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Effect of wall corrugations on scalar transfer to a wavy falling liquid film

Published online by Cambridge University Press:  28 November 2018

Georg F. Dietze Open the ORCID record for Georg F. Dietze [Opens in a new window]
Georg F. Dietze*
Affiliation:
Laboratoire FAST, Univ. Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France
*
†Email address for correspondence: dietze@fast.u-psud.fr
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Abstract

Direct numerical simulation is employed to study the effect of small-scale wall corrugations on scalar transfer through the wavy surface of a vertically falling liquid film in interaction with a strongly confined counter-current gas flow. Three wall geometries are considered: (i) a flat wall for reference; (ii) a sinusoidal corrugation typically found on structured packings in chemical engineering devices; and (iii) a heuristic design consisting of isolated semicircular bumps distanced by the wavelength of the surface waves. We consider the limiting case of a Dirichlet condition for the transported scalar (temperature or mass fraction) at the liquid–gas interface and focus on liquid-side transport. We consider convection-dominated regimes at moderate and large Péclet numbers, representative of heat and mass transfer respectively, and confront forced and noise-driven wave regimes. Our results show that sinusoidal wall corrugations increase transfer by up to 30 per cent in terms of the exchange length required to transfer a fixed amount of the transported quantity. A slightly greater intensification is achieved through the bump-shaped corrugations, which intermittently disrupt the moving-frame vortex forming within the large-amplitude solitary waves, allowing these to replenish with unsaturated liquid. However, when the velocity of the strongly confined gas flow is increased above a certain threshold, the bumps can trigger the flooding of the channel.

JFM classification

Mixing: Mixing Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 1098 - 1128
Copyright
© 2018 Cambridge University Press 

