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Self-similar clustering of inertial particles in homogeneous turbulence

Published online by Cambridge University Press:  19 April 2007

HIROSHI YOSHIMOTO  and
SUSUMU GOTO
HIROSHI YOSHIMOTO
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto, 606-8501, Japan
SUSUMU GOTO
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto, 606-8501, Japan
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Abstract

It is shown by direct numerical simulation that the preferential concentration of small heavy particles in homogeneous isotropic developed turbulence has a self-similar multi-scale nature when the particle relaxation time is within the inertial time scales of the turbulence. This is shown by the pair correlation function of the particle distribution extending over the entire inertial range, and the probability density function of the volumes of particle voids taking a power-law form. This self-similar multi-scale nature of particle clustering cannot be explained only by the centrifugal effect of the smallest-scale (i.e. the Kolmogorov scale) eddies, but also by the effect of co-existing self-similar multi-scale coherent eddies in the turbulence at high Reynolds numbers. This explanation implies that the preferential concentration of particles takes place even when the relaxation time of particles is much larger than the Kolmogorov time, provided it is smaller than the longest time scale of the turbulence, since even the largest-scale eddies bring about particle clustering.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 577 , 25 April 2007 , pp. 275 - 286
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Balkovsky, E., Falkovich, G. & Fouxon, A. 2001 Intermittent distribution of inertial particles in turbulent flows. Phys. Rev. Lett. 86, 2790–2793.CrossRefGoogle ScholarPubMed
Bec, J. 2003 Fractal clustering of inertial particles in random flows. Phys. Fluids 15, L81–L84.CrossRefGoogle Scholar
Bec, J. 2005 Multifractal concentration of inertial particles in smooth random flows. J. Fluid Mech. 528, 255–277.CrossRefGoogle Scholar
Boffetta, G., DeLillo, F. Lillo, F. & Gamba, A. 2004 Large scale inhomogeneity of inertial particles in turbulent flow. Phys. Fluids, 16, L20–L23.CrossRefGoogle Scholar
Cencini, M., Bec, J., Bifferale, L., Boffetta, G., Celani, A., Lanotte, A. S., Musacchio, S. & Toschi, F. 2006 Dynamnics and statistics of heavy particles in turbulent flows. J. Turbulence 7, 36.CrossRefGoogle Scholar
Chen, L., Goto, S. & Vassilicos, J. C. 2006 Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553, 143–154.CrossRefGoogle Scholar
Cuzzi, J. N., Hogan, R. C., Paque, J. M. & Dobrovolskis, A. R. 2001 Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence. Astrophys. J. 546, 496–508.CrossRefGoogle Scholar
Duncan, K., Mehlig, B., Östlund, S. & Wilkinson, M. 2005 Clustering by mixing flows. Phys. Rev. Lett. 95, 240602.CrossRefGoogle ScholarPubMed
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, Suppl. 169–209.CrossRefGoogle Scholar
Falkovich, G. & Pumir, A. 2004 Intermittent distribution of heavy particles in a turbulent flow. Phys. Fluids 16, L47–L50.CrossRefGoogle Scholar
Goto, S. & Kida, S. 2003 Enhanced stretching of material lines by antiparallel vortex pairs in turbulence. Fluid Dyn. Res. 33, 403–431.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, 115103.CrossRefGoogle Scholar
Kostinski, A. B. & Shaw, R. A. 2001 Scale-dependent droplet clustering in turbulent clouds. J. Fluid Mech. 434, 389–398.CrossRefGoogle Scholar
Landau, L. & Lifshitz, E. 1980 Statistical Physics. Pergamon.Google Scholar
Maxey, M. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow field. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Maxey, M. & Riley, J. 1983 Equation of motion of a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3, 1169–1179.CrossRefGoogle Scholar
Vaillancourt, P. A. & Yau, M. K. 2000 Review of particle-turbulence interactions and consequences for cloud physics. Bull. Am. Met. Soc. 81, 285–298.2.3.CO;2>CrossRefGoogle Scholar
Wang, L. P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy-particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.CrossRefGoogle Scholar
Yang, T. S. & Shy, S. S. 2005 Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J. Fluid Mech. 526, 171–216.CrossRefGoogle Scholar

Yoshimoto and Goto supplementary movie

Movie 1. Temporal evolution of inertial particles (white dots) of Stokes number equal to 2 inside a thin layer (side length is 3.4 times the integral length, width is 5 times the Kolmogorov length). Evolution until 1.1T (here T is the integral time) is shown. Reynolds number based on the Taylor length is 188. It is observed that it takes a long time, of the order of the integral time, for particle clustering to reach a statistically stationary state, and that not only small voids of particles but also voids as large as the integral length are created in the statistically stationary state.

Download Yoshimoto and Goto supplementary movie(Video)
Video 9.6 MB

Yoshimoto and Goto supplementary movie

Movie 1. Temporal evolution of inertial particles (white dots) of Stokes number equal to 2 inside a thin layer (side length is 3.4 times the integral length, width is 5 times the Kolmogorov length). Evolution until 1.1T (here T is the integral time) is shown. Reynolds number based on the Taylor length is 188. It is observed that it takes a long time, of the order of the integral time, for particle clustering to reach a statistically stationary state, and that not only small voids of particles but also voids as large as the integral length are created in the statistically stationary state.

Download Yoshimoto and Goto supplementary movie(Video)
Video 78.3 MB