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Extreme solitary waves on falling liquid films

Published online by Cambridge University Press:  24 March 2014

S. Chakraborty ,
P.-K. Nguyen ,
C. Ruyer-Quil  and
V. Bontozoglou
S. Chakraborty
Affiliation:
Université Pierre et Marie Curie, CNRS, Laboratoire FAST, Campus Universitaire, 91405 Orsay, France
P.-K. Nguyen
Affiliation:
University of Thessaly, Department of Mechanical Engineering, 38334 Volos, Greece
C. Ruyer-Quil
Affiliation:
Université Pierre et Marie Curie, CNRS, Laboratoire FAST, Campus Universitaire, 91405 Orsay, France Institut Universitaire de France
V. Bontozoglou*
Affiliation:
University of Thessaly, Department of Mechanical Engineering, 38334 Volos, Greece
*
†Email address for correspondence: bont@mie.uth.gr
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Abstract

Direct numerical simulation (DNS) of liquid film flow is used to compute fully developed solitary waves and to compare their characteristics with the predictions of low-dimensional models. Emphasis is placed on the regime of high inertia, where available models provide widely differing results. It is found that the parametric dependence of wave properties on inertia is highly non-trivial, and is satisfactorily approximated only by the four-equation model of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357–369). Detailed comparison of the asymptotic shapes of upstream and downstream tails is performed, and inherent limitations of all long-wave models are revealed. Local flow reversal in front of the main hump, which has been previously discussed in the literature, is shown to occur for an inertia range bounded from below and from above, and the boundaries are interpreted in terms of the capillary origin of the phenomenon. Computational results are reported for the entire range of Froude numbers, providing benchmark data for all wall inclinations.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 745 , 25 April 2014 , pp. 564 - 591
Copyright
© 2014 Cambridge University Press 

