Application of a two-phase flow model for hydrogen evolution in an electrochemical cell, Applied Mathematics and Computation,154, 507-519 (2004)
  12. Tomomi Uchiyama, Numerical prediction of added mass and damping for a cylinder oscillating in confined incompressible gasliquid, two-phase mixture, Nuclear Engineering and Design,22, 6878 (2003)
  13. Uchiyama T., ALE finite element method for gasliquid; two-phase flow including moving boundary based on an incompressible two-fluid model, Nuclear Engineering and Design,205, 6982 (2001)
  14. Gregory Rosebrock, Ahmed Elgafy, Thomas Beechem and Khalid Lafdi, Study of the growth and motion of graphitic foam bubbles, International Journal of Carbon,43, 30753087 (2005)
  15. Mitsuhiro Ohta, Eiji Iwasaki, Eiji Obata and Yutaka Yoshida, A numerical study of the motion of a spherical drop rising in shear-thinning fluid systems, International Journal of Non-Newtonian Fluid Mechanics,116, 95-111 (2003)
  16. Chen W.B., Reginald B.H. Tan, A model for steam bubble formation at a submerged nozzle in flowing subcooled water, International journal of heat and fluid flow,22, 552-560 (2001)
  17. Thomas Nierhaus, David Vanden Abeele and Herman Deconinck, Direct numerical simulation of bubbly flow in the turbulent boundary layer of a horizontal parallel plate electrochemical reactor, International Journal of Heat and Fluid Flow,28, 110 (2007)
  18. Study of Ionospheric Perturbations during Strong Seismic Activity by Correlation Analysis Method Gwal A.K., Jain Kumar Santosh, Panda Gopal and Gujar Y.S., Res. J. Recent Sci.,1(1), 2-9 (2012)
  19. Giusti A., Lucci F. and Soldati A., Influence of the lift force in direct numerical simulation of upward/downward turbulent channel flow laden with surfactant contaminated micro bubbles, International journal of Chemical Engineering Science,60, 61766187 (2005)
  20. Empirical Correlation of Various Inclusions on the Effect of Primary and Secondary Parameters for Estimation of (ETC) of Two Phase Materials Senthil Kumar A.P., Karthikeyan P., Prabhu Raja V., Ramu M., Somasundharam S. and Vasudevan V., Res. J. RecentSci., 1(1), 22-32 (2012)
  21. Wallis G.B., The terminal speed of single drop or bubbles in an infinite medium, International Journal of Multiphase Flow,1, 491, (1974)
  22. An Overview of Green Supply Chain Management in India Nimawat Dheeraj1 and Namdev Vishal, Res.J.Recent Sci.,1(6), 77-82(2012)
  23. Effective Factors on Determination of Audit Fees in Iran Khani Hamid and Yazdani Qanbar Ali, Res.J.Recent Sci.,1(6), 38-44(2012)
  24. Estimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural NetworkModels Agbo G.A., Ibeh G.F. and Ekpe J.E., Res.J.Recent Sci.,1(6), 27-31(2012)
  25. An Analysis of Malaysian Renewable energy target using Simulation Modelling Approach Akhwanzada, Salman Ahmad, Mat Tahar and Razman bin, Res. J. Recent Sci.,3(1),38-44(2014)