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

For citation:

Sennitskii V. L. Effects of a rotational motion of a liquid between curvilinear walls. Izvestiya VUZ. Applied Nonlinear Dynamics, 2025, vol. 33, iss. 2, pp. 219-232. DOI: 10.18500/0869-6632-003155, EDN: LMQFLO

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_2025-2_sennitskii_219-232.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Innovations in applied physics
Article type: 
Article
UDC: 
532.516, 532.517, 517.928
DOI: 
10.18500/0869-6632-003155
EDN: 
LMQFLO

Effects of a rotational motion of a liquid between curvilinear walls

Autors: 
Sennitskii Vladimir Leonidovich,
Abstract: 

The purpose of the work is the revealing and the researching of peculiarities of an average in time rotational motion of a viscous liquid which is bordering with solid bodies (curvilinear walls) under periodic in time influences which are characterized by the presence or the absence of a predominant direction in space.

Methods. The analytic investigational methods for boundary problems for Navier–Stokes and continuity equations are used that are the method
of perturbations (the method of a decomposition by degrees of a small parameter), the method of Fourier, an averaging.

Results. A new problem on the motion of a viscous liquid is formulated and solved. New hydro-mechanical effects are revealed.

Conclusion. The fulfilled investigation is a continuation of previous investigations of non-trivial dynamics of hydro-mechanical systems under periodic influences. In particular the work is directed to the determination of the range of possibilities to create quality changes of a hydro-mechanical systems dynamics by periodic influences. The obtained results can be used in a scientific researching of perspective approaches to the solving actual applied and fundamental problems.
 

