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Simulation of Counter-Current Gas Flow in Falling-Film Equipment for Moderate Reynolds Numbers

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Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020) (ICIE 2021)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

Joint motion of falling-down liquid film and counter-current gas is considered. Such types of flows occur in falling-film equipment (absorbers, evaporators, reactors) and take place in machines (pumps, compressors, turbines) that are widely used in many industries (energy, chemical, food, metallurgy, pharmaceutical, and biotech). Waves at gas–liquid interface significantly affect the overall process effectiveness, its operation cycle, dynamics, and safety. That makes the waves study quite important for machines design and control development. We present mathematical formalization of the problem, based on the first-principle approach. With the small parameter method, nonlinear non-stationary partial differential equation for the state of the liquid–gas interface is obtained, which describes the liquid–gas interface dynamics. In the equation scope, results of numerical simulation are shown. Wave profiles, phase velocities, amplitudes are calculated. The evolution of periodic disturbances is investigated: it is shown that regular wave profiles are formed at the liquid–gas interface, time formation of the regular waves is obtained. Gas flow effect on the liquid–gas interface is discussed.

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References

  1. Semyonov PA (1944) Techenie zhidkostu v tonkikh sloyah (Flowing of liquid in thin layers). Zhurnal Tekhnicheskoy Fiziki 14:425–437

    Google Scholar 

  2. Stainthorp FP, Batt RS (1967) The effect of co-current and counter-current air flow on the wave properties of falling liquid films. Tr Inst Chem Eng 45:372–387

    Google Scholar 

  3. Jones LO, Whitaker S (1966) An experimental study of falling liquid films. AIChE J 12:525–529. https://doi.org/10.1002/aic.690120324

    Article  Google Scholar 

  4. Portalski S, Clegg AJ (1972) An experimental study of wave inception on falling liquid films. Chem Eng Sci 27:1257–1265. https://doi.org/10.1016/0009-2509(72)80102-7

    Article  Google Scholar 

  5. Alekseenko SV, Nakoryakov VE, Pokusaev BG (1994) Wave flow of liquid films. Begell House, New York

    MATH  Google Scholar 

  6. Alekseenko SV, Markovich DM, Kharlamov SM et al (2004) Experimental study of the linear stability of a falling liquid film in the presence of a turbulent gas stream. Fluid Dyn 39:612–620. https://doi.org/10.1023/B:FLUI.0000045677.40730.18

    Article  MATH  Google Scholar 

  7. Alekseenko SV, Aktershev SP, Cherdantsev AV et al (2009) Primary instabilities of liquid film flow sheared by turbulent gas stream. Int J Mult Flow 35:617–627. https://doi.org/10.1016/j.ijmultiphaseflow.2009.03.003

    Article  Google Scholar 

  8. Mendez MA, Scheid B, Buchlin J-M (2017) Low Kapitsa falling liquid films. Chem Eng Sc 170:122–138. https://doi.org/10.1016/j.ces.2016.12.050

    Article  Google Scholar 

  9. Sergeev AD, Kholpanov LP, Nikolaev NA et al (1975) Measurement of the wave parameters of liquid film flow by the method of local electrical conductivity. J Eng Phys Thermophys 29:1400–1403. https://doi.org/10.1007/BF00858172

    Article  Google Scholar 

  10. Nosoko T, Yoshimura PN, Nagata T et al (1996) Characteristics of two-dimensional waves on a falling liquid film. Chem Eng J 51:725–732

    Article  Google Scholar 

  11. Nosoko T, Miyara A, Nagata T (2002) Characteristics of falling film flow on completely wetted horizontal tubes and the associated gas absorption. Int J Heat Mass Tr 45:2729–2738. https://doi.org/10.1016/S0017-9310(01)00357-X

    Article  Google Scholar 

  12. Park CD, Nosoko T, Gima S et al (2004) Wave-augmented mass transfer in a liquid film falling inside a vertical tube. Int J Heat Mass Tr 47:2587–2598. https://doi.org/10.1016/j.ijheatmasstransfer.2003.12.017

    Article  Google Scholar 

  13. Yoshimura PN, Nosoko T, Nagata T (1996) Enhancement of mass transfer into a falling laminar liquid film by two-dimensional surface waves—some experimental observations and modeling. Chem Eng Sc 51:1231–1240. https://doi.org/10.1016/0009-2509(95)00387-8

    Article  Google Scholar 

  14. Gross U, Storch Th, Philipp Ch et al (2009) Wave frequency of falling liquid films and the effect on reflux condensation in vertical tubes. Int J Mult Flow 35:398–409. https://doi.org/10.1016/j.ijmultiphaseflow.2009.01.001

    Article  Google Scholar 

  15. Meza CE, Balakotaiah V (2008) Modeling and experimental studies of large amplitude waves on vertically falling films. Chem Eng Sc 63:4704–4734. https://doi.org/10.1016/j.ces.2007.12.030

