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Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence

Published online by Cambridge University Press:  06 January 2012

Yoshiyuki Tagawa
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands International Collaboration for Turbulence Research
Julián Martínez Mercado
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands International Collaboration for Turbulence Research
Vivek N. Prakash
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands International Collaboration for Turbulence Research
Enrico Calzavarini
Affiliation:
Laboratoire de Mécanique de Lille CNRS/UMR 8107, Université Lille 1 and Polytech’Lille, Cité Scientifique Av. P. Langevin, 59650 Villeneuve d’Ascq, France International Collaboration for Turbulence Research
Chao Sun
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands International Collaboration for Turbulence Research
Detlef Lohse
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands International Collaboration for Turbulence Research
Corresponding

Abstract

Three-dimensional Voronoï analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data sets from numerics in the point particle limit and one experimental data set. We study the clustering behaviour at different density ratios, particle response times (i.e. Stokes numbers ) and two Taylor–Reynolds numbers ( and 180). The probability density functions (p.d.f.s) of the Voronoï cell volumes of light and heavy particles show different behaviour from that of randomly distributed particles, i.e. fluid tracers, implying that clustering is present. The standard deviation of the p.d.f. normalized by that of randomly distributed particles is used to quantify the clustering. The clustering for both light and heavy particles is stronger for higher . Light particles show maximum clustering for around 1–2 for both Taylor–Reynolds numbers. The experimental data set shows reasonable agreement with the numerical results. The results are consistent with previous investigations employing other approaches to quantify the clustering. We also present the joint p.d.f.s of enstrophy and Voronoï volumes and their Lagrangian autocorrelations. The small Voronoï volumes of light particles correspond to regions of higher enstrophy than those of heavy particles, indicating that light particles cluster in higher vorticity regions. The Lagrangian temporal autocorrelation function of Voronoï volumes shows that the clustering of light particles lasts much longer than that of heavy or neutrally buoyant particles. Due to inertial effects arising from the density contrast with the surrounding liquid, light and heavy particles remain clustered for much longer times than the flow structures which cause the clustering.

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Papers
Copyright
Copyright © Cambridge University Press 2012

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