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Wake behind contaminated bubbles in a solid-body rotating flow

Published online by Cambridge University Press:  10 December 2019

Marie Rastello Open the ORCID record for Marie Rastello [Opens in a new window]  and
Jean-Louis Marié Open the ORCID record for Jean-Louis Marié [Opens in a new window]
Marie Rastello*
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, UMR 5509, Université de Lyon, CNRS, Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000Grenoble, France
Jean-Louis Marié
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, UMR 5509, Université de Lyon, CNRS, Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, 36 avenue Guy de Collongue, 69134Ecully CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

A bubble injected into a flow rotating about a horizontal axis comes to an equilibrium location. The drag and lift exerted on the bubble can be measured and the bubble wake visualized (Rastello et al., J. Fluid Mech., vol. 624, 2009, pp. 159–178; Rastello et al., J. Fluid Mech., vol. 682, 2011, pp. 434–459; Rastello et al.,J. Fluid Mech., vol. 831, 2017, pp. 529–617). For a contaminated bubble, interface deformation remains limited. The bubble is freely rotating, which results in a complex separated wake, influenced by rotational flow and bubble spinning. The wake is described by analysing the near- and far-wake geometry and behaviour from laser-sheet visualizations, as a function of the relevant non-dimensional numbers: bubble Reynolds number $Re$, Rossby number $Ro$, and non-dimensional spinning rate $\unicode[STIX]{x1D6FA}^{\ast }$. As the far-wake length increases with $Re$, it deflects towards the rotation axis of the flow, the deflection angle increasing with $Re$ and being twice the angle that would occur without deflection. Deflection is stronger for bubbles located close to the rotation axis of the flow (small $Ro$). The far wake is more curved than the incoming streamlines. The near wake exhibits three distinct regimes as a function of $Re$. For $Re\leqslant 140$, the near wake is structured by the bubble spinning. Its size is related to $\unicode[STIX]{x1D6FA}^{\ast }$ and grows faster with $Re$ than for a stationary sphere in a uniform flow. As the bubble spinning is saturating ($140<Re\leqslant 240$), these differences vanish and $Re$ dependences for the two situations becomes comparable. For $Re>240$, wake instability generates a bubble precession that makes the near wake decrease rapidly for higher $Re$. These regimes coincide with the changes in the lift coefficients that we have noted in our studies.

JFM classification

Drops and Bubbles: Bubble dynamics Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A17
Copyright
© 2019 Cambridge University Press

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References

Bagchi, P. & Balachandar, S. 2002 Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re. Phys. Fluids 14 (8), 2719–2737.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
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
Fan, L.-S. & Tsuchiya, K. 1990 Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions. Butterworth-Heinemann.Google Scholar
Giacobello, M., Ooi, A. & Balanchandar, S. 2009 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J. Fluid Mech. 621, 103–130.CrossRefGoogle 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
Kim, D. 2009 Laminar flow past a sphere rotating in the transverse direction. J. Mech. Sci. Technol. 23, 578–589.CrossRefGoogle Scholar
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183–206.CrossRefGoogle Scholar
Nakamura, I. 1976 Steady wake behind a sphere. Phys. Fluids. 19, 5–8.CrossRefGoogle Scholar
Poon, E., Ooi, A., Giacobello, M. & Cohen, R. 2010 Laminar flow structures from a rotating sphere: effect of rotating axis angle. Intl J. Heat Fluid Flow 31, 961–972.CrossRefGoogle Scholar
Poon, E., Ooi, A., Giacobello, M., Iaccarino, G. & Cohen, R. 2013 Hydrodynamic forces on a rotating sphere. Intl J. Heat Fluid Flow 42, 278–288.CrossRefGoogle Scholar
Poon, E., Ooi, A., Giacobello, M., Iaccarino, G. & Chung, D. 2014 Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime. J. Fluid Mech. 759, 751–781.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. 2018 Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50, 25–48.CrossRefGoogle Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds. J. Phys. Soc. Japan 11, 1104–1108.CrossRefGoogle Scholar
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transition and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar