Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-14T09:52:45.424Z Has data issue: false hasContentIssue false
  • English
  • Français

Divergence and convergence of inertial particles in high-Reynolds-number turbulence

Published online by Cambridge University Press:  26 October 2020

Thibault Oujia Open the ORCID record for Thibault Oujia [Opens in a new window] ,
Keigo Matsuda Open the ORCID record for Keigo Matsuda [Opens in a new window]  and
Kai Schneider Open the ORCID record for Kai Schneider [Opens in a new window]
Thibault Oujia*
Affiliation:
Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université, CNRS and Centrale Marseille, 39 rue F. Joliot-Curie, 13453Marseille Cedex 13, France
Keigo Matsuda
Affiliation:
Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université, CNRS and Centrale Marseille, 39 rue F. Joliot-Curie, 13453Marseille Cedex 13, France Research Institute for Value-Added-Information Generation (VAiG), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 3173-25 Showa-machi, Kanazawa-ku, Yokohama, 236-0001Japan
Kai Schneider
Affiliation:
Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université, CNRS and Centrale Marseille, 39 rue F. Joliot-Curie, 13453Marseille Cedex 13, France
*
†Email address for correspondence: thibault.oujia@etu.univ-amu.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Inertial particle data from three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence at high Reynolds number are analysed using Voronoi tessellation of the particle positions and considering different Stokes numbers. A finite-time measure to quantify the divergence of the particle velocity by determining the volume change rate of the Voronoi cells is proposed. For inertial particles, the probability distribution function of the divergence deviates from that for fluid particles. Joint probability distribution functions of the divergence and the Voronoi volume illustrate that the divergence is most prominent in cluster regions and less pronounced in void regions. For larger volumes, the results show negative divergence values which represent cluster formation (i.e. particle convergence) and, for small volumes, the results show positive divergence values which represents cluster destruction/void formation (i.e. particle divergence). Moreover, when the Stokes number increases the divergence takes larger values, which gives some evidence why fine clusters are less observed for large Stokes numbers.

