On multiple manifestations of the second response branch in streamwise vortex-induced vibrations

Abstract

The structural motion and velocity field in the wake of a cylinder exhibiting vortex-induced vibration (VIV) in the streamwise direction were measured using Particle-Image Velocimetry. The effect of hysteresis on the amplitude response of the cylinder and the existence of multiple wake modes in the region of the second response branch were examined. As the reduced velocity was decreased, there was a reduction in the lock-in range; outside this range the amplitude response was found to be negligible and the A-II mode (which is similar to the von Kármán vortex street) was observed in the wake. When the reduced velocity was increased the second branch could be manifested in two forms, depending on whether the wake exhibited the SA or the A-IV mode (in which two and four vortices are shed per wake cycle, respectively). The A-IV mode has been observed in studies in which a cylinder was forced to oscillate in the streamwise direction; however, this represents the first time that it has been recorded in the wake of a freely oscillating body, and it was not previously known that the A-IV mode was capable of exciting self-sustaining vibrations. Both the SA and A-IV modes were stable and no intermittent mode-switching was observed; however, it was found to be unpredictable which mode would dominate as the reduced velocity was varied and the cylinder entered the second response branch. Analysis of the cylinder displacement signals measured while each mode was dominant indicated that the SA mode excited larger amplitude vibrations than the A-IV mode. A reduced velocity near the second response branch was identified at which the wake could exhibit either the SA, A-IV, or A-II modes, with the latter occurring as the reduced velocity was decreased. Although bi-modal behaviour is well established in VIV studies, as far as the authors are aware, this represents the first time that a point has been observed in the response regime of a freely oscillating structure in which three stable states have been observed, each corresponding to a different wake mode and vibration amplitude, for the same structural parameters, reduced velocity, and Reynolds number. This suggests that the mechanism determining which wake mode dominates and the fluid-structure interaction in the case of streamwise VIV may be more complex than has previously been thought. Finally, the vortex-formation and shedding processes associated with the A-II, SA, and A-IV modes were described using phase-averaged vorticity fields, and the differences between the SA and A-IV modes were discussed.