Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T16:47:56.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent pair dispersion of inertial particles

Published online by Cambridge University Press:  09 February 2010

J. BEC ,
L. BIFERALE ,
A. S. LANOTTE ,
A. SCAGLIARINI  and
F. TOSCHI
J. BEC
Affiliation:
Université de Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d'Azur, Laboratoire Cassiopée, Boulevard de l'Observatoire, 06300 Nice, France
L. BIFERALE
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
A. S. LANOTTE*
Affiliation:
ISAC-CNR, Istituto di Scienze dell'Atmosfera e del Clima, Via Fosso del Cavaliere 100, 00133 Roma and INFN, Sezione di Lecce, 73100 Lecce, Italy
A. SCAGLIARINI
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
F. TOSCHI
Affiliation:
Department of Physics and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, and Istituto per le Applicazioni del Calcolo CNR, Viale del Policlinico 137, 00161 Roma, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The relative dispersion of pairs of inertial point particles in incompressible, homogeneous and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ ~ 200 and Reλ ~ 400, corresponding to resolutions of 5123 and 20483 grid points, respectively. The evolution of both heavy and light particle pairs is analysed by varying the particle Stokes number and the fluid-to-particle density ratio. For particles much heavier than the fluid, the range of available Stokes numbers is St ∈ [0.1 : 70], while for light particles the Stokes numbers span the range St ∈ [0.1 : 3] and the density ratio is varied up to the limit of vanishing particle density. For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle velocity statistics, and it lasts until heavy particle velocities have relaxed towards the underlying flow velocities. At such large scales, a second regime starts where heavy particles separate as tracers' particles would do. As a consequence, at increasing inertia, a larger transient stage is observed, and the Richardson diffusion of simple tracers is recovered only at large times and large scales. These features also arise from a statistical closure of the equation of motion for heavy particle separation that is proposed and is supported by the numerical results. In the case of light particles with high density ratio, strong small-scale clustering leads to a considerable fraction of pairs that do not separate at all, although the mean separation increases with time. This effect strongly alters the shape of the probability density function of light particle separations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 645 , 25 February 2010 , pp. 497 - 528
Copyright
Copyright © Cambridge University Press 2010

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

Abrahamson, J. 1975 Collision rates of small particles in a vigorously turbulent fluid. Chem. Engng Sci. 30, 1371–1379.CrossRefGoogle Scholar
Ayyalasomayajula, S., Warhaft, Z. & Collins, L. R. 2008 Modeling inertial particle acceleration statistics in isotropic turbulence. Phys. Fluids 20, 095104.CrossRefGoogle Scholar
van Aartrijk, M. & Clercx, H. J. H. 2009 Dispersion of heavy particles in stably stratified turbulence. Phys. Fluids 21, 033304.CrossRefGoogle Scholar
Balkovsky, E., Falkovich, G. & Fouxon, A. 2001 Intermittent distribution of inertial particles in turbulent flows. Phys. Rev. Lett. 86, 2790–2793.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence II. The relative motion of particles. Proc. Camb. Philos. Soc. 48, 345–362.CrossRefGoogle Scholar
Bec, J. 2003 Fractal clustering of inertial particles in random flows. Phys. Fluids 15, L81–L84.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A. S., Musacchio, S. & Toschi, F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Cencini, M., Lanotte, A. S., Musacchio, S. & Toschi, F. 2007 a Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98, 084502.CrossRefGoogle ScholarPubMed
Bec, J., Biferale, L., Lanotte, A. S., Toschi, F. & Scagliarini, A. 2009 Intermittency in the velocity of heavy particles in turbulence. J. Fluid Mech (in press)CrossRefGoogle Scholar
Bec, J., Celani, A., Cencini, M. & Musacchio, S. 2005 Clustering and collisions of heavy particles in random smooth flows. Phys. Fluids 17, 073301.CrossRefGoogle Scholar
Bec, J., Cencini, M. & Hillerbrand, R. 2007 b Heavy particles in incompressible flows: the large Stokes number asymptotics. Physica D 226, 11–22.Google Scholar
Bec, J., Cencini, M., Hillerbrand, R. & Turitsyn, K. 2008 Stochastic suspensions of heavy particles. Physica D 237, 2037–2050.CrossRefGoogle Scholar
