Many experiments demonstrate that the bubble relative (slip) velocities in vertical turbulent sheared bubbly flows are significantly lower than those in quiescent infinite fluid. Moreover, vertical bubbly jet experiments performed by Sun and Faeth (1986, “Structure of Turbulent Bubbly Jets-1. Methods and Centerline Properties,” Int. J. Multiphase Flow, 12(1), pp. 99–114) indicate that bubble slip velocities have negative values in the high sheared zone near the injector. The present analysis shows that the phenomenon of the slip velocity inversion is associated with the effect of the turbulent part of the interfacial force. A new formulation of the turbulent contribution of the added mass force is proposed. This formulation is analyzed using the vertical bubbly jet experimental data. The results provide evidence that the turbulent contribution of the added mass force is at the origin of the slip velocity reduction and could explain the appearance of the negative values observed in bubbly jet experiments. As a whole, the turbulent contribution of the added mass force which comprises two terms (a nonlinear turbulent term and a convective acceleration term associated to the drift velocity) opposes the action of the gravity and their effect may be high enough to produce negative slip velocities. Taken separately, the two turbulent terms cannot explain the reversal and the reduction of slip through the entire section in the near injection zone of the bubbly jet. The combined effect of the two turbulent terms makes it possible to reproduce slip velocity profiles as observed in the near injection zone.
SELF-SIMILARITY OF VERTICAL BUBBLY JETS
