Skip to main content Accessibility help
×
Home

Why spheroids orient preferentially in near-wall turbulence

  • Lihao Zhao (a1) and Helge I. Andersson (a1)

Abstract

Non-spherical particles are known to orient preferentially in near-wall turbulence, but rod-like and disk-like particles align themselves differently relative to the mean vorticity direction. To uncover the mechanism that gives rise to such preferential particle orientations in anisotropic turbulence, Lagrangian statistics from a channel-flow simulation have been analysed. Ni et al. (J. Fluid Mech., vol. 743, 2014, R3) showed that the fluid vorticity and long rods independently aligned with the Lagrangian fluid stretching direction in isotropic turbulence. Following their approach, we deduced the left Cauchy–Green strain tensor along Lagrangian trajectories of tracer spheroids in channel-flow turbulence. The results showed that the alignment of the fluid vorticity vector with the strongest Lagrangian stretching direction in the channel centre, just as in isotropic turbulence, vanished in the vicinity of the walls. The analysis revealed that the directions of the strongest Lagrangian stretching and compression in near-wall turbulence are in the streamwise and wall-normal directions, respectively. All over the channel we found that the symmetry axis of prolate spheroids aligned with the direction of strongest Lagrangian stretching whereas oblate spheroids oriented with the direction of Lagrangian compression. This finding is apparently universal since the same trends were found in highly anisotropic wall turbulence as well as in isotropic turbulence. Contrary to the prevailing view, we have shown for the first time that the preferential orientation of the symmetry axis of long rods in the streamwise direction and of flat disks in the wall-normal direction is caused by Lagrangian stretching and not by fluid rotation. This finding fills a gap in our understanding of orientation and rotation of tracer spheroids in anisotropic wall turbulence.

Copyright

References

Hide All
Abbasi Hoseini, A., Lundell, F. & Andersson, H. I. 2015 Finite-length effects on dynamical behavior of rod-like particles in wall-bounded turbulent flow. Intl J. Multiphase Flow 76, 1321.
Andersson, H. I., Zhao, L. & Variano, E. 2015 On the anisotropic vorticity in turbulent channel flows. J. Fluids Engng 137, 084503.
Bettencourt, H. J., López, C. & Hernández-García, E. 2013 Characterization of coherent structures in three-dimensional turbulent flows using the finite-size Lyapunov exponent. J. Phys. A 46, 254022.
Byron, M., Einarsson, J., Gustavsson, K., Voth, G., Mehlig, B. & Variano, E. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27, 035101.
Capone, A. & Romano, P. G. 2015 Shape-dependence of particle rotation in isotropic turbulence. Phys. Fluids 27, 053303.
Carlsson, A., Söderberg, L. D. & Lundell, F. 2010 Fibre orientation measurements near a headbox wall. Nord. Pulp Paper 25, 204212.
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015a Orientation and rotation of inertial disk particles in wall turbulence. J. Fluid Mech. 766, R2.
Challabotla, N. R., Zhao, L. & Andersson, H. I. 2015b Shape effects on dynamics of inertia-free spheroids in wall turbulence. Phys. Fluids 27, 061703.
Chevillard, L. & Meneveau, C. 2013 Orientation dynamics of small, triaxial-ellipsoidal particles in isotropic turbulence. J. Fluid Mech. 737, 571596.
Green, M. A., Rowley, C. W. & Haller, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111120.
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373400.
Gustavsson, K., Einarsson, J. & Mehlig, B. 2014 Tumbling of small axisymmetric particles in random and turbulent flows. Phys. Rev. Lett. 112, 014501.
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137162.
Hunt, C., Tierney, L., Kramel, S. & Voth, G. 2015 Alignment of disks with Lagrangian stretching in turbulence. Bull. Am. Phys. Soc. 60, 21.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.
Leal, L. G. & Hinch, E. J. 1972 The rheology of a suspension of nearly spherical particles subject to Brownian rotations. J. Fluid Mech. 55, 745765.
Lundell, F., Söderberg, L. D. & Alfredsson, P. H. 2011 Fluid mechanics of papermaking. Annu. Rev. Fluid Mech. 43, 195217.
Marchioli, C., Fantoni, M. & Soldati, A. 2010 Orientation, distribution, and deposition of elongated, inertial fibers in turbulent channel flow. Phys. Fluids 22, 033301.
Marchioli, C., Zhao, L. & Andersson, H. I. 2016 On the relative rotational motion between rigid fibers and fluid in turbulent channel flow. Phys. Fluids 28, 013301.
Marcus, G. G., Parsa, S., Kramel, S., Ni, R. & Voth, G. A. 2014 Measurements of the solid-body rotation of anisotropic particles in 3D turbulence. New J. Phys. 16, 102001.
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J. & Boersma, B. J. 2008a On the orientation of ellipsoidal particles in a turbulent shear flow. Intl J. Multiphase Flow 34, 678683.
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J. & Boersma, B. J. 2008b Dynamics of prolate ellipsoidal particles in a turbulent channel flow. Phys. Fluids 20, 093302.
Ni, R., Kramel, S., Ouellette, N. T. & Voth, G. A. 2015 Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence. J. Fluid Mech. 766, 202225.
Ni, R., Ouellette, N. T. & Voth, G. A. 2014 Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence. J. Fluid Mech. 743, R3.
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109, 134501.
Parsa, S., Guasto, J. S., Kishore, M., Ouellette, N. T., Gollub, J. P. & Voth, G. A 2011 Rotation and alignment of rods in two-dimensional chaotic flow. Phys. Fluids 23, 043302.
Ruiz, J., Macas, D. & Peters, F. 2004 Turbulence increases the average settling velocity of phytoplankton cells. Proc. Natl Acad. Sci. USA 101, 1772017724.
Sabban, L., Cohen, A. & van Hout, R.2016 Combined measurements of the flow field and rigid, inertial fibre rotation/translation in near homogeneous isotropic turbulence. In 9th International Conference on Multiphase Flow (Firenze, Italy), http://www.aidic.it/icmf2016/webpapers/991sabban.pdf.
Voth, G. A. 2015 Disks aligned in a turbulent channel. J. Fluid Mech. 772, 14.
Yang, Y. & Pullin, D. I. 2011 Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. J. Fluid Mech. 674, 6792.
Zhang, H., Ahmadi, G., Fan, F.-G. & Mclaughlin, J. B. 2001 Ellipsoidal particles transport and deposition in turbulent channel flows. Intl J. Multiphase Flow 27, 9711009.
Zhao, L., Andersson, H. I. & Gillissen, J. J. J. 2013 On inertial effects of long fibers in wall turbulence: fiber orientation and fiber stresses. Acta Mech. 224, 23752384.
Zhao, L., Challabotla, N. R., Andersson, H. I. & Variano, E. 2015 Rotation of nonspherical particles in turbulent channel flow. Phys. Rev. Lett. 115, 244501.
Zhao, L., Marchioli, C. & Andersson, H. I. 2014 Slip velocity of rigid fibers in turbulent channel flow. Phys. Fluids 26, 063302.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed