High Temperature

, Volume 56, Issue 1, pp 61–69 | Cite as

Numerical Simulation of the Turbulent Upward Flow of a Gas-Liquid Bubble Mixture in a Vertical Pipe: Comparison with Experimental Data

  • D. A. Gubaidullin
  • B. A. Snigerev
Heat and Mass Transfer and Physical Gasdynamics


The results of numerical simulation of the structure of a two-phase flow of a gas–liquid bubble mixture in a vertical ascending flow in a pipe are presented. The mathematical model is based on the use of the Eulerian description of the mass and momentum conservation for the liquid and gas phases, recorded within the framework of the theory of interacting continua. To describe the bubble-size distribution, the equations of particle-number conservation for individual groups of bubbles with different constant sizes are used for each fraction, taking the processes of breakage and coalescence into account. Comparison of the results of numerical simulation with experimental data has shown that the proposed approach enables the simulation of bubble turbulent polydisperse flows in a wide range of gas concentrations.


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  1. 1.
    Jakobsen, H.A., Chemical Reactor Modeling. Multiphase Reactive Flows, Berlin: Springer, 2013.Google Scholar
  2. 2.
    Ishii, M. and Hibiki, T., Thermo-Fluid Dynamics of Two-Phase Flow, Berlin: Springer, 2011.CrossRefMATHGoogle Scholar
  3. 3.
    Nigmatulin, R.I., Osnovy mekhaniki geterogennykh sred (Fundamentals of Mechanics of Heterogeneous Media), Moscow: Nauka, 1978.Google Scholar
  4. 4.
    Nakoryakov, V.E., Pokusaev, B.G., and Shreiber, I.R., Volnovaya dinamika gazo-i parozhidkostnykh sred (Wave Dynamics of Gas and Vapor-Liquid Media), Moscow: Energoatomizdat, 1990.MATHGoogle Scholar
  5. 5.
    Varaksin, A.Yu., High Temp., 2013, vol. 51, no. 3, p. 377.CrossRefGoogle Scholar
  6. 6.
    Varaksin, A.Yu., High Temp., 2014, vol. 52, no. 5, p. 752.CrossRefGoogle Scholar
  7. 7.
    Burdukov, A.P., Valukina, N.V., and Nakoryakov, V.E., Prikl. Mekh. Tekh. Fiz., 1975, no. 4, p. 137.Google Scholar
  8. 8.
    Liu, T.J. and Bankoff, S.G., Int. J. Heat Mass Transfer, 1993, vol. 36, p. 1049.CrossRefGoogle Scholar
  9. 9.
    Nakoryakov, V.E., Kashinsky, O.N., Randin, V.V., and Timkin, L.S., J. Fluids Eng., 1996, vol. 118, p. 377.CrossRefGoogle Scholar
  10. 10.
    Hibiki, T., Ishii, M., and Xiao, Z., Int. J. Heat Mass Transfer, 2001, vol. 44, p. 1869.CrossRefGoogle Scholar
  11. 11.
    Lucas, D., Krepper, E., and Prasser, H.M., Int. J. Multiphase Flow, 2005, vol. 31, p. 1304.CrossRefGoogle Scholar
  12. 12.
    Gorelik, R.S., Kashinskii, O.N., and Nakoryakov, V.E., Appl. Mech. Tech. Phys., 1987, vol. 28, no. 1, p. 64.ADSCrossRefGoogle Scholar
  13. 13.
    Hibiki, T., Coda, H., Kim, S., et al., L. Int. J. Heat Mass Transfer, 2004, vol. 47, p. 1847.CrossRefGoogle Scholar
  14. 14.
    Kashinskii, O.N., Randin, V.V., Lobanov, P.D., and Bogosolovtsev, G.V., High Temp., 2005, vol. 12, no. 4, p. 635.Google Scholar
  15. 15.
    Kashinsky, O.N., Lobanov, P.D., and Pakhomov, M.A., et al., Int. J. Heat Mass Transfer, 2006, vol. 49, p. 3717.CrossRefGoogle Scholar
  16. 16.
    Ramkrishna, D., Population Balances: Theory and Applications to Particulate Systems in Engineering, New York: Academic, 2000.Google Scholar
  17. 17.
    Marchisio, D.L. and Fox, R.O., Computational Models for Polydisperse Particulate and Multiphase Systems, Cambridge: Cambridge Univ. Press, 2013.CrossRefGoogle Scholar
  18. 18.
