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Coherent clusters of inertial particles in homogeneous turbulence

Published online by Cambridge University Press:  03 November 2017

Lucia Baker Open the ORCID record for Lucia Baker [Opens in a new window] ,
Ari Frankel ,
Ali Mani Open the ORCID record for Ali Mani [Opens in a new window]  and
Filippo Coletti
Lucia Baker
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Ari Frankel
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Ali Mani
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Filippo Coletti
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

Despite the widely acknowledged significance of turbulence-driven clustering, a clear topological definition of particle cluster in turbulent dispersed multiphase flows has been lacking. Here we introduce a definition of coherent cluster based on self-similarity, and apply it to distributions of heavy particles in direct numerical simulations of homogeneous isotropic turbulence, with and without gravitational acceleration. Clusters show self-similarity already at length scales larger than twice the Kolmogorov length, as indicated by the fractal nature of their surface and by the power-law decay of their size distribution. The size of the identified clusters extends to the integral scale, with average concentrations that depend on the Stokes number but not on the cluster dimension. Compared to non-clustered particles, coherent clusters show a stronger tendency to sample regions of high strain and low vorticity. Moreover, we find that the clusters align themselves with the local vorticity vector. In the presence of gravity, they tend to align themselves vertically and their fall speed is significantly different from the average settling velocity: for moderate fall speeds they experience stronger settling enhancement than non-clustered particles, while for large fall speeds they exhibit weakly reduced settling. The proposed approach for cluster identification leverages the Voronoï diagram method, but is also compatible with other tessellation techniques such as the classic box-counting method.

JFM classification

Turbulent Flows: Homogeneous turbulence Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 833 , 25 December 2017 , pp. 364 - 398
Copyright
© 2017 Cambridge University Press 

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