Key words: 
viscous liquid
periodic in time influences
predominant direction in space
effects of rotational motion
Reference: 
  1. 1. Chelomei VN. Paradoxes in mechanics caused by vibrations. Doklady Akad. Nauk SSSR. 1983;270(1):62–67 (in Russian).
  2. Sennitskii VL. Motion of a circular cylinder in a vibrating liquid. Journal of Applied Mechanics and Technical Physics. 1985;(5):19–23 (in Russian).
  3. Sennitskii VL. The motion of a sphere in a liquid caused by vibrations of another sphere. Journal of Applied Mechanics and Technical Physics. 1986;(4):31–36 (in Russian).
  4. Lugovtsov BA, Sennitskii VL. Motion of a Body in a vibrating Liquid. Doklady Acad. Nauk SSSR. 1986;289(2):314–317 (in Russian).
  5. 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).
  6. Sennitskii VL. On the motion of a gas bubble in a viscous vibrating liquid. Journal of Applied Mechanics and Technical Physics. 1988;(6):107–113 (in Russian).
  7. Chelomei VN. Selected works. M.: Mashinostroenie; 1989. 336 p. (in Russian).
  8. Sennitskii VL. Predominantly unidirectional motion of a gas bubbe in a vibrating liquid. Doklady Akad. Nauk SSSR. 1991;319(1):117–119 (in Russian).
  9. Sennitskii VL. Predominantly unidirectional motion of a compressible solid body in a vibrating liquid. Journal of Applied Mechanics and Technical Physics. 1993;(1):100–101 (in Russian).
  10. Sennitskii VL. On motion of inclusions in uniformly and non-uniformly vibrating liquid. Proceedings of the International workshop on G jitter. Potsdam (USA): Clarkson University; 1993. P. 178–186.
  11. Lyubimov DV. New approach in the vibrational convection theory. Proc. 14 IMACs Congress on Computational and Applied Mathematics. Atlanta, Georgia, USA: Georgia Institute of Technonogy; 1994. P. 59–68.
  12. Lyubimov DV. Thermovibrational flows in nonuniform systems. Microgravity Quarterly. 1994;4(1): 221–225.
  13. Sennitskii VL. The motion of inclusions in an oscillating liquid. Siberian Physical Journal. 1995;(4):18–26 (in Russian).
  14. 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.
  15. Lyubimov DV, Lyubimova TP, Meradji S, Roux B. Vibrational control of crystal growth from liquid phase. J. Crystal Growth. 1997;180:648–659. DOI: 10.1016/S0022-0248(97)00294-7.
  16. Ivanova AA, Kozlov VG, Evesque P. Dynamics of a cylindrical body in a liquid-filled sector of a cylindrical layer under rotational vibration. Fluid Dynamics. 1998;33:488–496. DOI: 10.1007/BF02698213.
  17. Luybimov DV, Perminov AV, Cherepanov AA. Generation of averaged flows in a vibrational field close to the interface of mediums. In: Vibrational Effects in Hydrodynamics. Perm: Perm University Publishing; 1998. P. 204–221 (in Russian).
  18. Sennitskii VL. The motion of a ball in a liquid in the presence of a wall under oscillational influences. Applied Mechanics and Technical Physics. 1999;40(4):125–132 (in Russian).
  19. Lavrenteva OM. On the motion of particles in non-uniformly vibrating liquid. Europ. J. Appl. Math. 1999;10(3):251–263. DOI: 10.1017/S0956792599003745.
  20. Sennitskii VL. The motion of a pulsating rigid body in an oscillating viscous liquid. Applied Mechanics and Technical Physics. 2001;42(1):72–76 (in Russian).
  21. Lyubimov DV, Lyubimova TP, Cherepanov AA. Dynamics of Interfaces in Vibrational Fields. M.: Fizmatlit; 2003. 216 p. (in Russian).
  22. Pyatigorskaya OS, Sennitskii VL. Motion of a sphere in a liquid caused by vibrations of another sphere. Journal of Applied Mechanics and Technical Physics. 2004;45:542–545. DOI: 10.1023/B:JAMT.0000030331.35411.2e.
  23. 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.
  24. Lyubimov D, Lyubimova T, Vorobev A, Mojtabi A, Zappoli B. Thermal vibrational convection in near-critical fluids. Part I: Non-uniform heating. Journal of Fluid Mechanics. 2006;564:159–183. DOI: 10.1017/S0022112006001418.
  25. Hassan S, Lyubimova TP, Lyubimov DV, Kawaji M. Motion of a sphere suspended in a vibrating liquid-filled container. Journal of Applied Mechanics. 2006;73(1):72–78. DOI: 10.1115/1.1992516.
  26. Lyubimov DV, Lyubimova TP, Shklyaev SV. Behavior of a drop on an oscillating solid plate. Physics of Fluids. 2006;18:012101. DOI: 10.1063/1.2137358.
  27. 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. Physics of Fluids. 2007;19(1):017111. DOI: 10.1063/1.2409622.
  28. Sennitskii VL. Motion of an inclusion in uniformly and nonuniformly vibrating liquids. Journal of Applied Mechanics and Technical Physics. 2007;48(1):65-70. DOI: 10.1007/s10808-007-0009-8.
