Modeling and Qualitative Experiments on Swirling Bubbly Flows: Single Bubble With Rossby Number of Order 1

The behavior of an isolated bubble in a single-phase swirling flow is investigated theoretically and experimentally. The Rossby number is such that the liquid flow can be approximated by a solid-body rotation superposed to a uniform axial velocity. The equations of the motion of the bubble are solved analytically and numerically, by assuming that the bubble is small and does not modify the water flow. Two kinds of bubbles have been considered: clean bubbles and bubbles with a contaminated interface. In the latter case the bubble is treated as a solid sphere. In both cases a critical angular velocity $ωc$ for the rotating device is found. When $ω<ωc$ the trajectory of the bubble is a conical spiral which converges to the pipe axis, and when $ω>ωc$ the trajectory is a cosine conical spiral: the bubble migrates to the center in an oscillating manner. The numerical value of $ωc,$ together with the terminal velocity of the bubble, are found to be in good agreement with experimental observations, provided the bubble is treated as a solid sphere.