Settling disks in a linearly stratified fluid

We consider the unbounded settling dynamics of a circular disk of diameter $d$ and finite thickness $h$ evolving with a vertical speed $U$ in a linearly stratified fluid of kinematic viscosity $\unicode[STIX]{x1D708}$ and diffusivity $\unicode[STIX]{x1D705}$ of the stratifying agent, at moderate Rey...

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Veröffentlicht in:Journal of fluid mechanics 2020-02, Vol.885, Article A2
Hauptverfasser: Mercier, M. J., Wang, S., Péméja, J., Ern, P., Ardekani, A. M.
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Wang, S.
Péméja, J.
Ern, P.
Ardekani, A. M.
description We consider the unbounded settling dynamics of a circular disk of diameter $d$ and finite thickness $h$ evolving with a vertical speed $U$ in a linearly stratified fluid of kinematic viscosity $\unicode[STIX]{x1D708}$ and diffusivity $\unicode[STIX]{x1D705}$ of the stratifying agent, at moderate Reynolds numbers ( $Re=Ud/\unicode[STIX]{x1D708}$ ). The influence of the disk geometry (diameter $d$ and aspect ratio $\unicode[STIX]{x1D712}=d/h$ ) and of the stratified environment (buoyancy frequency $N$ , viscosity and diffusivity) are experimentally and numerically investigated. Three regimes for the settling dynamics have been identified for a disk reaching its gravitational equilibrium level. The disk first falls broadside-on, experiencing an enhanced drag force that can be linked to the stratification. A second regime corresponds to a change of stability for the disk orientation, from broadside-on to edgewise settling. This occurs when the non-dimensional velocity $U/\sqrt{\unicode[STIX]{x1D708}N}$ becomes smaller than some threshold value. Uncertainties in identifying the threshold value is discussed in terms of disk quality. It differs from the same problem in a homogeneous fluid which is associated with a fixed orientation (at its initial value) in the Stokes regime and a broadside-on settling orientation at low, but finite Reynolds numbers. Finally, the third regime corresponds to the disk returning to its broadside orientation after stopping at its neutrally buoyant level.
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J. ; Wang, S. ; Péméja, J. ; Ern, P. ; Ardekani, A. M.</creator><creatorcontrib>Mercier, M. J. ; Wang, S. ; Péméja, J. ; Ern, P. ; Ardekani, A. M.</creatorcontrib><description>We consider the unbounded settling dynamics of a circular disk of diameter $d$ and finite thickness $h$ evolving with a vertical speed $U$ in a linearly stratified fluid of kinematic viscosity $\unicode[STIX]{x1D708}$ and diffusivity $\unicode[STIX]{x1D705}$ of the stratifying agent, at moderate Reynolds numbers ( $Re=Ud/\unicode[STIX]{x1D708}$ ). The influence of the disk geometry (diameter $d$ and aspect ratio $\unicode[STIX]{x1D712}=d/h$ ) and of the stratified environment (buoyancy frequency $N$ , viscosity and diffusivity) are experimentally and numerically investigated. Three regimes for the settling dynamics have been identified for a disk reaching its gravitational equilibrium level. The disk first falls broadside-on, experiencing an enhanced drag force that can be linked to the stratification. A second regime corresponds to a change of stability for the disk orientation, from broadside-on to edgewise settling. This occurs when the non-dimensional velocity $U/\sqrt{\unicode[STIX]{x1D708}N}$ becomes smaller than some threshold value. Uncertainties in identifying the threshold value is discussed in terms of disk quality. It differs from the same problem in a homogeneous fluid which is associated with a fixed orientation (at its initial value) in the Stokes regime and a broadside-on settling orientation at low, but finite Reynolds numbers. 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J.</au><au>Wang, S.</au><au>Péméja, J.</au><au>Ern, P.</au><au>Ardekani, A. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Settling disks in a linearly stratified fluid</atitle><jtitle>Journal of fluid mechanics</jtitle><date>2020-02-25</date><risdate>2020</risdate><volume>885</volume><artnum>A2</artnum><issn>0022-1120</issn><eissn>1469-7645</eissn><abstract>We consider the unbounded settling dynamics of a circular disk of diameter $d$ and finite thickness $h$ evolving with a vertical speed $U$ in a linearly stratified fluid of kinematic viscosity $\unicode[STIX]{x1D708}$ and diffusivity $\unicode[STIX]{x1D705}$ of the stratifying agent, at moderate Reynolds numbers ( $Re=Ud/\unicode[STIX]{x1D708}$ ). The influence of the disk geometry (diameter $d$ and aspect ratio $\unicode[STIX]{x1D712}=d/h$ ) and of the stratified environment (buoyancy frequency $N$ , viscosity and diffusivity) are experimentally and numerically investigated. Three regimes for the settling dynamics have been identified for a disk reaching its gravitational equilibrium level. The disk first falls broadside-on, experiencing an enhanced drag force that can be linked to the stratification. A second regime corresponds to a change of stability for the disk orientation, from broadside-on to edgewise settling. This occurs when the non-dimensional velocity $U/\sqrt{\unicode[STIX]{x1D708}N}$ becomes smaller than some threshold value. Uncertainties in identifying the threshold value is discussed in terms of disk quality. It differs from the same problem in a homogeneous fluid which is associated with a fixed orientation (at its initial value) in the Stokes regime and a broadside-on settling orientation at low, but finite Reynolds numbers. 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subjects Aspect ratio
Brunt-vaisala frequency
Computational fluid dynamics
Diameters
Diffusion coefficients
Diffusivity
Disks
Drag
Dynamics
Fluids
Gravity
Kinematic viscosity
Kinematics
Orientation
Pollutants
Reynolds number
Settling
Stability
Stratification
Studies
Velocity
Viscosity
title Settling disks in a linearly stratified fluid
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