JFM classification

Turbulent Flows: Isotropic turbulence Multiphase and Particle-laden Flows: Multiphase flow Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 905 , 25 December 2020 , A14
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ariki, T., Yoshida, K., Matsuda, K. & Yoshimatsu, K. 2018 Scale-similar clustering of heavy particles in the inertial range of turbulence. Phys. Rev. E 97 (3), 033109.CrossRefGoogle ScholarPubMed
Aurenhammer, F. 1991 Voronoi diagrams-a survey of a fundamental geometric data structure. ACM Comput. Surv. 23 (3), 345–405.CrossRefGoogle Scholar
Baker, L., Frankel, A., Mani, A. & Coletti, F. 2017 Coherent clusters of inertial particles in homogeneous turbulence. J. Fluid Mech. 833, 364–398.CrossRefGoogle Scholar
Barber, C. B., Dobkin, D. P. & Huhdanpaa, H. T. 1996 The quickhull algorithm for convex hulls, ACM transactions on mathematical software. ACM Trans. Math. Softw. 22 (4), 469–483.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 (8), 084502.CrossRefGoogle ScholarPubMed
Bragg, A. D., Ireland, P. J. & Collins, L. R. 2015 Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. Phys. Rev. E 92 (2), 023029.CrossRefGoogle ScholarPubMed
Chen, L., Goto, S. & Vassilicos, J. C. 2006 Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553, 143–154.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
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.CrossRefGoogle Scholar
Dejoan, A. & Monchaux, R. 2013 Preferential concentration and settling of heavy particles in homogeneous turbulence. Phys. Fluids 25 (1), 013301.CrossRefGoogle Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.CrossRefGoogle Scholar
Elghobashi, S. 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech. 51, 217–244.CrossRefGoogle Scholar
Elperin, T., Kleeorin, N., L'vov, V. S., Rogachevskii, I. & Sokoloff, D. 2002 Clustering instability of the spatial distribution of inertial particles in turbulent flows. Phys. Rev. E 66 (3), 036302.CrossRefGoogle ScholarPubMed
Elperin, T., Kleeorin, N. & Rogachevskii, I. 1996 Self-excitation of fluctuations of inertial particle concentration in turbulent fluid flow. Phys. Rev. Lett. 77 (27), 5373–5376.CrossRefGoogle ScholarPubMed
Esmaily-Moghadam, M. & Mani, A. 2016 Analysis of the clustering of inertial particles in turbulent flows. Phys. Rev. Fluids 1 (8), 084202.CrossRefGoogle Scholar
Ferenc, J. S. & Néda, Z. 2007 On the size distribution of Poisson Voronoi cells. Physica A 385 (2), 518–526.CrossRefGoogle 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.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J. C. 2008 Sweep-stick mechanism of heavy particle clustering in fluid turbulence. Phys. Rev. Lett. 100 (5), 054503.CrossRefGoogle ScholarPubMed
Gustavsson, K. & Mehlig, B. 2011 Ergodic and non-ergodic clustering of inertial particles. Europhys. Lett. 96 (6), 60012.CrossRefGoogle Scholar
Gustavsson, K. & Mehlig, B. 2016 Statistical models for spatial patterns of heavy particles in turbulence. Adv. Phys. 65 (1), 1–57.CrossRefGoogle Scholar
Gustavsson, K., Vajedi, S. & Mehlig, B. 2014 Clustering of particles falling in a turbulent flow. Phys. Rev. Lett. 112 (21), 214501.CrossRefGoogle Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016 The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects. J. Fluid Mech. 796, 617–658.CrossRefGoogle Scholar
Matsuda, K. & Onishi, R. 2019 Turbulent enhancement of radar reflectivity factor for polydisperse cloud droplets. Atmos. Chem. Phys. 19, 1785.CrossRefGoogle Scholar
Matsuda, K., Onishi, R., Hirahara, M., Kurose, R., Takahashi, K. & Komori, S. 2014 Influence of microscale turbulent droplet clustering on radar cloud observations. J. Atmos. Sci. 71 (10), 3569–3582.CrossRefGoogle Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Momenifar, M. & Bragg, A. D. 2020 Local analysis of the clustering, velocities and accelerations of particles settling in turbulence. Phys. Rev. Fluids 5 (3), 034306.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a Voronoi analysis. Phys. Fluids 22 (10), 103304.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2012 Analyzing preferential concentration and clustering of inertial particles in turbulence. Intl J. Multiphase Flow 40, 1–18.CrossRefGoogle Scholar
Obligado, M., Teitelbaum, T., Cartellier, A., Mininni, P. & Bourgoin, M. 2014 Preferential concentration of heavy particles in turbulence. J. Turbul. 15 (5), 293–310.CrossRefGoogle Scholar
Onishi, R., Baba, Y. & Takahashi, K. 2011 Large-scale forcing with less communication in finite-difference simulations of stationary isotropic turbulence. J. Comput. Phys. 230 (10), 4088–4099.CrossRefGoogle Scholar
Petersen, A., Baker, L. & Coletti, F. 2019 Experimental study of inertial particles clustering and settling in homogeneous turbulence. J. Fluid Mech. 864, 925–970.CrossRefGoogle Scholar
Robinson, A. 1956 On the motion of small particles in a potential field of flow. Commun. Pure Appl. Maths 9 (1), 69–84.CrossRefGoogle Scholar
Salazar, J. P. L. C. & Collins, L. R. 2012 Inertial particle relative velocity statistics in homogeneous isotropic turbulence. J. Fluid Mech. 696, 45–66.CrossRefGoogle Scholar
Shaw, R. A. 2003 Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35 (1), 183–227.CrossRefGoogle 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.CrossRefGoogle Scholar
Tagawa, Y., Mercado, J. M., Prakash, V. N., Calzavarini, E., Sun, C. & Lohse, D. 2012 Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence. J. Fluid Mech. 693, 201–215.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Wilkinson, M. & Mehlig, B. 2005 Caustics in turbulent aerosols. Europhys. Lett. 71 (2), 186–192.CrossRefGoogle Scholar