Results are presented from an experimental investigation into the effects of proximity to a free surface on vortex-induced vibration (VIV) experienced by fully and semi-submerged spheres that are free to oscillate in the cross-flow direction. The VIV response is studied over a wide range of reduced velocities: $3\leqslant U^{\ast }\leqslant 20$, covering the mode I, mode II and mode III resonant response branches and corresponding to the Reynolds number range of $5000\lesssim Re\lesssim 30\,000$. The normalised immersion depth of the sphere is varied in small increments over the range $0\leqslant h^{\ast }\leqslant 1$ for the fully submerged case and $0\leqslant h^{\ast }\leqslant -0.75$ for the semi-submerged case. It is found that for a fully submerged sphere, the vibration amplitude decreases monotonically and gradually as the immersion ratio is decreased progressively, with a greater influence on the mode II and III parts of the response curve. The synchronisation regime becomes narrower as $h^{\ast }$ is decreased, with the peak saturation amplitude occurring at progressively lower reduced velocities. The peak response amplitude decreases almost linearly over the range of $0.5\leqslant h^{\ast }\leqslant 0.185$, beyond which the peak response starts increasing almost linearly. The trends in the total phase, $\unicode[STIX]{x1D719}_{total}$, and the vortex phase, $\unicode[STIX]{x1D719}_{vortex}$, reveal that the mode II response occurs for progressively lower $U^{\ast }$ values with decreasing $h^{\ast }$. On the other hand, when the sphere pierces the free surface, there are two regimes with different characteristic responses. In regime $\text{I}$ ($-0.5<h^{\ast }<0$), the synchronisation region widens and the vibration amplitude increases, surprisingly becoming even higher than for the fully submerged case in some cases, as $h^{\ast }$ decreases. However, in regime $\text{II}$ ($-0.5\leqslant h^{\ast }\leqslant -0.75$), the vibration amplitude decreases with a decrease in $h^{\ast }$, showing a very sharp reduction beyond $h^{\ast }<-0.65$. The response in regime II is characterised by two distinct peaks in the amplitude response curve. Careful analysis of the force data and phase information reveals that the two peaks correspond to modes I and II seen for the fully submerged vibration response. This two-peak behaviour is different to the classic VIV response of a sphere under one degree of freedom (1-DOF). The response was found to be insensitive to the Froude number ($Fr=U/\sqrt{gD}$, where $U$ is the free-stream velocity, $D$ is the sphere diameter and $g$ is the acceleration due to gravity) in the current range of $0.05\leqslant Fr\leqslant 0.45$, although higher Froude numbers resulted in slightly lower peak response amplitudes. The wake measurements in the cross-plane $1.5D$ downstream of the rear of the sphere reveal a reduction in the vorticity of the upper vortex of the trailing vortex pair, presumably through diffusion of vorticity into the free surface. For the piercing sphere case, the near-surface vorticity completely diffuses into the free surface, with only the opposite-signed vortex visible in the cross-plane at this downstream position. Interestingly, this correlates with an even higher oscillation amplitude than the fully submerged case. Finally, the effects of immersion ratio and diameter ratio ($D^{\ast }$ $=$ sphere diameter/support-rod diameter) are quantified, showing care needs to be taken with these factors to avoid unduly influencing VIV predictions.

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Vortex-induced vibration (VIV) of a sphere represents one of the most generic fundamental fluid-structure interaction problems. Since vortex-induced vibration can lead to structural failure, numerous studies have focused on understanding the underlying principles of VIV and its suppression. This paper reports on an experimental investigation of the effect of imposed axial rotation on the dynamics of vortex-induced vibration of a sphere that is free to oscillate in the cross-flow direction, by employing simultaneous displacement and force measurements. The VIV response was investigated over a wide range of reduced velocities (i.e. velocity normalised by the natural frequency of the system): 3 U * 18, corresponding to a Reynolds number range of 5000 < Re < 30 000, while the rotation ratio, defined as the ratio between the sphere surface and inflow speeds, α = |ω|D/(2U), was varied in increments over the range of 0 α 7.5. It is found that the vibration amplitude exhibits a typical inverted bell-shaped variation with reduced velocity, similar to the classic VIV response for a non-rotating sphere but without the higher reduced velocity response tail. The vibration amplitude decreases monotonically and gradually as the imposed transverse rotation rate is increased up to α = 6, beyond which the body vibration is significantly reduced. The synchronisation regime, defined as the reduced velocity range where large vibrations close to the natural frequency are observed, also becomes narrower as α is increased, with the peak saturation amplitude observed at progressively lower reduced velocities. In addition, for small rotation rates, the peak amplitude decreases almost linearly with α. The imposed rotation not only reduces vibration amplitudes, but also makes the body vibrations less periodic. The frequency spectra revealed the occurrence of a broadband spectrum with an increase in the imposed rotation rate. Recurrence analysis of the structural vibration response demonstrated a transition from periodic to chaotic in a modified recurrence map complementing the appearance of broadband spectra at the onset of bifurcation. Despite considerable changes in flow structure, the vortex phase (φ vortex ), defined as the phase between the vortex force and the body displacement, follows the same pattern as for the non-rotating case, with the φ vortex increasing gradually from low values in Mode I of the sphere vibration to almost 180• as the system undergoes a continuous transition to Mode II of the sphere vibration at higher reduced velocity. The total phase (φ total ), defined as the phase between the transverse lift force and the body displacement, only increases from low values after the peak amplitude † Email address for correspondence: jisheng.zhao@monash.edu response in Mode II has been reached. It reaches its maximum value (∼165• ) close to the transition from the Mode II upper plateau t...

