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Path oscillations and enhanced drag of light rising spheres

Published online by Cambridge University Press:  21 February 2018

Franck Auguste  and
Jacques Magnaudet Open the ORCID record for Jacques Magnaudet [Opens in a new window]
Franck Auguste
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, 31400 Toulouse, France
Jacques Magnaudet*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, 31400 Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of light spheres rising freely under buoyancy in a large expanse of viscous fluid at rest at infinity is investigated numerically. For this purpose, the computational approach developed by Mougin & Magnaudet (Intl J. Multiphase Flow, vol. 28, 2002, pp. 1837–1851) is improved to account for the instantaneous viscous loads induced by the translational and rotational sphere accelerations, which play a crucial role in the dynamics of very light spheres. A comprehensive map of the rise regimes encountered up to Reynolds numbers (based on the sphere diameter and mean rise velocity) of the order of $10^{3}$ is set up by varying independently the body-to-fluid density ratio and the relative magnitude of inertial and viscous effects in approximately 250 distinct combinations. These computations confirm or reveal the presence of several distinct periodic regions on the route to chaos, most of which only exist within a finite range of the sphere relative density and Reynolds number. The wake structure is analysed in these various regimes, evidencing the existence of markedly different shedding modes according to the style of path. The variation of the drag force with the flow parameters is also examined, revealing that only one of the styles of path specific to very light spheres yields a non-standard drag behaviour, with drag coefficients significantly larger than those measured on a fixed sphere under equivalent conditions. The outcomes of this investigation are compared with available experimental and numerical results, evidencing points of consensus and disagreement.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 228 - 266
Copyright
© 2018 Cambridge University Press 

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Footnotes

‡

Present address: Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), Université de Toulouse, CNRS-CECI, Toulouse, France.

