Study of bubble’s equilibrium in rotating flow

The equilibrium of small bubbles (d ∈ [0.2mm, 2mm]) in a solid body rotating flow around an horizontal axis is studied. The caracterisation of the reference flow (eg) the rotating flow without bubbles is led. Measurements show that the velocity profiles are linear as expected and that the axis of rotation of the flow exhibits motions of small amplitude (≈ ±0.1mm). The frequencies that appear in this motion are explored. One peak is the rotation rate of the tank, frequency that is also present in the bubble’s oscillating motion. The influence of the bubbles on this reference flow is then investigated. Depending of the size of the bubble and of its position relatively to the axis of rotation the bubble can feel back its own perturbation. The range of Reynolds and Strouhal numbers in which this occurs is quantified. When the incoming flow on the bubble is not influenced by the wake of the bubble, the drag and lift coefficients are considered. The two coefficients are determined from the measurement of the bubble’s equilibrium position. The resulting coefficients exhibit an increase of the drag with shear and a decrease of the lift. The lift coefficient tends asymptotically to 1 at high Reynolds number which is higher than the 0.5 value of Auton (1987)’s potential theory. The bubble never stabilizes on its equilibrium position, but slightly oscillates around this position. The spectrum of these oscillations shows three types of frequencies. One is equal to the rotation rate of the tank, another one is linked with a three-dimensional motion of the bubble and the last one is related to the interaction between the bubble and the shedding of vortices in the wake.