Numerical investigation of streamwise vibration of an elastically mounted circular cylinder in oscillatory flow

Vibration of an elastically mounted circular cylinder subjected to an oscillatory flow is investigated by two-dimensional numerical simulations. A low Reynolds number of Re = 150 and two Keulegan–Carpenter numbers of 5 and 10 are chosen in this study. A wide range of frequency ratios, which is defined as the ratio of the oscillatory flow frequency to the natural frequency, are studied. The cylinder, with mass ratios of 1, 2 and 3, is free to vibrate at zero damping ratio along the streamwise direction only. The vibration velocity of the cylinder relative to the fluid motion (referred to as relative velocity) is found to vary significantly with the frequency ratio. The amplitude of the relative velocity is greater than the amplitude of the oscillatory flow velocity as the frequency ratio is less than a critical value, which is slightly smaller than 1. The amplitude of the relative velocity significantly reduces as the frequency ratio is greater than this critical value. The change of the phase difference between the cylinder motion and fluid motion is identified as the cause for the increase or decrease of the relative velocity. The phase changes from −90° to 90° as the frequency ratio exceeds 1. The drag force is found to be zero at a frequency ratio of 1.