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

Renwei Mei, Christopher J. Lawrence, Ronald Adrian

Research output: Contribution to journalArticle

109 Citations (Scopus)

Abstract

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 Recks & 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.

Original languageEnglish (US)
Pages (from-to)613-631
Number of pages19
JournalJournal of Fluid Mechanics
Volume233
StatePublished - Dec 1991
Externally publishedYes

Fingerprint

free flow
drag
Drag
Reynolds number
flow theory
potential theory
unsteady flow
particle motion
Unsteady flow
Finite difference method
turbulent flow
Turbulent flow
diffusivity
Turbulence
turbulence
low frequencies
Data storage equipment
Fluids
fluids

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity. / Mei, Renwei; Lawrence, Christopher J.; Adrian, Ronald.

In: Journal of Fluid Mechanics, Vol. 233, 12.1991, p. 613-631.

Research output: Contribution to journalArticle

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N2 - 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 Recks & 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.

AB - 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 Recks & 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.

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