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ISSN Druckformat: 2169-2785
ISSN Online: 2167-857X
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INSTABILITY OF A GRAVITY-DRIVEN LIQUID FILM CONFINED IN AN INCLINED RECTANGULAR DUCT
ABSTRAKT
This study deals with the confinement effects due to top and side walls on the stability of a falling liquid film flowing down an incline. To this aim, we consider a liquid film flowing between two infinite plates and in rectangular ducts in the presence of an adjacent gas phase, focusing on the case of zero net gas flow rate. A rigorous linear stability analysis is conducted for three gas-liquid systems of particular interest in applications. This enables us to demonstrate the effect of the gas-liquid density ratio and viscosity ratio in small channels/ducts and shallow downward inclinations. Although the analysis considers all wave numbers, the neutral stability boundary is found to be defined mainly by long-wave perturbations in the two-plate (TP) geometry, as well as in the rectangular ducts. The decrease of the channel height for the considered liquid-gas systems always stabilizes the liquid film. However, the Kapitza criterion for the onset of Kapitza waves on the surface of a falling liquid film can either overpredict or underpredict the stability limits of the channel/duct flows, depending on the channel height, its aspect ratio, and the viscosity and density ratios of the phases. The falling liquid film, bounded by the side walls, becomes unstable at larger flow rates with the decrease of the duct aspect ratio. The presence of recirculating gas in the channel/duct is found to affect the stability through the dynamic shear stress components at the gas-liquid interface. Therefore, its presence must be taken into account.
-
Aksel, N. and Schorner, M., Films over Topography: From Creeping Flow to Linear Stability, Theory, and Experiments, A Review, ActaMech., vol. 229, pp. 1453-1482,2018.
-
Alekseenko, S.V., Nakoryakov, V.Y., and Pokusaev, B.G., Wave Formation on a Vertical Falling Liquid Film, AIChE J, vol. 31, pp. 1446-1460,1985.
-
Alekseenko, S.V. and Nakoryakov, V.E., Instability ofa Liquid Film Moving under the Effect of Gravity and Gas Flow, Int. J. Heat Mass Transf., vol. 38, pp. 2127-2134,1995.
-
Barmak, I., Gelfgat, A., Vitoshkin, H., Ullmann, A., and Brauner, N., Stability of Stratified Two-Phase Flows in Horizontal Channels, Phys. Fluids, vol. 28, p. 044101,2016a.
-
Barmak, I., Gelfgat, A., Ullmann, A., and Brauner, N., Stability of Stratified Two-Phase Flows in Inclined Channels, Phys. Fluids, vol. 28, p. 084101,2016b.
-
Barmak, I., Gelfgat, A., Ullmann, A., and Brauner, N., On the Squire's Transformation for Stratified Two-Phase Flows in Inclined Channels, Int. J. Multiphase Flow, vol. 88, pp. 142-151,2017.
-
Barmak, I., Gelfgat, A., Ullmann, A., and Brauner, N., Non-Modal Stability Analysis of Stratified Two-Phase Channel Flows, Int. J. Multiphase Flow, vol. 111, pp. 122-139,2019.
-
Benjamin, T.B., Wave Formation in Laminar Flow Down an Inclined Plane, J. FluidMech, vol. 2, pp. 554-574,1957.
-
Chang, H.C., Wave Evolution on a Falling Film, Annu. Rev. Fluid Mech., vol. 26, pp. 103-136,1994.
-
Chang, H.C. and Demekhin, E.A., Complex Wave Dynamics on Thin Films, Amsterdam, Netherlands: Elsevier, 2002.
-
Coleman, J.W. and Garimella, S., Characterization of Two-Phase Flow Patterns in Small Diameter Round and Rectangular Tubes, Int. J. Heat Mass Transf., vol. 42, pp. 2869-2881,1999.
-
Cornish, R.J., Flow in Pipes of Rectangular Cross Section, Proc. R. Soc. London, Ser. A, vol. 120, pp. 691-700,1928.
-
Craster, R.V. and Matar, O.K., Dynamics and Stability of Thin Liquid Films, Rev. Mod. Phys, vol. 81, pp. 1131-1198,2009.
-
Dietze, G.F., On the Kapitza Instability and the Generation of Capillary Waves, J. Fluid Mech, vol. 789, pp. 368-401,2016.
-
Gelfgat, A. and Brauner, N., Instability of Stratified Two-Phase Flows in Rectangular Ducts, Int. J. Multiphase Flow, vol. 131, p. 103395,2020.
-
Gelfgat, A., Barmak, I., and Brauner, N., Instability of Stratified Two-Phase Flows in Inclined Rectangular Ducts, Int. J. Multiphase Flow, vol. 138, p. 103586,2021.
-
Georgantaki, A., Vatteville, J., Vlachogiannis, M., and Bontozoglou, V., Measurements of Liquid Film Flow as a Function of Fluid Properties and Channel Width: Evidence for Surface-Tension-Induced Long-Range Transverse Coherence, Phys. Rev. E, vol. 84, p. 026325,2011.
-
Goldstein, A., Ullmann, A., and Brauner, N., Characteristic of Stratified Laminar Flows in Inclined Pipes, Int. J. Multiphase Flow, vol. 75, pp. 267-287,2015.
-
Hesla, T.I., Pranckh, F.R., and Preziosi, L., Squire's Theorem for Two Stratified Fluids, Phys. Fluids, vol. 29, pp. 2808-2811, 1986.
