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 simulations. The velocity and stress fields are discussed. Near-constant normal stress profiles over a region around the bubble apex could be generated by optimizing the wake angle of spherical cap bubbles. These wake angles agreed with relations in the literature. The flow in the region around the bubble apex was near-inviscid; further away deviation from inviscid flow was severe. A toroidal vortex was seen in the wake region, well approximated by Harper and Moore's modification to Hill's spherical vortex, confirming Bhaga and Weber's experimental findings. Nevertheless, a constant normal stress over the entire front of the rising spherical cap bubble could not be generated. This was, however, possible by optimizing an oblate elliptical cap shape. Data for this shape are given for a Reynolds number of 20.