Dynamics of a high-Reynolds-number bubble rising within a thin gap

Véronique Roig (1, 2) , Matthieu Roudet (1, 2) , Frédéric Risso (1, 2) , Anne-Marie Billet (3, 2)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 FERMAT - Fédération de Recherche Fluides, Energie, Réacteurs, Matériaux et Transferts
3 LGC - Laboratoire de Génie Chimique

We report an experimental analysis of path and shape oscillations of an air bubble of diameter d rising in water at high Reynolds number in a vertical Hele-Shaw cell of width h. Liquid velocity perturbations induced by the relative movement have also been investigated to analyze the coupling between the bubble motion and the wake dynamics. The confinement ratio h/d is lower than unity so that the bubble is flattened in between the walls of the cell. As the bubble diameter is increased, the Archimedes and the Bond numbers increase within 10 6 Ar 6 104 and 6 × 10−3 6 Bo 6 140. Mean shapes become more and more elongated. They first evolve from in-plane circles to ellipses, then to complicated shapes without fore-aft symmetry and finally to semi-circular capped bubbles. The scaling law Re = 0.5Ar is however valid for a large range of Ar, indicating that the liquid films between the bubble and the walls do no contribute significantly to the drag force exerted on the bubble. The coupling between wake dynamics, bubble path and shape oscillations evolves and a succession of contrasted regimes of oscillations is observed. The rectilinear bubble motion becomes unstable from a critical value Ar1 through an Hopf bifurcation while the bubble shape is still circular. The amplitude of path oscillations first grows as Ar increases above Ar1 but then surprisingly decreases beyond a second Archimedes number Ar2. This phenomenon, observed for steady ellipsoidal shape with moderate eccentricity, can be explained by the rapid attenuation of bubble wakes caused by the confinement. Shape oscillations around a significantly elongated mean shape starts for Ar > Ar3. The wake structure progressively evolves due to changes in the bubble shape. After the break-up of the fore-aft symmetry, a fourth regime involving complicated shape oscillations is then observed for Ar > Ar4. Vortex shedding disappears and unsteady attached vortices coupled to shape oscillations trigger path oscillations of moderate amplitude. Path and shape oscillations finally decrease when Ar is further increased. For Ar > Ar5, capped bubbles followed by a steady wake rise on a straight path.

Mots clés: Bubble dynamics; Multiphase flow; Wake; Vortex shedding

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

Véronique Roig, Matthieu Roudet, Frédéric Risso, Anne-Marie Billet. Dynamics of a high-Reynolds-number bubble rising within a thin gap. Journal of Fluid Mechanics, 2012, 707, pp.444-466. ⟨10.1017/jfm.2012.289⟩. ⟨hal-03531011⟩