References

Auguste, F.2010 Instabilités de sillage et trajectoires d’un corps solide cylindrique immergé dans un fluide visqueux. PhD thesis, Université Paul Sabatier, Toulouse, France (available online at http://thesesups.ups-tlse.fr/1186/).Google Scholar
Auguste, F., Magnaudet, J. & Fabre, D. 2013 Falling styles of disks. J. Fluid Mech. 719, 388–405.CrossRefGoogle Scholar
Bergé, P., Pomeau, Y. & Vidal, C. 1984 Order Within Chaos. Wiley.Google Scholar
Calmet, I. & Magnaudet, J. 1997 Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow. Phys. Fluids 9, 438–455.CrossRefGoogle Scholar
Cano-Lozano, J. C., Martínez-Bazán, C., Magnaudet, J. & Tchoufag, J. 2016 Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability. Phys. Rev. Fluids 1, 053604.CrossRefGoogle Scholar
Chrust, M., Bouchet, G. & Dušek, J. 2013 Numerical simulation of the dynamics of freely falling discs. Phys. Fluids 25, 044102.CrossRefGoogle Scholar
Chrust, M., Bouchet, G. & Dušek, J. 2014 Effect of solid body degrees of freedom on the path instabilities of freely falling or rising flat cylinders. J. Fluids Struct. 47, 55–70.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic Press.Google Scholar
Eckert, M. 2006 The Dawn of Fluid Dynamics. Wiley.Google Scholar
Fabre, D., Tchoufag, J. & Magnaudet, J. 2012 The steady oblique path of buoyancy-driven disks and spheres. J. Fluid Mech. 707, 24–36.CrossRefGoogle Scholar
Feuillebois, F. & Lasek, A. 1978 Rotational historic term in nonstationary Stokes flow. Q. J. Mech. Appl. Maths 31, 435–443.CrossRefGoogle Scholar
Gatignol, R. 1983 The Faxen formulas for a rigid particle in an unsteady non-uniform Stokes-flow. J. Méc. Théor. Appl. 2, 143–160.Google Scholar
Ghidersa, B. & Dušek, J. 2000 Breaking of axisymetry and onset of unsteadiness in the wake of a sphere. J. Fluid Mech. 423, 33–69.CrossRefGoogle Scholar
Horowitz, M. & Williamson, C. H. K. 2008 Critical mass ratio and a new periodic four-ring vortex wake mode for freely rising and falling spheres. Phys. Fluids 20, 101701.CrossRefGoogle Scholar
Horowitz, M. & Williamson, C. H. K. 2010 The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres. J. Fluid Mech. 651, 251–294.CrossRefGoogle Scholar
Jenny, M. & Dušek, J. 2004 Efficient numerical method for the direct numerical simulation of the flow past a single light moving spherical body in transitional regimes. J. Comput. Phys. 194, 215–232.CrossRefGoogle Scholar
Jenny, M., Dušek, J. & Bouchet, G. 2004 Instabilities and transition of a sphere falling or ascending in a Newtonian fluid. J. Fluid Mech. 508, 201–239.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to Reynolds number of 300. J. Fluid Mech. 378, 10–70.CrossRefGoogle Scholar
Karamanev, D. G. 2001 The study of the rise of buoyant spheres in gas reveals the universal behaviour of free rising rigid spheres in fluid in general. Intl J. Multiphase Flow 27, 1479–1486.CrossRefGoogle Scholar
Karamanev, D. G., Chavarie, C. & Mayer, R. C. 1996 Dynamics of the free rise of a light solid sphere in liquid. AIChE J. 42, 1789–1792.CrossRefGoogle Scholar
Karamanev, D. G. & Nikolov, L. N. 1992 Free rising spheres do not obey Newton’s law for free settling. AIChE J. 33, 1843–1846.CrossRefGoogle Scholar
Magnaudet, J. & Mougin, G. 2007 Wake instability of a fixed spheroidal bubble. J. Fluid Mech. 572, 311–337.CrossRefGoogle Scholar
Magnaudet, J., Rivero, M. & Fabre, J. 1995 Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow. J. Fluid Mech. 284, 97–135.CrossRefGoogle Scholar
Manneville, P. & Pomeau, Y. 1979 Intermittency and the Lorentz model. Phys. Lett. A 75, 1–2.CrossRefGoogle Scholar
Mittal, R. 1999 Planar symmetry in the unsteady wake of a sphere. AIAA J. 37, 388–390.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2002a The generalized Kirchhoff equations and their application to the interaction between a rigid body and an arbitrary time-dependent viscous flow. Intl J. Multiphase Flow 28, 1837–1851.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2002b Path instability of a rising bubble. Phys. Rev. Lett. 88, 014502.Google ScholarPubMed
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323–344.CrossRefGoogle Scholar
Orr, T. S., Domaradzki, J. A., Spedding, G. R. & Constantinescu, G. S. 2015 Numerical simulations of the near wake of a sphere moving in a steady, horizontal motion through a linearly stratified fluid at Re = 1000. Phys. Fluids 27, 035113.CrossRefGoogle Scholar
Ostmann, S., Chaves, H. & Brüker, C. 2017 Path instabilities of light particles rising in a liquid with background rotation. J. Fluids Struct. 70, 403–416.CrossRefGoogle Scholar
Pomeau, Y. & Manneville, P. 1980 Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys. 74, 189–197.CrossRefGoogle Scholar
Poon, E. K. W., Ooi, A. S. H., Giacobello, M., Iaccarino, G. & Chung, D. 2014 Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime. J. Fluid Mech. 759, 751–781.CrossRefGoogle Scholar
Rivero, M., Magnaudet, J. & Fabre, J. 1991 New results on the forces exerted on a spherical body by an accelerated flow. C. R. Acad. Sci. Paris II-B 312, 1499–1506.Google Scholar
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar
Turton, R. & Levenspiel, O. 1986 A short note on the drag correlation for spheres. Powder Technol. 47, 83–86.CrossRefGoogle Scholar
Uhlmann, M. & Dušek, J. 2014 The motion of a single heavy sphere in ambient fluid: a benchmark for interface-resolved particulate flow simulations with significant relative velocities. Intl J. Multiphase Flow 59, 221–243.CrossRefGoogle Scholar
Veldhuis, C. H. J. & Biesheuvel, A. 2007 An experimental study of the regimes of motion of spheres falling or ascending freely in Newtonian fluid. Intl J. Multiphase Flow 33, 1074–1087.CrossRefGoogle Scholar
Veldhuis, C. H. J., Biesheuvel, A. & Lohse, D. 2009 Freely rising light solid spheres. Intl J. Multiphase Flow 35, 312–322.CrossRefGoogle Scholar
Zhang, W. & Stone, H. A. 1998 Oscillatory motions of circular disks and nearly spherical particles in viscous flows. J. Fluid Mech. 367, 329–358.CrossRefGoogle Scholar
Zhou, W. & Dušek, J. 2015 Chaotic states and order in the chaos of the paths of freely falling and ascending spheres. Intl J. Multiphase Flow 75, 205–223.CrossRefGoogle Scholar