Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2. Liquid dynamics

Abstract

AbstractThe agitation of the liquid phase has been investigated experimentally in a homogeneous swarm of bubbles rising at high Reynolds number within a thin gap. Owing to the wall friction, the bubble wakes are strongly attenuated. Consequently, liquid fluctuations result from disturbances localized near the bubbles and direct interactions between them. The signature of the average wake rapidly fades and the probability density function of the fluctuations becomes Gaussian as the gas volume fraction $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\alpha $ increases. The energy of the fluctuations scales differently with $\alpha $ depending on the direction, indicating that hydrodynamic interactions are different in the horizontal and vertical directions. The spatial spectrum shows that the length scales of the fluctuations are independent of $\alpha $ and exhibits a $k^{-3}$ subrange, which results from localized random flow disturbances of various sizes. Comparisons with the dynamics of the gas phase show that liquid and bubble agitations are driven by the same mechanism in the vertical direction, whereas they turn out to be almost uncoupled in the horizontal direction. Comparisons with unconfined flows show that the generation of liquid fluctuations is very different. However, the cause of the $k^{-3}$ spectral subrange is the same for confined flows as for the spatial fluctuation of unconfined flows.