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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: marie.rastello@legi.cnrs.fr
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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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