Vortex dynamics and vibration modes of a tethered sphere

The flow-induced vibration of a tethered sphere was investigated through numerical simulations. A determination of the different modes of sphere vibration was made with simulations conducted at fixed Reynolds numbers (500, 1200 and 2000) with a sphere of mass ratio 0.8 over the reduced velocity range ∈ [3,32] . The flow was governed by the incompressible Navier-Stokes equations, while the dynamic motion of the sphere was governed by coupled Newtonian mechanics. A new fluid-structure interaction (FSI) solver was implemented to efficiently solve the coupled FSI system. The effect of Reynolds number was found to be significant in the mode I and II regimes. A progressive increase in the response amplitude was observed as the Reynolds number was increased, especially in the mode II regime. The overall sphere response at the highest Reynolds number was relatively close to the observed behaviour of previous higher- Re experimental studies. An aperiodic mode IV response was observed at higher reduced velocities beyond the mode II range in each case, without the intervening mode III regime. However, as the mass ratio increased from 0.8 to 80, the random response of the sphere (mode IV) gradually became more regular, showing a mode III response (characterized by a near-periodic sphere oscillation) at U* = 30. Thus, if the inertia of the system is low, mode IV appears at lower U* values, while for high-inertia systems, mode IV appears at high U* values beyond a mode III response.