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Alignment statistics of rods with the Lagrangian stretching direction in a channel flow

Published online by Cambridge University Press:  25 August 2020

Z. Cui Open the ORCID record for Z. Cui [Opens in a new window] ,
A. Dubey Open the ORCID record for A. Dubey [Opens in a new window] ,
L. Zhao Open the ORCID record for L. Zhao [Opens in a new window]  and
B. Mehlig Open the ORCID record for B. Mehlig [Opens in a new window]
Z. Cui
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, 100084Beijing, PR China
A. Dubey
Affiliation:
Department of Physics, Gothenburg University, SE-41296Gothenburg, Sweden
L. Zhao*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, 100084Beijing, PR China
B. Mehlig
Affiliation:
Department of Physics, Gothenburg University, SE-41296Gothenburg, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

In homogeneous isotropic turbulence, slender rods are known to align with the Lagrangian stretching direction. However, how the degree of alignment depends on the aspect ratio of the rod is not understood. Moreover, particle-laden flows are often anisotropic and inhomogeneous. Therefore we study the alignment of rods with the Lagrangian stretching direction in a channel flow, which is approximately homogeneous and isotropic near the centre but inhomogeneous and anisotropic near the walls. Our main question is how the distribution of relative angles between a rod and the Lagrangian stretching direction depends on the aspect ratio of the rod and upon the distance of the rod from the channel wall. We find that this distribution exhibits two regimes: a plateau at small angles corresponding to random uncorrelated motion, and power-law tails due to large excursions. We find that slender rods near the channel centre align better with the Lagrangian stretching direction compared with those near the channel wall. These observations are explained in terms of simple statistical models based on Jeffery's equation, qualitatively near the channel centre and quantitatively near the channel wall. Lastly we discuss the consequences of our results for the distribution of relative angles between the orientations of nearby rods (Zhao et al., Phys. Rev. Fluids, vol. 4, 2019, 054602).

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A16
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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