ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Sennitskii V. L. Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 2, pp. 197-208. DOI: 10.18500/0869-6632-003091, EDN: SMOTDZ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon and_2024-2_sennitskii_197-208.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Innovations in applied physics
Article type: 
Article
UDC: 
532.516, 532.517, 517.928
DOI: 
10.18500/0869-6632-003091
EDN: 
SMOTDZ

Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences

Autors: 
Sennitskii Vladimir Leonidovich,
Abstract: 

Purpose of the work is revealing and researching of peculiarities of a motion of a viscous liquid having a free boundary and undergoing periodic in time influences which are characterized by the absence of a predominant direction in space.

Methods. The analytic investigation methods of non-linear problems, of boundary problems for the system of Navier– Stokes and continuity equations are used that are the method of perturbations (the method of a small parameter) the method of Fourier (the method of a separation of variables), an averaging, a construction and studying of asymptotic formulas.

Results. A new problem on the motion of a viscous liquid is formulated and solved. Asymptotic representations of the found solution are constructed and explored. New hydromechanical effects are revealed.

Conclusion. The work is fulfilled in the development of a perspective direction in liquid mechanics that is of researching the dynamics of hydromechanical systems under periodic influences. The obtained results can be used in particular in further investigations of a non-trivial dynamics of hydromechanical systems, under working for the methods of a control of hydromechanical systems.

