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The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number

Published online by Cambridge University Press:  26 April 2006

Phillip M. Lovalenti  and
John F. Brady
Phillip M. Lovalenti
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
John F. Brady
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

The unsteady force acting on a sphere that is held fixed in a steady uniform flow with small-amplitude oscillations is evaluated to O(Re) for small Reynolds number Re. Good agreement is shown with the numerical results of Mei, Lawrence & Adrian (1991) up to Re ≈ 0.5. The analytical result is transformed by Fourier inversion to allow for an arbitrary time-dependent motion which is small relative to the steady uniform flow. This yields a history-dependent force which has an integration kernel that decays exponentially for large time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 607 - 614
Copyright
© 1993 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions, pp. 504–515. Dover.
Lovalenti, P.M. & Brady, J.F. 1993 The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561–605.Google Scholar
Maxworthy, T. 1965 Accurate measurements of sphere drag at low Reynolds numbers. J. Fluid Mech. 23, 369–372.Google Scholar
Mei, R. & Adrian, R. J. 1992 Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number. J. Fluid Mech. 237, 323–341 (referred to herein as MA).Google Scholar
Mei, R., Lawrence, C. J. & Adrian, R. J. 1991 Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity. J. Fluid Mech. 233, 613–631 (referred to herein as MLA).Google Scholar
Sano, T. 1981 Unsteady flow past a sphere at low Reynolds number. J. Fluid Mech. 112, 433–441.Google Scholar