Skip to main content
×
×
Home

Solitary waves on falling liquid films in the inertia-dominated regime

  • Fabian Denner (a1), Alexandros Charogiannis (a2), Marc Pradas (a2) (a3), Christos N. Markides (a2), Berend G. M. van Wachem (a1) (a4) and Serafim Kalliadasis (a2)...
Abstract

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Solitary waves on falling liquid films in the inertia-dominated regime
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Solitary waves on falling liquid films in the inertia-dominated regime
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Solitary waves on falling liquid films in the inertia-dominated regime
      Available formats
      ×
Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Email address for correspondence: fabian.denner@gmail.com
References
Hide All
Adomeit, P. & Renz, U. 2000 Hydrodynamics of three-dimensional waves in laminar falling films. Intl J. Multiphase Flow 26, 11831208.
Albert, C., Marschall, H. & Bothe, D. 2014 Direct numerical simulation of interfacial mass transfer into falling films. Intl J. Heat Mass Transfer 69, 343357.
Alekseenko, S., Antipin, V., Cherdantsev, A., Kharlamov, S. & Markovich, D. 2009 Two-wave structure of liquid film and wave interrelation in annular gas–liquid flow with and without entrainment. Phys. Fluids 21, 061701,1–4.
Alekseenko, S., Cherdantsev, A., Cherdantsev, M., Isaenkov, S., Kharlamov, S. & Markovich, D. 2012 Application of a high-speed laser-induced fluorescence technique for studying the three-dimensional structure of annular gas–liquid flow. Exp. Fluids 53, 7789.
Argyriadi, K., Serifi, K. & Bontozoglou, V. 2004 Nonlinear dynamics of inclined films under low-frequency forcing. Phys. Fluids 16, 24572468.
Benney, D. J. 1966 Long waves on liquid film. J. Math. Phys. 45, 150155.
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 Continuum method for modeling surface tension. J. Comput. Phys. 100, 335354.
Chakraborty, S., Nguyen, P.-K., Ruyer-Quil, C. & Bontozoglou, V. 2014 Extreme solitary waves on falling liquid films. J. Fluid Mech. 745, 564591.
Chang, H.-C. 1994 Wave evolution on a falling film. Annu. Rev. Fluid Mech. 26, 103136.
Chang, H.-C., Demekhin, E. A. & Kalaidin, E. N. 1995 Interaction dynamics of solitary waves on a falling film. J. Fluid Mech. 294, 123154.
Charogiannis, A., An, J. S. & Markides, C. N. 2015 A simultaneous laser-induced fluorescence, particle image velocimetry and particle tracking velocimetry technique for the investigation of liquid film flows. Exp. Therm. Fluid Sci. 68, 516536.
Charogiannis, A., Denner, F., van Wachem, B. G. M., Kalliadasis, S. & Markides, C. N. 2017 Detailed hydrodynamic characterization of harmonically excited falling-film flows: a combined experimental and computational study. Phys. Rev. Fluids 2, 014002.
Cherdantsev, A. V., Hann, D. B. & Azzopardi, B. J. 2014 Study of gas-sheared liquid film in horizontal rectangular duct using high-speed LIF technique: three-dimensional wavy structure and its relation to liquid entrainment. Intl J. Multiphase Flow 67, 5264.
Demekhin, E. A., Kalaidin, E. N., Kalliadasis, S. & Vlaskin, S. Yu. 2007 Three-dimensional localized coherent structures of surface turbulence. Part I. Scenarios of two-dimensional–three-dimensional transition. Phys. Fluids 19, 114103.
Denner, F., Evrard, F., Serfaty, R. & van Wachem, B. G. M. 2017b Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension. Comput. Fluids 143, 5972.
Denner, F., Pare, G. & Zaleski, S. 2017a Dispersion and viscous attenuation of capillary waves with finite amplitude. Eur. Phys. J. 226, 12291238.
Denner, F., Pradas, M., Charogiannis, A., Markides, C. N., van Wachem, B. G. M. & Kalliadasis, S. 2016 Self-similarity of solitary waves on inertia-dominated falling liquid films. Phys. Rev. E 93, 033121.
Denner, F. & van Wachem, B. G. M. 2014a Fully-coupled balanced-force VOF framework for arbitrary meshes with least-squares curvature evaluation from volume fractions. Numer. Heat Trans. B 65 (3), 218255.
