Geodesic
Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate Reynolds' numbers
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 4, pp. 30-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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Development of periodic disturbances on free surface of water film falling down vertical plane for Reynolds' number $Re \in [5; 10]$ is investigated. The investigation is implemented in a scope of the nonlinear differential equation for evolution of free surface of falling down liquid film. The equation is solved by a finite differencies method at rectangular uniformly spaced grid. By researching the growth of unit inaccuracy, the conditions on parameters of computation grid for inaccuracies to be not increasing are obtained. As a result, waveforms of water film, time spent to form the regular wave mode and amplitudes of periodic disturbances are calculated. Calculated amplitudes and experimental ones are compared.
Keywords: liquid film; amplitude; waveform; nonlinear evolution of disturbances. 
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     title = {Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate {Reynolds'} numbers},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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L. A. Prokudina; Ye. A. Salamatov. Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate Reynolds' numbers. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 4, pp. 30-39. http://geodesic.mathdoc.fr/item/VYURU_2015_8_4_a2/

[1] Kapitza P. L., “Wave Flow of Thin Layer of Viscous Fluid”, Zhurnal Eksperimental'noy i Teoreticheskoy Fiziki, 18:1 (1948), 3–18 (in Russian)

[2] Kapitza P. L., Kapitza S. P., “Wave Flow of Thin Layer of Viscous Fluid”, Zhurnal Eksperimental'noy i Teoreticheskoy Fiziki, 19:2 (1949), 105–120 (in Russian)

[3] Vellingiri R., “Dynamics of a Liquid Film Sheared by Co-Flowing Turbulent Gas”, Int. J. Multiphase Flow, 56 (2013), 93–104 | DOI

[4] Trifonof Y. Y., “Stability of the Wavy Film Falling Down a Vertical Plate: The DNS Computations and Floquet Theory”, Int. J. Multiphase Flow, 61 (2014), 73–82 | DOI | MR

[5] Dietse G. F., Al-Sibai F., Kneer R., “Experimental Study of Flow Separation in Laminar Falling Liquid Films”, J. Fluid Mech., 637 (2009), 73–104 | DOI

[6] Dietse G. F., Ruyer-Quil Ch., “Wavy Liquid Films in Interaction with a Confined Laminar Gas Flow”, J. Fluid Mech., 722 (2013), 348–393 | DOI | MR

[7] Meza C. E., Balakotaiah V., “Modeling and Experimental Studies of Large Amplitude Waves on Vertically Falling Films”, Chem. Eng. Sci., 68:19 (2008), 4707–4734 | DOI

[8] Ruyer-Quil Ch., Mannaville P., “Improved Modeling of Flows Down Inclined Planes”, The European Physical Journal B, 15 (2000), 357–369 | DOI

[9] Л. А. Прокудина, Г. П. Вяткин, “Самоорганизация возмущений в жидких пленках”, Доклады АН, 439:4 (2011), 481–484 | DOI

[10] Prokudina L. A., “Influence of Surface Tension Inhomogeneity on the Wave Flow of a Liquid Film”, J. Eng. Phys. Thermophys., 87:1 (2014), 165–173 | DOI

[11] Л. А. Прокудина, Г. П. Вяткин, “Неустойчивость неизотермической жидкой пленки”, Доклады АН, 362:6 (1998), 770–772 | MR | Zbl

[12] Prokudina L. A., Salamatov E. A., “Shear Stress Influence on Wave Characteristics of Liquid Film”, Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 2012, no. 7(34), 173–176 (in Russian)

[13] Berezin I. S., Zhidkov N. P., Computing Methods, Fizmatlit, M., 1959, 620 pp. (in Russian)

[14] Rogovaya I. A., Olevskiy V. M., Runova N. G., “Measurement of Parameters of Wavy Liquid Film Flow on Vertical Plate”, Theoretical Foundations of Chemical Engineering, 3:2 (1969), 200–208 (in Russian)

[15] Lel V. V., Al-Sibai F., Leefken A., Renz U., “Local Thickness and Wave Velocity Measurement of Wavy Films with a Chromatic Confocal Imaging Method and a Fluorescence Intensity Technique”, Exprements in Fluids, 39:5 (2005), 856–864 | DOI

[16] Penev V., Krylov V. S., Boyadjiev Ch., Vorotilin V. P., “Wavy Flow of Thin Liquid Films”, Int. J. Heat Mass Transfer, 15:7 (1972), 1395–1406 | DOI | Zbl