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Wavy liquid film in the presence of co- or counter-current turbulent gas flow

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Thermophysics and Aeromechanics Aims and scope

Abstract

The wavy downflow of a viscous liquid film in the presence of the turbulent gas flow was analyzed theoretically. Two-dimensional stationary running waves are calculated in a wide range of Reynolds numbers of liquid and gas. Hydrodynamics of liquid is calculated based on complete Navier-Stokes equations. The wave interface surface is considered as a small perturbation and equations in gas are linearized near the main turbulent flow. Different optimal downflow regimes are determined, and the main wave characteristics are compared in detail with and without the co- and counter-current gas flows. It is shown that at high velocities of the co-current gas flow, the calculated waves correspond to ripples observed in experiments.

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References

  1. W. Nusselt, Die Oberflächenkondensation des Wasserdampfes, Teil I, II, Z. VDI, 1916, Bd. 60, Nos. 27, 28, P. 541–546; 569–576.

    Google Scholar 

  2. P.L. Kapitza, Wavy flow of thin layers of viscous liquid. Part I. Free flow. Part II. The flow in contact with gas flow and heat transfer, J. Exp. Theor. Phys., 1948, Vol. 18, P. 3–28.

    Google Scholar 

  3. P.L. Kapitza and S.P. Kapitza, Wavy flow of thin layers of viscous liquid. Part III. Experimental investigation of the wavy flow regime, J. Exp. Theor. Phys., 1949, Vol. 19, P. 105–120.

    Google Scholar 

  4. L.O. Jones and S. Whitaker, An experimental study of falling liquid films, AIChE J., 1966, Vol. 12, P. 525–529.

    Article  Google Scholar 

  5. K.I. Chu and A.E. Dukler, Statistical characteristics of thin, wavy films. Part II. Studies of the substrate and its wave structure, AIChE J., 1974, Vol. 20, No. 4, P. 695–706.

    Article  Google Scholar 

  6. S.V. Alekseenko, V.E. Nakoryakov, and B.G. Pokusaev, Wave formation on a vertical falling liquid film, AIChE J., 1985, Vol. 31, No. 9, P. 1446–1460.

    Article  Google Scholar 

  7. S.W. Joo, S.H. Davis, and S.G. Bankoff, Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers, J. Fluid Mech., 1991, Vol. 230, P. 117–146.

    Article  MATH  ADS  Google Scholar 

  8. J. Liu, J.D. Paul, and J.P. Gollub, Measurements of the primary instabilities of film flow, J. Fluid Mech., 1993, Vol. 250, P. 69–101.

    Article  ADS  Google Scholar 

  9. J.J. Lee and C.C. Mei, Stationary waves on an inclined sheet of viscous fluid at high Reynolds and moderate Weber numbers, J. Fluid Mech., 1996, Vol. 307, P. 191–229.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  10. P.A. Semenov, Liquid flow in thin layers, Technical Physics, 1944, Vol. 14, No. 7–8, P. 427–437.

    Google Scholar 

  11. S.C. Lee and S.G. Bankoff, Parametric effects on the onset of flooding in flat-plate geometries, Int. J. Heat Mass Transf., 1984, Vol. 27, No. 12, P. 1691–1700.

    Article  Google Scholar 

  12. M. Biage, J.M. Delhaye, and P. Vernier, The flooding transition: a detailed experimental investigation of the liquid film before the flooding point, ANS Proceedings, National Heat Transfer Conf., ANS, 1989, P. 53–60.

    Google Scholar 

  13. A. Zapke and D.G. Kröger, Counter-current gas-liquid flow in inclined and vertical ducts. Part I. Flow patterns, pressure drop characteristics and flooding, Int. J. Multiphase Flow, 2000, Vol. 26, No. 9, P. 1439–1455.

    Article  MATH  Google Scholar 

  14. A. Zapke and D.G. Kröger, Counter-current gas-liquid flow in inclined and vertical ducts. Part II. The validity of the Froude—Ohnesorge number correlation for flooding, Int. J. Multiphase Flow, 2000, Vol. 26, No. 9, P. 1457–1468.

    Article  MATH  Google Scholar 

  15. N.A. Vlachos, S.V. Paras, A.A. Mouza, and A.J. Karabelas, Visual observations of flooding in narrow rectangular channels, Int. J. Multiphase Flow, 2001, Vol. 27, No. 8, P. 1415–1430.

    Article  MATH  Google Scholar 

  16. Y. Sudo, Mechanism and effects of predominant parameters regarding limitation of falling water in vertical counter-current two-phase flow, J. Heat Transf. (Transactions of the ASME), 1996, Vol. 118, No. 3, P. 715–724.

    Article  Google Scholar 

  17. E.I.P. Drosos, S.V. Paras, and A.J. Karabelas, Counter-current gas-liquid flow in a vertical narrow channel — liquid film characteristics and flooding phenomena, Int. J. Multiphase Flow, 2006, Vol. 32, No. 1, P. 51–81.