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References

Alekseenko, S. V., Nakoryakov, V. Y. & Pokusaev, B. G. 1985 Wave formation on a vertical falling liquid film. AIChE J. 31, 1446–1460.Google Scholar
Bach, P. & Villadsen, J. 1984 Simulation of the vertical flow of a thin wavy film using a finite element method. Intl J. Heat Mass Transfer 27, 815–827.Google Scholar
Balmforth, N. J. & Liu, J. J. 2004 Roll waves in mud. J. Fluid Mech. 519, 33–54.Google Scholar
Benney, D. J. 1966 Long waves on liquid films. J. Math. Phys. 45, 150–155.Google Scholar
Bontozoglou, V. & Serifi, K. 2008 Falling film flow along steep two-dimensional topography: the effect of inertia. Intl J. Multiphase Flow 34, 734–747.Google Scholar
Brevdo, L., Laure, P., Dias, F. & Bridges, T. J. 1999 Linear pulse structure and signalling in a film flow on an inclined plane. J. Fluid Mech. 396, 37–71.Google Scholar
Bunov, A., Demekhin, E. & Shkadov, V. Y. 1986 Bifurcations of solitary waves in a flowing liquid film. Vestnik Moskov. Univ. Ser. I Mat. Mekh. 41 (2), 37–38.Google Scholar
Chang, H.-C. & Demekhin, E. A. 2002 In Complex Wave Dynamics on Thin Films (ed. Möbius, D. & Miller, R.), Elsevier.Google Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131–1198.Google Scholar
Dietze, G. F., AL-Sibai, F. & Kneer, R. 2009 Experimental study of flow separation in laminar falling liquid films. J. Fluid Mech. 637, 73–104.CrossRefGoogle Scholar
Dietze, G. F., Leefken, A. & Kneer, R. 2008 Investigation of the backflow phenomenon in falling liquid films. J. Fluid Mech. 595, 435–459.Google Scholar
Doedel, E. J., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Sandstede, B. & Wang, X.-J.2007 Auto07: Continuation and bifurcation software for ordinary differential equations. Tech. Rep. Department of Computer Science, Concordia University, Montreal, Canada (available by FTP from ftp.cs.concordia.ca in directory pub/doedel/auto).Google Scholar
Gao, D., Morley, N. B. & Dhir, V. 2003 Numerical simulation of wavy falling film flow using VOF method. J. Comput. Phys. 192, 624–642.Google Scholar
Gjevik, B. 1970 Occurrence of finite-amplitude surface waves on falling liquid films. Phys. Fluids 13, 1918–1925.CrossRefGoogle Scholar
Ho, L.-W. & Patera, A. T. 1990 A legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Comput. Meth. Appli. Mech. Engng 80, 355–366.Google Scholar
Hoffmann, K. A. & Chiang, S. T. 2000 Computational Fluid Dynamics. EES.Google Scholar
Hood, P. 1976 Frontal solution program for unsymmetric matrices. Intl J. Numer. Meth. Engng 10, 379–399.Google Scholar
Jayanti, S. & Hewitt, G. F. 1996 Hydrodynamics and heat transfer of wavy thin film flow. Intl J. Heat Mass Transfer 40, 179–190.CrossRefGoogle Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films. Springer.Google Scholar
Kapitza, P. L. & Kapitza, S. P. 1949 Wave flow of thin layers of a viscous fluid: III. experimental study of undulatory flow conditions. In Collected papers of P. L. Kapitza (1965) (ed. Haar, D. T.), pp. 690–709. Pergamon, (Original paper in Russian: Zh. Ekper. Teor. Fiz. 19, 105–120).Google Scholar
Karapantsios, T. D., Paras, S. V. & Karabelas, A. J. 1989 Statistical characteristics of free falling films at high Reynolds numbers. Intl J. Multiphase Flow 15, 1–21.CrossRefGoogle Scholar
Kunugi, T. & Kino, C. 2005 DNS of falling film structure and heat transfer via MARS method. Comput. Struct. 83, 455–462.CrossRefGoogle Scholar
Leontidis, V., Vatteville, J., Vlachogiannis, M., Andritsos, N. & Bontozoglou, V. 2010 Nominally two-dimensional waves in inclined film flow in channels of finite width. Phys. Fluids 22, 112106.Google Scholar
Liu, J. & Gollub, J. P. 1994 Solitary wave dynamics of film flows. Phys. Fluids 6, 1702–1712.Google Scholar
Liu, Q. Q., Chen, L., Li, J. C. & Singh, V. P. 2005 Roll waves in overland flow. J. Hydrol. Engng 10 (2), 110–117.CrossRefGoogle Scholar
Malamataris, N., Vlachogiannis, M. & Bontozoglou, V. 2002 Solitary waves on inclined films: flow structure and binary interactions. Phys. Fluids 14, 1082–1094.Google Scholar
Miyara, A. 2000a Numerical analysis for a falling liquid film with interfacial waves on an inclined plate. part 2: Effects of interfacial waves on flow dynamics and heat transfer. Heat Transfer Asian Res. 29 (3), 233–248.Google Scholar
Miyara, A. 2000b Numerical simulation of wavy liquid film flowing down on a vertical wall and an inclined wall. Intl J. Therm. Sci. 39 (9), 1015–1027.Google Scholar
