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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

REFERENCES

Arns, C., Knackstedt, M. & Mecke, K. 2002 Characterising the morphology of disordered materials. In Morphology of Condensed Matter Physics and Geometry of Spatially Complex Systems (ed. Mecke, K. R. & Stoyan, D.). Lecture Notes in Physics, vol. 600, pp. 37–74. Springer.CrossRefGoogle Scholar
Ayyalasomayajula, S., Gylfason, A., Collins, L. R., Bodenschatz, E. & Warhaft, Z. 2006 Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys. Rev. Lett. 97, 144507.CrossRefGoogle ScholarPubMed
Babiano, A., Cartwright, J. H. E., Piro, O. & Provenzale, A. 2000 Dynamics of a Small Neutrally Buoyant Sphere in a Fluid and Targeting in Hamiltonian Systems. Phys. Rev. Lett. 84, 5764–5769.CrossRefGoogle Scholar
Bec, J. 2003 Fractal clustering of inertial particles in random flows. Phys. Fluids 15, L81–L84.CrossRefGoogle Scholar
Bec, J. 2005 Multifractal concentrations of inertial particles in smooth random flows. J. Fluid Mech. 528, 255–277.CrossRefGoogle Scholar
Bec, J., Biferale, L., Bofetta, G., Lanotte, A. S., Musacchio, S. & Toschi, F. 2006 a Lyapunov exponents of heavy particles in turbulence. Phys. Fluids 18, 091702.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A. S. & Toschi, F. 2006 b Effects of vortex filaments on the velocity of tracers and heavy particles in turbulence. Phys. Fluids 18, 081702.CrossRefGoogle Scholar
Bec, J., Cencini, M. & Hillerbrand, R. 2007 Heavy particles in incompressible flows: The large stokes number asymptotics. Physica D 226, 11–22.Google Scholar
van den Berg, T. H., Luther, S., Mazzitelli, I., Rensen, J., Toschi, F. & Lohse, D. 2006 Bubbly turbulence. J. Turb. 7, 1–12.CrossRefGoogle Scholar
Bewley, G. P., Lathrop, D. P. & Sreenivasan, K. R. 2006 Superfluid helium – visualization of quantized vortices. Nature 441, 588.CrossRefGoogle ScholarPubMed
Biferale, L., Boffetta, G., Celani, A., Lanotte, A. & Toschi, F. 2005 Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids 17, 021701.CrossRefGoogle Scholar
Boivin, M., Simonin, O. & Squires, K. 1998 Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235–263.CrossRefGoogle Scholar
Bourgoin, M., Ouellette, N. T., Xu, H. T., Berg, J. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311, 835–838.CrossRefGoogle ScholarPubMed
Calzavarini, E., van den Berg, T. H., Toschi, F. & Lohse, D. 2008 Quantifying microbubble clustering in turbulent flow from single-point me asurements. Phys. Fluids 20, 040702.CrossRefGoogle Scholar
Calzavarini, E., Cencini, M., Lohse, D. & Toschi, F. 2007 Quantifying turbulence induced segregation of inertial particles. Phys. Rev. Lett. (submitted).CrossRefGoogle Scholar
Celani, A., Falkovich, G., Mazzino, A. & Seminara, A. 2005 Droplet condensation in turbulent flows. Europhys. Lett. 70, 775–781.CrossRefGoogle Scholar
Chun, J., Koch, D. L., Rani, S. L., Ahluwalia, A. & Collins, L. R. 2005 Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech. 536, 219–251.CrossRefGoogle Scholar
Crowe, C. T., Troutt, T. & Chung, J. N. 1996 Numerical models for two-phase turbulent flows. Annu. Rev. Fluid Mech. 28, 11–43.CrossRefGoogle Scholar
Druzhinin, O. A. & Elghobashi, S. 2001 Direct numerical simulation of a three-dimensional spatially developing bubble-laden mixing layer with two-way coupling. J. Fluid Mech. 429, 23–61.CrossRefGoogle Scholar
Eckmann, J. P. & Ruelle, D. 1985 Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 67, 617.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech 242, 655–700.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids A 5, 1790–1801.CrossRefGoogle Scholar
