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Mean velocity, spreading and entrainment characteristics of weak bubble plumes in unstratified and stationary water

Published online by Cambridge University Press:  03 July 2019

Binbin Wang Open the ORCID record for Binbin Wang [Opens in a new window] ,
Chris C. K. Lai Open the ORCID record for Chris C. K. Lai [Opens in a new window]  and
Scott A. Socolofsky
Binbin Wang*
Affiliation:
Department of Civil and Environmental Engineering, University of Missouri, Columbia, MO 65211, USA
Chris C. K. Lai
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Scott A. Socolofsky
Affiliation:
Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this paper we present an experimental and theoretical study of weak bubble plumes in unstratified and stationary water. We define a weak bubble plume as one that spreads slower than the linear rate of a classic plume. This work focuses on the characteristics of the mean flow in the plume, including centreline velocity, plume spreading and entrainment of ambient water. A new theory based on diffusive spreading instead of an entrainment hypothesis is used to describe the lateral spreading of the bubbles and the associated plume. The new theory is supported by the experimental data. With the measured data of liquid volume fluxes and the new theory, we conclude that the weak bubble plume is a decreasing entrainment process, with the entrainment coefficient $\unicode[STIX]{x1D6FC}$ in the weak bubble plume decreasing with height $z$, following $\unicode[STIX]{x1D6FC}\sim z^{-1/2}$, and taking on values much smaller than those in a classic bubble plume. An additional non-dimensional diffusion coefficient, $\hat{E_{t}}\sim E_{t}U_{s}^{2}/B_{0}$, is also needed to describe the evolution of the volume and kinematic momentum fluxes for the mean flow in the weak bubble plume. Here, $E_{t}$ is the effective turbulent diffusion coefficient, $U_{s}$ is the terminal rise velocity of the bubbles, and $B_{0}$ is the kinematic buoyancy flux of the source. Finally, we provide a unified framework for the mean flow characteristics, including volume flux, momentum flux and plume spreading for the classic and weak bubble plumes, which also provides insight on the transition from classic to weak bubble plume behaviour.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 102 - 130
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Copyright
© 2019 Cambridge University Press 

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