  29. Ivanova AA, Kozlov VG, Kuzaev AF. Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity. Fluid Dynamics. 2008:43:194–202. DOI: 10.1134/S001546280802004X.
  30. 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.
  31. Ivanova AA, Kozlov VG, Shchipitsyn VD. A light cylinder under horizontal vibration in a cavity filled with a fluid. Fluid Dynamics. 2010;45:889–897. DOI: 10.1134/S0015462810060062.
  32. Kozlov VG, Ivanova AA, Schipitsyn VD, Stambouli M. Lift Force on the cylinder in viscous liquid under vibration. Acta Astronaut. 2012;79:44–51. DOI: 10.1016/j.actaastro.2012.04.013.
  33. Pyatigorskaya OS, Sennitskii VL. Example of motion of a cylindrical solid in a viscous liquid. Journal of Applied Mechanics and Technical Physics. 2013;54:237–242. DOI: 10.1134/S0021894413020089.
  34. Pyatigorskaya OS, Sennitskii VL. Motion of solid particles in an oscillating liquid. Journal of Applied Mechanics and Technical Physics. 2013;54:404–407. DOI: 10.1134/S0021894413030085.
  35. Lyubimov DV, Baydin AY, Lyubimova TP. Particle dynamics in a fluid under high frequency vibrations of linear polarization. Microgravity Science Technology. 2013;25:121–126. DOI: 10.1007/s12217-012-9336-3.
  36. 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;55:773–780. DOI: 10.1134/S002189441405006X.
  37. Alabujev AA. Behavior of a cylindrical bubble under vibrations. Computational Continuum Mechanics. 2014;7(2):151–161. DOI: 10.7242/1999-6691/2014.7.2.16.
  38. Sennitskii VL. On the prescribed orientation of a solid inclusion in a viscous liquid. Siberian Journal of Industrial Mathematics. 2015;18(1):123–128. DOI: 10.17377/SIBJIM.2015.18.110 (in Russian).
  39. Vlasova OA, Kozlov VG. The repulsion of flat body from the wall of vibrating container filled with liquid. Microgravity Sci. Technology. 2015;27:297–303. DOI: 10.1007/s12217-015-9460-y.
  40. Kozlov NV, Vlasova OA. Behaviour of a heavy cylinder in a horizontal cylindrical liquidfilled cavity at modulated rotation. Fluid Dyn. Res. 2016;48(5):055503. DOI: 10.1088/0169-5983/48/5/055503.
  41. Sennitskii VL. Paradoxical motion of a liquid.International Journal of Applied and Fundamental Research. 2017;(8–1):28–33 (in Russian). DOI: 10.17513/mjpfi.11753.
  42. Sennitskii VL. The predominantly unidirectional rotation of a solid body and a viscous liquid. Siberian Journal of Industrial Mathematics. 2017;20(2):93–97 (in Russian).
  43. Vlasova OA, 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;59:219–228. DOI: 10.1134/S0021894418020050.
  44. Konovalov VV, Lyubimova TP. Numerical study of the influence 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.
  45. Shchipitsyn VD. Vibrations of a nonaxisymmetric cylinder in a cavity filled with liquid and performing rotational oscillations. Tech. Phys. Lett. 2020;46:771–774. DOI: 10.1134/S1063785020080143.
  46. Sennitskii VL. The predominantly unidirectional flow of a viscous liquid. Siberian Journal of Industrial Mathematics. 2021;24(2):126–133 (in Russian). DOI: 10.33048/SIBJIM.2021.24.210.
  47. Sennitskii VL. On the flow of a viscous liquid in a gravity field. Thermophysics and Aeromechanics. 2021;28(3):347-351. DOI: 10.1134/S0869864321030057.
  48. Konovalov VV, Lyubimova TP. Influence of acoustic vibrations on the interaction of a gas bubble and a solid particle in a liquid. In: TP Lyubimova (ed.). 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, D.V. Lyubimov. Perm: Perm University Publishing; 2022. P. 254–261.
  49. 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.
  50. Sennitskii VL. Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences. Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(2):197–208. DOI: 10.18500/0869-6632-003091.
  51. Kapitsa PL. Pendulum with a vibrating suspension. Sov. Phys. Usp. 1951;44(1):7–20 (in Russian).
  52. Krilov NM, Bogolyubov NN. Introduction in Non-Linear Mechanics. Moscow-Ijevsk: NITs Reguliarnaya i haoticheskaya dinamika; 2004. 352 p. (in Russian).
  53. Bogolyubov NN, Mitropolskii YuA. Asimptotic Methods in the Theory of Non-Linear Oscillations. M.: GIF-ML; 1958. 408 p. (in Russian).
  54. Sennitskii VL. Force interaction of a sphere and a viscous liquid in the presence of a wall. Journal of Applied Mechanics and Technical Physics. 2000;41:50–54. DOI: 10.1007/BF02465236.
Received: 
26.06.2024
Accepted: 
30.08.2024
Available online: 
10.12.2024
Published: 
31.03.2025
  • 452 reads