The influence of higher harmonic flow forces on the response of a curved circular cylinder undergoing vortex-induced vibration

Abstract

Vortex-induced vibration (VIV) of a curved circular cylinder (a quarter of a ring, with no extension added to either end) free to oscillate in the crossflow direction was studied experimentally. Both the concave and the convex orientations (with respect to the oncoming flow direction) were considered. As expected, the amplitude of oscillations in both configurations was decreased compared to a vertical cylinder with the same mass ratio. Flow visualizations showed that the vortices were shed in parallel to the curved cylinder, when the cylinder was free to oscillate. The sudden jump in the phase difference between the flow forces and the cylinder displacement observed in the VIV of vertical cylinders was not observed in the curved cylinders. Higher harmonic force components at frequencies twice and three times the frequency of oscillations were observed in flow forces acting on the vertical cylinder, as well as the curved cylinder. Asymmetry in the wake was responsible for the 2nd harmonic force component and the relative velocity of the structure with respect to the oncoming flow was responsible for the 3rd harmonic force component. The lock-in occurred over the same range of reduced velocities for the curved cylinder in the convex orientation as for a vertical cylinder, but it was extended to higher reduced velocities for a curved cylinder in the concave orientation. Higher harmonic force components were found to be responsible for the extended lock-in range in the concave orientation. Within this range, the higher harmonic forces were even larger than the first harmonic force and the structure was being excited mainly by these higher harmonic forces.