Angular vortex-induced vibrations of a cylinder

We consider the response of a flexibly-mounted cylinder placed in flow and free to oscillate on a curved path about a pivot point. The curved path could be concave (i.e., bent toward the incoming flow) or convex (i.e., bent away from the incoming flow). We consider different radii of curvature for both the concave and the convex paths and show that oscillations are observed for radii of curvature larger than one cylinder diameter. In general, we show that the oscillations are of larger amplitudes in the convex orientation, reaching angles of oscillations of up to 38° and normalized (with respect to the cylinder's diameter) amplitudes of oscillations in the transverse and inline directions of up to 1.1 and 0.35, respectively. The oscillations on the concave path are of smaller amplitudes, but last up to higher values of reduced velocities than those in the convex orientation. The shedding and oscillation frequencies increase with increasing reduced velocity for the concave orientation reaching values of around 1.8 times the system's natural frequency in water at the end of the lock-in range, while for the convex orientation, the frequencies stay close to the natural frequency and only jump from values slightly lower than the natural frequency to values slightly higher than the natural frequency when the oscillation amplitude drops from an upper branch to a lower branch in the VIV amplitude response. Two single vortices are observed in the wake when oscillation amplitudes are relatively low, and two pairs of vortices of different sizes are observed in the wake when amplitudes are relatively larger. When two pairs of vortices are observed, the cylinder carries two bound vortices with it during its transverse oscillations and sheds them in the form of a pair of vortices of different sizes at the end of each half cycle. In the cases with the largest amplitudes of oscillations, besides the vortices that are shed synchronized with the oscillation frequency, several smaller-size vortices are shed in the wake as the cylinder traverses its crossflow path. We relate the reason for observing larger amplitudes of oscillations on the convex path to the relative orientation of the fluctuating forces that are exerted on the cylinder due to the shedding of vortices in its wake with respect to its oscillation path.