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Where do small, weakly inertial particles go in a turbulent flow?

Published online by Cambridge University Press:  27 March 2012

Mathieu Gibert ,
Haitao Xu  and
Eberhard Bodenschatz
Mathieu Gibert
Affiliation:
Max Planck Institute for Dynamics and Self Organization (MPIDS), 37077 Göttingen, Germany International Collaboration for Turbulence Research
Haitao Xu
Affiliation:
Max Planck Institute for Dynamics and Self Organization (MPIDS), 37077 Göttingen, Germany International Collaboration for Turbulence Research
Eberhard Bodenschatz*
Affiliation:
Max Planck Institute for Dynamics and Self Organization (MPIDS), 37077 Göttingen, Germany Institute for Nonlinear Dynamics, University of Göttingen, 37077 Göttingen, Germany Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA International Collaboration for Turbulence Research
*
†Email address for correspondence: [email protected]
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Abstract

We report experimental results on the dynamics of heavy particles of the size of the Kolmogorov scale in a fully developed turbulent flow. The mixed Eulerian structure function of two-particle velocity and acceleration difference vectors was observed to increase significantly with particle inertia for identical flow conditions. We show that this increase is related to a preferential alignment between these dynamical quantities. With increasing particle density the probability for those two vectors to be collinear was observed to grow. We show that these results are consistent with the preferential sampling of strain-dominated regions by inertial particles.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 698 , 10 May 2012 , pp. 160 - 167
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

‡

Present address: Institut NÉEL CNRS/UJF (Grenoble France).

References

1. 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, 77–105.CrossRefGoogle Scholar
2. 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), 2343–2353.CrossRefGoogle Scholar
3. Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
4. Berg, J., Lüthi, B., Mann, J. & Ott, S. 2006 Backwards and forwards relative dispersion in turbulent flow: An experimental investigation. Phys. Rev. E 74, 16304.CrossRefGoogle ScholarPubMed
5. Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1 (5), 497–504.CrossRefGoogle Scholar
6. Chun, J. H., 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
7. Collins, L. R. & Keswani, A. 2004 Reynolds number scaling of particle clustering in turbulent aerosols. New J. Phys. 6, 119.CrossRefGoogle Scholar
8. Ducasse, L. & Pumir, A. 2008 Intermittent particle distribution in synthetic free-surface turbulent flows. Phys. Rev. E 77 (6), 066304.CrossRefGoogle ScholarPubMed
9. Falkovich, G., Fouxon, A. & Stepanov, M. G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154.CrossRefGoogle ScholarPubMed
10. Falkovich, G., Gawȩdzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913.CrossRefGoogle Scholar
11. Falkovich, G. & Pumir, A. 2004 Intermittent distribution of heavy particles in a turbulent flow. Phys. Fluids 16 (7), L47–L50.CrossRefGoogle Scholar
12. Gibert, M., Xu, H. & Bodenschatz, E. 2010 Inertial effects on two-particle separation in a turbulent flows. Europhys. Lett. 90 (6), 64005.CrossRefGoogle Scholar
13. Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.Google Scholar
14. Hill, R. J. 2006 Opportunities for use of exact statistical equations. J. Turbul. 7 (43), 1–13.CrossRefGoogle Scholar
15. Homann, H. & Bec, J. 2010 Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J. Fluid Mech. 651, 81–91.CrossRefGoogle Scholar
16. Kholmyansky, M., Tsinober, A. & Yorish, S. 2001 Velocity derivatives in the atmospheric surface layer at . Phys. Fluids 13, 311.CrossRefGoogle Scholar
17. Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87.CrossRefGoogle Scholar
18. Mann, J., Ott, S. & Andersen, J. S. 1999 Experimental study of relative, turbulent diffusion. Risø–R–1036(EN).Google Scholar
19. Maxey, M. & Riley, J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.CrossRefGoogle Scholar
20. Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: A Voronoï analysis. Phys. Fluids 22, 103304.CrossRefGoogle Scholar
21. Ouellette, N. T., Xu, H. & Bodenschatz, E. 2006 A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp. Fluids 40, 301–313.CrossRefGoogle Scholar
22. Pumir, A., Shraiman, B. & Chertkov, M. 2001 The Lagrangian view of energy transfer in turbulent flow. Europhys. Lett. 56 (3), 379–385.CrossRefGoogle Scholar
23. Pumir, A., Xu, H. & Bodenschatz, E. 2012 Tetrad deformation and alignment of vorticity and strain in a turbulent flow (in preparation).CrossRefGoogle Scholar
24. Salazar, J. P. L. C & Collins, L. R 2012 Inertial particle relative velocity statistics in homogeneous isotropic turbulence. J. Fluid Mech. 696, 45–67.CrossRefGoogle Scholar
25. Salazar, J. P. L. C, Jong, J. D., Cao, L., Woodward, S. H., Meng, H. & Collins, L. R. 2008 Experimental and numerical investigation of inertial particle clustering in isotropic turbulence. J. Fluid Mech. 600, 245–256.CrossRefGoogle Scholar
26. Saw, E. W., Shaw, R. A., Ayyalasomayajula, S., Chuang, P. Y. & Gylfason, A. 2008 Inertial clustering of particles in high-Reynolds-number turbulence. Phys. Rev. Lett. 100 (21), 214501.CrossRefGoogle ScholarPubMed
27. Schmitt, F. C. & Seuront, L. 2008 Intermittent turbulence and copepod dynamics: Increase in encounter rates through preferential concentration. J. Mar. Syst. 70, 263–272.CrossRefGoogle Scholar
28. Shaw, R. A. 2003 Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227.CrossRefGoogle Scholar
29. Sundaram, S. & Collins, L. R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. 1. Direct numerical simulations. J. Fluid Mech. 335, 75–109.CrossRefGoogle Scholar
30. Wood, A. M., Hwang, W. & Eaton, J. K. 2005 Preferential concentration of particles in homogeneous and isotropic turbulence. Intl J. Multiphase Flow 31 (10–11), 1220–1230.CrossRefGoogle Scholar
31. Xu, H. 2008 Tracking Lagrangian trajectories in position-velocity space. Meas. Sci. Technol. 19 (7), 075105.CrossRefGoogle Scholar
32. 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
33. 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
34. Xu, H., Pumir, A. & Bodenschatz, E. 2011 The pirouette effect in turbulent flows. Nat. Phys. 7, 709–712.CrossRefGoogle Scholar
35. 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, 103018.CrossRefGoogle Scholar