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Lattice Boltzmann simulations of low-Reynolds-number flows past fluidized spheres: effect of inhomogeneities on the drag force

Published online by Cambridge University Press:  07 November 2017

Gregory J. Rubinstein Open the ORCID record for Gregory J. Rubinstein [Opens in a new window] ,
Ali Ozel ,
Xiaolong Yin ,
J. J. Derksen  and
Sankaran Sundaresan
Gregory J. Rubinstein
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
Ali Ozel
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
Xiaolong Yin
Affiliation:
Department of Petroleum Engineering, Colorado School of Mines, Golden, CO 80401, USA
J. J. Derksen
Affiliation:
School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK
Sankaran Sundaresan*
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: sundar@princeton.edu
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Abstract

The formation of inhomogeneities within fluidized beds, both in terms of the particle configurations and flow structures, have a pronounced effect on the interaction force between the fluid and particles. While recent numerical studies have begun to probe the effects of inhomogeneities on the drag force at the particle scale, the applicability of prior microscale constitutive drag relations is still limited to random, homogeneous distributions of particles. Since an accurate model for the drag force is needed to predict the fluidization behaviour, the current study utilizes the lessons of prior inhomogeneity studies in order to derive a robust drag relation that is both able to account for the effect of inhomogeneities and applicable as a constitutive closure to larger-scale fluidization simulations. Using fully resolved lattice Boltzmann simulations of systems composed of fluid and monodisperse spherical particles in the low-Reynolds-number (Re) regime, the fluid–particle drag force, normalized by the ideal Stokes drag force, is found to significantly decrease, over a range of length scales, as the extent of inhomogeneities increases. The extent of inhomogeneities is found to most effectively be quantified through one of two subgrid-scale quantities: the scalar variance of the particle volume fraction or the drift flux, which is the correlation between the particle volume fraction and slip velocity. Scale-similar models are developed to estimate these two subgrid measures over a wide range of system properties. Two new drag constitutive models are proposed that are not only functions of the particle volume fraction and the Stokes number ( $St$ ), but also dependent on one of these subgrid measures for the extent of inhomogeneities. Based on the observed, appreciable effect of inhomogeneities on drag, these new low-Re drag models represent a significant advancement over prior constitutive relations.

JFM classification

Multiphase and Particle-laden Flows: Fluidized beds Low-Reynolds-number flows: Low-Reynolds-number flows Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows

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Papers
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Journal of Fluid Mechanics , Volume 833 , 25 December 2017 , pp. 599 - 630
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© 2017 Cambridge University Press 

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