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Bubble behaviour in a horizontal high-speed solid-body rotating flow

Published online by Cambridge University Press:  27 August 2021

Majid Rodgar ,
Hélène Scolan ,
Jean-Louis Marié ,
Delphine Doppler  and
Jean-Philippe Matas Open the ORCID record for Jean-Philippe Matas [Opens in a new window]
Majid Rodgar
Affiliation:
Univ Lyon, Ecole Centrale de Lyon, Univ Claude Bernard Lyon 1, CNRS, INSA Lyon, LMFA, UMR5509, 69130, Ecully, France
Hélène Scolan
Affiliation:
Univ Lyon, Ecole Centrale de Lyon, Univ Claude Bernard Lyon 1, CNRS, INSA Lyon, LMFA, UMR5509, 69130, Ecully, France
Jean-Louis Marié*
Affiliation:
Univ Lyon, Ecole Centrale de Lyon, Univ Claude Bernard Lyon 1, CNRS, INSA Lyon, LMFA, UMR5509, 69130, Ecully, France
Delphine Doppler
Affiliation:
Univ Lyon, Ecole Centrale de Lyon, Univ Claude Bernard Lyon 1, CNRS, INSA Lyon, LMFA, UMR5509, 69130, Ecully, France
Jean-Philippe Matas
Affiliation:
Univ Lyon, Ecole Centrale de Lyon, Univ Claude Bernard Lyon 1, CNRS, INSA Lyon, LMFA, UMR5509, 69130, Ecully, France
*
†Email address for correspondence: jean-philippe.matas@univ-lyon1.fr
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Abstract

