A NUMERICAL INVESTIGATION OF BUBBLES RISING AT INTERMEDIATE REYNOLDS AND LARGE WEBER NUMBERS

The steady state rise of bubbles at intermediate Reynolds numbers and large Weber numbers has been investigated using finite element simulat ions. The velocity and stress fields are discussed. Near-constant norm al stress profiles over a region around the bubble apex could be gener ated by optimizing the wake angle of spherical cap bubbles. These wake angles agreed with relations in the literature. The flow in the regio n around the bubble apex was near-inviscid; further away deviation fro m inviscid flow was severe. A toroidal vortex was seen in the wake reg ion, well approximated by Harper and Moore's modification to Hill's sp herical vortex, confirming Bhaga and Weber's experimental findings. Ne vertheless, a constant normal stress over the entire front of the risi ng spherical cap bubble could not be generated. This was, however, pos sible by optimizing an oblate elliptical cap shape. Data for this shap e are given for a Reynolds number of 20.