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Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers

Published online by Cambridge University Press:  20 July 2017

J. R. Agudo Open the ORCID record for J. R. Agudo [Opens in a new window] ,
C. Illigmann ,
G. Luzi ,
A. Laukart ,
A. Delgado  and
A. Wierschem
J. R. Agudo
Affiliation:
Institute of Fluid Mechanics, FAU Busan Campus, University of Erlangen-Nuremberg, 618-230 Busan, Republic of Korea
C. Illigmann
Affiliation:
Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), D-91058, Erlangen, Germany
G. Luzi
Affiliation:
Institute of Fluid Mechanics, FAU Busan Campus, University of Erlangen-Nuremberg, 618-230 Busan, Republic of Korea
A. Laukart
Affiliation:
Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), D-91058, Erlangen, Germany
A. Delgado
Affiliation:
Institute of Fluid Mechanics, FAU Busan Campus, University of Erlangen-Nuremberg, 618-230 Busan, Republic of Korea Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), D-91058, Erlangen, Germany
A. Wierschem*
Affiliation:
Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), D-91058, Erlangen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

We study the incipient motion of single spheres in steady shear flow on regular substrates at low particle Reynolds numbers. The substrate consists of a monolayer of regularly arranged fixed beads, in which the spacing between beads is varied resulting in different angles of repose and exposures of the particle to the main flow. The flow-induced forces and the level of flow penetration into the substrate are determined numerically. Since experiments in this range had shown that the critical Shields number is independent of inertia but strongly dependent on the substrate geometry, the particle Reynolds number was fixed to 0.01 in the numerical study. Numerics indicates that rolling motion is always preferred to sliding and that the flow penetration is linearly dependent on the spacing between the substrate particles. Besides, we propose an analytical model for the incipient motion. The model is an extension of Goldman’s classical result for a single sphere near a plain surface taking into account the angle of repose, flow orientation with respect to substrate topography and shielding of the sphere to the linear shear flow. The effective level of flow penetration is the only external parameter. The model, applied to triangular and quadratic arrangements with different spacings, is able to predict the dependence of the critical Shields number on the geometry and on the orientation of the substrate. The model is in very good agreement with numerical results. For well-exposed particles, we observed that the minimum critical Shields number for a certain angle of repose does not depend sensitively on the considered arrangement. At large angles of repose, as expected in fully armoured beds, the model is consistent with experimental results for erodible beds at saturated conditions.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 284 - 314
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© 2017 Cambridge University Press 

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