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.
Similar content being viewed by others
References
W. Nusselt, Die Oberflächenkondensation des Wasserdampfes, Teil I, II, Z. VDI, 1916, Bd. 60, Nos. 27, 28, P. 541–546; 569–576.
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.
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.
L.O. Jones and S. Whitaker, An experimental study of falling liquid films, AIChE J., 1966, Vol. 12, P. 525–529.
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.
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.
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.
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.
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.
P.A. Semenov, Liquid flow in thin layers, Technical Physics, 1944, Vol. 14, No. 7–8, P. 427–437.
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.
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.
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.
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.
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.
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.
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.
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.
G.F. Hewitt and N.S. Hall Taylor, Annular two-phase flow, Pergamon Press, Oxford, 1970.
B.J. Azzopardi, Gas-Liquid Flows, Begell House, New York, 2006.
D.E. Woodmansee and T.J. Hanratty, Base film over which roll waves propagate, AIChE J., 1969, Vol. 15, No. 5, P. 712–715.
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.
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.
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.
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.
T.B. Benjamin, Shearing flow over a wavy boundary, J. Fluid Mech., 1959, Vol. 6, P. 161–205.
J.W. Miles, On the generation of surface waves by shear flows, J. Fluid Mech., 1957, Vol. 3, P. 185–204.
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.
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.
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.
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.
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.
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.
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).
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
The work is financially supported by the Russian Foundation for Basic Research (Project code 10-08-00259).
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0869864314030068