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References

Adomeit, P., Leefken, A. & Renz, U. 2000 Experimental and numerical investigations on wavy films. In Proceedings of the 3rd European Thermal Sciences Conference (ed. Hahne, E. W. P., Heidemann, W. & Spindler, K.), pp. 1003–1009. ETS.Google Scholar
Aksel, N. & Schörner, M. 2018 Films over topography: from creeping flow to linear stability, theory, and experiments, a review. Acta Mechanica 229, 1453–1482.Google Scholar
Albert, C., Marschall, H. & Bothe, D. 2013 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
Azzopardi, B. J., Mudde, R. F., Lo, S., Morvan, H., Yan, Y. & Zhao, D. 2011 Hydrodynamics of Gas–Liquid Reactors: Normal Operation and Upset Conditions. Wiley.Google Scholar
Bontozoglou, V. 1998 A numerical study of interfacial transport to a gas-sheared wavy liquid. Intl J. Heat Mass Transfer 41 (15), 2297–2305.Google Scholar
Bontozoglou, V. & Papapolymerou, G. 1997 Laminar film flow down a wavy incline. Intl J. Multiphase Flow 23 (1), 69–79.Google Scholar
Bontozoglou, V. & Papapolymerou, G. 1998 Wall-triggered interfacial resonance in laminar gas–liquid flow. Intl J. Multiphase Flow 24 (1), 131–143.Google Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modelling surface tension. J. Comput. Phys. 100, 335–354.Google Scholar
Brauer, H. 1971 Stoffaustausch einschließlich chemischer Reaktion. Verlag Sauerländer.Google Scholar
Brauner, N. 1987 Roll wave celerity and average film thickness in turbulent wavy film flow. Chem. Engng Sci. 42, 265–273.Google Scholar
Calhoun, D.1999 A Cartesian grid method for solving the streamfunction-vorticity equations in irregular geometries. PhD thesis, University of Washington.Google Scholar
Cao, Z., Vlachogiannis, M. & Bontozoglou, V. 2013 Experimental evidence for a short-wave global mode in film flow along periodic corrugations. J. Fluid Mech. 718, 304–320.Google Scholar
Chang, H. C. & Demekhin, E. A. 2002 Complex Wave Dynamics on thin Films, Studies in Interface Science, vol. 14. Elsevier.Google Scholar
Chang, H. C., Demekhin, E. A. & Kalaidin, E. 1996a Simulation of noise-driven wave dynamics on a falling film. AIChE J. 42 (6), 1553–1568.Google Scholar
Chang, H. C., Demekhin, E. A., Kalaidin, E. & Ye, Y. 1996b Coarsening dynamics of falling-film solitary waves. Phys. Rev. E 54 (2), 1467–1477.Google Scholar
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comp. 22, 745–762.Google Scholar
Dávalos-Orozco, L. A. 2007 Nonlinear instability of a thin film flowing down a smoothly deformed surface. Phys. Fluids 19, 074103.Google Scholar
Dietze, G. F. 2016 On the Kapitza instability and the generation of capillary waves. J. Fluid Mech. 789, 368–401.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. & Ruyer-Quil, C. 2013 Wavy liquid films in interaction with a confined laminar gas flow. J. Fluid Mech. 722, 348–393.Google Scholar
Fair, J. R. & Bravo, J. L. 1990 Distillation columns containing structured packing. Chem. Engng Prog. 86 (1), 19–29.Google Scholar
Gaskell, P. H., Jimack, P. K., Sellier, M. & Thompson, H. M. 2006 Flow of evaporating, gravity-driven thin liquid films over topography. Phys. Fluids 18, 013601.Google Scholar
Haroun, Y.2008 Etude du transfert de masse réactif gaz-liquide le long de plans corrugués par simulation numérique avec suivi d’interface. PhD thesis, Université de Toulouse.Google Scholar
Haroun, Y., Legendre, D. & Raynal, L. 2010 Direct numerical simulation of reactive absorption in gas–liquid flow on structured packing using interface capturing method. Chem. Engng Sci. 65, 351–356.Google Scholar
Heining, C., Bontozoglou, V., Aksel, N. & Wierschem, A. 2009 Nonlinear resonance in viscous films on inclined wavy planes. Intl J. Multiphase Flow 35, 78–90.Google Scholar
Higbie, R. 1935 The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. Amer. Inst. Chem. Eng. 31, 365–389.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
Islam, M. A., Miyara, A. & Setoguchi, T. 2009 Numerical investigation of steam absorption in falling film of libr aqueous solution with solitary waves. Intl J. Refrig. 32 (7), 1597–1603.Google Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films, Applied Mathematical Sciences, vol. 176. Springer.Google Scholar
Kapitza, P. L. 1948 Wave flow of thin layer of viscous fluid (in Russian). Zh. Eksp. Teor. Fiz. 18 (1), 3–28.Google Scholar
Kohrt, M., Ausner, I., Wozny, G. & Repke, J.-U. 2011 Texture influence on liquid-side mass transfer. Chem. Engng Res. Des. 89, 1405–1413.Google Scholar
Kunugi, T. & Kino, C. 2005 DNS of falling film structure and heat transfer via MARS method. Comput. Struct. 83 (6–7), 455–462.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
Markides, C. N., Mathie, R. & Charogiannis, A. 2016 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, 872–888.Google Scholar
Miyara, A. 1999 Numerical analysis on flow dynamics and heat transfer of falling liquid films with interfacial waves. Heat Mass Transfer 35, 298–306.Google Scholar
Nagasaki, T. & Hijikata, K. 1990 Numerical simulation of CO2 absorption into wavy water film (in Japanese). In Proceedings of the 3rd JSME Symposium on Numerical Dynamics, pp. 47–48. The Japan Society of Mechanical Engineers.Google Scholar
Nusselt, W. 1923 Der Wärmeaustausch am Berieselungskühler. VDI-Zeitschrift 67, 206–210.Google Scholar
Oron, A. & Heining, C. 2008 Weighted-residual integral boundary-layer model for the nonlinear dynamics of thin liquid films falling on an undulating vertical wall. Phys. Fluids 20, 082102.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Taylor & Francis.Google Scholar
Pollak, T. & Aksel, N. 2013 Crucial flow stabilization and multiple instability branches of gravity-driven films over topography. Phys. Fluids 25, 024103.Google Scholar
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190, 572–600.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.Google Scholar
Rastaturin, A., Demekhin, E. & Kalaidin, E. 2006 Optimal regimes of heat-mass transfer in a falling film. J. Non-Equilib. Thermodyn. 31, 1–10.Google Scholar
Roberts, R. M. & Chang, H.-C. 2000 Wave-enhanced interfacial transfer. Chem. Engng Sci. 55, 1127–1141.Google Scholar
Rudman, M. 1997 Volume-tracking methods for interfacial flows calculations. Intl J. Numer. Methods Fluids 24 (7), 671–691.Google Scholar
Schagen, A. & Modigell, M. 2005 Luminescence technique for the measurement of local concentration distribution in thin liquid films. Exp. Fluids 38 (2), 174–184.Google Scholar
Schörner, M. & Aksel, N. 2018 The stability cycle – a universal pathway for the stability of films over topography. Phys. Fluids 30, 012105.Google Scholar
Schörner, M., Reck, D. & Aksel, N. 2016 Stability phenomena far beyond the nusselt flow – revealed by experimental asymptotics. Phys. Fluids 28, 022102.Google Scholar
Schörner, M., Reck, D., Aksel, N. & Trifonov, Y. Y. 2018 Switching between different types of stability isles in films over topographies. Acta Mechanica 229, 423–436.Google Scholar
Serifi, K. & Bontozoglou, V. 2004 Transient flow and heat transfer phenomena in inclined wavy films. Intl J. Therm. Sci. 43, 761–767.Google Scholar
Trifonov, Y. Y. 1998 Viscous liquid film flows over a periodic surface. Intl J. Multiphase Flow 24, 1139–1161.Google Scholar
Trifonov, Y. Y. 2007a Stability and nonlinear wavy regimes in downward film flows on a corrugated surface. J. Appl. Mech. Tech. Phys. 48 (1), 91–100.Google Scholar
Trifonov, Y. Y. 2007b Stability of a viscous liquid film flowing down a periodic surface. Intl J. Multiphase Flow 33, 1186–1204.Google Scholar
Trifonov, Y. Y. 2010a Counter-current gas–liquid wavy film flow between the vertical plates analyzed using the Navier–Stokes equations. AIChE J. 56 (8), 1975–1987.Google Scholar
Trifonov, Y. Y. 2010b Flooding in two-phase counter-current flows: numerical investigation of the gas–liquid wavy interface using the Navier–Stokes equations. Intl J. Multiphase Flow 36, 549–557.Google Scholar
Trifonov, Y. Y. 2011 Counter-current gas–liquid flow between vertical corrugated plates. Chem. Engng Sci. 66, 4851–4866.Google Scholar
Trifonov, Y. Y. 2014 Stability of a film flowing down an inclined corrugated plate: the direct Navier–Stokes computations and Floquet theory. Phys. Fluids 26, 114101.Google Scholar
Trifonov, Y. Y. 2017 Nonlinear waves on a liquid film falling down an inclined corrugated surface. Phys. Fluids 29, 054104.Google Scholar
Tseluiko, D., Blyth, M. G. & Papageorgiou, D. T. 2013 Stability of film flow over inclined topography based on a long-wave nonlinear model. J. Fluid Mech. 729, 638–671.Google Scholar
Tseluiko, D. & Kalliadasis, S. 2011 Nonlinear waves in counter-current gas–liquid film flow. J. Fluid Mech. 673, 19–59.Google Scholar
Valluri, P., Matar, O. K., Hewitt, G. F. & Mendes, M. A. 2005 Thin film flow over structured packings at moderate Reynolds numbers. Chem. Engng Sci. 60, 1965–1975.Google Scholar
Veremieiev, S., Thompson, H. M. & Gaskell, P. H. 2015 Free-surface film flow over topography: full three-dimensional finite element solutions. Comput. Fluids 122, 66–82.Google Scholar
Vlachogiannis, M. & Bontozoglou, V. 2002 Experiments on laminar film flow along a periodic wall. J. Fluid Mech. 457, 133–156.Google Scholar
Vlachos, N. A., Paras, S. V., Mouza, A. A. & Karabelas, A. J. 2001 Visual observations of flooding in narrow rectangular channels. Intl J. Multiphase Flow 27, 1415–1430.Google Scholar
Wierschem, A., Pollak, T., Heining, C. & Aksel, N. 2010 Suppression of eddies in films over topography. Phys. Fluids 22, 113603.Google Scholar
Wierschem, A., Scholle, M. & Aksel, N. 2003 Vortices in film flow over strongly undulated bottom profiles at low Reynolds numbers. Exp. Fluids 15 (2), 426–435.Google Scholar
Yoshimura, P. N., Nosoko, P. & Nagata, T. 1996 Enhancement of mass transfer into a falling laminar liquid film by two-dimensional surface waves-some experimental observations and modeling. Chem. Engng Sci. 51 (8), 1231–1240.Google Scholar
Youngs, D. L. 1982 Time-dependent multi-material flow with large fluid distortion. In Numerical Methods for Fluid Dynamics, pp. 273–285. Academic Press.Google Scholar

