Three-dimensional flow field measurements in the wake of a tethered sphere crossing the onset of vortex induced vibrations

The changing three-dimensional vortex shedding topology of a heavy, tethered sphere exposed to uniform flow crossing the onset of vortex induced vibrations (VIV) is reported together with simultaneously tracked sphere positions. Transient upstream flow conditions were imposed by increasing the reduced velocity from $U^{*} = 2.2$ to 4.5 (‘lock-in’, mode I). Three-dimensional vortex shedding under these transient conditions strongly resembled those at steady conditions at the same $U^{*}$ . Changes in the wake accompanying the onset of VIV indicated several well-defined stages associated with the changing instantaneous location of the velocity deficit centroid and the wake's symmetry plane's orientation. Before the onset of VIV, the appearance of induced vortices led to lock-in of streamwise sphere oscillations prior to lock-in in the transverse direction. Shortly after ( $U^{*} \approx 3.6$ ), preferential vortex shedding (wake symmetry plane aligned with tether) was lost. Upon reaching $U^{*} = 4.5$ , flow–structure interaction reorganised vortex shedding and sphere motion, resulting in steady state conditions after some delay. At this stage, the symmetry plane was aligned perpendicular to the tether and pairs of alternately shed, single hairpins exerted transverse forcing on the sphere. At $U^{*} = 7.2$ (mode II, steady upstream flow), pairs of double hairpins were shed per oscillation period with maximum instantaneous vortex force coefficients that were higher than at $U^{*} = 4.5$ . While the present Reynolds numbers ( $Re$ ) were chosen low, the different identified stages in the onset of VIV are also expected to be relevant at a higher $Re$ range.