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

Fullmer, William D.; Liu, Guodong; Yin, Xiaolong; Hrenya, Christine M.

doi:10.1017/jfm.2017.295

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

Journal Article · Tue Jun 20 00:00:00 EDT 2017 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2017.295· OSTI ID:1832979

^[1]; Liu, Guodong ^[2]; Yin, Xiaolong ^[3]; Hrenya, Christine M. ^[4]

Univ. of Colorado, Boulder, CO (United States); Univ of Colorado at Boulder
Harbin Inst. of Technology (China)
Colorado School of Mines, Golden, CO (United States)
Univ. of Colorado, Boulder, CO (United States)

In this paper 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Fossil Energy (FE)

Grant/Contract Number:: FE0026298

OSTI ID:: 1832979

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 823; ISSN 0022-1120

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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