Dietze supplementary movie 1

Repeated extrusion of scalar plumes from the interfacial scalar boundary layer (figure 5). Case 4 (table 1): periodically-forced waves, long sinusoidal wall corrugation, strongly-dominant convection (Pe=4590).

Download Dietze supplementary movie 1(Video)
Video 2.3 MB

Dietze supplementary movie 2

Repeated de- and acceleration of the leading front of surface waves moving over the long sinusoidal corrugation. Case 4 (table 1): periodically-forced waves.

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Video 1.7 MB

Dietze supplementary movie 3

Redistribution of liquid within a wave hump as it moves over a bump-shaped corrugation (figures 7 and 8). Case 5 (table 1): periodically-forced waves, strongly-dominant convection (Pe=4590).

Download Dietze supplementary movie 3(Video)
Video 2 MB

Dietze supplementary movie 4

Cascade of flooding events at successive bump-shaped corrugations after increasing the gas flow (figure 12). Case 5 (table 1) with additional stepwise increase of counter-current gas flow rate (figure 11a).

Download Dietze supplementary movie 4(Video)
Video 1.4 MB

Dietze supplementary movie 5

Flooding at the third bump-shaped corrugation after increasing the gas flow rate (figure 12b). Case 5 (table 1) with additional stepwise increase of counter-current gas flow rate (figure 11a). Contours show the streamwise velocity component (blue: upward flow; red: downward flow).

Download Dietze supplementary movie 5(Video)
Video 1.2 MB