Biferale, L., Boffetta, G., Celani, A., Devenish, B. J., Lanotte, A. S. & Toschi, F. 2005 Lagrangian statistics of particle pairs in homogeneous isotropic turbulence. Phys. Fluids 17, 115101.CrossRefGoogle Scholar
Biferale, L., Boffetta, G., Celani, A., Lanotte, A. S. & Toschi, F. 2006 Lagrangian statistics of fully developed turbulence. J. Turbul. 7, 6 (1–12).CrossRefGoogle Scholar
Boffetta, G., De Lillo, F. & Gamba, A. 2004 Large scale inhomogeneity of inertial particles in turbulent flows. Phys. Fluids 16, L20–L24.CrossRefGoogle Scholar
Boffetta, G. & Sokolov, M. 2002 Statistics of two-particle dispersion in two-dimensional turbulence. Phys. Fluids 14, 3224–3232.CrossRefGoogle Scholar
Bourgoin, M., Ouelette, N. T., Xu, H., 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 a Quantifying microbubble clustering in turbulent flow from single-point measurements. Phys. Fluids 20, 040702-040702-6.CrossRefGoogle Scholar
Calzavarini, E., Kerscher, M., Lohse, D. & Toschi, F. 2008 b Dimensionality and morphology of particle and bubble clusters in turbulent flow. J. Fluid Mech. 607, 13–24.CrossRefGoogle Scholar
Cencini, M., Bec, J., Biferale, L., Boffetta, G., Celani, A., Lanotte, A. S., Musacchio, S. & Toschi, F. 2006 Dynamics and statistics of heavy particles in turbulent flows. J. Turbul. 7, 36 (1–16).CrossRefGoogle Scholar
Chen, S., Doolen, G. D., Kraichnan, R. H. & She, Z.-S. 1993 On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence. Phys. Fluids A 5, 458–463.CrossRefGoogle Scholar
Chen, L., Goto, S. & Vassilicos, J. C. 2006 Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553, 143–154.Google Scholar
Chun, J., Koch, D. L., Rani, S., Ahluwalia, A. & Collins, L. R. 2005 Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech. 536, 219–251.CrossRefGoogle Scholar
Collins, L. R. & Keswani, A. 2004 Reynolds number scaling of particle clustering in turbulent aerosols. New J. Phys. 6, 119.CrossRefGoogle Scholar
Csanady, G. 1980 Turbulent Diffusion in the Environment. Geophysics and Astrophysics Monographs, vol. 3. D. Reidel Publishing Company.Google Scholar
Derevich, I. V. 2008 Relative particle velocity in a turbulent flow. Fluid Dyn. 43, 357–368.CrossRefGoogle Scholar
Derevyanko, S. A., Falkovich, G., Turitsyn, K. & Turitsyn, S. 2007 Lagrangian and Eulerian descriptions of inertial particles in random flows. J. Turbul. 8, 16 (1–19).CrossRefGoogle Scholar
Douady, S., Couder, Y. & Brachet, M.-E. 1991 Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986.CrossRefGoogle ScholarPubMed
Eaton, J. K. & Fessler, J. L. 1994 Preferential concentrations of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.CrossRefGoogle Scholar
El Maihy, A. & Nicolleau, F. 2005 Investigation of the dispersion of heavy-particle pairs and Richardson's law using kinematic simulation. Phys. Rev. E 71, 046307.CrossRefGoogle ScholarPubMed
Falkovich, G., Gawedzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913–975.CrossRefGoogle Scholar
Falkovich, G., Fouxon, A. & Stepanov, M. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154.CrossRefGoogle ScholarPubMed
Falkovich, G. & Pumir, A. 2004 Intermittent distribution of heavy particles in a turbulent flow. Phys. Fluids 16, L47–L51.CrossRefGoogle Scholar
Falkovich, G. & Pumir, A. 2007 Sling effect in collision of water droplet in turbulent clouds. J. Atm. Sci. 64, 4497–4505.CrossRefGoogle Scholar
Fouxon, I. & Horvai, P. 2008 Separation of heavy particles in turbulence. Phys. Rev. Lett. 100 040601.CrossRefGoogle ScholarPubMed
Frisch, U. 1995 Turbulence. The legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gerashchenko, S., Sharp, N. S., Neuscamman, S. & Warhaft, Z. 2008 Lagrangian measurements of inertial particle accelerations in a turbulent boundary layer. J. Fluid Mech. 617, 255–281.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J. C. 2008 Sweep-stick mechanism of heavy particle clustering in fluid turbulence. Phys. Rev. Lett. 100, 054503.CrossRefGoogle ScholarPubMed
Gotoh, T. & Fukayama, D. 2001 Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 86, 3775–3778.CrossRefGoogle ScholarPubMed
Gylfason, A., Ayyalasomayajula, S., Bodenschatz, E. & Warhaft, Z. 2006 Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys. Rev. Lett 97, 144507.Google Scholar
Jullien, M.-C., Paret, J. & Tabeling, P. 1999 Richardson pair dispersion in two-dimensional turbulence. Phys. Rev. Lett. 82, 2872–2876.CrossRefGoogle Scholar
Maxey, M. R. 1987 The motion of small spherical particles in a cellular flow field. Phys. Fluids 30, 1915–1928.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. 1983 Equation of motion of a small rigid sphere in a non-uniform flow. Phys. Fluids 26, 883–889.CrossRefGoogle Scholar
