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Linear instability of the path of a freely rising spheroidal bubble

Published online by Cambridge University Press:  24 June 2014

Joël Tchoufag ,
Jacques Magnaudet  and
David Fabre
Joël Tchoufag
Affiliation:
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France
Jacques Magnaudet*
Affiliation:
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
David Fabre
Affiliation:
Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France
*
†Email address for correspondence: magnau@imft.fr
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Abstract

Path and wake instabilities of buoyancy-driven oblate spheroidal bubbles with a prescribed shape rising freely in a viscous fluid otherwise at rest are studied using global stability analysis, following the technique recently developed for a coupled fluid $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}+$ body system by Tchoufag, Fabre & Magnaudet (J. Fluid Mech. vol. 740, 2014, pp. 278–311). The essential role of the wake on the path instability is evidenced by comparing the shape of the global stability diagram with that obtained in the case of a fixed bubble. However, dramatic differences are also found, since the critical curve of the coupled system mostly involves low- and high-frequency oscillating modes, whereas that of a fixed bubble only involves stationary modes. Comparison of the present predictions with results obtained through direct numerical simulation is achieved in several regimes, confirming the predictions of the linear approach but also highlighting some of its limitations when the system successively encounters several unstable modes.

JFM classification

Drops and Bubbles: Drops and Bubbles Instability: Instability Wakes/Jets: Wakes/Jets
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , R4
Copyright
© 2014 Cambridge University Press 

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References

Assemat, P., Fabre, D. & Magnaudet, J. 2012 The onset of unsteadiness of two-dimensional bodies falling or rising freely in a viscous fluid: a linear study. J. Fluid Mech. 690, 173–202.CrossRefGoogle Scholar
Auguste, F., Magnaudet, J. & Fabre, D. 2013 Falling styles of disks. J. Fluid Mech. 719, 388–405.Google Scholar
Blanco, A. & Magnaudet, J. 1995 The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Phys. Fluids 7, 1265–1274.Google Scholar
Cano-Lozano, J. C., Bohorquez, P. & Martinez-Bazan, C. 2013 Wake instability of a fixed axisymmetric bubble of realistic shape. Intl J. Multiphase Flow 51, 11–21.Google Scholar
Chrust, M., Bouchet, G. & Dusek, J. 2013 Numerical simulation of the dynamics of freely falling discs. Phys. Fluids 25, 044102.Google Scholar
Chrust, M., Bouchet, G. & Dusek, 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.Google Scholar
Ellingsen, K. & Risso, F. 2001 On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity. J. Fluid Mech. 440, 235–268.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.Google Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659–708.Google Scholar
Magnaudet, J. & Mougin, G. 2007 Wake instability of a fixed spheroidal bubble. J. Fluid Mech. 572, 311–337.Google Scholar
Mougin, G.2002 Interactions entre la dynamique d’une bulle et les instabilités de son sillage. PhD thesis, Inst. Nat. Polytech. Toulouse, France.Google Scholar
Mougin, G. & Magnaudet, J. 2002 Path instability of a rising bubble. Phys. Rev. Lett. 88, 014502.Google Scholar
Mougin, G. & Magnaudet, J. 2006 Wake-induced forces and torques on a zigzagging/spiralling bubble. J. Fluid Mech. 567, 185–194.Google Scholar
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323–344.Google Scholar
Prosperetti, A. 2004 Bubbles. Phys. Fluids 16, 1852–1865.Google Scholar
Prosperetti, A., Ohl, C., Tijink, A., Mougin, G. & Magnaudet, J. 2003 Leonardo’s paradox (Appendix to ‘The added mass of an expanding bubble’ by C. D. Ohl, A. Tijink and A. Prosperetti). J. Fluid Mech. 482, 271–290.Google Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean-flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.Google Scholar
Tchoufag, J., Fabre, D. & Magnaudet, J. 2014 Global linear stability analysis of the wake and path of buoyancy-driven disks and thin cylinders. J. Fluid Mech. 740, 278–311.Google Scholar
Tchoufag, J., Magnaudet, J. & Fabre, D. 2013 Linear stability and sensitivity of the flow past a fixed oblate spheroidal bubble. Phys. Fluids 25, 054108.Google Scholar
Veldhuis, C., Biesheuvel, A. & van Wijngaarden, L. 2008 Shape oscillations on bubbles rising in clean and in tap water. Phys. Fluids 20, 040705.Google Scholar
de Vries, A., Biesheuvel, A. & van Wijngaarden, L. 2002 Notes on the path and wake of a gas bubble rising in pure water. Intl J. Multiphase Flow 28, 1823–1835.Google Scholar
van Wijngaarden, L. 2005 Bubble velocities induced by trailing vortices behind neighbours. J. Fluid Mech. 541, 203–229.Google Scholar
Zenit, R. & Magnaudet, J. 2008 Path instability of rising spheroidal air bubbles: a shape-controlled process. Phys. Fluids 20, 061702.Google Scholar
Zenit, R. & Magnaudet, J. 2009 Measurements of the streamwise vorticity in the wake of an oscillating bubble. Intl J. Multiphase Flow 35, 195–203.CrossRefGoogle Scholar