We study experimentally the behaviour of a bubble injected into a horizontal liquid solid-body rotating flow, in a range of rotational velocities where the bubble is close to the axis of rotation. We first study the stretching of the bubble as a function of its size and of the rotation of the cell. We show that the bubble aspect ratio can be predicted as a function of the bubble Weber number by the model of Rosenthal (J. Fluid Mech., vol. 12, 1962, 358–366) provided an appropriate correction due to the impact of buoyancy is included. We next deduce the drag and lift coefficients from the mean bubble position. For large bubbles straddling the axis of rotation, we show that the drag coefficient $C_D$ is solely dependent on the Rossby number $Ro$, with $C_D \approx 1.5/Ro$. In the same limit of large bubbles, we show that the lift coefficient $C_L$ is controlled by the shear Reynolds number $Re_{shear}$ at the scale of the bubble. For $Re_{shear}$ larger than 3000 we observe a sharp transition, wherein large fluctuations in the bubble aspect ratio and mean position occur, and can lead to the break-up of the bubble. We interpret this regime as a resonance between the periodic forcing of the rotating cell and the eigenmodes of the stretched bubble.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Breakup/coalescence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 925 , 25 October 2021 , A34
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Adoua, R., Legendre, D. & Magnaudet, J. 2009 Reversal of the lift force on an oblate bubble in a weakly viscous shear flow. J. Fluid Mech. 628, 23–41.CrossRefGoogle Scholar
Auton, T.R. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199–218.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Bluemink, J.J., Lohse, D., Prosperetti, A. & Van Wijngaarden, L. 2008 A sphere in a uniformly rotating or shearing flow. J. Fluid Mech. 600, 201–233.CrossRefGoogle Scholar
Bluemink, J.J., Lohse, D., Prosperetti, A. & Van Wijngaarden, L. 2010 Drag and lift forces on particles in a rotating flow. J. Fluid Mech. 643, 1–31.CrossRefGoogle Scholar
Cabut, D., Michard, M., Simoens, S., Méès, L., Todoroff, V., Hermange, C. & Le Chenadec, Y. 2021 Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry. Phys. Fluids 33, 032101.CrossRefGoogle Scholar
Choi, J.K. & Chahine, G.L. 2003 Non-spherical bubble behavior in vortex flow fields. Comput. Mech. 32, 281–290.CrossRefGoogle Scholar
Clift, R., Grace, J.R. & Weber, M.E. 1978 Bubbles, Drops and Particles. Academic.Google Scholar
Duineveld, P.C. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325–332.CrossRefGoogle Scholar
Ervin, E.A. & Tryggvason, G. 1997 The rise of bubbles in a vertical shear flow. Trans. ASME J. Fluid Engng 119, 443.CrossRefGoogle Scholar
Green, S.I. 1995 Fluid Vortices. Springer Science+Business Media Dordrech.CrossRefGoogle Scholar
Hayashi, K., Legendre, D. & Tomiyama, A. 2020 Lift coefficients of clean ellipsoidal bubbles in linear shear flows. Intl J. Multiphase Flow 129, 103350.CrossRefGoogle Scholar
Jah, N.K. & Govardhan, R.N. 2015 Interaction of a vortex ring with a single bubble: bubble and vorticity dynamics. J. Fluid Mech. 773, 460–497.Google Scholar
Johnson, T.A. & Patel, V.C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.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 Engineering Joint Conference, Honolulu, Hawaii, pp. 261–267.Google Scholar
Lamb, H. 1934 Hydrodynamics, 6th edn. Dover.Google Scholar
Magnaudet, J. & Eames, I. 2000 Dynamics of high $Re$ bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659–708.CrossRefGoogle Scholar
Magnaudet, J. & Legendre, D. 1998 Some aspects of the lift force on a spherical bubble. Appl. Sci. Res. 58, 441–461.CrossRefGoogle Scholar
Marten, M.K., Shariff, K., Psarakos, S. & White, D.J. 1996 Ring bubbles of dolphins. Sci. Am. 275, 82–87.CrossRefGoogle ScholarPubMed
Mudde, R.F. 2005 Gravity driven bubbly flows. Annu. Rev. Fluid Mech. 37, 393–423.CrossRefGoogle Scholar
Naciri, A. 1992 Contribution à l’étude des forces exercées par un liquide sur une bulle de gaz: portance, masse ajoutée et interactions hydrodynamiques. PhD thesis, Ecole Centrale de Lyon.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
Phillips, O.M. 1960 Centrifugal waves. J. Fluid Mech. 3, 340–352.CrossRefGoogle Scholar
Prosperetti, A. 2017 Vapor bubble. Annu. Rev. Fluid Mech. 49, 221–248.CrossRefGoogle Scholar
Rastello, M. & Marié, J.L. 2020 Wake behind contaminated bubbles in a solid-body rotating flow. J. Fluid Mech. 884, A17.CrossRefGoogle Scholar
Rastello, M., Marié, J.L., Grosjean, N. & Lance, M. 2009 Drag and lift forces on interface-contaminated bubbles spinning in a rotating flow. J. Fluid Mech. 624, 159–178.CrossRefGoogle Scholar
Rastello, M., Marié, J.L. & Lance, M. 2011 Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid-body rotating flow. J. Fluid Mech. 682, 434–459.CrossRefGoogle Scholar
Rastello, M., Marié, J.L. & Lance, M. 2017 Clean versus contaminated bubbles in a solid-body rotating flow. J. Fluid Mech. 831, 529–617.CrossRefGoogle Scholar
Risso, F. 2000 The mechanisms of deformation and breakup of drops and bubbles. Multiphase Sci. Technol. 12, 1–50.CrossRefGoogle Scholar
Risso, F. 2018 Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50, 25–48.CrossRefGoogle Scholar
Rosenthal, D.K. 1962 The shape and stability of a bubble at the axis of a rotating liquid. J. Fluid Mech. 12, 358–366.CrossRefGoogle Scholar
Saffman, P.G. 1965 The lift force on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.CrossRefGoogle Scholar
Sauma-Pérez, T., Johnson, C.G., Yang, Y. & Mullin, T. 2018 An experimental study of the motion of a light sphere in a rotating viscous fluid. J. Fluid Mech. 847, 119–133.CrossRefGoogle Scholar
Schiller, L. & Naumann, A.Z. 1933 Uber die grundlegenden Berechnungen bei der Schwerkraftaufberei-tung. Ver. Deut. Ing. 77, 318–320.Google Scholar
Serizawa, A., Kataoka, I. & Michiyoshi, I. 1975 Turbulence structure of air-water bubbly flow. II. Intl J. Multiphase Flow 2, 235–246.CrossRefGoogle Scholar
Sridhar, G. & Katz, J. 1995 Drag and lift forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7 (2), 389–399.CrossRefGoogle Scholar
Tagaki, S. & Matsumoto, Y. 2011 Surfactant effect on bubble motion and bubbly flows. Annu. Rev. Fluid Mech. 43, 615–636.CrossRefGoogle Scholar
Takemura, F., Magnaudet, J. & Dimitrakopoulos, P. 2009 Migration and deformation of bubbles rising in a wall-bounded shear flow at finite Reynolds number. J. Fluid Mech. 634, 463–486.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

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