    Article  MATH  Google Scholar 

  18. D.M. Maron and A.E. Dukler, Flooding and upward film flow in vertical tubes. Part II. Speculations on film flow mechanisms, Int. J. Multiphase Flow, 1984, Vol. 10, No. 5, P. 599–621.

    Article  Google Scholar 

  19. G.F. Hewitt and N.S. Hall Taylor, Annular two-phase flow, Pergamon Press, Oxford, 1970.

    Google Scholar 

  20. B.J. Azzopardi, Gas-Liquid Flows, Begell House, New York, 2006.

    Google Scholar 

  21. D.E. Woodmansee and T.J. Hanratty, Base film over which roll waves propagate, AIChE J., 1969, Vol. 15, No. 5, P. 712–715.

    Article  Google Scholar 

  22. K.I. Chu and A.E. Dukler, Statistical characteristics of thin, wavy films. Part III. Structure of the large waves and their resistance to gas flow, AIChE J., 1975, Vol. 21, No. 3, P. 583–593.

    Article  Google Scholar 

  23. J.C. Asali and T.J. Hanratty, Ripples generated on a liquid film at high gas velocities, Int. J. Multiphase Flow, 1993, Vol. 19, No. 2, P. 229–243.

    Article  MATH  Google Scholar 

  24. B.J. Azzopardi and P.B. Whalley, Artificial waves in annular two-phase flow, ASME Winter Annual Meeting, Chicago, 1980, Basic Mechanisms in Two-Phase Flow and Heat Transfer, P. 1–8.

    Google Scholar 

  25. E.A. Demekhin, G.Yu. Tokarev, and V.Ya. Shkadov, Instability and nonlinear waves in a vertical liquid film counter-current to the turbulent gas flow, Theor. Found. Chem. Engng., 1989, Vol. 23, No. 1, P. 64–70.

    Google Scholar 

  26. T.B. Benjamin, Shearing flow over a wavy boundary, J. Fluid Mech., 1959, Vol. 6, P. 161–205.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. J.W. Miles, On the generation of surface waves by shear flows, J. Fluid Mech., 1957, Vol. 3, P. 185–204.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. Yu.Ya. Trifonov, Flooding in two-phase counter-current flows: numerical investigation of the gas-liquid wavy interface using the Navier—Stokes equations, Int. J. Multiphase Flow, 2010, Vol. 36, No. 7, P. 549–557.

    Article  Google Scholar 

  29. Yu.Ya. Trifonov, Counter-current gas-liquid wavy film flow between the vertical plates analyzed using the Navier—Stokes equations, AIChE J., 2010, Vol. 56, No. 8, P. 1975–1987.

    MathSciNet  Google Scholar 

  30. V.V. Guguchkin, E.A. Demekhin, G.N. Kalugin, E.E. Markovich, and V.G. Pikin, Linear and nonlinear stability of combined plane-parallel flow of a film of liquid and gas, Fluid Dynamics, 1979, Vol. 14, No. 1, P. 26–31.

    Article  ADS  Google Scholar 

  31. E.A. Demekhin, Nonlinear waves in a liquid film entrained by a turbulent gas stream, Fluid Dynamics, 1981, Vol. 16, No. 2, P. 188–193.

    Article  MATH  ADS  Google Scholar 

  32. S.V. Alekseenko, A.V. Cherdantsev, O.M. Heinz, S.M. Kharlamov, and D.M. Markovich, An image analysis method as applied to study the space-temporal evolution of waves in an annular gas-liquid flow, Pattern Recognition and Image Analysis, 2011, Vol. 21, No. 3, P. 441–445.

    Article  Google Scholar 

  33. S.V. Alekseenko, A.V. Cherdantsev, O.M. Heinz, S.M. Kharlamov, and D.M. Markovich, Application of the image analysis method to studies of the space-time wave evolution in an annular gas-liquid flow, Pattern Recognition and Image Analysis, 2013, Vol. 23, No. 1, P. 229–243.

    Article  Google Scholar 

  34. Yu.Ya. Trifonov, Stability and bifurcations of the wavy film flow down a vertical plate: the results of integral approaches and full-scale computations, Fluid Dyn. Res., 2012, Vol. 44, No. 3, P. 031418(19).

    Article  MathSciNet  ADS  Google Scholar 

  35. Yu.Ya. Trifonov, Wavy flow of a liquid film in the presence of a co-current turbulent gas flow, J. Appl. Mech. Techn. Phys., 2013, Vol. 54, No. 5, P. 762–772.

    Article  ADS  Google Scholar 

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Correspondence to Yu. Ya. Trifonov.

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The work is financially supported by the Russian Foundation for Basic Research (Project code 10-08-00259).

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Trifonov, Y.Y. Wavy liquid film in the presence of co- or counter-current turbulent gas flow. Thermophys. Aeromech. 21, 319–336 (2014). https://doi.org/10.1134/S0869864314030068

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  • DOI: https://doi.org/10.1134/S0869864314030068

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