Abstract
We have investigated the characteristics and the causes of the zigzag periodic motions followed by solid bodies rising freely under the effect of buoyancy in liquid otherwise at rest. The frequencies, amplitudes and relative phases of the body velocity and orientation have been determined for a large range of parameters. Thanks to the determination of the body kinematics and using the force and torque balances provided by the generalized Kirchhoff equations, we have analyzed the dynamics of the body periodic motion.
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References
A. Andersen, U. Pesavento, and ZJ. Wang. Unsteady aerodynamics of fluttering and tumbling plates. J. Fluid. Mech., 541:65–90, 2005.
C. Brücker. Structure and dynamics of the wake of bubbles and its relevance for bubble interaction. Phys. Fluids, 11:1781–1796, 1999.
K. Ellingsen and F. Risso. On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid — induced velocity. J. Fluid. Mech., 440:235–268, 2001.
P. Ern, P.C. Fernandes, F. Risso, and J. Magnaudet. Evolution of wake structure and wake-induced loads along the path of freely rising axisymmetric bodies. Phys. Fluids, 19:113302, 2007.
P. C. Fernandes. Etude expérimentale de la dynamique de corps mobiles en ascension dans un fluide peu visqueux. The`se de Doctorat, Institut National Polytechnique de Toulouse, France, 2302, 2005.
P.C. Fernandes, P. Ern, F. Risso, and J. Magnaudet. On the zigzag dynamics of freely moving axisymmetric bodies. Phys. Fluids, 17:098107, 2005.
P.C. Fernandes, P. Ern, F. Risso, and J. Magnaudet. Dynamics of axisymmetric bodies rising along a zigzag path. J. Fluid Mech., 606:209–223, 2008.
P.C. Fernandes, F. Risso, P. Ern, and J. Magnaudet. Oscillatory motion and wake instability of freely-rising axisymmetric bodies. J. Fluid Mech., 573:479–502, 2007.
S. Field, M. Klaus, M. Moore, and F. Nori. Chaotic dynamics of falling disks. Nature, 388:252–254, 1997.
M. Howe. On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at low and high Reynolds numbers. Q. J. Mech. Appl. Math., 48:401–426, 1995.
M. Jenny, J. Dusek, and G. Bouchet. Instabilities and transition of a sphere falling or ascending in a newtonian fluid. J. Fluid. Mech., 508:201–239, 2004.
M.A. Jones and M.J. Shelley. Falling cards. J. Fluid. Mech., 540:393–425, 2005.
P. Kry and R. List. Angular motions of freely falling spheroidal hailstone models. Phys. Fluids, 17(6):1093–1102, 1974.
H.J. Lugt. Autorotation. Ann. Rev. Fluid. Mech., 15:123–147, 1983.
J. Magnaudet and I. Eames. The motion of high-Reynolds-number bubbles in inhomogeneous flows. Ann. Rev. Fluid Mech., 32:659–708, 2000.
G. Mougin and J. Magnaudet. The generalized Kirchhoff equations and their application to the interaction between a rigid body and an arbitrary time-dependent viscous flow. Int. J. Multiphase Flow, 28:1837–1851, 2002.
G. Mougin and J. Magnaudet. Path instability of a rising bubble. Phys. Rev. Lett., 88(1):14502, 2002.
G. Mougin and J. Magnaudet. Wake-induced forces and torques on a zigzagging/spiralling bubble. J. Fluid Mech., 567:185–194, 2006.
W. Shew, S. Poncet, and J.-F. Pinton. Force measurements on rising bubbles. J. Fluid Mech., 569:51–60, 2006.
G.E. Stringham, D.B. Simons, and H.P. Guy. The behavior of large particles falling in quiescent liquids. US Geol. Surv. Prof. Pap., 562-C:C1–C36, 1969.
Z.J. Wang. Dissecting insect flight. Ann. Rev. Fluid Mech., 37:183–210, 2005.
W. Willmarth, N. Hawk, and R. Harvey. Steady and unsteady motions and wakes of freely falling disks. Phys. Fluids, 7(2):197–208, 1964.
Acknowledgments
We are very grateful to D. Fabre, H. Ayroles, S. Cazin, E. Cid, C. Trupin, J.-P. Escafit, J.-J. Huc and O. Eiff for technical assistance and helpful discussions.
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Fernandes, P., Ern, P., Risso, F., Magnaudet, J. (2009). Dynamics of Oblate Freely Rising Bodies. In: Braza, M., Hourigan, K. (eds) IUTAM Symposium on Unsteady Separated Flows and their Control. IUTAM Bookseries, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9898-7_18
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DOI: https://doi.org/10.1007/978-1-4020-9898-7_18
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