Denner, F. & van Wachem, B. G. M. 2014b Compressive VOF method with skewness correction to capture sharp interfaces on arbitrary meshes. J. Comput. Phys. 279, 127144.
Denner, F. & van Wachem, B. G. M. 2015 Numerical time-step restrictions as a result of capillary waves. J. Comput. Phys. 285, 2440.
Dietze, G. F., Al-Sibai, F. & Kneer, R. 2009 Experimental study of flow separation in laminar falling liquid films. J. Fluid Mech. 637, 73104.
Dietze, G. F., Leefken, A. & Kneer, R. 2008 Investigation of the backflow phenomenon in falling liquid films. J. Fluid Mech. 595, 435459.
Dietze, G. F. & Ruyer-Quil, C. 2013 Wavy liquid films in interaction with a confined laminar gas flow. J. Fluid Mech. 722, 348393.
Dietze, G. F. 2016 On the Kapitza instability and the generation of capillary waves. J. Fluid Mech. 789, 368401.
Doro, E. O. & Aidun, C. K. 2013 Interfacial waves and the dynamics of backflow in falling liquid films. J. Fluid Mech. 726, 261284.
Gao, D., Morley, N. B. & Dhir, V. 2003 Numerical simulation of wavy falling film flow using VOF method. J. Comput. Phys. 192 (2), 624642.
Hinch, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463465.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201225.
Kaehler, C. J., Scharnowski, S. & Cierpka, C. 2012 On the uncertainty of digital PIV and PTV near walls. Exp. Fluids 52, 16411656.
Kaehler, C. J., Scholz, U. & Ortmanns, J. 2006 Wall-shear-stress and near-wall turbulence measurements up to single pixel resolution by means of long-distance micro-PIV. Exp. Fluids 41, 327341.
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films, Springer Series on Applied Mathematical Sciences, vol. 176. Springer.
Kapitza, P. L. 1948 Wave flow of thin layers of a viscous fluid. Zh. Eksp. Teor. Fiz. 18, 328.
Kapitza, P. L. & Kapitza, S. P. 1949 Wave flow on thin layers of a viscous fluid. Zh. Eksp. Teor. Fiz. 19, 105120.
Karimi, G. & Kawaji, M. 2000 Flooding in vertical counter-current annular flow. Nucl. Engng Des. 200, 95105.
Kelly, R. E., Goussis, D. A., Lin, S. P. & Hsu, F. K. 1989 The mechanism for surface wave instability in film flow down an inclined plane. Phys. Fluids A 1 (5), 819828.
Kunugi, T. & Kino, C. 2005 DNS of falling film structure and heat transfer via MARS method. Comput. Struct. 83 (6–7), 455462.
Lel, V. V., Al-Sibai, F., Leefken, A. & Renz, U. 2005 A local thickness and wave velocity measurement of wavy films with a chromatic confocal imaging method and a fluorescence intensity technique. Exp. Fluids 39, 856864.
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.
Liu, J. & Gollub, J. P. 1993 Onset of spatially chaotic waves on flowing films. Phys. Rev. Lett. 70 (15), 22892292.
Liu, J. & Gollub, J. P. 1994 Solitary wave dynamics of film flows. Phys. Fluids 6 (5), 17021712.
Liu, J., Paul, J. D. & Gollub, J. P. 1993 Measurements of the primary instabilities of film flows. J. Fluid Mech. 250, 69101.
Malamataris, N. A. & Balakotaiah, V. 2008 Flow structure underneath the large amplitude waves of a vertically falling film. AIChE J. 54 (7), 17251740.
Malamataris, N. A., Vlachogiannis, M. & Bontozoglou, V. 2002 Solitary waves on inclined films: flow structure and binary interactions. Phys. Fluids 14 (3), 10821094.
Markides, C. N., Mathie, R. & Charogiannis, A. 2015 An experimental study of spatiotemporally resolved heat transfer in thin liquid-film flows falling over an inclined heated foil. Intl J. Heat Mass Transfer 93, 872888.
Maron, D. M., Brauner, N. & Hewitt, G. F. 1989 Flow patterns in wavy thin films: numerical simulation. Intl Commun. Heat Mass Transfer 16, 655666.
