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Doklady Physics

, Volume 63, Issue 6, pp 253–256 | Cite as

The Force Acting on a Cylinder in a Ring Flow of a Viscous Fluid with a Small Eccentric Displacement

Mechanics
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Abstract

A system consisting of two circular cylinders one inside the other with parallel axes is considered. The outer cylinder of radius R2 is fixed, and the inner cylinder of radius R1 rotates with a sufficiently large angular velocity. The region between the cylinders is filled with an incompressible viscous fluid and, in the case of coaxial cylinders, Couette flow along circular trajectories arises. Upon an eccentric small displacement of the axis of the inner cylinder, the symmetry of the flow is disturbed and a force exerted on the inner cylinder by the fluid is created. Within the ideal fluid model, the force depends linearly on the transverse velocities and accelerations of the cylinder. In a viscous fluid, the force depends on the previous motion of the cylinder. It is expressed in terms of the velocity functional by analogy with the Basset force acting on a ball moving in a viscous fluid with a variable velocity.

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References

  1. 1.
    P. L. Kapitsa, Zh. Tekh. Fiz. 9 (2), 124 (1939).Google Scholar
  2. 2.
    V. F. Kopiev, S. A. Chernyshev, and M. A. Yudin. J. Appl. Math. Mech. 81 (2), 148 (2017).MathSciNetCrossRefGoogle Scholar
  3. 3.
    H. Lamb, Hydrodynamics, 6th ed. (University Press, Cambridge, 1932; OGIZ, Moscow–Lenigrad, 1947).MATHGoogle Scholar
  4. 4.
    L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1975; Nauka, Moscow, 1986).Google Scholar
  5. 5.
    A. G. Petrov, Analytical Hydrodynamics (Fizmatlit, Moscow, 2009) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Ishlinskii Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

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