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A Lagrangian probability-density-function model for collisional turbulent fluid–particle flows

Published online by Cambridge University Press:  11 January 2019

A. Innocenti Open the ORCID record for A. Innocenti [Opens in a new window] ,
R. O. Fox Open the ORCID record for R. O. Fox [Opens in a new window] ,
M. V. Salvetti  and
S. Chibbaro
A. Innocenti
Affiliation:
Sorbonne Université, Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond D’Alembert, F-75005 Paris, France Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso 8, 56122 Pisa, Italy
R. O. Fox
Affiliation:
Department of Chemical and Biological Engineering, 618 Bissell Road, Iowa State University, Ames, IA 50011-1098, USA
M. V. Salvetti
Affiliation:
Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso 8, 56122 Pisa, Italy
S. Chibbaro*
Affiliation:
Sorbonne Université, Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond D’Alembert, F-75005 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These clusters, in turn, can generate and sustain turbulence in the fluid phase, which we refer to as cluster-induced turbulence (CIT). In the present work, we tackle the problem of developing a framework for the stochastic modelling of moderately dense particle-laden flows, based on a Lagrangian probability-density-function formalism. This framework includes the Eulerian approach, and hence can be useful also for the development of two-fluid models. A rigorous formalism and a general model have been put forward focusing, in particular, on the two ingredients that are key in moderately dense flows, namely, two-way coupling in the carrier phase, and the decomposition of the particle-phase velocity into its spatially correlated and uncorrelated components. Specifically, this last contribution allows us to identify in the stochastic model the contributions due to the correlated fluctuating energy and to the granular temperature of the particle phase, which determine the time scale for particle–particle collisions. The model is then validated and assessed against direct-numerical-simulation data for homogeneous configurations of increasing difficulty: (i) homogeneous isotropic turbulence, (ii) decaying and shear turbulence and (iii) CIT.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 449 - 489
Copyright
© 2019 Cambridge University Press 

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