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Sedimentation and fluttering of a cylinder in a confined liquid

Maria Veronica D'Angelo* and Mario Cachile

Jean-Pierre Hulin and Harold Auradou§

  • Universidad de Buenos-Aires, Facultad de Ingeniería, GMP-LIA-FMF, CONICET, Paseo Colón 850, 1063, Buenos Aires, Argentina

  • Laboratoire FAST, Univ. Paris Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France

  • *vdangelo@fi.uba.ar
  • mcachil@fi.uba.ar
  • hulin@fast.u-psud.fr
  • §auradou@fast.u-psud.fr

Phys. Rev. Fluids 2, 104301 – Published 5 October, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.104301

Abstract

The sedimentation and fluttering (angular oscillation of the axis) of straight cylinders are studied in a viscous fluid at rest filling a vertical Hele-Shaw cell for different density contrasts ρsρf and fluid viscosities μf and for two cylinder densities ρs and diameters D. The influence of confinement in the cell is studied by comparing the present results to those of the literature for nonconfined fluids. While the confinement and the cylinder length L both influence strongly the mean sedimentation velocity Vs, the characteristics of the fluttering instability are much more similar in the confined and nonconfined cases. While the drag coefficient is nearly constant in a nonconfined fluid, it is larger here and depends both on L (due to flow blockage) and on the Reynolds number ReD=VsDρf/μf; the inertial and viscous drag components have equal magnitudes for ReD40. For fluttering, instead, the key parameter is the Froude number Fr=Vs/Vg [Vg=(ρsρf)gL/ρf], and the fluttering oscillations vanish below Fr0.07 for all cylinders and fluids investigated. Above this threshold, the angular amplitude increases with Fr up to a plateau value, while that of the horizontal oscillations is, at first, very large and then decreases; both amplitudes are reduced when the viscous drag is dominant, but, if inertial drag is dominant, all data points follow a common trend. For all fluids and cylinders, too, the fluttering frequency varies as f=0.102Vg/L. These features of fluttering are generally qualitatively similar to those reported in nonconfined fluids, but this instability is observable down to lower ReD values (24 instead of 200).

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References (23)

  1. J. C. Maxwell, On a particular case of the descent of a heavy body in a resisting medium, Camb. Dublin Math. J. 9, 145 (1854).
  2. G. Kirchhoff, Uber die Bewegung eines Rotationskorpers in einer Flussigkeit, J. Reine Angew. Math. (Crelle) 71, 237 (1869).
  3. P. Ern, F. Risso, and J. Magnaudet, Wake-induced oscillatory paths of bodies freely rising or falling in fluids, Annu. Rev. Fluid Mech. 44, 97 (2012).
  4. A. Belmonte, H. Eisenberg, and E. Moses, From Flutter to Tumble: Inertial Drag and Froude Similarity in Falling Paper, Phys. Rev. Lett. 81, 345 (1998).
  5. F. Fonseca and H. J. Herrmann, Simulation of the sedimentation of a falling oblate ellipsoid, Physica A 345, 341 (2005).
  6. S. B. Field, M. Klaus, M. G. Moore, and F. Nori, Chaotic dynamics of falling disks, Nature (London) 388, 252 (1997).
  7. L. Mahadevan, H. Aref, and S. W. Jones, Comment on “Behavior of a Falling Paper,” Phys. Rev. Lett. 75, 1420 (1995).
  8. A. Andersen, U. Pesavento, and Z. J. Wang, Unsteady aerodynamics of fluttering and tumbling plates, J. Fluid Mech. 541, 65 (2005).
  9. A. Andersen, U. Pesavento, and Z. J. Wang, Analysis of transitions between fluttering, tumbling and steady descent of falling cards, J. Fluid Mech. 541, 91 (2005).
  10. P. C. Fernandes, P. Ern, F. Risso, and J. Magnaudet, On the zigzag dynamics of freely moving axisymmetric bodies, Phys. Fluids 17, 098107 (2005).
  11. P. C. Fernandes, F. Risso, P. Ern, and J. Magnaudet, Oscillatory motion and wake instability of freely rising axisymmetric bodies, J. Fluid Mech. 573, 479 (2007).
  12. M. N. Bulova, K. Nosova, D. Willberg, and J. Lassek, Benefits of the novel fiber-laden low-viscosity fluid system in fracturing low-permeability tight gas formations, in Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 Sept 2006 (Society of Petroleum Engineers, 2006), paper SPE 102956.
  13. M. N. Bulova, A. N. Cheremisin, K. E. Nosova, J. T. Lassek, and D. Willberg, Evaluation of the proppant-pack permeability in fiber-assisted hydraulic fracturing treatments for low-permeability formations, in Proceedings of the SPE Gas Technology Symposium, Calgary, Alberta, Canada, 15–17 May 2006 (Society of Petroleum Engineers, 2006), paper SPE 100556.
  14. E. K. Marchildon, A. Clamen, and W. H. Gauvin, Drag and oscillatory motion of freely falling cylindrical particles, Can. J. Chem. Eng. 42, 178 (1964).
  15. A. C. Chow and E. E. Adams, Prediction of drag coefficient and secondary motion of free-falling rigid cylindrical particles with and without curvature at moderate Reynolds number, J. Hydraul. Eng. 137, 1406 (2011).
  16. M. V. D'Angelo, J. P. Hulin, and H. Auradou, Oscillations and translation of a free cylinder in a confined viscous flow, Phys. Fluids 25, 014102 (2013).
  17. L. Gianorio, M. V. D'Angelo, M. Cachile, J. P. Hulin, and H. Auradou, Influence of confinement on the oscillations of a free cylinder in a viscous flow, Phys. Fluids 26, 084106 (2014).
  18. B. Semin, J. P. Hulin, and H. Auradou, Influence of flow confinement on the drag force on a static cylinder, Phys. Fluids 21, 103604 (2009).
  19. B. Semin, A. Decoene, J. P. Hulin, M. L. M. Francois, and H. Auradou, New oscillatory instability of a confined cylinder in a flow below the vortex shedding threshold, J. Fluid Mech. 690, 345 (2012).
  20. R. G. Cox, The motion of long slender bodies in a viscous fluid. Part 1. General theory, J. Fluid Mech. 44, 791 (1970).
  21. A. Vakil and S. I. Green, Drag and lift coefficients of inclined finite circular cylinders at moderate Reynolds number, Comput. Fluids 38, 1771 (2009).
  22. Lord Rayeigh, LIII. On the resistance of fluids, Philos. Mag. (5th Ser.) 2, 430 (1876).
  23. A. Fage, and F. C. Johansen, On the flow of air behind an inclined flat plate of infinite span, Proc. R. Soc. London A 116, 170 (1927).

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