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Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes number. Part 1. DNS and fluctuating force model

Published online by Cambridge University Press:  06 October 2011

Partha S. Goswami  and
V. Kumaran
Partha S. Goswami
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India
V. Kumaran*
Affiliation:
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India
*
†Email address for correspondence: kumaran@chemeng.iisc.ernet.in
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Abstract

The fluctuating force model is developed and applied to the turbulent flow of a gas–particle suspension in a channel in the limit of high Stokes number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a ‘moving Eulerian’ reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 1 - 40
Copyright
Copyright © Cambridge University Press 2011

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