Falconer, K. J. 1990 Fractal Geometry. John Wiley & Sons.Google Scholar
Falkovich, G., Fouxon, A. & Stepanov, M. G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154.CrossRefGoogle ScholarPubMed
Gatignol, R. 1983 The Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow. J. Méc. Théori. Appl. 1, 143–160.Google Scholar
Grassberger, P. & Procaccia, I. 1984 Dimensions and entropies of strange attractors from a fluctuating dynamics approach. Physica D 13, 34–54.Google Scholar
Hadwiger, H. 1957 Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer.CrossRefGoogle Scholar
Herminghaus, S., Jacobs, K., Mecke, K., Bischof, J., Fery, A., Ibn-Elhaj, M. & Schlagowski, S. 1998 Spinodal dewetting in liquid crystal and liquid metal films. Science 282, 916–919.CrossRefGoogle ScholarPubMed
Hoyer, K., Holzner, M., Luethi, B., Guala, M., Lieberzon, A. & Kinzelback, W. 2005 3D scanning particle tracking velocimetry. Exps. Fluids 39, 923–934.CrossRefGoogle Scholar
Kerscher, M. 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. Mecke, K. R. & Stoyan, D.). Lecture Notes in Physics, vol. 554. Springer.Google Scholar
Kerscher, M., Mecke, K., Schmalzing, J., Beisbart, C., Buchert, T. & Wagner, H. 2001 Morphological fluctuations of large–scale structure: the PSCz survey. Astron. Astrophys. 373, 1–11.CrossRefGoogle Scholar
Kerscher, M., Schmalzing, J., Retzlaff, J., Borgani, S., Buchert, T., Gottlöber, S., Müller, V., Plionis, M. & Wagner, H. 1997 Minkowski functionals of Abell/ACO clusters. Mon. Not. R. Astron. Soc. 284, 73–84.CrossRefGoogle Scholar
Malkiel, E., Abras, J. N., Widder, E. A. & Katz, J. 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, 149–170.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283–315.CrossRefGoogle Scholar
Maxey, M. & Riley, J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.CrossRefGoogle Scholar
Mazzitelli, I., Lohse, D. & Toschi, F. 2003 a The effect of microbubbles on developed turbulence. Phys. Fluids 15, L5–L8.CrossRefGoogle Scholar
Mazzitelli, I., Lohse, D. & Toschi, F. 2003 b On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283–313.CrossRefGoogle Scholar
Mecke, K. 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. Mecke, K. & Stoyan, D.). Lecture Notes in Physics, vol. 554. Springer.CrossRefGoogle Scholar
Mecke, K. R., Buchert, T. & Wagner, H. 1994 Robust morphological measures for large–scale structure in the Universe. Astron. Astrophys. 288, 697–704.Google Scholar
Mecke, K. R. & Wagner, H. 1991 Euler characteristic and related measures for random geometric sets. J. Statist. Phys. 64, 843–850.CrossRefGoogle Scholar
Porta, A. L., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019.CrossRefGoogle ScholarPubMed
Upstill-Goddard, R. C. 2006 Air-sea gas exchange in the coastal zone. Esturine Coastal Shelf Sci. 70, 388–404.CrossRefGoogle Scholar
Vaillancourt, P. A., Yau, M. K., Bartello, P. & Grabowski, W. W. 2002 Microscopic approach to cloud droplet growth by condensation. part ii: Turbulence, clustering, and condensational growth. J. Atmos. Sci. 59, 3421–3435.2.0.CO;2>CrossRefGoogle Scholar
Wang, L. & Maxey, M. 1993 Settling velocity and concentration distribution of heavy particl es in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.CrossRefGoogle Scholar
Wilkin, S. L., Barenghi, C. F. & Shukurov, A. 2007 Magnetic structures produced by the small-scale dynamo. Phys. Rev. Lett. 99, 134301.CrossRefGoogle ScholarPubMed

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