Developed ‘laminar’ bubbly flow with non-uniform bubble sizes

  • Luo Rui 
  • Song Qiang 
  • Yang Xianyong 
  • Wang Zhou 


Bubbles with different sizes have different dynamic and kinetic behavior in a two-phase bubbly flow. A common two-fluid model based on the uniform bubble size assumption is not suitable for a bubbly flow with non-uniform bubble sizes. To deal with non-uniform bubbly flows, a multi-fluid model is established, with which bubbles are divided into several groups according to their sizes and a set of basic equations is derived for each group of bubbles with almost the same size. Through analyzing the bubble-bubble and bubble-pipe wall interactions, two new constitutive laws for the wall-force and pressure difference between the liquid phase and interface are developed to close the averaged basic equations. The respective phase distributions for each group of bubbles measured by a specially designed three-dimensional photographic method are used to check the model. Comparison between model-predicted values and experimental data shows that the model can describe laminar bubbly flow with non-uniform bubble sizes.

Key words

multi-fluid model non-uniform bubbly flow phase distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Antal, S. P., Lahey, R. T. Jr. Flaherty, J. E., Analysis of phase distribution in fully developed laminar bubbly two-phase flow, Int. J. Multiphase Flow, 1991, 17: 635.MATHCrossRefGoogle Scholar
  2. 2.
    Nakoryakov, V. E., Kashinsky, O. N., Randin, V. V. et al., Gas-liquid bubbly flow in vertical pipes, Journal of Fluid Engineering, 1996, 118: 377.CrossRefGoogle Scholar
  3. 3.
    Kashinsky, O. N., Timkin, L. S., Cartellier, A., Experimental study of “laminar” bubbly flows in a vertical pipe, Experiments in Fluids, 1993, 14: 308.Google Scholar
  4. 4.
    Song, Q., Theoretical and experimental research on bubbly flow in a vertical pipe, Ph. D. Thesis, Tsinghua University, 1999 Beijing, China.Google Scholar
  5. 5.
    Kataoka, M., Ishii, M., Serizawa, A., Local formulation of interfacial area concentration, Int. J. Multiphase Flow, 1986, 12: 505.MATHCrossRefGoogle Scholar
  6. 6.
    Drew, D. A., Mathematical modeling of two-phase flow, Annual Review of Fluid Mechanics, 1983, 15: 261.CrossRefGoogle Scholar
  7. 7.
    Nigmatulin, R. I., Spatial averaging in the mechanics of heterogeneous and dispersed systems, Int. J. Multiphase Flow, 1979 5: 353.MATHCrossRefGoogle Scholar
  8. 8.
    Sato, Y., Sadatomi, M., Sekoguchi, K., Momentum and heat transfer in two-phase bubbly flow-I, Int. J. Multiphase Flow, 1981, 7: 167.MATHCrossRefGoogle Scholar
  9. 9.
    Ishii, M., Mishima, K., Two-fluid modeling and hydrodynamic constitutive relations, Nucl. Engng. Des., 1984, 82: 107.CrossRefGoogle Scholar
  10. 10.
    Drew, D. A., Lahey, R. T. Jr., The virtual mass and lift force on a sphere in rotating and straining invicid flow, Int. J. Multiphase Flow, 1987, 13: 113.MATHCrossRefGoogle Scholar
  11. 11.
    Cherkutat, P., McLaughlin, J. B., Wall-induced lift on a sphere, Int. J. Multiphase Flow, 1990, 16: 899.CrossRefGoogle Scholar
  12. 12.
    Tomiyama, A., Zun, I., Higaki, H. et al., A three-dimensional particle tracking method for bubbly flow simulation, Nucl. Engng. Des., 1997, 175: 77.CrossRefGoogle Scholar
  13. 13.
    Van Wijingaarden, L., The mean rise velocity of pairwise-interacting bubbles in liquid, J. Fluid Mech., 1993, 251: 55.CrossRefGoogle Scholar
  14. 14.
    Stuhmiller, J. H., The influence of interfacial pressure on the character of two-phase flow model equations, Int. J. Multiphase Flow, 1977, 3: 551.MATHCrossRefGoogle Scholar

Copyright information

© Science in China Press 2001

Authors and Affiliations

  • Luo Rui 
    • 1
  • Song Qiang 
    • 2
  • Yang Xianyong 
    • 1
  • Wang Zhou 
    • 1
  1. 1.Department of Thermal EngineeringTsinghua UniversityBeijingChina
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingChina

Personalised recommendations