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Interaction of two axisymmetric bodies falling side by side at moderate Reynolds numbers

Published online by Cambridge University Press:  11 February 2014

Patricia Ern*
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France CNRS, IMFT, F-31400 Toulouse, France
Nicolas Brosse
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France CNRS, IMFT, F-31400 Toulouse, France
Email address for correspondence:


We consider the interaction of two identical disks freely falling side by side in a fluid at rest for Reynolds numbers ranging from 100 to 300, corresponding to rectilinear and oscillatory paths. For the three aspect ratios of the disks investigated, we observed that the bodies always repel one another when the horizontal distance between their centres of gravity is less than 4.5 diameters. They never come closer for distances spanning between 4.5 and 6 diameters. Beyond the latter distance, the disks appear indifferent to each other. For both rectilinear and periodic paths, the repulsion effect is weak, leading to an overall horizontal drift lower than 3 % of the vertical displacement. We propose a model for the repulsion coefficient Cr, which decreases with the separation distance between the bodies and is inversely proportional to the aspect ratio of the bodies, Cr thus being stronger for the thicker ones. Furthermore, in the case of the oscillatory paths, we show that the effect of the interaction reduces to the repulsion effect, since the characteristics of the oscillatory motion of each disk appear unaffected by the presence of the companion disk and no synchronization is observed between the paths, nor between the wakes, of the two disks.

© 2014 Cambridge University Press 

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Aidun, C. K., Lu, Y. & Ding, E. J. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287311.CrossRefGoogle Scholar
Fernandes, P. C. 2005 Etude expérimentale de la dynamique de corps mobiles en ascension dans un fluide peu visqueux. PhD thesis, Institut National Polytechnique de Toulouse.Google Scholar
Fernandes, P. C., Ern, P., Risso, F. & Magnaudet, J. 2008 Dynamics of axisymmetric bodies rising along a zigzag path. J. Fluid Mech. 606, 209223.Google Scholar
Fernandes, P. C., Risso, F., Ern, P. & Magnaudet, J. 2007 Oscillatory motion and wake instability of freely rising axisymmetric bodies. J. Fluid Mech. 573, 479502.Google Scholar
Kim, I., Elghobashi, S. & Sirignano, W. A. 1993 Three-dimensional flow over two spheres placed side by side. J. Fluid Mech. 246, 465488.Google Scholar
Legendre, D., Magnaudet, J. & Mougin, G. 2003 Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J. Fluid Mech. 497, 133166.Google Scholar
Pan, T. W., Joseph, D. D. & Glowinski, R. 2005 Simulating the dynamics of fluid-ellipsoid interactions. Comput. Struct. 83 (6-7), 463478.Google Scholar
Peschard, I. & Le Gal, P. 1996 Coupled wakes of cylinders. Phys. Rev. Lett. 77 (15), 31223125.Google Scholar
Schouveiler, L., Brydon, A., Leweke, T. & Thompson, M. C. 2004 Interactions of the wakes of two spheres placed side by side. Eur. J. Mech. B/Fluids 23 (1), 137145.CrossRefGoogle Scholar
Takemura, F. & Magnaudet, J. 2003 The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number. J. Fluid Mech. 495, 235253.CrossRefGoogle Scholar
Williamson, C. H. K. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 118.CrossRefGoogle Scholar
Wu, J. & Manasseh, R. 1998 Dynamics of dual-particles settling under gravity. Intl J. Multiphase Flow 24 (8), 13431358.Google Scholar
Yoon, D.-H. & Yang, K.-S. 2007 Flow-induced forces on two nearby spheres. Phys. Fluids 19 (9), 098103.Google Scholar