Flow-induced vibration of a cantilevered cylinder in oscillatory flow at high KC

Flow-induced vibrations of a cantilevered circular cylinder are measured in sinusoidal, oscillatory, water flows with amplitude of reduced velocity in the range 1.9≤U_r≤4.4 and Keulegan–Carpenter number in the range 120≤KC≤900 respectively. Flow velocities are measured using laser Doppler anemometry, and forces and moments are measured using a 6-axis load cell; the two-degree-of-freedom (2-DOF) cylinder motions are determined from the measured moments. The dominant type of vibration occurring within the flow half-period is shown to depend mainly on U_r, with predominantly in-line vibration occurring for U_r⪅2.7, figure-8 vibration occurring for 2.7⪅U_r⪅4, and transverse vibration occurring for U_r⪆4. In-line vibration frequency, f_x, is close to, or slightly higher than the cylinder's natural frequency in still-water, while transverse vibration frequency, f_y, is generally close to the vortex shedding frequency given by Strouhal number St=0.2. Some unsteadiness is seen in the transverse vibration frequency in that accelerating flow f_y is consistently higher than decelerating flow f_y for the same instantaneous reduced velocity u_r. The most notable unsteady effect is seen in the in-line vibration amplitude, A_x, which is much higher during flow deceleration than during flow acceleration; maximum A_x occurs at decelerating u_r≈2 for all three vibration types. Transverse vibration amplitude, A_y, increases with increasing u_r and shows only slight asymmetry between accelerating and decelerating flow. Experiments with the cylinder placed within a large array of similar cylinders with a spacing between cylinders of six cylinder diameters, show that cylinder vibrations within the array are more variable than those of the isolated cylinder, but exhibit similar average vibration amplitudes and frequencies as the isolated cylinder. An empirical model for unsteady in-line vibration based on theoretical considerations and the experimental data is presented. Model-predicted and measured in-line vibration amplitudes through the flow half-period show good agreement for in-line, figure-8 and transverse vibrations.