    Ekambara, K., Dhotre, M.T., and Joshi, J.B., Chem. Eng. Sci., 2005, vol. 60, no. 4, p. 6733.CrossRefGoogle Scholar
  19. 19.
    Yeoh, G.H. and Tu, J.Y., Appl. Math. Modell., 2006, vol. 30, p. 1067.CrossRefGoogle Scholar
  20. 20.
    McGraw, R., Aerosol Sci. Technol., 1997, vol. 27, p. 255.ADSCrossRefGoogle Scholar
  21. 21.
    Buffo, A., Vanni, M., Marchisio, D., and Fox, R.O., Int. J. Multiphase Flow, 2013, vol. 50, p. 41.CrossRefGoogle Scholar
  22. 22.
    Selma, B., Bannari, R., and Proulx, P., Chem. Eng. Sci., 2010, vol. 65, p. 1925.CrossRefGoogle Scholar
  23. 23.
    Deju, L., Cheung, S.C.P., Yeoh, G.H., and Tu, J.Y., Appl. Math. Modell., 2013, vol. 37, p. 8557.CrossRefGoogle Scholar
  24. 24.
    Kocamustafaogullari, G. and Ishii, M., Int. J. Heat Mass Transfer, 1995, vol. 38, p. 481.CrossRefGoogle Scholar
  25. 25.
    Hibiki, T. and Ishii, M., Int. J. Heat Mass Transfer, 2001, vol. 45, p. 2331.Google Scholar
  26. 26.
    Wu, Q., Kim, S., Ishii, M., and Beus, S.G., Int. J. Heat Mass Transfer, 1998, vol. 41, p. 1103.CrossRefGoogle Scholar
  27. 27.
    Hibiki, T. and Ishii, M.J., Int. J. Heat Mass Transfer, 2000, vol. 43, p. 2711.CrossRefGoogle Scholar
  28. 28.
    Yao, W. and Morel, C., Int. J. Heat Mass Transfer, 2004, vol. 47, p. 307.CrossRefGoogle Scholar
  29. 29.
    Terekhov, V.I. and Pakhomov, M.A., High Temp., 2008, vol. 46, no. 6, p. 854.CrossRefGoogle Scholar
  30. 30.
    Pakhomov, M.A. and Terekhov, V.I., Fluid Dyn., 2015, vol. 50, no. 2, p. 229.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Pakhomov, M.A. and Terekhov, V.I., Tech. Phys., 2015, vol. 60, no. 9, p. 1268.CrossRefGoogle Scholar
  32. 32.
    Pakhomov, M.A. and Terekhov, V.I., High Temp., 2016, vol. 54, no. 1, p. 150.CrossRefGoogle Scholar
  33. 33.
    Zaichik, L.I., Skibin, A.P., and Solov’ev, S.L., High Temp., 2004, vol. 42, no. 1, p. 101.CrossRefGoogle Scholar
  34. 34.
    Zaichik, L.I., Mukin, R.V., Mukina, L.S., Strizhov, V.F., and Filippov, A.S., High Temp., 2012, vol. 50, no. 1, p. 70.CrossRefGoogle Scholar
  35. 35.
    Zaichik, L.I., Mukin, R.V., Mukin, L.S., and Strizhov, V.F., High Temp., 2012, vol. 50, no. 5, p. 621.CrossRefGoogle Scholar
  36. 36.
    Mukin, R.V., Int. J. Multiphase Flow, 2014, vol. 62, p. 52.MathSciNetCrossRefGoogle Scholar
  37. 37.
    Troshko, A.A. and Hasan, Y.A., Int. J. Multiphase Flow, 2001, vol. 27, p. 1965.CrossRefGoogle Scholar
  38. 38.
    Politano, M.S., Carrica, P.M., and Converti, J., Int. J. Multiphase Flow, 2003, vol. 29, p. 1153.CrossRefGoogle Scholar
  39. 39.
    Drew, D.A., Ann. Rev. Fluid Mech., 1983, vol. 15, p. 261.ADSCrossRefGoogle Scholar
  40. 40.
    Lahey, J.R.T. and Drew, D.A., Chem. Eng. Commun., 1992, vol. 118, p. 124.CrossRefGoogle Scholar
  41. 41.
    Wang, T., Wang, J., and Jin, Y., AIChE J., 2006, vol. 52, p. 125.CrossRefGoogle Scholar
  42. 42.
    Pfleger, D., Gomes, S., Wagner, G.H., and Gilbert, N., Chem. Eng. Sci., 1999, vol. 54, no. 4, p. 5091.CrossRefGoogle Scholar
  43. 43.
    Prince, M.J. and Blanch, H.W., AIChE. J., 1990, vol. 36, p. 1485.CrossRefGoogle Scholar
  44. 44.
    Luo, H. and Svendsen, H., AIChE. J., 1996, vol. 46, p. 1225.CrossRefGoogle Scholar
  45. 45.
    Weller, N.G., Tabor, G., and Jasak, H., Comput. Phys., 1998, vol. 12, p. 620.ADSCrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Mechanics and Engineering, Kazan Scientific CenterRussian Academy of SciencesKazanRussia
  2. 2.Kazan Federal UniversityKazanRussia

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