Vortex-induced vibration of elastically-mounted spheres: a comparison of the response of three degrees of freedom and one degree of freedom systems

In published literature of the vortex-induced vibration of a sphere, limited attention has been devoted to spheres having three degrees of freedom (DOF) motion and the effect on the vibration response. In this study, the vortex-induced vibration response of a 3-DOF elastically-mounted sphere was examined numerically. The response of a sphere allowed to oscillate in all three spatial directions (3-DOF motion) was compared with the response of a sphere whose motion was restricted to only the transverse direction (1-DOF). Simulations were conducted over the reduced velocity range U ^∗ ≡U∕(Df _n )∈[3.5,16], using a sphere of mass ratio m ^∗ ≡ρ _s ∕ρ=3, at a fixed Reynolds number of 2000, where U is the free-stream velocity of the flow, f _n is the natural frequency of the system, ρ _s and ρ are the solid and fluid densities, respectively. When the sphere was allowed 3-DOF movement, it was initially excited to vibrate along a linear path in the transverse direction, synchronized with the two-sided shedding of vortex loops behind the sphere. As the simulation time advanced, the sphere trajectory eventually converted into a circular orbit with a spiralling wake behind it. The transition time between these two modes was found to increase with decreasing Reynolds number. The vibration amplitude was significantly smaller when the sphere motion was in all three spatial directions than when it was restricted only to the transverse direction. The maximum vibration amplitudes were approximately 0.6 and 0.8 diameters, for 3-DOF and 1-DOF motion, respectively. In the synchronization regime, the maximum time-averaged drag coefficient was approximately 100% greater than that of a stationary sphere, when the sphere had 3-DOF, similar to previous observations for a tethered sphere. However, the maximum change to the time-averaged drag coefficient was only 76% when the motion was restricted to the transverse direction.