A phase-resolved force analysis of bubble trapping behind cylinders in liquid-gas flows

A liquid-gas flow across a bluff body can result in non-uniform distribution of void fraction due to the interaction of the bubbles with the bluff-body wake. This experimental investigation was conducted to characterize a bubble-trapping region and the clustering dynamics of two distinct bubble sizes in an upward water channel with a rectangular cross-section. Bubble trapping in the near wake of a cylinder is shown as a function of bubble size, liquid flow rate, and gas flow rate through patterns of local void fraction. Particle tracking velocimetry and particle image velocimetry were used to calculate time-averaged trajectories of 3 mm diameter and 0.5 mm diameter bubbles as they flowed around a cylinder. The liquid Reynolds number (Re), based on the cylinder diameter of 9.5 mm, was varied from Re = 100 to Re = 3,000. In addition, the injection of liquid flow tracers and application of particle shadow image velocimetry allowed measurements of the time-averaged liquid velocities in the wake. The phase-resolved tracking results were evaluated to determine the effects of the added mass, pressure gradient, lift, drag, and buoyancy forces acting on the air bubbles. Trapping of both bubble sizes was observed across a range of operating conditions; however, this behavior was not explained solely by the Reynolds number of the flow. The force balance analysis revealed that inertial forces and lift forces acting on the bubbles both contributed to the clustering, which occurred when either the inertial forces or the lift forces acting on the bubble were sufficiently high compared to the bubble drag forces. Both the inertia- and lift-to-drag ratios were necessary to predict the bubble clustering dynamics of the distinct bubble sizes investigated.