The nonlinear partial differential equation, defining the state of the free surface of a viscous liquid layer (film) interacting with a backward gas flow, is presented. The evolution of the periodic disturbances of this fi lm, resulting in the establishment of a regular regime of its flow, was numerically investigated. For a water fi lm falling vertically down under the conditions of its interaction with a reverse gas flow, the shapes of the waves on the gas–liquid contact surface were constructed and the wave characteristics of a regular regime of flow of the water film (the frequency of the waves and their increment and phase velocity) and the time of establishment of this regime were calculated.
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References
P. A. Semenov, Flow of thin liquid layers, Zh. Tekh. Fiz., 14, No. 7, pp. 425–437 (1944).
F. P. Stainthorp and R. S. W. Batt, The effect of co-current and counter-current air flow on the wave properties of falling liquid films, Tr. Inst. Chem. Engs., 45, Issue 9, 372–387 (1967).
L. O. Jones and S. Whitaker, An experimental study of falling liquid films, AIChE, 12, Issue 3, 525–529 (1966).
M. A. Mendez, B. Scheid, and J.-M. Buchlin, Low Kapitza falling liquid films, Chem. Eng. Sci., 170, 122–138 (2016).
A. D. Sergeev, L. P. Kholpanov, N. A. Nikolaev, V. A. Malyusov, and N. M. Zhavoronkov, Measurement of the wave parameters of liquid film flow by the method of local electrical conductivity, J. Eng. Phys. Thermophys., 29, No. 5, 1400–1403 (1975).
T. Nosoko, A. Miyara, and T. Nagata, Characteristics of falling film flow on completely wetted horizontal tubes and the associated gas absorption, Int. J. Heat Mass Transf., 45, Issue 13, 2729–2738 (2002).
C. E. Meza and V. Balakotaiah, Modeling and experimental studies of large amplitude waves on vertically falling films, Chem. Eng. Sci., 63, Issue 19, 4704–4734 (2008).
I. A. Rogovaya, V. M. Olevskii, and N. G. Runova, Measurement of parameters of a wave film flow over a vertical plate, Teor. Osnovy Khim. Tekhnol., 3, No. 2, 200–208 (1969).
V. M. Olevskii, V. R. Ruchinskii, A. M. Kashnikov, and V. I. Chernyshev, Film Heat and Mass Exchange Apparatus (Processes and Apparatus of the Chemical and Petrochemical Industries) [in Russian], Khimiya, Moscow (1988).
W. Strobel and S. Whitaker, The effect of surfactants on the flow characteristics of falling liquid films, AIChE, 15, Issue 4, 527–532 (1969).
P. L. Kapitsa, Wave flow of viscous liquid thin layers. Flow making contact with a gas flow and heat transfer, Zh. Éksp. Tekh. Fiz., 18, No. 1, 19–28 (1948).
L. P. Kholpanov and V. Ya. Shkadov, Hydrodynamics and Heat Mass Exchange with an Interface [in Russian], Nauka, Moscow (1990).
Yu. P. Korotaev and A. A. Tochigin, Effect of a gas stream on the wave flow of thin layers of a viscous liquid, J. Eng. Phys. Thermophys., 17, No. 6, 989–994 (1969).
D. Tseluiko and S. Kalliadasis, Nonlinear waves in counter-current gas-liquid film flow, J. Fluid Mech., 673, 19–59 (2011).
A. N. Beloglazkin and V. Ya. Shkadov, Nonlinear waves in the liquid film–gas flow system, Izv. RAN, Mekh. Zhidkosti Gaza, No. 6, 32–49 (2012).
C. Ruyer-Quil and P. Manneville, Improved modeling of fl ows down inclined planes, Eur. Phys. J., 15, Issue 2, 357–369 (2000).
G. F. Dietze, C. Ruyer-Quil, and S. Mergui, Wavy liquid films in interaction with a confi ned laminar gas flow, J.Fluid Mech., 722, 348–393 (2013).
L. A. Prokudina and G. P. Vyatkin, Ins tability of a nonisothermal liquid film, Dokl. Akad. Nauk, 362, No. 6, 770–772 (1998).
L. A. Prokudina and G. P. Vyatkin, Sel f-organization of disturbances in liquid films, Dokl. Akad. Nauk, 439, No. 4, 481–484 (2011).
L. A. Prokudina, Nonlinear evolution of the disturbances in a thin liquid layer with waves, Zh. Éksp. Tekh. Fiz., 145, No. 3, 549–558 (2014).
L. A. Prokudina, Influence of surface tension inhomogeneity on the wave flow of a liquid film, J. Eng. Phys. Thermophys., 87, No. 1, 165–173 (2014).
D. Anderson, J. Tannehill, and R. Plet cher, Computational Fluid Mechanics and Heat Transfer [Russian translation], Mir, Moscow (1990).
I. S. Berezin and N. P. Zhidkov, Metho ds of Calculations [in Russian], GIFML, Moscow (1959).
L. A. Prokudina and E. A. Salamatov, I nfl uence of the shear stress of a liquid fi lm on its wave characteristics, Vestn. YuUrGU, Ser. Mat. Mekh. Fiz., 7, No. 34, 173–176 (2012).
L. A. Prokudina and E. A. Salamatov, M athematical simulation of the wave surface of a liquid fi lm fl owing down over a vertical plane at moderate Reynolds numbers, Vestn, YuUrGU, Ser. Mat. Model. Program., 8, No. 4, 30–39 (2015).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 95, No. 1, pp. 125–133, January–February, 2022.
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Prokudina, L.A., Salamatov, E.A. Numerical Investigation of the Wave Flows of Liquid Films Interacting with a Gas Flow. J Eng Phys Thermophy 95, 123–131 (2022). https://doi.org/10.1007/s10891-022-02460-8
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DOI: https://doi.org/10.1007/s10891-022-02460-8