Experimental investigation of the turbulence induced by a bubble swarm rising within incident turbulence

Abstract

This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high Reynolds numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction $\unicode[STIX]{x1D6FC}$ and the velocity fluctuations $u_{0}^{\prime }$ of the carrier flow before bubble injection are varied, respectively, in the ranges $0\,\%<\unicode[STIX]{x1D6FC}<0.93\,\%$ and $2.3~\text{cm}~\text{s}^{-1}<u_{0}^{\prime }<5.5~\text{cm}~\text{s}^{-1}$. The so-called bubblance parameter ($b=V_{r}^{2}\unicode[STIX]{x1D6FC}/u_{0}^{\prime 2}$, where $V_{r}$ is the bubble relative rise velocity) is used to compare the ratio of the kinetic energy generated by the bubbles to the one produced by the incident turbulence, and is varied from 0 to 1.3. Conditional measurements of the velocity field downstream of the bubbles in the vertical direction allow us to disentangle three regions that have specific statistical properties, namely the primary wake, the secondary wake and the far field. While the fluctuations in the primary wake are similar to that of a single bubble rising in a liquid at rest, the statistics of the velocity fluctuations in the far field follow a Gaussian distribution, similar to that produced by the homogenous and isotropic turbulence at the largest scales. In the secondary wake region, the conditional probability density function of the velocity fluctuations is asymmetric and shows an exponential tail for the positive fluctuations and a Gaussian one for the negative fluctuations. The overall agitation thus results from the combination of these three contributions and depends mainly on the bubblance parameter. For $0<b<0.7$, the overall velocity fluctuations in the vertical direction evolve as $b^{0.4}$ and are mostly driven by the far-field agitation, whereas the fluctuations increase as $b^{1.3}$ for larger values of the bubblance parameter ($b>0.7$), in which the significant contributions come both from the secondary wake and the far field. Thus, the bubblance parameter is a suitable parameter to characterise the evolution of liquid agitation in bubbly turbulent flows.