Vortex-induced vibrations of an elastically mounted sphere: The effects of Reynolds number and reduced velocity

The dynamics and wake modes of vortex-induced vibrations of a sphere mounted on elastic supports in all three spatial directions are systematically investigated via numerical simulations. In our previous work (Behara et al. 2011), we studied this problem for a sphere of m*=2 at Re=300 and reduced velocity in the range of U*=0–9. We showed that for 4.8≤U*≤9 the sphere exhibits two distinct synchronized oscillation regimes each associated with a distinct wake mode: the hairpin mode (hairpin vortices shed in the wake) and the spiral mode (intertwined vortices shed in the wake). Here we contribute new physical insights into the dynamics of the elastically mounted sphere by probing vibration modes and vortex shedding patterns for a greater range of reduced velocities (U*=0−13) at Re=300 and for the range of Reynolds numbers 300≤Re≤1000 for a fixed reduced velocity U*=9. For the Re=300 case the lock-in regime is observed for 5.8≤U*≤12.2 with the spiral mode, while the lock-in region with the hairpin mode exists only for 4.8≤U*≤8. The hairpin mode is found to become unstable and merge with the response branch of the spiral mode at U*=9. In the lock-in regime corresponding to the spiral shedding mode the vibrating sphere moves along a circular orbit on the transverse plane. The hairpin shedding mode reappears in the wake after the synchronization region corresponding to the spiral mode ends. Varying Reynolds number (300≤Re≤1000) for fixed reduced velocity (U*=9), we find that the synchronized oscillations persist up to Re=1000, but the wake mode and sphere trajectories depend strongly on Reynolds number. The sphere sheds spiral vortices up to Re∼500, but the wake transitions from the spiral to the hairpin shedding mode in the range of Re=500–600. During this wake transition the sphere trajectory on the transverse plane changes from circular to elliptical orbits. The sphere exhibits periodic oscillations in the spiral mode for Re≤500, whereas for Re≥600, when the wake is in the hairpin mode, oscillations become non-stationary.