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The effect of nonlinear drag on the rise velocity of bubbles in turbulence

Published online by Cambridge University Press:  04 August 2021

Daniel J. Ruth Open the ORCID record for Daniel J. Ruth [Opens in a new window] ,
Marlone Vernet Open the ORCID record for Marlone Vernet [Opens in a new window] ,
Stéphane Perrard Open the ORCID record for Stéphane Perrard [Opens in a new window]  and
Luc Deike Open the ORCID record for Luc Deike [Opens in a new window]
Daniel J. Ruth
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA
Marlone Vernet
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA Département de Physique, ENS, PSL Université, CNRS, 24 rue Lhomond, 75005 Paris, France
Stéphane Perrard
Affiliation:
Département de Physique, ENS, PSL Université, CNRS, 24 rue Lhomond, 75005 Paris, France
Luc Deike*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA High Meadows Environmental Institute, Princeton University, NJ 08544, USA
*
†Email address for correspondence: ldeike@princeton.edu
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Abstract

We investigate how turbulence in liquid affects the rising speed of gas bubbles within the inertial range. Experimentally, we employ stereoscopic tracking of bubbles rising through water turbulence created by the convergence of turbulent jets and characterized with particle image velocimetry performed throughout the measurement volume. We use the spatially varying, time-averaged mean water velocity field to consider the physically relevant bubble slip velocity relative to the mean flow. Over a range of bubble sizes within the inertial range, we find that the bubble mean rise velocity $\left \langle v_z \right \rangle$ decreases with the intensity of the turbulence as characterized by its root-mean-square fluctuation velocity, $u'$. Non-dimensionalized by the quiescent rise velocity $v_{q}$, the average rise speed follows $\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$ at high ${\textit {Fr}}$, where ${\textit {Fr}}=u'/\sqrt {dg}$ is a Froude number comparing the intensity of the turbulence to the bubble buoyancy, with $d$ the bubble diameter and $g$ the acceleration due to gravity. We complement these results by performing numerical integration of the Maxey–Riley equation for a point bubble experiencing nonlinear drag in three-dimensional, homogeneous and isotropic turbulence. These simulations reproduce the slowdown observed experimentally, and show that the mean magnitude of the slip velocity is proportional to the large-scale fluctuations of the flow velocity. Combining the numerical estimate of the slip velocity magnitude with a simple theoretical model, we show that the scaling $\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$ originates from a combination of the nonlinear drag and the nearly isotropic behaviour of the slip velocity at large ${\textit {Fr}}$ that drastically reduces the mean rise speed.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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