This experimental study investigates the effect of imposed rotary oscillation on the flow-induced vibration of a sphere that is elastically mounted in the cross-flow direction, employing simultaneous displacement, force and vorticity measurements. The response is studied over a wide range of forcing parameters, including the frequency ratio $f_{R}$ and velocity ratio $\unicode[STIX]{x1D6FC}_{R}$ of the oscillatory forcing, which vary between $0\leqslant f_{R}\leqslant 5$ and $0\leqslant \unicode[STIX]{x1D6FC}_{R}\leqslant 2$ . The effect of another important flow parameter, the reduced velocity, $U^{\ast }$ , is also investigated by varying it in small increments between $0\leqslant U^{\ast }\leqslant 20$ , corresponding to the Reynolds number range of $5000\lesssim Re\lesssim 30\,000$ . It has been found that when the forcing frequency of the imposed rotary oscillations, $f_{r}$ , is close to the natural frequency of the system, $f_{nw}$ , (so that $f_{R}=f_{r}/f_{nw}\sim 1$ ), the sphere vibrations lock on to $f_{r}$ instead of $f_{nw}$ . This inhibits the normal resonance or lock-in leading to a highly reduced vibration response amplitude. This phenomenon has been termed ‘rotary lock-on’, and occurs for only a narrow range of $f_{R}$ in the vicinity of $f_{R}=1$ . When rotary lock-on occurs, the phase difference between the total transverse force coefficient and the sphere displacement, $\unicode[STIX]{x1D719}_{total}$ , jumps from $0^{\circ }$ (in phase) to $180^{\circ }$ (out of phase). A corresponding dip in the total transverse force coefficient $C_{y\,(rms)}$ is also observed. Outside the lock-on boundaries, a highly modulated amplitude response is observed. Higher velocity ratios ( $\unicode[STIX]{x1D6FC}_{R}\geqslant 0.5$ ) are more effective in reducing the vibration response of a sphere to much lower values. The mode I sphere vortex-induced vibration (VIV) response is found to resist suppression, requiring very high velocity ratios ( $\unicode[STIX]{x1D6FC}_{R}>1.5$ ) to significantly suppress vibrations for the entire range of $f_{R}$ tested. On the other hand, mode II and mode III are suppressed for $\unicode[STIX]{x1D6FC}_{R}\geqslant 1$ . The width of the lock-on region increases with an increase in $\unicode[STIX]{x1D6FC}_{R}$ . Interestingly, a reduction of VIV is also observed in non-lock-on regions for high $f_{R}$ and $\unicode[STIX]{x1D6FC}_{R}$ values. For a fixed $\unicode[STIX]{x1D6FC}_{R}$ , when $U^{\ast }$ is progressively increased, the response of the sphere is very rich, exhibiting characteristically different vibration responses for different $f_{R}$ values. The phase difference between the imposed rotary oscillation and the sphere displacement $\unicode[STIX]{x1D719}_{rot}$ is found to be crucial in determining the response. For selected $f_{R}$ values, the vibration amplitude increases monotonically with an increase in flow velocity, reaching magnitudes much higher than the peak VIV response for a non-rotating sphere. For these cases, the vibrations are always locked to the forcing frequency, and there is a linear decrease in $\unicode[STIX]{x1D719}_{rot}$ . Such vibrations have been termed ‘rotary-induced vibrations’. The wake measurements in the cross-plane $1.5D$ downstream of the sphere position reveal that the sphere wake consists of vortex loops, similar to the wake of a sphere without any imposed rotation; however, there is a change in the timing of vortex formation. On the other hand, for high $f_{R}$ values, there is a reduction in the streamwise vorticity, presumably leading to a decreased total transverse force acting on the sphere and resulting in a reduced response.

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