The budget of turbulent kinetic energy in bubble plumes by acoustic Doppler velocimetry*

We present an experimental investigation on the TKE budget of a two-phase air-water bubble plume in an otherwise quiescent ambient. The required three-dimensional turbulent velocity field was measured by a profiling acoustic Doppler velocimeter. Experiments were carried out in a square water tank of 1m$^3$ and covered both adjustment phase (z/D $<$ 5) and asymptotic regime (z/D $\ge$ 5) of the plume in which the latter is characterized by a constant local $Fr_{p}$. The dynamic length scale $D$ has previously been derived from a two-fluid approach and delineates the two regimes. Data on the mean flow establish the existence of an asymptotic regime when $z/D > 8$ with an entrainment coefficient of 0.095 and a $Fr_{p}$ of 1.63. The data also corroborate well with previous measurements of large-scale bubble plumes. A budget of TKE was performed using curve-fits derived from the radial profiles of second- and third-order moments of turbulent velocities. From the budget, TKE production by bubbles was found to be larger than that by fluid shear. Approximately 55-60\% of the total work done by bubbles is used to create fluid turbulence.