-
Kalliadasis, S., Ruyer-Quil, C., Scheid, B., and Velarde, M.G., Falling Liquid Films, Applied Mathematical Sciences, vol. 176, London, UK: Springer-Verlag, 2012.
-
Kapitza, P.L. and Kapitza, S.P., Wave Flow of Thin Layers of a Viscous Fluid, Zh. Eksp. Teor. Fiz., vol. 18, pp. 3-28,1948.
-
Kushnir, R., Segal, V., Ullmann, A., and Brauner, N., Inclined Two-Layered Stratified Channel Flows: Long Wave Stability Analysis of Multiple Solution Regions, Int. J. Multiphase Flow, vol. 62, pp. 17-29,2014.
-
Kushnir, R., Ullmann, A., and Brauner, N., Closure Relations Effects on the Prediction of the Stratified Two-Phase Flow Stability via the Two-Fluid Model, Int. J. Multiphase Flow, vol. 97, pp. 78-93,2017.
-
Kushnir, R., Barmak, I., Ullman, A., and Brauner, N., Stability of Gravity-Driven Thin-Film Flow in the Presence of an Adjacent Gas Phase, Int. J. Multiphase Flow, vol. 135, p. 103443,2021.
-
Landman, M.J., Non-Unique Holdup and Pressure Drop in Two-Phase Stratified Inclined Pipe Flow, Int. J. Multiphase Flow, vol. 17, pp. 377-394,1991.
-
Lavalle, G., Li, Y., Mergui, S., Grenier, N., and Dietze, G.F., Suppression of the Kapitza Instability in Confined Falling Liquid Films, J. FluidMech, vol. 860, pp. 608-639,2019.
-
Leontidis, V., Vatteville, J., Vlachogiannis, M., Andritsos, N., and Bontozoglou, V., Nominally Two-Dimensional Waves in Inclined Film Flow in Channels of Finite Width, Phys. Fluids, vol. 22, p. 112106,2010.
-
Li, G., Guo, L., and Chen, X., The Behavior and Characteristics of the Interfacial Waves in Gas-Liquid Two-Phase Separated Flow through Downward Inclined Rectangular Channel, J. Thermal Sci., vol. 7, pp. 29-36,1998.
-
Lu, Q. and Suryanarayana, N.V., Interfacial Waves with Condensation of a Vapor Flowing inside a Horizontal, Rectangular Duct, Exp. Heat Transf., vol. 7, pp. 303-318,1994.
-
Oron, A., Davis, S.H., and Bankoff, S.G., Long-Scale Evolution of Thin Liquid Films, Rev. Mod. Phys., vol. 69, pp. 931-980, 1997.
-
Pollak, T., Haas, A., and Aksel, N., Side Wall Effects on the Instability of Thin Gravity-Driven Films-From Long-Wave to Short-Wave Instability, Phys. Fluids, vol. 23, p. 094110,2011.
-
Tang, Y.P. and Himmelblau, D.M., Interphase Mass Transfer for Laminar Concurrent Flow of Carbon Dioxide and Water between Parallel Plates, AIChEJ, vol. 9, pp. 630-635,1963.
-
Thibault, D., Munoz, J.M., and Line, A., Multiple Holdup Solutions in Laminar Stratified Flow in Inclined Channels, Int. J. Multiphase Flow, vol. 73, pp. 275-288,2015.
-
Tilley, B.S., Davis, S.H., and Bankoff, S.G., Linear Stability of Two-Layer Fluid Flow in an Inclined Channel, Phys. Fluids, vol. 6, pp. 3906-3922,1994.
-
Ullmann, A., Zamir, M., Ludmer, Z., and Brauner, N., Stratified Laminar Countercurrent Flow of Two Liquid Phases in Inclined Tubes, Int. J. Multiphase Flow, vol. 29, pp. 1583-1604,2003a.
-
Ullmann, A., Zamir, M., Gat, S., and Brauner, N., Multi-Holdups in Co-Current Stratified Flow in Inclined Tubes, Int. J. Multiphase Flow, vol. 29, pp. 1565-1581,2003b.
-
Ullmann, A., Goldstien, A., Zamir, M., and Brauner, N., Closure Relations for the Shear Stresses in Two-Fluid Models for Stratified Laminar Flows, Int. J. Multiph. Flow, vol. 30, pp. 877-900,2004.
-
Vlachogiannis, M., Samandas, A., Leontidis, V., and Bontozoglou, V., Effect of Channel Width on the Primary Instability of Inclined Film Flow, Phys. Fluids, vol. 22, p. 012106, 2010.
-
Wilmarth, T. and Ishii, M., Two-Phase Flow Regimes in Narrow Rectangular Vertical and Horizontal Channels, Int. J. Heat Mass Transf., vol. 37, pp. 1749-1758,1994.
-
Xu, J.L., Cheng, P., and Zhao, T.S., Gas-Liquid Two-Phase Flow Regimes in Rectangular Channels with Mini/Micro Gaps, Int. J. Multiphase Flow, vol. 25, pp. 411-432,1999.
-
Yih, C.-S., Stability of Liquid Flow down an Inclined Plane, Phys. Fluids, vol. 6, pp. 321-334,1963.
-
Zhao, Y., Chen, G., and Yuan, Q., Liquid-Liquid Two-Phase Flow Patterns in a Rectangular Microchannel, AIChE J, vol. 52, pp. 4052-4060,2006.