A phase-resolved force analysis of bubbly flows allows prediction of bubble holdup in the wake of circular cylinders

The wakes of cylinders in a bubbly cross-flow can induce a non-uniform distribution of void fraction due to the interaction of the bubbles with the wake. This hold up of bubbles can increase flow resistance and promote bubble coalescence, which can reduce the dispersed phase interfacial area and species transport. Here, we investigate the bubble trapping phenomenon by performing velocimetry of a bubbly flow flowing across a 9.5 mm diameter circular cylinder in an upward water channel. Velocimetry of both phases were performed by using tracer particles and shadow image velocimetry in addition to bubble tracking. Cylinder Reynolds numbers ranging from Re = 100 to 3,000 were investigated along with two distinct bubble sizes, 3 mm in diameter and 0.5 mm in diameter, to examine the impact of bubble size on the hydrodynamic forces leading to bubble trapping. A force balance analysis revealed that both the inertia- and lift-to-drag ratios were necessary to predict the bubble clustering dynamics. We captured these effects in an order-of-magnitude analysis to create a bubble trapping parameter, which allows these conditions to be predicted based on the free-stream flow parameters.