Abstract
The paper is devoted to the study of the problem of high-frequency low-amplitude harmonic oscillations of a circular cylinder in a viscous incompressible fluid. The study develops the classical method of successive asymptotic expansions of a solution into internal and outer, steady and oscillating components in terms of a small parameter. The case of finite streaming Reynolds numbers is considered. Using the original method for calculation of the hydrodynamic force components from external flow characteristics, analytical expressions for four terms of the force expansion were found. The obtained results allow to evaluate not only a linear response to perturbations of flow caused by oscillations of the cylinder, but also the effect of the non-linear interaction of harmonics in the boundary layer.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. G. Stokes, “On the effect of the internal friction of fluids on the motion of pendulums,” Trans. Camb. Phil. Soc. 9, 8–106 (1851).
T. Sarpkaya and M. Isaacson, Mechanics of Wave Forces on Offshore Structures (Van Nostrand Reinhold, New York, 1981).
N. D. P. Barltrop and A. J. Adams, Dynamics of Fixed Marine Structures (Butterworth-Heinemann, London, 1991).
E. Naudascher, Flow-Induced Vibrations, An Engineering Guide (Balkema, 1994).
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).
P. W. Bearman, M. J. Downie, J. M. R. Graham, and E. D. Obasaju, “Forces on cylinders in viscous oscillatory flow at low Keulegan-Carpenter numbers,” J. Fluid Mech. 154, 337–356 (1985).
P. Justesen, “A numerical study of oscillating flow around a circular cylinder,” J. Fluid Mech. 222, 157–196 (1991).
A. N. Nuriev, A. G. Egorov, and O. N. Zaitseva, “Numerical analysis of secondary flows around an oscillating cylinder,” J. Appl. Mech. Tech. Phys. 59, 451–459 (2018).
A. G. Egorov, A. M. Kamalutdinov, and A. N. Nuriev, “Evaluation of aerodynamic forces acting on oscillating cantilever beams based on the study of the damped flexural vibration of aluminium test samples,” J. Sound Vibrat. 421, 334–347 (2018).
J. Stuart, “Double boundary layers in oscillatory viscous flow,” J. Fluid Mech. 24, 673–687 (1966).
H. Schlichting, “Berechnung ebener periodischer Grenzschichtströmungen,” Phys. Zeit. 33, 327–335 (1932).
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).
E. W. Haddon and N. Riley, “The steady streaming induced between oscillating circular cylinders,” Q. J. Mech. Appl. Math. 32, 265–282 (1979).
S. K. Kim, “Streaming flows generated by high-frequency small-amplitude oscillations of arbitrarily shaped cylinders,” Phys. Fluids, A: Fluid Dyn. 1, 975–985 (1989).
F. Noca, D. Shiels, and D. Jeon, “A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives,” J. Fluids Struct. 13, 551–578 (1999).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Nuriev, A.N., Egorov, A.G. Asymptotic Investigation of Hydrodynamic Forces Acting on an Oscillating Cylinder at Finite Streaming Reynolds Numbers. Lobachevskii J Math 40, 794–801 (2019). https://doi.org/10.1134/S1995080219060180
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080219060180