Steady Flows of a Fluid Oscillating in an Axisymmetric Channel of Variable Cross-Section, Versus the Dimensionless Frequency

  • 12 Accesses


The averaged flows excited by oscillations of fluid in an axisymmetric channel, which transverse section periodically changes with longitudinal coordinate, are experimentally studied. Oscillations are caused by harmonious change of a volume of the fluid, which is pumped over via the channel. Researches are executed within the broad range of dimensionless frequency which characterizes the ratio of the cross size of the channel to the thickness of Stokes boundary layers. It is shown that oscillations of fluid excite an averaged flows in the form of a system of toroidal vortex structures in each segment of the channel. The intensity of averaged flows increases with the increase in amplitude and frequency of fluid oscillation and is defined by the pulsational Reynolds number and the dimensionless frequency in the channel of the set geometry. It is shown that in the limit of low dimensionless frequencies, when viscous forces define the oscillating component of flow in the whole channel, the primary vortices occupy all the volume of the channel. The cross size of the primary vortices decreases with the increase in dimensionless frequency, and at high frequencies the vortexes are localized in viscous boundary layer near the side border in a narrow part of the channel. At the same time, the secondary vortices having opposite turning are formed outside the primary boundary layer vortexes in the bulk of the channel. The transformation of the structure of averaged flows and their intensity versus the dimensionless frequency are studied.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  1. Aleksandrov, V., Kopysov, S., Tonkov, L.: Vortex flows in the liquid layer and droplets on a vibrating flexible plate. Microgravity Sci. Technol. 30(1–2), 85–93 (2018)

  2. Dyakova, V., Kozlov, V., Polezhaev, D.: Oscillation-induced sand dunes in a fluid-filled rotating cylinder. Phys. Rev. 94(6), 063109 (2016)

  3. Gershuni, G.Z., Lyubimov, D.V.: Thermal Vibrational Convection, 358 p. Wiley, New York (1998)

  4. Guibert, R., Plouraboue, F., Bergeon, A.: Steady streaming confined between three-dimensional wavy surfaces. J. Fluid Mech. 657, 430–455 (2010)

  5. Ivanova, A.A., Kozlov, V.G.: Vibrational convection in a nontranslationally oscillating cavity (isothermal case). Fluid Dyn. 38(2), 186–192 (2003)

  6. Ivanova, A.A., Kozlov, V.G., Liubimov, D.V., Liubimova, T.P., Meragy, S., Roux, B.: Structure of averaged flow driven by a vibrating body with a large-curvature edge. Fluid Dyn. 33(5), 659–665 (1998)

  7. Kozlov, V.G., Kozlov, N.V., Schipitsyn, V.D.: Steady flows in an oscillating deformable container: effect of the dimensionless frequency. Phys. Rev. Fluids. 2, 094501 (2017)

  8. Kozlov, V.G., Sabirov, R.R., Subbotin, S.V.: Steady flows in an oscillating spheroidal cavity with elastic wall. Fluid Dyn. 53(2), 189–199 (2018)

  9. Kozlov, N.V., Vjatkin, A.A., Schipitsyn, V.D., Stambouli, M.: Steady flows excited by local oscillations of flexible boundary of a container with fluid. Microgravity Sci. Technol. 821–831 (2019)

  10. Lighthill, M.J.: Acoustic streaming. J. Sound Vib. 61(3), 391–418 (1978)

  11. Liubimov, D.V., Liubimova, T.P., Cherepanov, A.A.: Dynamics of interfaces in vibration fields. M.: Fizmatlit. 216 p (2003)

  12. Nishimura, T., Arakawa, S., Murakami, S., Kawamura, Y.: Oscillatory viscous flow in symmetric wavy-walled channels. Chem. Eng. Sci. 44, 2137–2148 (1989)

  13. Nyborg, W.L.M.: Acoustic streaming. In: Mason, W.P. (ed.) Physical Acoustics, vol. II B, p. 265. Academic, New York (1965)

  14. Ralph, M.E.: Oscillatory flows in wavy-walled tubes. J. Fluid Mech. 168, 515–540 (1986)

  15. Riley, N.: Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65 (2001)

  16. Schlichting, H.: Boundary Layer Theory. McGraw-Hill, New York (1979)

  17. Subbotin, S.V., Dyakova, V.V.: Inertial waves and steady flows in a liquid filled librating cylinder. Microgravity Sci. Technol. 30(4), 383–392 (2018)

  18. Thielicke, W., Stamhuis, E.J.: PIVLAB-towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J. Open Res. Softw. 2, e30 (2014)

  19. Ye, X., Shimizu, M.: Augmented longitudinal diffusion in grooved tubes for oscillatory flow. Int. J. Heat Mass Transf. 44(3), 633–644 (2001)

Download references


The work is supported by the Russian Foundation for Basic Research (Grant № 17-41-590773).

Author information

Correspondence to Olga Vlasova.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article belongs to the Topical Collection: Multiphase Fluid Dynamics in Microgravity

Guest Editors: Tatyana P. Lyubimova, Jian-Fu Zhao

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Vlasova, O., Karpunin, I., Latyshev, D. et al. Steady Flows of a Fluid Oscillating in an Axisymmetric Channel of Variable Cross-Section, Versus the Dimensionless Frequency. Microgravity Sci. Technol. (2020).

Download citation


  • Axisymmetric channel
  • Varying cross section
  • Oscillations
  • Steady flows
  • Dimensionless frequency