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Investigation of the backflow phenomenon in falling liquid films

Published online by Cambridge University Press:  08 January 2008

GEORG F. DIETZE ,
A. LEEFKEN  and
R. KNEER
GEORG F. DIETZE
Affiliation:
Institute of Heat and Mass Transfer, RWTH Aachen University, Aachen, 52056, Germany
A. LEEFKEN
Affiliation:
Institute of Heat and Mass Transfer, RWTH Aachen University, Aachen, 52056, Germany
R. KNEER
Affiliation:
Institute of Heat and Mass Transfer, RWTH Aachen University, Aachen, 52056, Germany
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Abstract

The phenomenon of backflow in the capillary wave region of laminar falling liquid films is studied in detail. For the first time, the mechanism leading to the origination of the phenomenon is identified and explained. It is shown that backflow forms as the result of a separation eddy developing at the bounding wall similar to the case of classical flow separation. Results show that the adverse pressure distribution causing the separation of the flow in the capillary wave region is induced by the strong third-order deformation (i.e. change in curvature) of the liquid–gas free surface there. This deformation acts on the interfacial pressure jump, and thereby the wall pressure distribution, as a result of surface tension forces. It is shown that only the capillary waves, owing to their short wavelength and large curvature, impose a pressure distribution satisfying the conditions for flow separation. The effect of this capillary separation eddy on momentum and heat transfer is investigated from the perspective of modelling approaches for falling liquid films. The study is centred on a single case of inclined liquid film flow in the visco-capillary regime with surface waves externally excited at a single forcing frequency. Investigations are based on temporally and spatially highly resolved numerical data obtained by solving the Navier–Stokes equations for both phases. Computation of phase distribution is performed with the volume of fluid method and the effect of surface tension is modelled using the continuum surface force approach. Numerical data are compared with experimental data measured in the developed region of the flow. Laser-Doppler velocimetry is used to measure the temporal distribution of the local streamwise velocity component, and confocal chromatic imaging is employed to measure the temporal distribution of film thickness. Excellent agreement is obtained with respect to film thickness and reasonable agreement with respect to velocity.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 435 - 459
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Adomeit, P., Leefken, A. & Renz, U. 2000 Experimental and numerical investigations on wavy films. In 3rd European Thermal Sciences Conf., pp. 1003–1009. ETS, Heidelberg.Google Scholar
Albrecht, H. E., Borys, M., Damaschke, N. & Tropea, C. 2003 Laser Doppler and Phase Doppler Measurement Techniques. Springer.Google Scholar
Alekseenko, S. V., Nakoryakov, V. E. & Pokusaev, B. G. 1994 Wave Flow of Liquid Films. Begell House.CrossRefGoogle Scholar
Benjamin, T. B. 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2, 554–574.CrossRefGoogle 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. 1956 Strömung und Wörmeübergang bei Rieselfilmen. VDI Forschungsheft 457, 22.Google Scholar
Cohen-Sabban, J., Gaillard-Groleas, J. & Crepin, P.-J. 2001 Quasi-confocal extended field surface sensing. In Proc. SPIE (ed. Duparre, A. & Singh, B.), Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, vol. 4449, pp. 178–183.Google Scholar
Davies, J. T. 1961 Interfacial Phenomena, pp. 267–268. Academic.Google Scholar
Elsäer, A. 1998 Kraftstoffaufbereitung in Verbrennungskraftmaschinen: Grundlagen der Strömung schubspannungsgetriebener Wandfilme. PhD thesis, Technische Universität Karlsruhe.Google Scholar
Friedman, S. J. & Miller, C. O. 1941 Indust. Engng Chem. Fund. 33, 885.Google Scholar
Frisk, D. P. & Davis, E. J. 1972 The enhancement of heat transfer by waves in stratified gas–liquid flow. Intl J. Heat Mass Transfer 15, 1537–1552.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
Hjemfelt, A. T. & Mockros, L. F. 1966 Motion of discrete particles in a turbulent fluid. Appl. Sci. Res. 16, 149.CrossRefGoogle Scholar
Kapitza, P. L. 1948 Wave flow of thin layers of a viscous fluid (in russian). Sov. Phys., J. Exp. Theor. Phys. 3, 3–28.Google Scholar
Kapitza, P. L. & Kapitza, S. P. 1965 Wave flow on thin layers of a viscous fluid: experimental study of undulatory flow conditions. In Collected Papers of P. L. Kapitza (ed. Ter Haar, D.), vol. 2. Pergamon.Google Scholar
Kunugi, T. & Kino, C. 2005 DNS of falling film structure and heat transfer via mars method. Comput. Struct. 83, 455–462.CrossRefGoogle Scholar
Kunugi, T., Kino, C. & Serizawa, A. 2005 Surface wave structure and heat transfer of vertical liquid film flow with artificial oscillation. In 5th Intl Symp. Multiphase Flow, Heat Mass Ttransfer and Energy Conversion.Google Scholar
Leefken, A. & Renz, U. 2001 Numerical analysis on hydrodynamics and heat transfer of laminar-wavy falling films. In Proc. 1st Intl Berlin Workshop (IBW1) on Transport Phenomena with Moving Boundaries (ed. Schindler, F.-P.), vol. 738, pp. 134–143. VDI, Berlin.Google Scholar
Leefken, A., Al-Sibai, F. & Renz, U. 2004 LDV measurement of the velocity distribution in periodic waves of laminar falling films. In Proc. 5th Intl Conf. on Multiphase Flow.Google Scholar
Lel, V. V., Al-Sibai, F. & Leefken, A. 2005 Local thickness and wave velocity measurement of wavy films with a chromatic confocal imaging method and a fluorescence intensity technique. Exps Fluids 39, 856–864.Google Scholar
Mudawar, I. & Houpt, R. A. 1993 Measurement of mass and momentum transport in wavy-laminar falling liquid films. Intl J. Heat Mass Transfer 36, 4151–4162.CrossRefGoogle Scholar
Mudunuri, R. R. & Balakotaiah, V. 2006 Solitary waves on thin falling films in the very low forcing frequency limit. AIChE J.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
Nusselt, W. 1916 Der Wärmeaustausch am Berieselungskühler. Zeitschrift des VDI 67, 206–210.Google Scholar
Portalski, S. 1964 Eddy formation in film flow down a vertical plate. Indust. Engng Chem. Fund. 3, 49–53.Google Scholar
Prandtl, L. 1961 Über Flüssigkeitsbewegung bei sehr kleiner Reibung. In Gesammelte Abhandlungen zur angewandten Mechanik, Hydro- und Aerodynamik (ed. Tolmien, W., Schlichting, H. & Görtler, H.), vol. 2, chap. 4. Springer.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2000 Improved modeling of flows down inclined planes. Eur. Phys. J. B 15, 357–369.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
Sychev, V. V. 1998 Asymptotic Theory of Separated Flows. Cambridge University Press.CrossRefGoogle Scholar
Takase, K., Yoshida, H., Ose, Y., Kano, T., Satake, S. & Kunugi, T. 2003 Large-scale numerical simulations of multiphase flow behavior in an advanced light-water reactor core. Annu Rep. Earth Simulator Center.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley.Google Scholar
Wilke, W. 1962 Wärmeübergang an Rieselfilme. VDI Fortschritte 490.Google Scholar
Youngs, D. L. 1982 Numerical Methods in Fluid Dynamics, pp. 273–285. Academic.Google Scholar