In this paper the popup height of rising buoyant spheres is studied over a range of distinct release depths along with the accompanying velocities and accelerations near the free surface. In the past, regimes of motion due to vortex induced vibrations have been classified based on trajectories below the free surface. This study focuses on the popup height, velocity and acceleration at free surface exit, and vortex shedding in order to further define regimes of motion experienced by a rising buoyant sphere. Varying the release depth below the free surface reveals varying exit angles, velocities, accelerations, and popup heights at surface exit. Vortex shedding prior to free surface exit causes decelerations contributing to the variation in exit velocities and resulting popup heights. Using high-speed imaging and particle image velocimetry, we examine the trajectories, accelerations, velocities and vortex shedding events for spheres of different mass ratios over a range of Reynolds number (2e4 >Re> 6e5). At lower Re, spheres released from shallow release depths result in greater accelerations and velocities at free surface exit along with greater popup heights compared to releases from deeper depths. After reaching a depth which results in a minimum popup height, further increasing the release depth reveals an increase in popup height demonstrating an oscillatory pattern due to the sphere being released from vortex forces after shedding. This pattern is repeated as the popup height again decreases with greater release depths. For spheres of greater Re, popup height increases linearly with release depth, demonstrating continued accelerations at free surface exit.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





popup, oblique, oscillating, free surface, trajectory, vortex