Forces on a high-Reynolds-number spherical bubble in a turbulent flow

The forces acting on a clean spherical bubble fixed on the axis of a turbulent pipe flow are computed using large-eddy simulation for a bubble Reynolds number Re₁\, =\, 500 (based on the bubble diameter and centreline velocity in the pipe) and a bulk Reynolds number Re\, =\, 6000 (based on the pipe diameter and bulk velocity). The force is found to be influenced by all the length and time scales down to the Kolmogorov microscales. The results show that the lift force experiences much larger fluctuations than the drag force, an effect which is shown to be specific to clean bubbles as compared with solid spheres. Using the instantaneous undisturbed velocity and vorticity at the centre of the bubble, the drag force is well predicted by Moore's drag law while Auton's expression for the shear-induced lift force yields a good description of the transverse force.