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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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References

Andersson, H. I. & Soldati, A. 2013 Anisotropic particles in turbulence: status and outlook. Acta Mechanica 224 (10), 2219–2223.Google Scholar
Ashurst, Wm. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30, 2343.Google Scholar
Benzi, R., Biferale, L., Calzavarini, E., Lohse, D. & Toschi, F. 2009 Velocity-gradient statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame. Phys. Rev. E 80, 066318.Google Scholar
Blum, D. B., Kunwar, S. B., Johnson, J. & Voth, G. A. 2010 Effects of nonuniversal large scales on conditional structure functions in turbulence. Phys. Fluids 22 (1), 015107.Google Scholar
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4, 782–793.Google Scholar
Chevillard, L. & Meneveau, C. 2013 Orientation dynamics of small, triaxial ellipsoidal particles in isotropic turbulence. J. Fluid Mech. 737, 571–596.Google Scholar
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373–400.Google Scholar
Gustavsson, K., Einarsson, J. & Mehlig, B. 2014 Tumbling of small axisymmetric particles in random and turbulent flows. Phys. Rev. Lett. 112, 014501.Google Scholar
Herzhaft, B., Guazzelli, E., Mackaplow, M. B. & Shaqfeh, E. S. G 1996 Experimental investigation of the sedimentation of a dilute fiber suspension. Phys. Rev. Lett. 77 (2), 290–293.CrossRefGoogle ScholarPubMed
Hoyer, K., Holzner, M., Lüthi, B., Guala, M., Liberzon, A. & Kinzelbach, W. 2005 3D scanning particle tracking velocimetry. Exp. Fluids 39, 923–934.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Jumars, P. A., Trowbridge, J. H., Boss, E. & Lee, K.-B. 2009 Turbulence-plankton interactions: a new cartoon. Mar. Ecol.-Evol. Persp. 30 (2), 133–150.Google Scholar
Karp-Boss, L., Azevedo, L. & Boss, E. 2007 LISST-100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape. Limnol. Oceanogr. 5, 396–406.CrossRefGoogle Scholar
Koch, D. L. & Shaqfeh, E. S. G. 1989 The instability of a dispersion of sedimenting spheroids. J Fluid Mech. 209, 521–542.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in an incompressible fluid at very high Reynolds number. Dokl. Akad. Nauk SSSR 30, 299.Google Scholar
Korolev, A. & Isaac, G. 2003 Roundness and aspect ratio of particles in ice clouds. J. Atmos. Sci. 60, 1795–1808.Google Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Tsinober, A. & Kinzelbach, W. 2014 A combined scanning PTV/LIF technique to simultaneously measure the full velocity gradient tensor and the 3d density field. Meas. Sci. Technol. 25, 065301.Google Scholar
Leal, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435–476.Google Scholar
Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87–118.Google Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245.Google Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004 Experimental Lagrangian acceleration probability density function measurement. Physica D 193, 245–251.Google Scholar
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.Google Scholar
Olson, J. A. & Kerekes, R. J. 1998 The motion of fibres in turbulent flow. J Fluid Mech. 377, 47–64.Google Scholar
Ouellette, N. T., Xu, H.-T. & Bodenschatz, E. 2006 A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp. Fluids 40, 301–313.Google Scholar
Parsa, S.2013 Rotational dynamics of rod particles in fluid flows. PhD thesis, Wesleyan University.Google Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys Rev. Lett. 109 (13), 134501.Google Scholar
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 (4), 043302.Google Scholar
Parsa, S. & Voth, G. A. 2014 Inertial range scaling in rotations of long rods in turbulence. Phys. Rev. Lett. 112 (2), 024501.Google Scholar
Pinsky, M. B., Khain, A. P. & Shapiro, M. 2007 Collisions of cloud droplets in a turbulent flow. part IV: droplet hydrodynamic interaction. J. Atmos. Sci. 64 (7), 2462–2482.Google Scholar
Pumir, A., Bodenschatz, E. & Xu, H. 2013 Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow. Phys. Fluids 25, 035101.Google Scholar
Pumir, A. & Wilkinson, M. 2011 Orientation statistics of small particles in turbulence. New J. Phys. 13, 093030.Google Scholar
Rosen, T., Lundell, F. & Aidun, C. K. 2014 Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow. J Fluid Mech. 738, 563–590.Google Scholar
Shapiro, M. & Goldenberg, M. 1993 Deposition of glass-fiber particles from turbulent air-flow in a pipe. J. Aero. Sci. 24 (1), 65–87.Google Scholar
Shaw, R. A. 2003 Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227.Google Scholar
Shin, M. & Koch, D. L. 2005 Rotational and translational dispersion of fibres in isotropic turbulent flows. J. Fluid Mech. 540, 143–173.Google Scholar
Szeri, A. J. & Leal, L. G. 1993 Microstructure suspended in 3-dimensional flows. J. Fluid Mech. 250, 143–167.Google Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.Google Scholar
Wallace, J. M. & Vukoslavc̆ević, P. V. 2010 Measurement of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 42, 157–181.Google Scholar
Wan, M.2008 On the Lagrangian study of the turbulent energy and circulation cascades. PhD thesis.Google Scholar
Zhang, H. F., Ahmadi, G., Fan, F. G. & McLaughlin, J. B. 2001 Ellipsoidal particles transport and deposition in turbulent channel flows. Intl J. Multiphase Flow 27 (6), 971–1009.Google Scholar