    Article  Google Scholar 

  16. Kapitsa PL (1948) Volnovoe techenie tonkikh sloyev vyazkoi zhidkosti (Wavy flow of thin layers of viscous fluid). Zhulnal Experimental’noi i Teoreticheskoi Fiziki 18:3–28

    Google Scholar 

  17. Kapitsa PL, Kapitsa SP (1949) Volnovoe techenie tonkikh sloyev vyazkoi zhidkosti (Wavy flow of thin layers of viscous fluid). Zhulnal Experimental’noi i Teoreticheskoi Fiziki 19:105–120

    Google Scholar 

  18. Benney DJ (1966) Long waves on liquid films. J Math Phys 45:150–155. https://doi.org/10.1002/sapm1966451150

    Article  MathSciNet  MATH  Google Scholar 

  19. Shkadov VY (1967) Wave flow regimes of a thin layer of viscous fluid subject to gravity. Fluid Dyn 2:29–34. https://doi.org/10.1007/BF01024797

    Article  Google Scholar 

  20. Esmail MN, Shkadov VY (1971) Nonlinear theory of waves in a viscous liquid layer. Fluid Dyn 6:599–603. https://doi.org/10.1007/BF01013621

    Article  Google Scholar 

  21. Nakoryakov VE, Shreiber IR (1973) Waves on the surface of a thin layer of viscous liquid. J Appl Mech Tech Phys 14:237–241. https://doi.org/10.1007/BF01200661

    Article  Google Scholar 

  22. Ivanilov PY (1961) Katyashchiesya volny v naklonnom kanale (Roll waves in inclined channel). Zhurnal Vychislitel’noy Matematiki i Matematicheskoy Fiziki 6:1061–1076

    Google Scholar 

  23. Korotaev YP, Tochigin AA (1969) Effect of a gas stream on the wave flow of thin layers of a viscous liquid. J Eng Phys Thermophys 17:1469–1473. https://doi.org/10.1007/BF00832502

    Article  Google Scholar 

  24. Lin T-S, Tseluiko D, Kalliadasis S (2014) Numerical study of a non-local weakly nonlinear model for a liquid film sheared by a turbulent gas. Proc. IUTAM 11:98–109. https://doi.org/10.1016/j.piutam.2014.01.052

    Article  Google Scholar 

  25. Ruyer-Quil C, Manneville P (2000) Improved modeling of flows down inclined planes. Eur Phys J B 15:357–369. https://doi.org/10.1007/s100510051137

    Article  MATH  Google Scholar 

  26. Dietze GF, Ruyer-Quil C (2013) Wavy liquid films in interaction with a confined laminar gas flow. J Fluid Mech 722:348–603. https://doi.org/10.1017/jfm.2013.98

    Article  MathSciNet  MATH  Google Scholar 

  27. Prokudina LA, Vyatkin GP (1998) Instability of a nonisotermal liquid film. Dokl Phys 43:652–654

    MathSciNet  MATH  Google Scholar 

  28. Prokudina LA, Vyatkin GP (2011) Self-organization of perturbations in liquid films. Dokl Phys 56:444–447. https://doi.org/10.1134/S1028335811080039

    Article  Google Scholar 

  29. Prokudina LA (2014) Nonlinear evolution of perturbations in a thin fluid layer during wave formation. J Exp Theor Phys 118:480–488. https://doi.org/10.1134/S1063776114020046

    Article  Google Scholar 

  30. Prokudina LA, Salamatov YA (2015) Mathematical modelling of wavy surface of liquid film falling down a vertical plane at moderate Reynolds’ numbers. Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe modelirovanie i programmirovanie 8:30–39

    Google Scholar 

  31. Prokudina LA, Salamatov YA (2012) Vliyanie kasatel’nogo napryazheniya navolnovye kharakteristiki zhydkoy plyenki (Shear stress influence on wave characteristics of liquid film). Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematike. Mekhanika. Fizika 7:173–176

    Google Scholar 

  32. Kholpanov LP, Shkadov VY (1990) Hydrodynamics and heat-and-mass transfer with an interface surface. Nauka, Moscow

    Google Scholar 

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Authors and Affiliations

  1. South Ural State University, 76 Lenin Avenue, Chelaybinsk, 454080, Russia

    L. Prokudina

  2. Metran, Emerson Process Management, 15 Novogradskii Prospekt, Chelyabinsk, 454003, Russia

    Ye. Salamatov

Authors
  1. L. Prokudina
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  2. Ye. Salamatov
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Correspondence to Ye. Salamatov .

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Editors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Andrey A. Radionov

  2. Mechatronics and Automation Department, South Ural State University, Chelyabinsk, Russia

    Vadim R. Gasiyarov

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Prokudina, L., Salamatov, Y. (2021). Simulation of Counter-Current Gas Flow in Falling-Film Equipment for Moderate Reynolds Numbers. In: Radionov, A.A., Gasiyarov, V.R. (eds) Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020). ICIE 2021. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-54814-8_118

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  • DOI: https://doi.org/10.1007/978-3-030-54814-8_118

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54813-1

  • Online ISBN: 978-3-030-54814-8

  • eBook Packages: EngineeringEngineering (R0)

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