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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.
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