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Dimensionality and morphology of particle and bubble clusters in turbulent flow


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.

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S. Ayyalasomayajula , A. Gylfason , L. R. Collins , E. Bodenschatz & Z. Warhaft 2006 Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys. Rev. Lett. 97, 144507.

A. Babiano , J. H. E. Cartwright , O. Piro & A. Provenzale 2000 Dynamics of a Small Neutrally Buoyant Sphere in a Fluid and Targeting in Hamiltonian Systems. Phys. Rev. Lett. 84, 57645769.

J. Bec 2003 Fractal clustering of inertial particles in random flows. Phys. Fluids 15, L81L84.

J. Bec 2005 Multifractal concentrations of inertial particles in smooth random flows. J. Fluid Mech. 528, 255277.

J. Bec , L. Biferale , G. Bofetta , A. S. Lanotte , S. Musacchio & F. Toschi 2006 aLyapunov exponents of heavy particles in turbulence. Phys. Fluids 18, 091702.

J. Bec , L. Biferale , M. Cencini , A. S. Lanotte & F. Toschi 2006 bEffects of vortex filaments on the velocity of tracers and heavy particles in turbulence. Phys. Fluids 18, 081702.

T. H. van den Berg , S. Luther , I. Mazzitelli , J. Rensen , F. Toschi & D. Lohse 2006 Bubbly turbulence. J. Turb. 7, 112.

G. P. Bewley , D. P. Lathrop & K. R. Sreenivasan 2006 Superfluid helium – visualization of quantized vortices. Nature 441, 588.

L. Biferale , G. Boffetta , A. Celani , A. Lanotte & F. Toschi 2005 Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids 17, 021701.

M. Boivin , O. Simonin & K. Squires 1998 Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235263.

M. Bourgoin , N. T. Ouellette , H. T. Xu , J. Berg & E. Bodenschatz 2006 The role of pair dispersion in turbulent flow. Science 311, 835838.

E. Calzavarini , T. H. van den Berg , F. Toschi & D. Lohse 2008 Quantifying microbubble clustering in turbulent flow from single-point me asurements. Phys. Fluids 20, 040702.

A. Celani , G. Falkovich , A. Mazzino & A. Seminara 2005 Droplet condensation in turbulent flows. Europhys. Lett. 70, 775781.

J. Chun , D. L. Koch , S. L. Rani , A. Ahluwalia & L. R. Collins 2005 Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech. 536, 219251.

C. T. Crowe , T. Troutt & J. N. Chung 1996 Numerical models for two-phase turbulent flows. Annu. Rev. Fluid Mech. 28, 1143.

O. A. Druzhinin & S. Elghobashi 2001 Direct numerical simulation of a three-dimensional spatially developing bubble-laden mixing layer with two-way coupling. J. Fluid Mech. 429, 2361.

S. Elghobashi & G. Truesdell 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech 242, 655700.

S. Elghobashi & G. Truesdell 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids A 5, 17901801.

G. Falkovich , A. Fouxon & M. G. Stepanov 2002 Acceleration of rain initiation by cloud turbulence. Nature 419, 151154.

H. Hadwiger 1957 Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer.

S. Herminghaus , K. Jacobs , K. Mecke , J. Bischof , A. Fery , M. Ibn-Elhaj & S. Schlagowski 1998 Spinodal dewetting in liquid crystal and liquid metal films. Science 282, 916919.

K. Hoyer , M. Holzner , B. Luethi , M. Guala , A. Lieberzon & W. Kinzelback 2005 3D scanning particle tracking velocimetry. Exps. Fluids 39, 923934.

M. Kerscher 2000 Statistical analysis of large–scale structure in the Universe. In Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation (ed. K. R. Mecke & D. Stoyan ). Lecture Notes in Physics, vol. 554. Springer.

M. Kerscher , K. Mecke , J. Schmalzing , C. Beisbart , T. Buchert & H. Wagner 2001 Morphological fluctuations of large–scale structure: the PSCz survey. Astron. Astrophys. 373, 111.

M. Kerscher , J. Schmalzing , J. Retzlaff , S. Borgani , T. Buchert , S. Gottlöber , V. Müller , M. Plionis & H. Wagner 1997 Minkowski functionals of Abell/ACO clusters. Mon. Not. R. Astron. Soc. 284, 7384.

E. Malkiel , J. N. Abras , E. A. Widder & J. Katz 2006 On the spatial distribution and nearest neighbor distance between particles in the water column determined from in situ holographic measurements. J. Plankton Res. 28, 149170.

C. Marchioli & A. Soldati 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283315.

M. Maxey & J. Riley 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883889.

I. Mazzitelli , D. Lohse & F. Toschi 2003 aThe effect of microbubbles on developed turbulence. Phys. Fluids 15, L5L8.

I. Mazzitelli , D. Lohse & F. Toschi 2003 b On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283313.

K. Mecke 2000 Additivity, convexity, and beyond: Application of minkowski functionals in statistical physics. In Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial structures and Pattern Formation (ed. K. Mecke & D. Stoyan ). Lecture Notes in Physics, vol. 554. Springer.

K. R. Mecke & H. Wagner 1991 Euler characteristic and related measures for random geometric sets. J. Statist. Phys. 64, 843850.

A. L. Porta , G. A. Voth , A. M. Crawford , J. Alexander & E. Bodenschatz 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 10171019.

R. C. Upstill-Goddard 2006 Air-sea gas exchange in the coastal zone. Esturine Coastal Shelf Sci. 70, 388404.

P. A. Vaillancourt , M. K. Yau , P. Bartello & W. W. Grabowski 2002 Microscopic approach to cloud droplet growth by condensation. part ii: Turbulence, clustering, and condensational growth. J. Atmos. Sci. 59, 34213435.

L. Wang & M. Maxey 1993 Settling velocity and concentration distribution of heavy particl es in homogeneous isotropic turbulence. J. Fluid Mech. 256, 2768.

S. L. Wilkin , C. F. Barenghi & A. Shukurov 2007 Magnetic structures produced by the small-scale dynamo. Phys. Rev. Lett. 99, 134301.

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Journal of Fluid Mechanics
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Type Description Title

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.

 Video (6.7 MB)
6.7 MB

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).

 Video (7.4 MB)
7.4 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.

 Video (7.5 MB)
7.5 MB


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