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Coherent clusters of inertial particles in homogeneous turbulence

Published online by Cambridge University Press:  03 November 2017

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

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.

Type
Papers
Copyright
© 2017 Cambridge University Press 

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References

Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J. C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77105.Google Scholar
Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30 (8), 23432353.Google Scholar
Bec, J. 2003 Fractal clustering of inertial particles in random flows. Phys. Fluids 15 (11), L81L84.CrossRefGoogle Scholar
Bec, J. 2005 Multifractal concentrations of inertial particles in smooth random flows. J. Fluid Mech. 528, 255277.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98, 084502.Google Scholar
Bec, J., Homann, H. & Ray, S. S. 2014 Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phys. Rev. Lett. 112, 184501.CrossRefGoogle ScholarPubMed
Bergougnoux, L., Bouchet, G., Lopez, D. & Guazzelli, E. 2014 The motion of solid spherical particles falling in a cellular flow field at low Stokes number. Phys. Fluids 26 (9), 093302.Google Scholar
Bermejo-Moreno, I., Pullin, D. I. & Horiuti, K. 2009 Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence. J. Fluid Mech. 620, 121166.Google Scholar
Bragg, A. D. & Collins, L. R. 2014 New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles. New J. Phys. 16 (5), 055013.Google Scholar
Buxton, O. R. H. & Ganapathisubramani, B. 2010 Amplification of enstrophy in the far field of an axisymmetric turbulent jet. J. Fluid Mech. 651, 483502.CrossRefGoogle Scholar
Calzavarini, E., Kerscher, M., Lohse, D. & Toschi, F. 2008 Dimensionality and morphology of particle and bubble clusters in turbulent flow. J. Fluid Mech. 607, 1324.Google Scholar
Chen, L., Goto, S. & Vassilicos, J. C. 2006 Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553, 143154.Google Scholar
Coleman, S. W. & Vassilicos, J. C. 2009 A unified sweep-stick mechanism to explain particle clustering in two-and three-dimensional homogeneous, isotropic turbulence. Phys. Fluids 21 (11), 113301.Google Scholar
Dejoan, A. & Monchaux, R. 2013 Preferential concentration and settling of heavy particles in homogeneous turbulence. Phys. Fluids 25 (1), 013301.Google Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169209.Google Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309329.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655700.Google Scholar
Esmaily-Moghadam, M. & Mani, A. 2016 Analysis of the clustering of inertial particles in turbulent flows. Phys. Rev. Fluids 1 (8), 084202.Google Scholar
Falconer, K. 2004 Fractal Geometry: Mathematical Foundations and Applications. Wiley.Google Scholar
Falkovich, G. & Pumir, A. 2004 Intermittent distribution of heavy particles in a turbulent flow. Phys. Fluids 16 (7), L47L50.CrossRefGoogle Scholar
Ferenc, J. S. & Néda, Z. 2007 On the size distribution of Poisson Voronoi cells. Physica A 385 (2), 518526.Google Scholar
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6 (11), 37423749.CrossRefGoogle Scholar
Frankel, A., Pouransari, H., Coletti, F. & Mani, A. 2016 Settling of heated particles in homogeneous turbulence. J. Fluid Mech. 792, 869893.Google Scholar
Good, G. H., Gerashchenko, S. & Warhaft, Z. 2012 Intermittency and inertial particle entrainment at a turbulent interface: the effect of the large-scale eddies. J. Fluid Mech. 694, 371398.CrossRefGoogle Scholar
Good, G. H., Ireland, P. J., Bewley, G. P., Bodenschatz, E., Collins, L. R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.Google Scholar
Goto, S. & Vassilicos, J. C. 2006 Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence. Phys. Fluids 18 (11), 115103.Google Scholar
Goto, S. & Vassilicos, J. C. 2008 Sweep-stick mechanism of heavy particle clustering in fluid turbulence. Phys. Rev. Lett. 100, 054503.Google Scholar
Grassberger, P. & Procaccia, I. 1983 Characterization of strange attractors. Phys. Rev. Lett. 50, 346349.Google Scholar
Gualtieri, P., Picano, F. & Casciola, C. M. 2009 Anisotropic clustering of inertial particles in homogeneous shear flow. J. Fluid Mech. 629, 2539.Google Scholar
Gustavsson, K. & Mehlig, B. 2016 Statistical models for spatial patterns of heavy particles in turbulence. Adv. Phys. 65 (1), 157.Google Scholar
Gustavsson, K., Vajedi, S. & Mehlig, B. 2014 Clustering of particles falling in a turbulent flow. Phys. Rev. Lett. 112, 214501.Google Scholar
Hamlington, P. E., Schumacher, J. & Dahm, W. J. A. 2008 Direct assessment of vorticity alignment with local and nonlocal strain rates in turbulent flows. Phys. Fluids 20 (11), 111703.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program. Stanford University.Google Scholar
Ijzermans, R. H. A., Meneguz, E. & Reeks, M. W. 2010 Segregation of particles in incompressible random flows: singularities, intermittency and random uncorrelated motion. J. Fluid Mech. 653, 99136.Google Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016 The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects. J. Fluid Mech. 796, 659711.Google Scholar
Kidanemariam, A. G., Chan-Braun, C., Doychev, T. & Uhlmann, M. 2013 Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15 (2), 025031.Google Scholar