Mehlig, B. & Wikinson, M. 2004 Coagulation by random velocity fields as a Kramers problem. Phys. Rev. Lett. 92, 250602.CrossRefGoogle Scholar
Meneveau, C. 1996 Transition between viscous and inertial-range scaling of turbulence structure functions. Phys. Rev. E 54, 3657–3663.CrossRefGoogle ScholarPubMed
Monin, A. S. & Yaglom, A. M. 2007 Statistical Fluid Mechanics, Volume 2: Mechanics of Turbulence. MIT.Google Scholar
Olla, P. 2002 Transport properties of heavy particles in high Reynolds number turbulence. Phys. Fluids 14, 4266–4277.CrossRefGoogle Scholar
Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223.CrossRefGoogle Scholar
Ouellette, N. T., Xu, H., Bourgoin, M. & Bodenschatz, E. 2006 An experimental study of turbulent relative dispersion models. New J. Phys. 8, 109 (1–22).CrossRefGoogle Scholar
Post, S. & Abraham, J. 2002 Modeling the outcome of drop-drop collisions in Diesel sprays. Intl J. Multiphase Flow 28, 997–1019.CrossRefGoogle Scholar
Qureshi, N. M., Arrieta, U., Baudet, C., Cartellier, A., Gagne, Y. & Bourgoin, M. 2008 Acceleration statistics of inertial particles in turbulent flow. Eur. Phys. J. B 66, 531–536.CrossRefGoogle Scholar
Qureshi, N. M., Bourgoin, M., Baudet, C., Cartellier, A. & Gagne, Y. 2007 Turbulent transport of material particles: an experimental study of finite-size effects. Phys. Rev. Lett 99, 184502.CrossRefGoogle ScholarPubMed
Reade, W. C. & Collins, L. R. 2000 A numerical study of the particle size distribution of an aerosol undergoing turbulent coagulation. J. Fluid Mech. 415, 45–64.CrossRefGoogle Scholar
Richardson, L. F. 1926 Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. Lond. Ser. A 110, 709–737.Google Scholar
Salazar, J. P. L. C. & Collins, L. R. 2009 Two-particle dispersion in isotropic turbulent flows. Ann. Rev. Fluid Mech 41, 405–432.CrossRefGoogle Scholar
Sawford, B. 2001 Turbulent relative dispersion. Ann. Rev. Fluid Mech. 33, 289–317.CrossRefGoogle Scholar
Sawford, B., Yeung, P. K. & Hackl, J. F. 2008 Reynolds number dependence of relative dispersion statistics in isotropic turbulence. Phys. Fluids 20, 065111 (1–13).CrossRefGoogle Scholar
Shaw, R. A. 2003 Particle–turbulence interactions in atmospheric clouds. Ann. Rev. Fluid Mech. 35, 183–227.CrossRefGoogle Scholar
Sigurgeirsson, H. & Stuart, A. M. 2002 A Model for preferential concentration. Phys. Fluids 14, 4352–4361.CrossRefGoogle Scholar
Simonin, O., Février, P. & Laviéville, J. 2002 On the spatial distribution of heavy-particle velocities in turbulent flow: from continuous field to particulate chaos. J. Turbul. 3, 40.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3, 1169–1178.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Ann. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Volk, R., Calzavarini, E., Verhille, G., Lohse, D., Mordant, N., Pinton, J.-F. & Toschi, F. 2008 Acceleration of heavy and light particles in turbulence: comparison between experiments and direct numerical simulations. Physica D: Nonlinear Phenomena 237, 2084–2089.CrossRefGoogle Scholar
Volk, R., Mordant, N., Verhille, G. & Pinton, J.-F. 2008 Laser Doppler measurement of inertial particle and bubble accelerations in turbulence. Europhys. Lett. 81, 34002.CrossRefGoogle Scholar
Weinan, E. & Vanden Eijnden, E. 2000 Generalized flows, intrinsic stochasticity, and turbulent transport. Proc. Nat. Acad. Sci. (USA) 97, 8200–8205.Google Scholar
Wilkinson, M. & Mehlig, B. 2005 Caustics in turbulent aerosols. Europhys. Lett. 71, 186–192.CrossRefGoogle Scholar
Xu, H. & Bodenschatz, E. 2008 Motion of inertial particles with size larger than Kolmogorov scale in turbulent flows. Physica D 237, 2095–2100.CrossRefGoogle Scholar
Xu, H., Ouellette, N. T., Vincenzi, D. & Bodenschatz, E. 2007 Acceleration correlations and pressure structure functions in high-Reynolds number turbulence. Phys. Rev. Lett. 99, 204501.CrossRefGoogle ScholarPubMed
Yeung, P. K. & Borgas, M. S. 2004 Relative dispersion in isotropic turbulence: part 1. Direct numerical simulations and Reynolds number dependence. J. Fluid Mech. 503, 125–160.CrossRefGoogle Scholar
Zaichik, L. I. & Alipchenkov, V. M. 2008 Acceleration of heavy particles in isotropic turbulence. Intl J. Multiphase Flow 34, 865–868.CrossRefGoogle Scholar
Zaichik, L. I., Simonin, O. & Alipchenkov, V. M. 2003 Two statistical models for predicting collision rates of inertial particles in homogeneous isotropic turbulence. Phys. Fluids 15, 2995–3005.CrossRefGoogle Scholar