Skip to main content
SpringerLink
Log in

A New Approach in Modeling Phase Distribution in Fully Developed Bubbly Pipe Flow

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

Turbulent two-phase flow equations are derived and solved for fully developed pipe flow using a composite eddy-viscosity model and a new void-fraction equation. The void fraction profile is first specified from experiments and the velocity field is calculated to validate the eddy-viscosity model. Consequently, a new equation is presented for calculation of the void fraction. This void-fraction equation incorporates the gradient of turbulent normal stresses in the radial direction, the conventional lift force, and a contribution from the unsteady drag force. The implications of this new equation, for the bubbly flow regime, are investigated by calculating the void-fraction distribution for a given velocity field. Inclusion of the normal turbulent stresses in the radial direction is shown to simulate correctly the experimentally observed trends of the phase distribution, both for upward and downward bubbly flow, without the need for a fictitious term such as the so called ``lubrication force''.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahmadi, G. and Ma, D., A thermodynamical formulation for dispersed multiphase turbulence flows. Part 1: Basic theory. Report No. MIE-143, Department of Mechanical and Industrial Engineering, Postdam, NY (1987).

    Google Scholar 

  2. Alajbegovic, A., Kurul, N. and Podowski, M.Z., Multiphase modeling in CFX4. In: Proceedings 3rd International Users Conference, Chesham, Buckinghamshire, U.K. (1996).

    Google Scholar 

  3. Antal, S.P., Lahey Jr., R.T. and Flaherty, J.E., Analysis of phase distribution in fully developed laminar bubbly two-phase flow. Internat. J. Multiphase Flow 17(5) (1991) 635-652.

    Article  MATH  Google Scholar 

  4. Baldwin, B.S. and Lomax, H., Thin-layer approximation and algebraic model for separated turbulent flows. AIAA Paper 78-257, Huntsville, AL (1978).

  5. Bertodano, M.L., Lee, S.-J., Lahey Jr., R.T. and Drew, D.A., The prediction of two-phase turbulence and phase distribution phenomena using Reynolds stress model. J. Fluids Engrg. 112 (1990) 107-113.

    Google Scholar 

  6. Besnard, D.C. and Harlow, F.H., Turbulence in multiphase flow. Internat. J. Multiphase Flow 14 (1988) 679.

    Article  MATH  Google Scholar 

  7. Bao, J. and Soo, S.L., Measurement of bubble flow properties in a suspension by a laser system. Powder Technol. 85 (1995) 261-268.

    Article  Google Scholar 

  8. Cebeci, T. and Smith, A.M.O., Analysis of Turbulent Boundary Layers, Series in Applied Mathematics & Mechanics, Vol. XV. Academic Press, New York (1974).

    MATH  Google Scholar 

  9. Celik, I. and Gel, A., Time-averaged steady state equations for two-phase flow in fluidized bed reactors. Final Report U.S. DOE Morgantown Energy Technology Center, Morgantown, WV. Contract No. DE-AP21-91MCS53942 (1993).

  10. Celik, I., and Gel, A., Modeling of two-phase turbulence in bubbly flow regime. Forum on Cavitation and Multiphase Flow, Proceedings of the 1997 ASME Fluids Engineering Division Summer Meeting (FEDSM'97) Vancouver, British Columbia, Canada, June 22-26. ASME, New York (1997) CD-ROM, Paper No. ASME-FEDSM97-3261.

  11. Celik, I. and Wang, Y.-Z., Numerical simulation of circulation in gas-liquid column reactors: Isothermal, bubbly, laminar flow. Internat. J. Multiphase Flow 20(6) (1994) 1053-1070.

    Article  MATH  Google Scholar 

  12. Chang, K.C., Wu, W.J. and Wang, M.R., Limitations of stochastic approach in two-phase turbulent flow calculations. Atomization and Sprays 6(2) (1996) 211-225.

