Journal of Fluid Mechanics

Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity

Renwei  Mei a1p1, Christopher J.  Lawrence a1 and Ronald J.  Adrian a1
a1 Department of Theoretical & Applied Mechanics, University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801, USA

Article author query
mei r   [Google Scholar] 
lawrence cj   [Google Scholar] 
adrian rj   [Google Scholar] 


Unsteady flow over a stationary sphere with small fluctuations in the free-stream velocity is considered at finite Reynolds number using a finite-difference method. The dependence of the unsteady drag on the frequency of the fluctuations is examined at various Reynolds numbers. It is found that the classical Stokes solution of the unsteady Stokes equation does not correctly describe the behaviour of the unsteady drag at low frequency. Numerical results indicate that the force increases linearly with frequency when the frequency is very small instead of increasing linearly with the square root of the frequency as the classical Stokes solution predicts. This implies that the force has a much shorter memory in the time domain. The incorrect behaviour of the Basset force at large times may explain the unphysical results found by Reeks & Mckee (1984) wherein for a particle introduced to a turbulent flow the initial velocity difference between the particle and fluid has a finite contribution to the long-time particle diffusivity. The added mass component of the force at finite Reynolds number is found to be the same as predicted by creeping flow and potential theories. Effects of Reynolds number on the unsteady drag due to the fluctuating free-stream velocity are presented. The implications for particle motion in turbulence are discussed.

(Published Online April 26 2006)
(Received March 20 1990)
(Revised June 13 1991)

p1 Present address: Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL 32611, USA.