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Stationary plume induced by carbon dioxide dissolution

Published online by Cambridge University Press:  19 February 2013

F. Nadal ,
P. Meunier ,
B. Pouligny  and
E. Laurichesse
F. Nadal
Affiliation:
Commissariat à l’Énergie Atomique (CEA), 33314 Le Barp, France
P. Meunier*
Affiliation:
IRPHE UMR 7342, CNRS, Aix Marseille Université, Centrale Marseille, 13013 Marseille, France
B. Pouligny
Affiliation:
CRPP UPR 8641, CNRS, Université Bordeaux I, 33600 Pessac, France
E. Laurichesse
Affiliation:
CRPP UPR 8641, CNRS, Université Bordeaux I, 33600 Pessac, France
*
†Email address for correspondence: meunier@irphe.univ-mrs.fr
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Abstract

In this paper, laminar convection flows induced by carbon dioxide absorption are addressed from experimental, numerical and theoretical points of view. A vertical glass tube (of centimetre scale) filled with distilled water is subjected to a sudden increase in the partial pressure of carbon dioxide. As a result of the diffusion of the gas into the unsaturated solution, a thin layer of fluid located underneath the surface becomes heavier. This initial density gradient first destabilizes to form a plume, which goes downwards through the entire cell. After a first transient pulsating regime (periodic succession of such Rayleigh–Bénard plumes), a stationary flow settles in the tube, which is maintained by the constant supply of gas at the surface. At late stages, this stationary regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution (thermodynamic equilibrium). The present study only focuses on the stationary regime, whose characteristics appear to be almost independent of the Bond number and the aspect ratio but strongly dependent on the chemical Rayleigh number. Three decades of Rayleigh numbers are explored using particle image velocimetry measurements, which allows for a precise determination of the scaling exponents for the vertical velocity amplitude and the plume width. The assumption that gravity and a constant pressure gradient balance the viscous effects enables us to derive an analytic expression for the stationary vertical velocity on the axis, which scales as ${\mathit{Ra}}^{2/ 3} \mathop{(\ln \mathit{Ra})}\nolimits ^{1/ 3} $. As a consequence, the width of the plume scales as ${\mathit{Ra}}^{- 1/ 6} \mathop{(\ln \mathit{Ra})}\nolimits ^{- 1/ 3} $ and the mass Nusselt number as $\mathop{(\mathit{Ra}/ \ln \mathit{Ra})}\nolimits ^{1/ 3} $. These scalings are in excellent agreement with the experimental and numerical results. The multiplicative constants of these scalings can also be calculated and show a fairly good agreement if a rigid boundary condition (no-slip) is assumed at the free surface.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 203 - 229
Copyright
©2013 Cambridge University Press

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Nadal et al. supplementary movie

Temporal evolution of a plume created by carbone dioxide dissolution at the surface with Ra=1.9 106, h=3 and Bo=4.9, corresponding to P=4bars, H=18mm and Rc=6mm. The movie is accelerated 16 times.

Download Nadal et al. supplementary movie(Video)
Video 16.8 MB