On the bubble rise velocity of a continually released bubble chain in still water and with crossflow

The rise velocities of in-chain bubbles continually released from a single orifice in still water with and without crossflow are investigated in a series of laboratory experiments for wobbling ellipsoidal bubbles with moderate Reynolds number. For the limiting case in still water, that is, crossflow velocity = 0, the theoretical turbulent wake model correctly predicts the in-chain bubble rise velocity. In this case, the bubble rise velocities V-B are enhanced compared to the terminal velocities of the isolated bubbles V-0 due to wake drafting and are scaled with flow rate Q and bubble diameter D. Here, we also derive an updated wake model with consideration of the superposition of multiple upstream bubble wakes, which removes the nonlinear behavior of the non-distant (i.e., local) wake model. For the cases with crossflow, the enhancement of the in-chain bubble rise velocity can be significantly reduced, and imaging of the experiments shows very organized paring and grouping trajectories of rising bubbles not observed in still water under different crossflow velocities. The in-chain bubble rise velocities in crossflow are described by two models. First, an empirical model is used to correct the still-water equation for the crossflow effect. In addition, a semitheoretical model considering the turbulent wake flow and the crossflow influence is derived and used to develop a theoretical normalization of bubble rise velocity, crossflow velocity, and the released bubble flow rate. The theoretical model suggests there are two different regimes of bubble-bubble interaction, with strong interaction occurring for the non-dimensional crossflow velocity U-c(+) = pi(UcDV0)-D-3-V-3/(18g beta Q(2)) less than 0.06 and weaker interaction occurring for U-c(+) greater than 0.06, where U-c is the crossflow velocity, g is the acceleration of gravity, and beta is the mixing length coefficient. (C) 2015 AIP Publishing LLC.