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

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...

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Veröffentlicht in:Journal of fluid mechanics 2017-08, Vol.825, p.284-314
Hauptverfasser: Agudo, J. R., Illigmann, C., Luzi, G., Laukart, A., Delgado, A., Wierschem, A.
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container_issue
container_start_page 284
container_title Journal of fluid mechanics
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creator Agudo, J. R.
Illigmann, C.
Luzi, G.
Laukart, A.
Delgado, A.
Wierschem, A.
description 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.
doi_str_mv 10.1017/jfm.2017.370
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R. ; Illigmann, C. ; Luzi, G. ; Laukart, A. ; Delgado, A. ; Wierschem, A.</creator><creatorcontrib>Agudo, J. R. ; Illigmann, C. ; Luzi, G. ; Laukart, A. ; Delgado, A. ; Wierschem, A.</creatorcontrib><description>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. 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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. 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R.</au><au>Illigmann, C.</au><au>Luzi, G.</au><au>Laukart, A.</au><au>Delgado, A.</au><au>Wierschem, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2017-08-25</date><risdate>2017</risdate><volume>825</volume><spage>284</spage><epage>314</epage><pages>284-314</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><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.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2017.370</doi><tpages>31</tpages><orcidid>https://orcid.org/0000-0003-0025-6252</orcidid></addata></record>
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source Cambridge University Press Journals Complete
subjects Angle of repose
Angles (geometry)
Banks (topography)
Beads
Computational fluid dynamics
Fluid flow
Fluid mechanics
Forces (mechanics)
Incipient motion
Inertia
Mathematical models
Movement
Orientation
Penetration
Reynolds number
Rolling (ship motion)
Rolling motion
Sediments
Shear flow
Shielding
Slope
Spheres
Substrates
Topography
Topography (geology)
title Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers
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