    Google Scholar 

  13. Chang, K.C. and Yang, J.C., Unsteady drag consideration in stochastic Eulerian-Lagrangian formulation of two-phase flow. AIAA J. 37(4) (1999) 434-442.

    Article  MathSciNet  Google Scholar 

  14. Daily, J.W. and Harleman, D.R.F., Fluid Dynamics. Addison Wesley, Reading, MA (1973).

    Google Scholar 

  15. Dasgupta, S., Jackson, R. and Sundaresan, S., Turbulent gas-bubble flow in vertical risers. AIChE J. 40 (1994) 215.

    Article  Google Scholar 

  16. Drew, D.A. and Lahey, R.T., The analysis of phase distribution in fully developed twophase flows. In: Proceedings 2nd Multi-Phase Flow and Heat Transfer Symposium-Workshop. Hemisphere, New York (1979).

    Google Scholar 

  17. Drew, D.A. and Lahey, R.T., Phase-distribution mechanisms in turbulent low-quality two-phase flow in a circular pipe. J. Fluid Mech. 117 (1982) 91-106.

    Article  MATH  ADS  Google Scholar 

  18. Drew, D.A., Mathematical modeling of two-phase flow. Annual Rev. Fluid Mech. 15 (1983) 261-291.

    Article  MATH  ADS  Google Scholar 

  19. Drew, D.A., The plane Poiseuille flow of a bubble-fluid mixture. ASME J. Fluids Engrg. 112 (1990) 362-366.

    Article  Google Scholar 

  20. Elgobashi, S.E. and Abou-Arab, T.W., A two-equation turbulence closure for two-phase flows. Phys. Fluids 26 (1983) 931-938.

    Article  ADS  Google Scholar 

  21. Gel, A., Modeling of bubble-induced turbulence effects in gas-liquid flows by using timeaveraged equations. M.Sc. Thesis, MAE Department, West Virginia University, Morgantown, WV (1994).

    Google Scholar 

  22. Gel, A. and Celik, I., Fully developed two-phase flow analysis: Theory and application in bubbly flow regime. In: Coleman, H., et al. (eds), Cavitation and Multiphase Flow Forum, Proceedings of the ASME Fluids Engineering Conference, San Diego, CA, July 7-11, FED-Vol. 236. ASME, New York (1996) pp. 557-563.

    Google Scholar 

  23. Gharat, S.D. and Joshi, J.B., Transport phenomena in bubble column reactors I: Flow pattern. Chem. Engrg. J. 48 (1992) 141-151.

    Article  Google Scholar 

  24. Gidaspow, D., Tsuo, Y.P. and Luo, K.M., Computed and experimental cluster formation in velocity profiles in circulating fluidized beds. In: Grace, J.R., et al. (eds), International Fluidization Conference, Banff, Alberta, Canada. Engineering Foundation, New York (1989).

    Google Scholar 

  25. Grossetete, C., Experimental investigation and preliminary numerical simulations of void pro-file development in a vertical cylinderical pipe. In: Proceedings 2nd International Conference on Multiphase Flow, Kyoto, Japan, April 3-7 (1995) pp. (IF1-1)-(IF1-10).

  26. Hestroni, G., Bubbles-turbulence interaction. Internat. J. Multiphase Flow 15(5) (1989) 735-746.

    Article  Google Scholar 

  27. Hunt, J.C.R. and Belcher, S.E., Turbulent flow over hills and waves. Annual Rev. Fluid Mech. 30 (1998) 507-538.

    Article  MathSciNet  ADS  Google Scholar 

  28. Hutchinson, P., Hewitt, G.F. and Dukler, A.E., Deposition of liquid or solid dispersion from turbulent gas streams: A stochastic model. Chem. Engrg. Sci. 26 (1971) 419-439.

    Article  Google Scholar 

  29. Kashinsky, O.N., Timkin, L.S. and Cartellier, A., Experimental study of laminar bubbly flow in a vertical pipe. Exp. Fluids 15(4/5) (1993) 308-314.

