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Numerical study of double-diffusive sedimentation in thermally stratified fluid

Published online by Cambridge University Press:  27 April 2020

Chen-Yen Hung ,
Yang-Yao Niu  and
Yi-Ju Chou Open the ORCID record for Yi-Ju Chou [Opens in a new window]
Chen-Yen Hung
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei10617, Taiwan
Yang-Yao Niu
Affiliation:
Department of Aerospace Engineering, Tamkang University, New Taipei City25137, Taiwan
Yi-Ju Chou*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei10617, Taiwan Center of Advanced Study of Theoretical Sciences, National Taiwan University, Taipei10617, Taiwan
*
†Email address for correspondence: yjchou@iam.ntu.edu.tw
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Abstract

We conduct Eulerian–Lagrangian simulations to study double-diffusive sedimentation in stratified flows. The results show the pattern of double-diffusive sedimentation and the transition to the pattern of Rayleigh–Taylor instability when the size of particles increases. In cases of double-diffusive sedimentation, our simulation results show little variation in the temperature-to-particle flux ratio among cases with various particle sizes and initial concentrations, which is consistent with previous theoretical derivations and experimental observations. The energy budget is analysed to show that the settling enhancement is a result of the thermal effect combined with shear dissipation and that the thermal contribution decreases as the size increases. Based on the balance of the energy budget, velocity scaling was derived for the quasi-steady state in the thermally controlled region, which can be used to characterize the plumes’ final velocity of double-diffusive sedimentation. Moreover, adopting some values from the simulation results yields a velocity criterion with which to distinguish different sedimentation patterns. Finally, we investigate changes in the particle-laden plumes below the region of the apparent temperature gradient at which secondary instabilities occur in the form of significant horizontal flow motion. We show that the resulting initial shift of the dominant modes can be approximated with the existing theoretical analysis of collective instabilities for salt fingers. A simple scaling argument for the change in the total cross-sectional area of particle-laden plumes is presented, which is then used to scale the resulting enhanced sedimentation.

JFM classification

Convection: Double diffusive convection Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 893 , 25 June 2020 , A27
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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