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Dimensionality and morphology of particle and bubble clusters in turbulent flow

Published online by Cambridge University Press:  30 June 2008

ENRICO CALZAVARINI ,
MARTIN KERSCHER ,
DETLEF LOHSE  and
FEDERICO TOSCHI
ENRICO CALZAVARINI
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Center for Fluid Dynamics, and Impact-Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands International Collaboration for Turbulence Research
MARTIN KERSCHER
Affiliation:
Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstrasse 39, D-80333 München, Germany
DETLEF LOHSE
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Center for Fluid Dynamics, and Impact-Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands International Collaboration for Turbulence Research
FEDERICO TOSCHI
Affiliation:
IAC-CNR, Istituto per le Applicazioni del Calcolo, Viale del Policlinico 137, I-00161 Roma, Italy and INFN, via Saragat 1, I-44100 Ferrara, Italy International Collaboration for Turbulence Research
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Abstract

We conduct numerical experiments to investigate the spatial clustering of particles and bubbles in simulations of homogeneous and isotropic turbulence. On varying the Stokes parameter and the densities, striking differences in the clustering of the particles can be observed. To quantify these visual findings we use the Kaplan–Yorke dimension. This local scaling analysis shows a dimension of approximately 1.4 for the light bubble distribution, whereas the distribution of very heavy particles shows a dimension of approximately 2.6. However, clearly different parameter combinations yield the same dimensions. To overcome this degeneracy and to further develop the understanding of clustering, we perform a morphological (geometrical and topological) analysis of the particle distribution. For such an analysis, Minkowski functionals have been successfully employed in cosmology, in order to quantify the global geometry and topology of the large-scale distribution of galaxies. In the context of dispersed multiphase flow, these Minkowski functionals – being morphological order parameters – allow us to discern the filamentary structure of the light particle distribution from the wall-like distribution of heavy particles around empty interconnected tunnels. Movies are available with the online version of the paper.

JFM classification

Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 607 , 25 July 2008 , pp. 13 - 24
Copyright
Copyright © Cambridge University Press 2008

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References

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Calzavarini et al. supplementary movie

Movie 1. Visualization of particle distribution in a turbulent flow field (Re = 75). Three-dimensional snapshot of light particles (bubbles) with St = 0.6 and β=3. In the model system used in this numerical study, particles are characterized by two parameters: the Stokes number St (which is the ratio between the particle response time and the Kolmogorov time scale) and the parameter β which is related to the particle--fluid density ratio ( β = 3 ρ_f /(ρ_f + 2 ρ_p) ). Particles lighter than the fluid cluster in highly vortical regions, the opposite happens for heavy particles (see Movie 3), while neutrally buoyant particles remains on average homogeneously distributed (see Movie 2).

Download Calzavarini et al. supplementary movie(Video)
Video 7.4 MB

Calzavarini et al. supplementary movie

Movie 2. Visualization of particle distribution in a turbulent flow field (Re = 75). Three-dimensional snapshot of neutrally buoyant particles with St = 0.6 and β=1.

Download Calzavarini et al. supplementary movie(Video)
Video 6.7 MB

Calzavarini et al. supplementary movie

Movie 3. Visualization of particle distribution in a turbulent flow field (Re = 75). Three-dimensional snapshot of heavy particles with St = 0.6 and β=0.

Download Calzavarini et al. supplementary movie(Video)
Video 7.5 MB