Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T02:45:09.571Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase diagram for the onset of circulating waves and flow reversal in inclined falling films

Published online by Cambridge University Press:  17 December 2014

Wilko Rohlfs  and
Benoit Scheid
Wilko Rohlfs*
Affiliation:
Institute of Heat and Mass Transfer, RWTH Aachen University, Augustinerbach 6, 52056 Aachen, Germany
Benoit Scheid
Affiliation:
TIPs, Université Libre de Bruxelles, C.P. 165/67, Avenue F. D. Roosevelt 50, 1050 Bruxelles, Belgium
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The onset of circulating waves, i.e. waves with a circulating eddy in the main wave hump, and the onset of flow reversal, i.e. a vortex in the first capillary minimum, in inclined falling films is investigated as a function of the Reynolds number and inclination number using the weighted integral boundary layer (WIBL) model and direct numerical simulations (DNS). Analytical criteria for the onset of circulating waves and flow reversal based on the wave celerity, the average film thickness and the maximum and minimum film thickness have been approximated using self-similar parabolic velocity profiles. This approximation has been validated by second-order WIBL and DNS simulations. It is shown that the onset of circulating waves in the phase diagram for homoclinic solutions (waves of infinite wavelength) is strongly dependent on the inclination, but independent of the streamwise viscous dissipation effect. On the contrary, the onset of flow reversal shows a clear dependence on the viscous dissipation. Furthermore, simulation results for limit cycles (finite wavelength) reveal a strong increase of the corresponding critical Reynolds number with the excitation frequency. Additionally, a critical ratio between the maximum and substrate film thickness (value of approximately 2.5) was found for the onset of circulating waves, which is independent of wavelength, inclination, viscous dissipation and Reynolds number.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 322 - 351
Check for updates
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, C., Marschall, H. & Bothe, D. 2014 Direct numerical simulation of interfacial mass transfer into falling films. Intl J. Heat Mass Transfer 69, 343–357.Google Scholar
Alekseenko, S. V., Antipin, V. A., Bobylev, A. V. & Markovich, D. M. 2007 Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder. Exp. Fluids 43 (2–3), 197–207.Google Scholar
Alekseenko, S. V., Nakoryakov, V. E. & Pokusaev, B. G. 1994 Wave Flow of Liquid Films. Begell House.Google Scholar
Binz, M., Rohlfs, W. & Kneer, R. 2014 Direct numerical simulations of a thin liquid film coating an axially oscillating cylindrical surface. Fluid Dyn. Res. 46, 041402.CrossRefGoogle Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354.Google Scholar
Brauner, N. & Maron, D. M. 1983 Modeling of wavy flow in inclined thin films. Chem. Engng Sci. 38 (5), 775–788.Google Scholar
Chakraborty, S., Nguyen, P.-K., Ruyer-Quil, C. & Bontozoglou, V. 2014 Extreme solitary waves on falling liquid films. J. Fluid Mech. 745, 564–591.Google Scholar
Chang, H.-C. & Demekhin, E. A. 2002 Complex Wave Dynamics on Thin Films (ed. Möbius, D. & Miller, R.). Elsevier.Google Scholar
Davies, J. T. 1960 The importance of surfaces in chemical engineering. Trans. Inst. Chem. Engrs 38, 289–293.Google Scholar
Dietze, G. F.2010 Flow separation in falling liquid films. PhD thesis, RWTH Aachen.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.Google 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
Dietze, G. F., Rohlfs, W., Nährich, K., Kneer, R. & Scheid, B. 2014 Three-dimensional flow structures in laminar falling films. J. Fluid Mech. 743, 75–123.CrossRefGoogle Scholar
Doedel, E. J.2008 AUTO07P continuation and bifurcation software for ordinary differential equations. Montreal Concordia University.Google Scholar
Doro, E. O. & Aidun, C. K. 2013 Interfacial waves and the dynamics of back flow in falling liquid films. J. Fluid Mech. 726, 261–284.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
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225.Google Scholar
Hu, J., Yang, X., Yu, J. & Dai, G. 2014 Numerical simulation of carbon dioxide ( $\text{CO}_{2}$ ) absorption and interfacial mass transfer across vertically wavy falling film. Chem. Engng Sci. 116, 243–253.Google Scholar
Islam, M. A.2009 Wave dynamics and simultaneous heat and mass transfer of falling liquid film. PhD thesis, Graduate School of Science and Engineering, Saga University, Japan.Google Scholar
Jasak, H.1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College, University of London.Google Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2013 Falling Liquid Films. Springer.Google Scholar
Kouhikamali, R., Abadi, S. M. A. N. R. & Hassani, M. 2014 Numerical investigation of falling film evaporation of multi-effect desalination plant. Appl. Therm. Engng 70 (1), 477–485.Google Scholar
Liu, J. & Gollub, J. P. 1994 Solitary wave dynamics of film flows. Phys. Fluids 6 (5), 1702–1712.Google Scholar
Malamataris, N. A. & Balakotaiah, V. 2008 Flow structure underneath the large amplitude waves of a vertically falling film. AIChE J. 54 (7), 1725–1740.Google Scholar
Malamataris, N. A., Vlachogiannis, M. & Bontozoglou, V. 2002 Solitary waves on inclined films: flow structure and binary interactions. Phys. Fluids 14 (3), 1082–1094.Google Scholar
Maron, D. M., Brauner, N. & Hewitt, G. F. 1989 Flow patterns in wavy thin films: numerical simulation. Intl Commun. Heat Mass Transfer 16 (5), 655–666.Google Scholar
Miyara, A. 2000 Numerical simulation of wavy liquid film flowing down on a vertical wall and an inclined wall. Intl J. Therm. Sci. 39 (9–11), 1015–1027.Google Scholar
Ooshida, T. 1999 Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number. Phys. Fluids 11 (11), 3247–3269.Google Scholar
Portalski, S. 1964 Eddy formation in film flow down a vertical plate. Ind. Engng Chem. Fundam. 3 (1), 49–53.Google Scholar
Roberts, R. M. & Chang, H.-C. 2000 Wave-enhanced interfacial transfer. Chem. Engng Sci. 55 (6), 1127–1141.Google Scholar
Rohlfs, W., Binz, M. & Kneer, R. 2014 On the stabilizing effect of a liquid film on a cylindrical core by oscillatory motions. Phys. Fluids 26, 022101.Google Scholar
Rusche, H.2002 Computational fluid dynamics of dispersed two-phase flows at high phase fractions. PhD thesis, Imperial Collage, University of London.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2000 Improved modeling of flows down inclined planes. Eur. Phys. J. B 15, 357–369.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
Scheid, B., Ruyer-Quil, C., Thiele, U., Kabov, P. 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. 562, 183–222.Google Scholar
Ubbink, O.1997 Numerical prediction of two fluid systems with sharp interfaces. PhD thesis, Imperial College, University of London.Google Scholar
Wasden, F. K. & Dukler, A. E. 1989 Insights into the hydrodynamics of free falling wavy films. AIChE J. 35 (2), 187–195.Google Scholar