Massot, C., Irani, F. & Lightfoot, E. N. 1966 Modified description of wave motion in a falling film. AIChE J. 12 (3), 445455.
Mathie, R., Nakamura, H. & Markides, C. N. 2013 Heat transfer augmentation in unsteady conjugate thermal systems. Part II. Applications. Intl J. Heat Mass Transfer 56, 819833.
Miyara, A. 2000 Numerical simulation of wavy liquid film flowing down on a vertical wall and an inclined wall. Intl J. Therm. Sci. 39, 10151027.
Moran, K., Inumaru, J. & Kawaji, M. 2002 Instantaneous hydrodynamics of a laminar wavy liquid film. Intl J. Multiphase Flow 28, 731755.
Nosoko, T. & Miyara, A. 2004 The evolution and subsequent dynamics of waves on a vertically falling liquid film. Phys. Fluids 16 (4), 11181126.
Nosoko, T., Yoshimura, P. N., Nagata, T. & Oyakawa, K. 1996 Characteristics of two-dimensional waves on a falling liquid film. Chem. Engng Sci. 51 (5), 725732.
Nusselt, W. 1916 Die Oberflaechenkondensation des Wasserdampfes. VDI Zeit. 60, 541546.
Ooshida, T. 1999 Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number. Phys. Fluids 11, 32473269.
Portalski, S. 1964 Eddy formation in film flow down a vertical plate. Ind. Chem. Engng Fund. 3 (1), 4953.
Pradas, M., Tseluiko, D. & Kalliadasis, S. 2011 Rigorous coherent-structure theory for falling liquid films: viscous dispersion effects on bound-state formation and self-organization. Phys. Fluids 23, 044104.
Pradas, M., Tseluiko, D., Ruyer-Quil, C. & Kalliadasis, S. 2014 Pulse dynamics in a power-law falling film. J. Fluid Mech. 747, 460480.
Ramaswamy, B., Chippada, S. & Joo, S. W. 1996 A full-scale numerical study of interfacial instabilities in thin-film flows. J. Fluid Mech. 325, 163194.
Roberts, R. M. & Chang, H.-C. 2000 Wave-enhanced interfacial transfer. Chem. Engng Sci. 55, 11271141.
Rohlfs, W., Pischke, P. & Scheid, B. 2017 Hydrodynamic waves in films flowing under an inclined plane. Phys. Rev. Fluids 2, 044003.
Rohlfs, W. & Scheid, B. 2015 Phase diagram for the onset of circulating waves and flow reversal in inclined falling films. J. Fluid Mech. 763, 322351.
Ruyer-Quil, C. & Manneville, P. 1998 Modeling film flows down inclined planes. Eur. Phys. J. B 6, 227292.
Ruyer-Quil, C. & Manneville, P. 2000 Improved modeling of flows down inclined planes. Eur. Phys. J. B 15, 357369.
Ruyer-Quil, C. & Manneville, P. 2002 Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations. Phys. Fluids 14, 170183.
Scheid, B., Ruyer-Quil, C. & Manneville, P. 2006 Wave patterns in film flows: modelling and three-dimensional waves. J. Fluid Mech. 562, 183222.
Schlagen, A., Modigell, M., Dietze, G. F. & Kneer, R. 2006 Simultaneous measurement of local film thickness and temperature distribution in wavy liquid films using a luminescence technique. Intl J. Heat Mass Transfer 49, 50495061.
Shkadov, V. 1967 Wave flow regimes of a thin layer of a viscous liquid under the action of gravity. Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 2 (1), 4351.
Shkadov, V. 1977 Solitary waves in a layer of viscous liquid. Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 12 (1), 6366.
Smith, M. K. 1990 The mechanism for the long-wave instability in thin liquid films. J. Fluid Mech. 217, 469485.
Yih, C. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6 (3), 321324.
Zadrazil, I., Matar, O. K. & Markides, C. N. 2014a An experimental characterization of downwards gas–liquid annular flow by laser-induced fluorescence: flow regimes and film statistics. Intl J. Multiphase Flow 60, 87102.
Zadrazil, I., Matar, O. K. & Markides, C. N. 2014b An experimental characterization of liquid films in downwards co-current gas–liquid annular flow by particle image and tracking velocimetry. Intl J. Multiphase Flow 68, 112.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed