Abstract
The problem of generation of steady streaming by an oscillating circular cylinder is considered. For the case of a finite oscillation frequency, the asymptotic expansion of the solution in terms of a small oscillation amplitude is constructed. In the leading steady term the two possible regimes of secondary streaming are analyzed. The fluid pumping effect of secondary streaming is studied. Energy efficient pumping regime is determined. The limits of applicability of high-frequency asymptotic solutions are established.
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REFERENCES
G. G. Stokes, ‘‘On the effect of the internal friction of fluids on the motion of pendulums,’’ Trans. Cambridge Philos. Soc. 9, 8–106 (1851).
C. Zhang, X. Guo, L. Royon, and P. Brunet, ‘‘Unveiling of the mechanisms of acoustic streaming induced by sharp edges,’’ Phys. Rev. E 102, 043110 (2020).
A. G. Yegorov and O. S. Zakharova, ‘‘The energy-optimal motion of a vibration-driven robot in a resistive medium,’’ J. Appl. Math. Mech. 74, 443–451 (2010).
D. Ahmed, M. Lu, A. Nourhani, et al., ‘‘Selectively manipulable acoustic-powered microswimmers,’’ Sci. Rep. 5, 9744 (2015).
K. Chong, S. D. Kelly, S. T. Smith, and J. D. Eldredge, ‘‘Transport of inertial particles by viscous streaming in arrays of oscillating probes,’’ Phys. Rev. E 93, 013109 (2016).
H. Zhu, P. Zhang, Z. Zhong, et al., ‘‘Acoustohydrodynamic tweezers via spatial arrangement of streaming vortices,’’ Sci. Adv. 7, eabc7885 (2021).
H. Schlichting, ‘‘Berechnung ebener periodischer Grenzschichtströmungen,’’ Phys. Zeitschr. 33, 327–335 (1932).
J. Stuart, ‘‘Double boundary layers in oscillatory viscous flow,’’ J. Fluid Mech. 24, 673–687 (1966).
C. Y. Wang, ‘‘On high-frequency oscillating viscous flows,’’ J. Fluid Mech. 32, 55–68 (1968).
N. Riley, ‘‘The steady streaming induced by a vibrating cylinder,’’ J. Fluid Mech. 68, 801–812 (1975).
A. N. Nuriev and A. G. Egorov, ‘‘Asymptotic investigation of hydrodynamic forces acting on an oscillating cylinder at finite streaming Reynolds numbers,’’ Lobachevskii J. Math. 40 (6), 794–801 (2019).
A. Nuriev, A. Egorov, and A. Kamalutdinov, ‘‘Hydrodynamic forces acting on the elliptic cylinder performing high-frequency low-amplitude multi-harmonic oscillations in a viscous fluid,’’ J. Fluid Mech. 913, A40 (2021).
J. Holtsmark, I. Johnsen, T. Sikkeland, and S. Skavlem, ‘‘Boundary layer flow near a cylindrical obstacle in an oscillating incompressible fluid,’’ Acoust. Soc. Am. 26, 26–39 (1954).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, Oxford, 1987).
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(Submitted by D. A. Gubaidullin)
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Egorov, A.G., Nuriev, A.N. Steady Streaming Generated by Low-Amplitude Oscillations of a Cylinder. Lobachevskii J Math 42, 2102–2108 (2021). https://doi.org/10.1134/S1995080221090067
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DOI: https://doi.org/10.1134/S1995080221090067