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Reversal of the lift force on an oblate bubble in a weakly viscous linear shear flow

Published online by Cambridge University Press:  01 June 2009

RICHARD ADOUA ,
DOMINIQUE LEGENDRE  and
JACQUES MAGNAUDET
RICHARD ADOUA
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
DOMINIQUE LEGENDRE
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
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
*
†Email address for correspondence: [email protected]
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Abstract

We compute the flow about an oblate spheroidal bubble of prescribed shape set fixed in a viscous linear shear flow in the range of moderate to high Reynolds numbers. In contrast to predictions based on inviscid theory, the numerical results reveal that for weak enough shear rates, the lift force and torque change sign in an intermediate range of Reynolds numbers when the bubble oblateness exceeds a critical value that depends on the relative shear rate. This effect is found to be due to the vorticity generated at the bubble surface which, combined with the velocity gradient associated with the upstream shear, results in a system of two counter-rotating streamwise vortices whose sign is opposite to that induced by the classical inviscid tilting of the upstream vorticity around the bubble. We show that this lift reversal mechanism is closely related to the wake instability mechanism experienced by a spheroidal bubble rising in a stagnant liquid.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 23 - 41
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Adoua, S. R. 2007 Hydrodynamique d'une bulle déformée dans un écoulement cisaillé. Thèse de Doctorat, Inst. Nat. Polytech. Toulouse (available online at http://ethesis.inp-toulouse.fr/archive/00000458/).Google Scholar
Auton, T. R. 1987 The lift force on a spherical body in rotational flow. J. Fluid Mech. 183, 199–218.CrossRefGoogle Scholar
Auton, T. R., Hunt, J. C. R. & Prud'homme, M. 1988 The force exerted on a body in an inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257.CrossRefGoogle Scholar
Ervin, E. A. & Tryggvason, G. 1997 The rise of bubbles in a vertical shear flow. J. Fluids Engng 119, 443–449.CrossRefGoogle Scholar
Kariyasaki, A. 1987 Behavior of a single gas bubble in a liquid flow with a linear velocity profile. In Proceedings of ASME-JSME Thermal Engng Joint Conf., Honolulu Hawaii, pp. 261–267.Google Scholar
Lamb, H. 1945 Hydrodynamics, 6th ed. Cambridge University Press.Google Scholar
Legendre, D. & Magnaudet, J. 1998 The lift force on a spherical bubble in a viscous linear shear flow. J. Fluid Mech. 368, 81–126.CrossRefGoogle Scholar
Lighthill, J. 1956 Drift. J. Fluid Mech. 1, 31–53.CrossRefGoogle Scholar
Magnaudet, J. & Mougin, G. 2007 Wake instability of a fixed spheroidal bubble. J. Fluid Mech. 572, 311–337.CrossRefGoogle Scholar
Magnaudet, J., Takagi, S. & Legendre, D. 2003 Drag, deformation and lateral migration of a buoyant drop moving near a vertical wall. J. Fluid Mech. 476, 115–157.CrossRefGoogle Scholar
Miloh, T. 2003 The motion of solids in inviscid uniform vortical fields. J. Fluid Mech. 479, 287–385.CrossRefGoogle Scholar
Moore, D. W. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749–766.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2002 Path instability of a rising bubble. Phys. Rev. Lett. 88, 014502.Google ScholarPubMed
Naciri, A. 1992 Contribution à l'étude des forces exercées par un liquide sur une bulle de gaz: portance, masse ajoutée et interactions hydrodynamiques. Thèse de Doctorat, Ec. Centrale Lyon, France.Google Scholar
van Nierop, E. A., Luther, S., Bluemink, J. J., Magnaudet, J., Prosperetti, A. & Lohse, D. 2007 Drag and lift forces on bubbles in a rotating flow. J. Fluid Mech. 571, 439–454.CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1995 The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J. Fluid. Mech. 287, 151–171.CrossRefGoogle Scholar
Sankaranarayanan, K. & Sundaresan, S. 2002 Lift force in bubbly suspensions. Chem. Engng Sci. 57, 3521–3542.CrossRefGoogle Scholar
Serizawa, A., Kataoka, I. & Michiyoshi, I. 1975 Turbulence structure of air–water bubbly flow II. Local properties. Intl J. Multiph. Flow 2, 235–246.CrossRefGoogle Scholar
Tomiyama, A., Tamai, H., Zun, I. & Hosokawa, S. 2002 Transverse migration of single bubbles in simple shear flows. Chem. Engng Sci. 57, 1849–1859.CrossRefGoogle Scholar
Tran-Cong, S., Marié, J. L. & Perkins, R. J. 2008 Bubble migration in a turbulent boundary layer. Intl J. Multiph. Flow 34, 786–807.CrossRefGoogle Scholar
Wells, J. C. 1996 A geometrical interpretation of force on a translating body in rotational flow. Phys. Fluids 8, 442.CrossRefGoogle Scholar
Zenit, R. & Magnaudet, J. 2008 Path instability of spheroidal rising bubbles: a shape-controlled process. Phys. Fluids 20, 061702.CrossRefGoogle Scholar