Kostinski, A. B. & Shaw, R. A. 2001 Scale-dependent droplet clustering in turbulent clouds. J. Fluid Mech. 434, 389398.Google Scholar
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277 (1), 109134.Google Scholar
Leung, T., Swaminathan, N. & Davidson, P. A. 2012 Geometry and interaction of structures in homogeneous isotropic turbulence. J. Fluid Mech. 710, 453481.Google Scholar
Lundgren, T. S. 2003 Linearly forced isotropic turbulence. In Annual Research Briefs, Center for Turbulence Research, pp. 461473. Stanford University.Google Scholar
Matsuda, K., Onishi, R. & Takahashi, K. 2017 Influence of gravitational settling on turbulent droplet clustering and radar reflectivity factor. Flow Turbul. Combust. 98 (1), 327340.Google Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441465.Google Scholar
Maxey, M. R. & Corrsin, S. 1986 Gravitational settling of aerosol particles in randomly oriented cellular flow fields. J. Atmos. Sci. 43 (11), 11121134.Google Scholar
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111133.Google Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a Voronoï analysis. Phys. Fluids 22 (10), 103304.Google Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2012 Analyzing preferential concentration and clustering of inertial particles in turbulence. Intl J. Multiphase Flow 40, 118.CrossRefGoogle Scholar
Ni, R., Ouellette, N. T. & Voth, G. A. 2014 Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence. J. Fluid Mech. 743, R3.Google Scholar
Nielsen, P. 1993 Turbulence effects on the settling of suspended particles. J. Sedim. Res. 63 (5).Google Scholar
Nilsen, C., Andersson, H. I. & Zhao, L. 2013 A Voronoï analysis of preferential concentration in a vertical channel flow. Phys. Fluids 25 (11), 115108.Google Scholar
Obligado, M., Teitelbaum, T., Cartellier, A., Mininni, P. & Bourgoin, M. 2014 Preferential concentration of heavy particles in turbulence. J. Turbul. 15 (5), 293310.Google Scholar
Park, Y. & Lee, C. 2014 Gravity-driven clustering of inertial particles in turbulence. Phys. Rev. E 89, 061004.Google Scholar
Pouransari, H. & Mani, A. 2017 Effects of preferential concentration on heat transfer in particle-based solar receivers. J. Sol. Energy Eng. 139 (2), 021008.Google Scholar
Pouransari, H., Mortazavi, M. & Mani, A. 2015 Parallel variable density particle-laden turbulence simulation. In Annual Research Briefs, Center for Turbulence Research, pp. 4354.Google Scholar
Rabencov, B. & van Hout, R. 2015 Voronoi analysis of beads suspended in a turbulent square channel flow. Intl J. Multiphase Flow 68, 1013.Google Scholar
Rosa, B., Parishani, H., Ayala, O. & Wang, L. P. 2016 Settling velocity of small inertial particles in homogeneous isotropic turbulence from high-resolution DNS. Intl J. Multiphase Flow 83, 217231.Google Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17 (9), 095106.Google Scholar
Saw, E. W., Shaw, R. A., Ayyalasomayajula, S., Chuang, P. Y. & Gylfason, Á. 2008 Inertial clustering of particles in high-Reynolds-number turbulence. Phys. Rev. Lett. 100, 214501.Google Scholar
de Silva, C. M., Philip, J., Chauhan, K., Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers. Phys. Rev. Lett. 111, 044501.Google Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 11691178.Google Scholar
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23 (1), 539604.Google Scholar
Sumbekova, S., Cartellier, A., Aliseda, A. & Bourgoin, M. 2017 Preferential concentration of inertial sub-Kolmogorov particles: the roles of mass loading of particles, Stokes numbers, and Reynolds numbers. Phys. Rev. Fluids 2 (2), 024302.Google Scholar
Sundaram, S. & Collins, L. R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75109.CrossRefGoogle Scholar
Tagawa, Y., Mercado, J. M., Prakash, V. N., Calzavarini, E., Sun, C. & Lohse, D. 2012 Three-dimensional Lagrangian Voronoi analysis for clustering of particles and bubbles in turbulence. J. Fluid Mech. 693, 201215.Google Scholar
Tsinober, A., Kit, E. & Dracos, T. 1992 Experimental investigation of the field of velocity gradients in turbulent flows. J. Fluid Mech. 242, 169192.Google Scholar
Uhlmann, M. & Doychev, T. 2014 Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion. J. Fluid Mech. 752, 310348.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 120.Google Scholar
Wang, L. P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 2768.Google Scholar
Wang, L. P., Wexler, A. S. & Zhou, Y. 2000 Statistical mechanical description and modelling of turbulent collision of inertial particles. J. Fluid Mech. 415, 117153.CrossRefGoogle Scholar
Woittiez, E. J. P., Jonker, H. J. J. & Portela, L. M. 2009 On the combined effects of turbulence and gravity on droplet collisions in clouds: a numerical study. J. Atmos. Sci. 66 (7), 19261943.Google Scholar
Wood, A. M., Hwang, W. & Eaton, J. K. 2005 Preferential concentration of particles in homogeneous and isotropic turbulence. Intl J. Multiphase Flow 31 (10), 12201230.Google Scholar
Yoshimoto, H. & Goto, S. 2007 Self-similar clustering of inertial particles in homogeneous turbulence. J. Fluid Mech. 577, 275286.Google Scholar
Zaichik, L. I. & Alipchenkov, V. M. 2009 Statistical models for predicting pair dispersion and particle clustering in isotropic turbulence and their applications. New J. Phys. 11 (10), 103018.Google Scholar
Zamansky, R., Coletti, F., Massot, M. & Mani, A. 2016 Turbulent thermal convection driven by heated inertial particles. J. Fluid Mech. 809, 390437.Google Scholar