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Simulation of sedimentation of two spheres with different densities in a square tube

Published online by Cambridge University Press:  29 May 2020

Deming Nie Open the ORCID record for Deming Nie [Opens in a new window]  and
Jianzhong Lin Open the ORCID record for Jianzhong Lin [Opens in a new window]
Deming Nie
Affiliation:
Institute of Fluid Mechanics, China Jiliang University, Hangzhou, Zhejiang310018, PR China
Jianzhong Lin*
Affiliation:
State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, Zhejiang310027, PR China
*
†Email address for correspondence: mecjzlin@public.zju.edu.cn
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Abstract

We simulated the sedimentations of two unequal spheres with different densities in a square tube for Galileo numbers (Ga) from 5 to 25, resulting in a Reynolds number range of $0.8\leqslant Re_{T}\leqslant 17.3$ based on the terminal settling velocity. The sedimentation of spheres with different densities is dynamically more complex than that of identical spheres. At high Ga the spheres oscillate in the centreline plane of the tube, where they are initially released from rest. By contrast, the spheres move to the diagonal or reverse–diagonal plane of the tube at low Ga, reaching a steady or periodic state depending on the density difference between them. A phase diagram illustrates the transitions between different sedimentation behaviours depending on Ga and the density difference. A possible mechanism for these behaviours is also presented. Furthermore, we compare two-dimensional (2-D) and three-dimensional computations for our system to attain a better understanding of the hydrodynamic interactions between two unequal spheres at low but finite Reynolds number. Comparing relative trajectories, periods of oscillation and flow features shows that 2-D circular cylinders oscillate much more strongly and frequently than spheres under the same flow conditions. In particular, spheres do not have the discontinuity in period that arises in the 2-D case from the change in rotation sign of a heavy particle.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A12
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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