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Motion of a particle near a rough wall in a viscous shear flow

Published online by Cambridge University Press:  14 October 2021

F. Charru ,
E. Larrieu ,
J.-B. Dupont  and
R. Zenit
F. Charru
Affiliation:
Institut de Mécanique des Fluides de Toulouse-UMR CNRS/INPT/UPS 5502, 2, Avenue Camille Soula, 31400 Toulouse, France
E. Larrieu
Affiliation:
Institut de Mécanique des Fluides de Toulouse-UMR CNRS/INPT/UPS 5502, 2, Avenue Camille Soula, 31400 Toulouse, France
J.-B. Dupont
Affiliation:
Institut de Mécanique des Fluides de Toulouse-UMR CNRS/INPT/UPS 5502, 2, Avenue Camille Soula, 31400 Toulouse, France
R. Zenit
Affiliation:
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, México D.F. 04510, México
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Abstract

The motion of a spherical particle along a rough bed in a simple shear viscous flow is studied experimentally for a wide range of parameters, varying the particle size and density, the fluid viscosity and the shear rate γ. The instantaneous particle velocity is calculated in the stream, transverse and vertical directions, using a high-speed video imaging system. It is found that the normalized streamwise mean particle velocity U/US, where US is the Stokes settling velocity, depends only on the dimensionless shear rate μ γ/(Δ ρ g d), this relationship being independent of the particle Reynolds number Rep. This result holds for small Rep, which was the case in our experiments (Rep < 10). The characteristic amplitude and frequency of the velocity fluctuations are also given and discussed. A model is then proposed for the mean streamwise velocity, based on ideas of Bagnold (Proc. R. Soc. Lond. A, vol. 332, 1973, p. 473) and calculations of Goldman et al. (Chem. Engng Sci., vol. 22, 1967b, p. 653) for the velocity of a particle close to a smooth plane. From this model an equivalent bed roughness and an effective friction coefficient are deduced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 431 - 453
Copyright
Copyright © Cambridge University Press 2007

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