Abstract
A theoretical analysis of a downward viscous film flow on corrugated surfaces is reported. The study is based on Navier–Stokes equations (for one‐ and two‐dimensional surfaces) and on an integral model (for a three‐dimensional surface with double corrugation). The calculations were carried out in a wide range of Reynolds numbers and geometric characteristics of the surface with due allowance for the surface‐tension force. The shape of the free surface of the liquid film and other characteristics of the flow are calculated. It is shown that, in the case of a one‐dimensional surface, there exists a range of parameters where the flow is predominantly governed by surface‐tension forces; this flow can be adequately treated with the integral approach. In this range of parameters, on the surface with double corrugation, the average quantities of the downward flow in wide corrugation valleys are determined by the fine‐texture geometry.
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REFERENCES
W. Nusselt, “Die Oberflächenkondensation des Wasserdampfes,”Zeitschrift VDI 60, 541-546 (1916).
S. V. Alekseenko, V. E. Nakoryakov, and B. G. Pokusaev,Wavy Liquid Film Flow [in Russian], Nauka, Novosibirsk (1992).
H.-C. Chang, “Wave evolution on a falling film,”Ann. Rev. Fluid Mech. 26, 103-136 (1994).
Yu. Ya. Trifonov and O. Yu. Tsvelodub, “Nonlinear waves on the surface of a falling liquid film. Pt 1. Waves of the first family and their stability,”J. Fluid Mech. 229, 531-554 (1991).
L. T. Nguyen and V. Balakotaiah, “Modeling and experimental studies of wave evolution on free falling viscous films,”Phys. Fluids 12, 2236-2256 (2000).
J. R. Fair and J. R. Bravo, “Distillation columns containing structure packing,”Chem. Eng. Progr. 86, 19-29 (1990).
J. M. DeSantos, T. R. Melli, and L. E. Scriven, “Mechanics of gas-liquid flow in packed-bed contactors,”Ann. Rev. Fluid Mech. 23, 233-260 (1991).
R. K. Shah and W. W. Focke, “Plate heat exchangers and their design theory,” in: Heat transfer equipment design, Hemisphere, Washington (1988), pp. 227-254.
R. L. Webb,Principles of Enhanced Heat Transfer, Wiley, New York (1994).
L. Zhao and R. L. Cerro, “Experimental characterization of viscous film flows over complex surfaces,”Int. J. Multiphase Flow 6, 495-516 (1992).
M. Vlachogiannis and V. Bontozoglou, “Experiments on laminar film flow along a periodic wall,”J. Fluid Mech. 457, 133-156 (2002).
C. Y. Wang, “Liquid film flowing slowly down a wavy incline,”AIChE J. 27, 207-212 (1981).
F. Kang and K. Chen, “Gravity-driven two-layer flow down a slightly wavy periodic incline at low Reynolds numbers,”Int. J. Multiphase Flow 3, 501-513 (1995).
C. Pozrikidis, “The flow of a liquid film along a periodic wall,”J. Fluid Mech. 188, 275-300 (1988).
S. Shetty and R. L. Cerro, “Flow of a thin film over a periodic surface,”Int. J. Multiphase Flow 6, 1013-1027 (1993).
V. Bontozoglou and G. Papapolymerou, “Laminar film flow down a wavy incline,”Int. J. Multiphase Flow 1, 69-79 (1997).
Yu. Ya. Trifonov, “Viscous liquid film flows over a periodic surface,”Int. J. Multiphase Flow 24, 1139-1161 (1998).
Yu. Ya. Trifonov, “Viscous liquid film flows over a vertical corrugated surface and the film free surface stability,”Russ. J. Eng. Thermophys. 10, No. 2, 129-145 (2000).
Yu. Ya. Trifonov, “Viscous liquid film flows over a vertical corrugated surface. Calculation of heat and mass transfer,” in: Advanced computational methods in heat transfer VI. WITpress, Southhampton, UK (2000), pp. 373-382.
V. Ya. Shkadov, “Wavy modes of gravity-driven viscous thin-film flow,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1, 43-51(1967).
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Trifonov, Y.Y. Viscous Film Flow down Corrugated Surfaces. Journal of Applied Mechanics and Technical Physics 45, 389–400 (2004). https://doi.org/10.1023/B:JAMT.0000025021.41499.e1
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DOI: https://doi.org/10.1023/B:JAMT.0000025021.41499.e1