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Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Published online by Cambridge University Press:  04 February 2015

Rui Ni ,
Stefan Kramel ,
Nicholas T. Ouellette  and
Greg A. Voth
Rui Ni*
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA Department of Mechanical Engineering & Materials Science, Yale University, New Haven, CT 06520, USA
Stefan Kramel
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
Nicholas T. Ouellette
Affiliation:
Department of Mechanical Engineering & Materials Science, Yale University, New Haven, CT 06520, USA
Greg A. Voth*
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We present simultaneous experimental measurements of the dynamics of anisotropic particles transported by a turbulent flow and the velocity gradient tensor of the flow surrounding them. We track both rod-shaped particles and small spherical flow tracers using stereoscopic particle tracking. By using scanned illumination, we are able to obtain a high enough seeding density of tracers to measure the full velocity gradient tensor near the rod. The alignment of rods with the vorticity and the eigenvectors of the strain rate from experimental results agree well with numerical findings. A full description of the tumbling of rods in turbulence requires specifying a seven-dimensional joint probability density function (jPDF) of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the rod. If these seven parameters are known, then Jeffery’s equation specifies the rod tumbling rate and any statistic of rod rotations can be obtained as a weighted average over the jPDF. To look for a lower-dimensional projection to simplify the problem, we explore conditional averages of the mean-squared tumbling rate. The conditional dependence of the mean-squared tumbling rate on the magnitude of both the vorticity and the strain rate is strong, as expected, and similar. There is also a strong dependence on the orientation between the rod and the vorticity, since a rod aligned with the vorticity vector tumbles due to strain but not vorticity. When conditioned on the alignment of the rod with the eigenvectors of the strain rate, the largest tumbling rate is obtained when the rod is oriented at a certain angle to the eigenvector that corresponds to the smallest eigenvalue, because this particular orientation maximizes the contribution from both the vorticity and strain.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 202 - 225
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Copyright
© 2015 Cambridge University Press 

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