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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

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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