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Clustering instabilities in sedimenting fluid–solid systems: critical assessment of kinetic-theory-based predictions using direct numerical simulation data

Published online by Cambridge University Press:  20 June 2017

William D. Fullmer Open the ORCID record for William D. Fullmer [Opens in a new window] ,
Guodong Liu ,
Xiaolong Yin  and
Christine M. Hrenya
William D. Fullmer
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA
Guodong Liu
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China
Xiaolong Yin
Affiliation:
Petroleum Engineering Department, Colorado School of Mines, Golden, CO 80401, USA
Christine M. Hrenya*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: hrenya@colorado.edu
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Abstract

In this work the quantitative and qualitative ability of a kinetic-theory-based two-fluid model (KT-TFM) is assessed in a state of fully periodic sedimentation (fluidization), with a focus on statistically steady, unstable (clustered) states. The accuracy of KT-TFM predictions is evaluated via direct comparison to direct numerical simulation (DNS) data. The KT-TFM and DNS results span a rather wide parameter space: mean-flow Reynolds numbers on the order of 1 and 10, mean solid volume fractions from 0.1 to 0.4, solid-to-fluid density ratios from 10 to 1000 and elastic and moderately inelastic (restitution coefficient of 0.9) conditions. Data from both KT-TFM and DNS display a rich variety of statistically steady yet unstable structures (clusters). Instantaneous snapshots of KT-TFM and DNS demonstrate remarkable qualitative agreement. This qualitative agreement is quantified by calculating the critical density ratio at which the structure transitions from a chaotic, dynamic state to a regular, plug-flow state, with good overall comparisons. Further quantitative assessments of mean and fluctuating velocities show good agreement at high density ratios but weaker agreement at intermediate to low density ratios depending on the mean-flow Reynolds numbers and solid fractions. Deviations of the KT-TFM results from the DNS data were traced to a breakdown in one of the underlying assumptions of the kinetic theory derivation: high thermal Stokes number. Surprisingly, however, even though the low Knudsen number assumption, also associated with the kinetic theory derivation, is violated throughout most of the parameter space, it does not seem to affect the good quantitative accuracy of KT-TFM simulations.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions
Type
Papers
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Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 433 - 469
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© 2017 Cambridge University Press 

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Fullmer et al. supplementary movie

Chaotic regime: Evolution of particles from a single DNS realization in a dp-thick xy-slice about the z-centerline colored by filtered solids concentration. Conditions are: Ar = 1432, <φ> = 0.15, e = 1.0, and ρ* = 30.

Download Fullmer et al. supplementary movie(Video)
Video 3.9 MB

Fullmer et al. supplementary movie

Chaotic regime: Evolution of solids concentration from KT-TFM simulation in the xy-plane at the z-centerline. Conditions are: Ar = 1432, <φ> = 0.15, e = 1.0, and ρ* = 32.

Download Fullmer et al. supplementary movie(Video)
Video 5.3 MB

Fullmer et al. supplementary movie

2-D plug regime: Evolution of particles from a single DNS realization in a dp-thick xy-slice about the z-centerline colored by filtered solids concentration. Conditions are: Ar = 1432, <φ> = 0.15, e = 1.0, and ρ* = 100.

Download Fullmer et al. supplementary movie(Video)
Video 12 MB

Fullmer et al. supplementary movie

2-D plug regime: Evolution of solids concentration from KT-TFM simulation in the xy-plane at the z-centerline. Conditions are: Ar = 1432, <φ> = 0.15, e = 1.0, and ρ* = 100.

Download Fullmer et al. supplementary movie(Video)
Video 4.9 MB

Fullmer et al. supplementary movie

1-D plug regime: Evolution of particles from a single DNS realization in a dp-thick xy-slice about the z-centerline colored by filtered solids concentration. Conditions are: Ar = 1432, <φ> = 0.15, e = 1.0, and ρ* = 1000.

Download Fullmer et al. supplementary movie(Video)
Video 14.1 MB

Fullmer et al. supplementary movie

1-D plug regime: Evolution of solids concentration from KT-TFM simulation in the xy-plane at the z-centerline. Conditions are: Ar = 1432, <φ> = 0.15, e = 1.0, and ρ* = 1000.

Download Fullmer et al. supplementary movie(Video)
Video 4.7 MB