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Stationary plume induced by carbon dioxide dissolution

  • F. Nadal (a1), P. Meunier (a2), B. Pouligny (a3) and E. Laurichesse (a3)
Abstract
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.

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Email address for correspondence: meunier@irphe.univ-mrs.fr
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G. Alendal , H. Drange & P. M. Haugan 1994 Modelling of deep-sea gravity currents using an integrated plume model. In The Polar Oceans and Their Role in Shaping the Global Environment (ed. O. M. Johannessen, R.D. Muench & J.E. Overland), pp. 237246. American Geophysical Union.

D. Anderson 1975 Chemical plumes in the mantle. Geol. Soc. Am. Bull. 86, 15931600.

G. K. Batchelor 1954 Heat convection and buoyancy effects in fluids. Q. J. R. Meteorol. Soc. 80, 339358.

C. Dombrowski , B. Lewellyn , A. I. Pesci , J. M. Restrepo , J. O. Kessler & R. E. Goldstein 2005 Coiling, entrainment, and hydrodynamic coupling of decelerated fluid jets. Phys. Rev. Lett. 95, 184501.

T. Fujii 1963 Theory of the steady laminar natural convection above a horizontal line heat source and a point heat source. Intl J. Heat Mass Transfer 6, 597.

A. Hebach , A. Oberhof & N. Dahmen 2004 Density of water$~+ $ carbon dioxide at elevated pressures: measurements and correlation. J. Chem. Eng. Data 49 (5), 950953.

E. J. List 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189212.

P. Meunier & T. Leweke 2003 Analysis and optimization of the error caused by high velocity gradients in particle image velocimetry. Exp. Fluids 35 (5), 408421.

B. R. Morton , G. I. Taylor & J. S. Turner 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.

P. Olson , G. Schubert & C. Anderson 1993 Structure of axisymmetric mantle plumes. J. Geophys. Res. 98, 68296844.

L. Pera & G. Gebhart 1971 On the stability of laminar plumes: some numerical solutions and experiments. Intl J. Heat Mass Transfer 14, 975984.

A. I. Pesci , M. A. Porter & M. A. Goldstein 2003 Inertially driven buckling and overturning of jets in a Hele-Shaw cell. Phys. Rev. E 68, 056305.

G. O. Roberts 1977 Fast viscous convection. Geophys. Astrophys. Fluid Dyn. 8, 197233.

D. Schlien & R. Boxman 1979 Temperature field measurement in an axisymmetric laminar plume. Phys. Fluids 22, 631634.

S. P. Schofield & J. M. Restrepo 2010 Stability of planar buoyant jets in stratified fluids. Phys. Fluids 22, 053602.

J. S. Turner 1969 Buoyant plumes and thermals. Annu. Rev. Fluid Mech. 1, 2944.

A. W. Woods 2010 Turbulent plumes in nature. Annu. Rev. Fluid Mech. 42, 391412.

M. G. Worster 1986 The axisymmetric laminar plume: asymptotic solution for large Prandtl number. Stud. Appl. Math. 75, 139152.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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Type Description Title
VIDEO
Movie

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.

 Video (10.7 MB)
10.7 MB