Key words: 
viscous liquid
free boundary
periodic in time influences
predominant direction in space
stationary motion
Reference: 
  1. Sennitskii VL. Predominantly unidirectional motion of a gas bubbe in a vibrating liquid. Proceedings of the Academy of Sciences of the USSR. 1991;319(1):117–119 (in Russian).
  2. Sennitskii VL. Predominantly unidirectional motion of a compressible solid body in a vibrating liquid. Journal of Applied Mechanics and Technical Physics. 1993;34(1):96–97. DOI: 10.1007/ BF00851812.
  3. Lyubimov DV. New approach in the vibrational convection theory. In: Proc. 14 IMACs Congresson Computational and Applied Mathematics. Atlanta, Georgia, USA: Georgia Institute of Technonogy; 1994. P. 59–68.
  4. Lyubimov DV. Thermovibrational flows in nonuniform systems. Microgravity Quarterly. 1994;4(1): 221–225.
  5. Kozlov VG. Solid-body dynamics in cavity with liquid under high-frequency rotational vibration. Europhysics Letters. 1996;36(9):651–656. DOI: 10.1209/epl/i1996-00282-0.
  6. Lyubimov DV, Lyubimova TP, Meradji S, Roux B. Vibrational control of crystal growth from liquid phase. Journal of Crystal Growth. 1997;180(3–4):648–659. DOI: 10.1016/S0022-0248(97)00294-7.
  7. Ivanova АА, Kozlov VG, Evesque P. Dynamics of a cylindrical body in a liquid-filled sector of a cylindrical layer under rotational vibration. Fluid Dynamics. 1998;33(4):488–496. DOI: 10.1007/ BF02698213.
  8. Luybimov DV, Perminov AV, Cherepanov AA. Generation of mean flows in vibrational field near the interface. In: Vibration Effects in Hydrodynamics. Perm: Perm State University Publishing; 1998. P. 204–221 (in Russian).
  9. Sennitskii VL. Motion of a pulsating rigid body in an oscillating viscous liquid. Journal of Applied Mechanics and Technical Physics. 2001;42(1):72–76. DOI: 10.1023/A:1018808628235.
  10. Lyubimov DV, Lyubimova TP, Cherepanov AA. Dynamics of Interfaces in Vibrationalfields. Moscow: Fizmatlit; 2003. 216 p. (in Russian).
  11. Ivanova AA, Kozlov VG, Kuzaev AF. Vibrational lift force acting on a body in a fluid near a solid surface. Doklady Physics. 2005;50(6):311–314. DOI: 10.1134/1.1958123.
  12. Lyubimov D, Lyubimova T, Vorobev A, Mojtabi A, Zappoli B. Thermal vibrational convection in near-critical fluids. Part 1. Non-uniform heating. Journal of Fluid Mechanics. 2006;564:159–183. DOI: 10.1017/S0022112006001418.
  13. Hassan S, Lyubimova TP, Lyubimov DV, Kawaji M. Motion of a sphere suspended in a vibrating liquid-filled container. J. Appl. Mech. 2006;73(1):72–78. DOI: 10.1115/1.1992516.
  14. Lyubimov DV, Lyubimova TP, Shklyaev SV. Behavior of a drop on an oscillating solid plate. Phys. Fluids. 2006;18(1):012101. DOI: 10.1063/1.2137358.
  15. Shevtsova V, Melnikov D, Legros JC, Yan Y, Saghir Z, Lyubimova T, Sedelnikov G, Roux B. Influence of vibrations on thermodiffusion in binary mixture: A benchmark of numerical solutions. Phys. Fluids. 2007;19(1):017111. DOI: 10.1063/1.2409622.
  16. Ivanova AA, Kozlov VG, Kuzaev AF. Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity. Fluid Dynamics. 2008;43(2):194–202. DOI: 10.1134/S0015462 80802004X.
  17. Sennitskii VL. Pulsating motion of an inhomogeneous solid sphere in a vibrating liquid. Journal of Applied Mechanics and Technical Physics. 2009;50(6):936–943. DOI: 10.1007/s10808-009- 0127-6.
  18. Ivanova AA, Kozlov VG, Shchipitsyn VD. A light cylinder under horizontal vibration in a cavity filled with a fluid. Fluid Dynamics. 2010;45(6):889–897. DOI: 10.1134/S0015462810060062.
  19. Kozlov V, Ivanova A, Schipitsyn V, Stambouli M. Lift force acting on the cylinder in viscous liquid under vibration. Acta Astronautica. 2012;79:44–51. DOI: 10.1016/j.actaastro.2012.04.013.
  20. Lyubimov DV, Baydin AY, Lyubimova TP. Particle dynamics in a fluid under high frequency vibrations of linear polarization. Microgravity Sci. Technol. 2013;25(2):121–126. DOI: 10.1007/ s12217-012-9336-3.
  21. Ivanova AA, Kozlov VG, Shchipitsyn VD. Lift force acting on a cylindrical body in a fluid near the boundary of a cavity performing translational vibrations. Journal of Applied Mechanics and Technical Physics. 2014;55(5):773–780. DOI: 10.1134/S002189441405006X.
  22. Alabuzhev АА. Behavior of a cylindrical bubble under vibrations. Computational Continuum Mechanics. 2014;7(2):151–161 (in Russian). DOI: 10.7242/1999-6691/2014.7.2.16.
  23. Sennitskii VL. On a prescribed orientation of a solid inclusion in a viscous liquid. Journal of Applied and Industrial Mathematics. 2015;18(1):123–128 (in Russian). DOI: 10.17377/ SIBJIM.2015.18.11.
  24. Kozlov V, Vlasova O. The repulsion of flat body from the wall of vibrating container filled with liquid. Microgravity Sci. Technol. 2015;27(4):297–303. DOI: 10.1007/s12217-015-9460-y.
  25. Kozlov NV, Vlasova OA. Behavior of a heavy cylinder in a horizontal cylindrical liquid-filled cavity at modulated rotation. Fluid Dyn. Res. 2016;48(5):055503. DOI: 10.1088/0169- 5983/48/5/055503.
  26. Sennitskii VL. Paradoxical motion of a liquid. International Journal of Applied and Basic Research. 2017;(8–1):28–33 (in Russian). DOI: 10.17513/mjpfi.11753.
  27. Vlasova ОА, Kozlov VG, Kozlov NV. Lift force acting on a heavy solid in a rotating liquid-filled cavity with a time-varying rotation rate. Journal of Applied Mechanics and Technical Physics. 2018;59(2):219–228. DOI: 10.1134/S0021894418020050.
  28. Konovalov ВВ, Lyubimova ТP. Numerical study of the effect of vibrations on the interaction in an ensemble of gas bubbles and solid particles in a liquid. Computational Continuum Mechanics. 2019;12(1):48–56 (in Russian). DOI: 10.7242/1999-6691/2019.12.1.5.
  29. Shchipitsyn VD. Vibrations of a nonaxisymmetric cylinder in a cavity filled with liquid and performing rotational oscillations. Tech. Phys. Lett. 2020;46(8):771–774. DOI: 10.1134/S106378 5020080143.
  30. Konovalov VV, Lyubimova TP. Influence of acoustic vibrations on the interaction of a gas bubble and a solid particle in a liquid. In: Lyubimova TP, editor. Perm Hydrodynamical Scientific Readings. Digest of Articles by the Materials of VIII All-Russian Conference Dedicated for the Memory of Professors G. Z. Gershuny, E. M. Juhovitskii and D. V. Lyubimov. Perm: Perm State National Research University; 2022. P. 254–261 (in Russian).
  31. Sennitskii VL. On peculiarities of a liquid flow in a gravity field. Siberian Electronic Mathematical Reports. 2022;19(1):241–247 (in Russian). DOI: 10.33048/semi.2022.19.018.
  32. Chelomei VN. Paradoxes in mechanics caused by vibrations. Proceedings of the Academy of Sciences of the USSR. 1983;270(1):62–67 (in Russian).
  33. Sennitskii VL. Motion of a circular cylinder in a vibrating liquid. Journal of Applied Mechanics and Technical Physics. 1985;26(5):620–623. DOI: 10.1007/BF00915307.
  34. Sennitskii VL. Motion of a sphere in fluid caused by vibrations of another sphere. Journal of Applied Mechanics and Technical Physics. 1986;27(4):501–505. DOI: 10.1007/BF00910190.
  35. Lugovtsov BA, Sennitskii VL. Motion of a body in a vibrating liquid. Proceedings of the Academy of Sciences of the USSR. 1986;289(2):314–317 (in Russian).
  36. Lyubimov DV, Lyubimova TP, Cherepanov AA. On the motion of a solid body in a vibrating fluid. In: Convective Flows. Perm: Perm Pedagogical Institute Publishing; 1987. P. 61–71 (in Russian).
  37. Chelomei VN. Selected Works. Moscow: Mashinostroenie; 1989. 336 p. (in Russian).
  38. Sennitskii VL. Motion of a gas bubble in a viscous vibrating liquid. Journal of Applied Mechanics and Technical Physics. 1988;29(6):865–870. DOI: 10.1007/BF00858387.
  39. Kapitsa PL. Pendulum with a vibrating suspension. Sov. Phys. Usp. 1951;44(1):7–20 (in Russian). DOI: 10.3367/UFNr.0044.195105b.0007.
  40. Krylov NM, Bogoliubov NN. Introduction in Non-linear Mechanics. Moscow-Izhevsk: Research Center Regular and Chaotic Dynamics; 2004. 352 p. (in Russian).
  41. Bogoliubov NN, Mitropolsky YA. Asymptotic Methods in the Theory of Non-linear Oscillations. New York: Gordon and Breach; 1961. 537 p.
Received: 
29.08.2023
Accepted: 
23.10.2023
Available online: 
08.02.2024
Published: 
29.03.2024
  • 281 reads