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Numerical study of convective sedimentation through a sharp density interface

Published online by Cambridge University Press:  06 July 2017

Yun-Chuan Shao ,
Chen-Yen Hung  and
Yi-Ju Chou Open the ORCID record for Yi-Ju Chou [Opens in a new window]
Yun-Chuan Shao
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
Chen-Yen Hung
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
Yi-Ju Chou*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan Taida Institute of Mathematical Sciences, National Taiwan University, Taipei, 106, Taiwan Ocean Technology Research Center, National Taiwan University, Taipei, 106, Taiwan
*
†Email address for correspondence: [email protected]
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Abstract

We conduct numerical simulations using the Eulerian–Lagrangian approach to investigate the formation of the leaking, finger, and stable-settling modes in convective sedimentation when a sediment-laden fluid layer descends through a sharply stratified ambient flow. We show that the temporal evolution of the sedimentation process for the leaking mode can be divided into three stages, including (in temporal order) Rayleigh–Taylor instability, convection, and leaking stages. The presence of sheet-like descending plumes of suspended particles is an important characteristic of the leaking mode, which marks the existence of the leaking stage. For larger particles, the motion is more dominated by gravitational settling and less affected by buoyancy-induced flow motion. The resulting lack of the leaking stage for the larger-particle case leads to persistent finger-like plumes of suspended particles, known as the finger mode. The stable-settling mode occurs when the particles are large and the concentration is dilute such that flow motion due to Rayleigh–Taylor instability has no effect on the particle motion, and the convective motion of suspended particles is insignificant. For the third stage of the leaking mode, which is also the final stationary state, we derive the criterion for the occurrence of the leaking pattern from a scaling argument of the viscous boundary layer. The criterion is further confirmed by the present simulation results and previous laboratory experiments. Through analysis of the energy budget and the vertical flux, we show that although the settling of individual particles is accelerated, the presence of the sheet-like descending plumes in the leaking mode does not contribute to an efficient settling enhancement compared with the finger mode and the Rayleigh–Taylor instability, i.e., the cases with no background stratification. This implies a negative effect on the settling enhancement for small suspended particles when a stable background density stratification exists. In addition, simulations using the equilibrium Eulerian description for the suspended particles are also conducted to examine the difference between the present Lagrangian particle approach and the conventional Eulerian model.

JFM classification

Convection: Buoyancy-driven instability Geophysical and Geological Flows: Geophysical and Geological Flows Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 513 - 549
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Copyright
© 2017 Cambridge University Press 

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