Vortex dynamics and associated fluid forcing in the near wake of a light and heavy tethered sphere in uniform flow

Abstract

Time-resolved particle image velocimetry measurements of vortex-induced vibrations of a negatively (“heavy”) and positively (“light”) buoyant tethered sphere in uniform flow, and its wake characteristics were performed in a closed-loop water channel. Experiments for both spheres were performed at similar bulk velocities, ranging between 0.048 < U < 0.32 m/s, corresponding to reduced velocities, 2.2 < U * < 13.5. Initially stationary, with increasing U, the amplitude response displayed periodic oscillations beyond the Hopf bifurcation as a result of “lock-in” between vortex shedding and the natural structural frequency. However, while the heavy sphere’s amplitude decreased beyond U * = 7.0, the light sphere’s amplitude continuously increased. In the periodic oscillation region, flow field characteristics in the wakes of both spheres (at comparable U * ) were similar, characterized by alternately shed hairpin vortices having a horizontal symmetry plane. Primary vortex trajectories in the frame of reference of the sphere collapsed for different U * (but not for different m * ) when scaled by f 2,s/U, where f 2,s is the sphere’s transverse oscillation frequency. This allows determination of vortex positions based on sphere dynamics and bulk flow conditions only. Associated vortex convection velocities as a function of downstream position from the sphere also nearly collapsed when normalized by U. In addition, fluid forcing and energy transfer from fluid to sphere were estimated based on an analogy between aircraft trailing vortices and hairpin vortices. Maximum forcing occurred at vortex pinch-off. For the highest comparable U * , despite different amplitudes, total transferred energy during one oscillation period was similar for both spheres. Changes in sphere dynamics must therefore be related to differences in inertia.