Nguyen, L. T. & Balakotaiah, V. 2000 Modeling and experimental studies of wave evolution on free falling viscous films. Phys. Fluids 12, 2236–2256.Google Scholar
Nosoko, T. & Miyara, A. 2004 The evolution and subsequent dynamics of waves on a vertically falling liquid film. Phys. Fluids 16, 1118–1126.CrossRefGoogle Scholar
Ooshida, T. 1999 Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number. Phys. Fluids 11, 3247–3269.Google Scholar
Oron, A., Gottlieb, O. & Novbari, E. 2009 Numerical analysis of a weighted-residual integral boundary-layer model for nonlinear dynamics of falling liquid films. Eur. J. Mech. B/Fluids 28, 1–36.Google Scholar
Panga, M. K. R. & Balakotaiah, V. 2003 Low-dimensional models for vertically falling viscous films. Phys. Rev. Lett. 90 (15), 154501.Google Scholar
Pradas, M., Kalliadasis, S., Nguyen, P.-K. & Bontozoglou, V. 2013 Bound-state formation in interfacial turbulence: direct numerical simulations and theory. J. Fluid Mech. 716 (R2).Google Scholar
Pumir, A., Manneville, P. & Pomeau, Y. 1983 On solitary waves running down an inclined plane. J. Fluid Mech. 135, 27–50.Google Scholar
Ramaswamy, B., Chippada, S. & Joo, S. W. 1996 A full-scale numerical study of interfacial instabilities in thin-film flows. J. Fluid Mech. 325, 163–194.Google Scholar
Roberts, A. J. 1996 Low-dimensional models of thin film fluid dynamics. Phys. Lett. A 212, 63–71.Google Scholar
Roberts, A. J. & Li, Z.-Q. 2006 An accurate and comprehensive model of thin fluid flows with inertia on curved substrates. J. Fluid Mech. 553, 33–73.Google Scholar
Ruyer-Quil, C. & Kalliadasis, S. 2012 Wavy regimes of film flow down a fibre. Phys. Rev. E 85, 046302.CrossRefGoogle Scholar
Ruyer-Quil, C. & Manneville, P. 1998 Modeling film flows down inclined planes. Eur. Phys. J. B 6, 277–292.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2000 Improved modelling of flows down inclined planes. Eur. Phys. J. B 15, 357–369.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2002 Further accuracy and convergence results on the modelling of flows down inclined planes by weighted-residual approximations. Phys. Fluids 14, 170–183.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2005 On the speed of solitary waves running down a vertical wall. J. Fluid Mech. 531, 181–190.Google Scholar
Ruyer-Quil, C., Treveleyan, P., Giorgiutti-Dauphiné, F., Duprat, C. & Kalliadasis, S. 2008 Modelling film flows down a fibre. J. Fluid Mech. 603, 431–462.Google Scholar
Salamon, T. R., Armstrong, R. C. & Brown, R. A. 1994 Traveling waves on vertical films: numerical analysis using the finite element method. Phys. Fluids 6, 2202–2220.Google Scholar
Samanta, A., Goyeau, B. & Ruyer-Quil, C. 2013 A falling film on a porous medium. J. Fluid Mech. 716, 414–444.CrossRefGoogle Scholar
Samanta, A., Ruyer-Quil, C. & Goyeau, B. 2011 A falling film down a slippery inclined plane. J. Fluid Mech. 684, 353–383.Google Scholar
Scheid, B., Ruyer-Quil, C. & Manneville, P. 2006 Wave patterns in film flows: modelling and three-dimensional waves. J. Fluid Mech. 562, 183–222.Google Scholar
Scheid, B., Ruyer-Quil, C., Thiele, U., Kabov, O. A., Legros, J. C. & Colinet, P. 2005 Validity domain of the Benney equation including the Marangoni effect for closed and open flows. J. Fluid Mech. 527, 303–335.Google Scholar
Shkadov, V. Ya. 1967 Wave flow regimes of a thin layer of viscous fluid subject to gravity. Izv. Ak. Nauk SSSR, Mekh. Zhidk Gaza 1, 43–51; English translation in Fluid Dyn. 2, 29–34, 1970 (Faraday Press, NY).Google Scholar
Shkadov, V. Ya. 1977 Solitary waves in a layer of viscous liquid. Izv. Ak. Nauk SSSR, Mekh. Zhidk Gaza 1, 63–66.Google Scholar
Thomas, H. A.1939 The propagation of waves in steep prismatic conduits In Proc. Hydraulics Conf., Univ. of Iowa, pp. 214–229.Google Scholar
Tihon, J., Serifi, K., Argyiriadi, K. & Bontozoglou, V. 2006 Solitary waves on inclined films: their characteristics and the effects on wall shear stress. Exp. Fluids 41, 79–89.CrossRefGoogle Scholar
Trifonov, Y. Y. 2012 Stability and bifurcations of the wavy film flow down a vertical plate: the results of integral approaches and full-scale computations. Fluid Dyn. Res. 44, 031418.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley & Sons.Google Scholar
Yu, L.-Q., Wasden, F. K., Dukler, A. E. & Balakotaiah, V. 1995 Nonlinear evolution of waves on falling films at high Reynolds numbers. Phys. Fluids 7, 1886–1902.Google Scholar