    Google Scholar 

  30. Kataoka, I. and Serizawa, A., Basic equations of turbulence in gas-liquid two-phase flow. Internat. J. Multiphase Flow 5 (1989) 843-855.

    Article  MATH  Google Scholar 

  31. Liu, T.J. and Bankoff, S.G., Structure of air-water bubbly flow in a vertical pipe-I. Liquid mean velocity and turbulence measurements. Internat. J. Heat Mass Transfer 36 (1993) 1049-1060.

    Article  Google Scholar 

  32. Liu, T.J. and Bankoff, S.G., Structure of air-water bubbly flow in a vertical pipe-II. Void fraction, bubble velocity and bubble size distributions. Internat. J. Heat Mass Transfer 36 (1993) 1061-1072.

    Article  Google Scholar 

  33. Loth, E., Experimental bubble dispersion in a turbulent boundary layer. Poster presentation at the ONR 2000 Workshop on Free Surface Turbulence and Bubbly Flows, CalTech, Pasadena, CA, March 1-3, and Private Communication.

  34. Michiyoshi, I. and Serizawa, A., Turbulence in two-phase bubbly flow. Nuclear Engrg. Design 95 (1986) 253-267.

    Article  Google Scholar 

  35. Mobbs, S.D. and Lucas, G.P., A turbulence model for inclined, bubbly flows. Appl. Sci. Res. 51 (1993) 263-268.

    Article  MATH  Google Scholar 

  36. Nakaryakov, V.E., Kashinsky, O.N., Randin, V.V. and Timkin, L.S., Gas-liquid bubbly flow in vertical pipes. J. Fluids Engrg. 118 (1996) 377-382.

    Google Scholar 

  37. Nikitopoulos, D.E. and Michaelides, E.E., Phenomenological model for dispersed bubbly flow in pipes. AIChE J. 41(1) (1995) 12-22.

    Article  Google Scholar 

  38. Riviere, N. and Cartellier, A., Wall shear stress and void fraction in Poiseuille bubbly flow: Part I: Simple analytical predictions. European J. Mech. B/Fluids 18 (1999) 823-846.

    Article  MATH  Google Scholar 

  39. Riviere, N., Cartellier, A., Timkin, L. and Kashinsky, O., Wall shear stress and void fraction in Poiseuille bubbly flow: Part II: Experiments and validity of analytical predictions. European J. Mech. B/Fluids 18 (1999) 847-867.

    Article  MATH  Google Scholar 

  40. Sadatomi, M., Sato, Y. and Sekoguchi, K., Momentum and heat transfer in two-phase bubbly flow-I. Theory. Internat. J. Multiphase Flow 2 (1981) 79-95.

    Google Scholar 

  41. Schnitzlein, M.G. and Weinstein, H., Flow characterization in high-velocity fluidized beds using pressure fluctuations. Chem. Engrg. Sci. 43 (1988) 2605.

    Article  Google Scholar 

  42. Sano, T., Unsteady flow past a sphere at low Reynolds numbers. J. Fluid Mech. 112 (1981) 433-441.

    Article  MATH  ADS  Google Scholar 

  43. Syamlal, M. and O'Brien, T.J., Simulation of granular layer inversion in liquid fluidized beds. Internat. J. Numer. Methods Fluids 14 (1988) 473-481.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical & Aerospace Engineering Department, West Virginia University, Morgantown, WV, 26506-6106, U.S.A.

    Ismail Celik & Aytekin Gel

Authors
  1. Ismail Celik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aytekin Gel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Celik, I., Gel, A. A New Approach in Modeling Phase Distribution in Fully Developed Bubbly Pipe Flow. Flow, Turbulence and Combustion 68, 289–311 (2002). https://doi.org/10.1023/A:1021765605698

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021765605698

Search

Navigation