Numerical investigation of two-degree-of-freedom vortex-induced vibration of a circular cylinder in oscillatory flow

Two-degree-of-freedom (2dof) vortex-induced vibration (VIV) of a circular cylinder in oscillatory flow is investigated numerically. The direction of the oscillatory flow is perpendicular to the spanwise direction of the circular cylinder. Simulations are carried out for the Keulegan-Carpenter (KC) numbers of 10, 20 and 40 and the Reynolds numbers ranging from 308 to 9240. The ratio of the Reynolds number to the reduced velocity is 308. At KC1/410, the amplitude of the primary frequency component is much larger than those of other frequency components. Most vibrations for KC1/420 and 40 have multiple frequencies. The primary frequency of the response in the cross-flow direction decreases with the increasing reduced velocity, except when the reduced velocity is very small. Because the calculated primary frequencies of the response in the cross-flow direction are multiple of the oscillatory flow frequency in most of the calculated cases, the responses are classified into single-frequency mode, double-frequency mode, triple frequency mode, etc. If the reduced velocity is in the range where the VIV is transiting from one mode to another, the vibration is very irregular. For each KC number the range of the reduced velocity can be divided into a cross-flow-in-phase regime (low Vr), where the response and the hydrodynamic force in the cross-flow direction synchronize, and a cross-flow-anti-phase regime (high Vr), where the response and the hydrodynamic force in the cross-flow direction are in anti-phase with each other. The boundary values of Vr between the cross-flow-in-phase and the cross-flow-anti-phase regimes are 7, 9 and 11 for KC1/410, 20 and 40, respectively. For KC1/420, another cross-flow-anti-phase regime is found between 15≤Vr≤19. Similarly the in-line-in-phase and the in-line-anti-phase regimes are also identified for the response in the in-line direction. It is found that the boundary value of Vr between the in-line-in-phase and the in-line-anti-phase regimes is greater than that in the cross-flow direction. They are 14 and 26 for KC1/410 and 20, respectively. Maximum amplitude occurs at the boundary value of the reduced velocity between in-phase regime and anti1/4phase regime in both the x- and the y-directions.