From a steady plume to periodic puffs during confined carbon dioxide dissolution

Patrice Meunier (1) , F. Nadal (2)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 Loughborough University

In this paper, the stability of a laminar plume due to solutal convection is addressed from experimental, numerical and theoretical points of view. A topless vertical tube containing water is put in a pressure cell filled with carbon dioxide (CO 2). The diffusion of CO 2 at the free surface creates a thin layer of heavy fluid underneath the surface. This unstable density gradient generates a steady laminar plume which goes downward through the entire tube. A quasi-steady flow settles in the tube, filling gradually the bottom of the tube with heavy fluid. During this laminar regime, the velocity of the plume slowly decreases due to the build-up of the background density gradient. Surprisingly, despite the decrease of the Reynolds number, the laminar plume suddenly destabilizes via a varicose mode into periodic pulsed puffs after an onset time which depends on the height of the tube and on the chemical Rayleigh number Ra. This periodic regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution. The wavelength, frequency, onset time and phase velocity of the instability are explored using Particle Image Velocimetry (PIV) measurements over two decades of Rayleigh numbers. The characteristics of the instability appear to be almost independent of the Bond number but strongly dependent on the chemical Rayleigh number and the aspect ratio. The phase velocity is very close to the fluid velocity of the plume before the instability, which has been predicted in various works to scale as Ra 2/3 (ln Ra) 1/3. The wavelength is close to 4.5 times the radius of the cylinder (independent of aspect ratio, Bond number and Rayleigh number) such that the frequency scales as the phase velocity. The onset time, which is proportional to the height of the cylinder, scales as Ra −0.55 and depends on the Bond number. A simplified model inspired from Lorenz' waterwheel is proposed to explain the destabilization process after partial fill-up of the cylinder. Although very qualitative, the model captures the key features of the experimental observations.

Domaines: Mécanique des fluides [physics.class-ph]

Patrice Meunier, F. Nadal. From a steady plume to periodic puffs during confined carbon dioxide dissolution. Journal of Fluid Mechanics, 2018, 855, pp.1-27. ⟨10.1017/jfm.2018.564⟩. ⟨hal-02103711⟩