Self-Similarity of Vertical Bubbly Jets

Abstract

-An integral model for vertical bubbly jets with nearly monodisperse bubble sizes is presented. The model is based on the Gaussian type self-similarity of mean liquid velocity, bubble velocity and void fraction, as well as on functional relationships for initial liquid jet velocity and radius, bubble diameter and relative velocity. Adjusting the model to experimental data available in the literature for a wide range of densimetric Froude numbers provide constant values for the entrainment coefficient, momentum amplification factor, and spreading ratio of the bubble core for different flow conditions. Consistency and sensitivity of key model parameters are also verified. Overall, the deviations between model predictions and axial/radial profiles of mean liquid velocity, bubble velocity and void fraction are lower than about 20%, which suggests that bubbly jets tend to behave as self-preserving shear flows, similarly to single-phase jets and plumes. Furthermore, model simulations indicate a behavior similar to those of single-phase buoyant jets and slurry jets, but some differences with respect to confined bubbly jets are highlighted. This article provides not only a contribution to the problem of self-similarity in two-phase jets, but also a comprehensive model that can be used for analysis of artificial aeration/mixing systems involving bubbly jets.

Bubbling to Jetting Transition during Argon Injection in Molten Steel

“…At subsonic velocities (M < 1) the jetting regime is unstable [14] and for y > H j the continuous jet is transformed into a bubble stream, as is observed in Figure 1. Jet heights were determined from the phase distributions and are depicted in Figure 2 Figure 3 shows that the argon volume fraction exhibits a Gaussian distribution inside the jets as reported experimentally in [24] and numerically in [25] [26]. Besides, in Figure 3 it is observed that the volume fraction and the width of the jets are increased as the injection velocity is increased.…”