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Bubble shape oscillations in a turbulent environment

Published online by Cambridge University Press:  11 December 2024

Aliénor Rivière Open the ORCID record for Aliénor Rivière [Opens in a new window] ,
Kamel Abahri  and
Stéphane Perrard Open the ORCID record for Stéphane Perrard [Opens in a new window]
Aliénor Rivière
Affiliation:
PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France
Kamel Abahri
Affiliation:
PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France
Stéphane Perrard*
Affiliation:
PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France
*
†Email address for correspondence: stephane.perrard@espci.fr
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Abstract

We study single bubble deformation statistics in an homogeneous and isotropic turbulent flow by means of direct numerical simulations. We consider bubbles at low Weber number ($We <3$) that have not been broken. We show that we can reproduce bubble deformations with a linear dynamics for each spherical harmonic mode. Inferring the coefficients of the linear model from the DNS data, we find that the natural frequency corresponds to the Rayleigh frequency, derived in a quiescent flow. However, the effective damping increases by a factor 7 compared with the quiescent case, at Taylor Reynolds number $\textit {Re}_\lambda = 55$. Looking at the flow structure around the bubble, we argue that the enhanced damping originates from a thick boundary layer surrounding the bubble. We demonstrate that the effective forcing, originating from the turbulent flow forcing on the bubble surface, is independent of bubble deformability. Therefore, the interface deformations are only one-way coupled to the flow. From this model we conclude that bubbles break rather from turbulent fluctuations than from a resonant mechanism. Eventually, we investigate the pressure modes’ statistics in the absence of bubbles and compare them with the effective forcing statistics. We show that both fields share the same probability distribution function, characterized by exponential tails, and a characteristic time scale corresponding to the eddy turnover time at the mode scale.

JFM classification

Drops and Bubbles: Bubble dynamics Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1001 , 25 December 2024 , A26
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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