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Computationally generated constitutive models for particle phase rheology in gas-fluidized suspensions

Published online by Cambridge University Press:  04 December 2018

Yile Gu Open the ORCID record for Yile Gu [Opens in a new window] ,
Ali Ozel ,
Jari Kolehmainen Open the ORCID record for Jari Kolehmainen [Opens in a new window]  and
Sankaran Sundaresan
Yile Gu*
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08540, USA
Ali Ozel
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08540, USA School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
Jari Kolehmainen
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08540, USA
Sankaran Sundaresan
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08540, USA
*
†Email address for correspondence: [email protected]
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Abstract

Developing constitutive models for particle phase rheology in gas-fluidized suspensions through rigorous statistical mechanical methods is very difficult when complex inter-particle forces are present. In the present study, we pursue a computational approach based on results obtained through Eulerian–Lagrangian simulations of the fluidized state. Simulations were performed in a periodic domain for non-cohesive and mildly cohesive (Geldart Group A) particles. Based on the simulation results, we propose modified closures for pressure, bulk viscosity, shear viscosity and the rate of dissipation of pseudo-thermal energy. For non-cohesive particles, results in the high granular temperature $T$ regime agree well with constitutive expressions afforded by the kinetic theory of granular materials, demonstrating the validity of the methodology. The simulations reveal a low $T$ regime, where the inter-particle collision time is determined by gravitational fall between collisions. Inter-particle cohesion has little effect in the high $T$ regime, but changes the behaviour appreciably in the low $T$ regime. At a given $T$, a cohesive particle system manifests a lower pressure at low particle volume fractions when compared to non-cohesive systems; at higher volume fractions, the cohesive assemblies attain higher coordination numbers than the non-cohesive systems, and experience greater pressures. Cohesive systems exhibit yield stress, which is weakened by particle agitation, as characterized by $T$. All these effects are captured through simple modifications to the kinetic theory of granular materials for non-cohesive materials.

JFM classification

Rarefied Gas Flow: Kinetic theory Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Rheology
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 318 - 349
Copyright
© 2018 Cambridge University Press 

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