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Turbulent transport mechanisms in oscillating bubble plumes

The detailed investigation of an unstable meandering bubble plume created in a 2-m-diameter vessel with a water depth of 1.5 m is reported for void fractions up to 4% and bubble size of the order of 2.5 mm. Simultaneous particle image velocity (PIV) measurements of bubble and liquid velocities and video recordings of the projection of the plume on two vertical perpendicular planes were produced in order to characterize the state of the plume by the location of its centreline and its equivalent diameter. The data were conditionally ensemble averaged using only PIV sets corresponding to plume states in a range as narrow as possible, separating the small-scale fluctuations of the flow from the large-scale motions, namely plume meandering and instantaneous cross-sectional area fluctuations. Meandering produces an apparent spreading of the average plume velocity and void fraction profiles that were shown to remain self-similar in the instantaneous plume cross-section. Differences between the true local time-average relative velocities and the difference of the averaged phase velocities were measured; the complex variation of the relative velocity was explained by the effects of passing vortices and by the fact that the bubbles do not reach an equilibrium velocity as they migrate radially, producing momentum exchanges between high- and low-velocity regions. Local entrainment effects decrease with larger plume diameters, contradicting the classical dependence of entrainment on the time-averaged plume diameter. Small plume diameters tend to trigger ‘entrainment eddies’ that promote the inward-flow motion. The global turbulent kinetic energy was found to be dominated by the vertical stresses. Conditional averages according to the plume diameter showed that the large-scale motions did not affect the instantaneous turbulent kinetic energy distribution in the plume, suggesting that large scales and small scales are not correlated. With conditional averaging, meandering was a minor effect on the global kinetic energy and the Reynolds stresses. In contrast, plume diameter fluctuations produce a substantial effect on these quantities.