Three-dimensional numerical simulation of two-degree-of-freedom VIV of a circular cylinder with varying natural frequency ratios at Re = 500

The two-degree-of-freedom (2DOF) vortex-induced vibration (VIV) of a circular cylinder with varying in-line to cross-flow natural frequency ratios (f* = fnx/fny) is studied using a three-dimensional (3D) computational fluid dynamics (CFD) approach. Numerical simulation is carried out for a constant mass ratio of 2 at a fixed Reynolds number Re = 500. The reduced velocity ranges from 2 to 12. Three natural frequency ratios are considered, i.e., f* = 1, 1.5 and 2. The structural damping is set to zero to maximise the response of the cylinder. The main objective of this study is to investigate the effect of f* on the 2DOF VIV responses and the 3D characteristics of the flow. It is discovered that there is a significant increase in the vibration amplitude, and the peak amplitude shifts to a higher reduced velocity when f* increases from 1 to 2. A single-peak cross-flow response is observed for the identical in-line and cross-flow mass ratios when f* = 2. Dual resonance is found to exist over the range of f* studied. The preferable trajectories of the cylinder in the lock-in range are counterclockwise figure-eight orbits. Oblique figure-eight trajectories appear at Vr = 6, 7 and 8 when f* = 1. The third harmonic component which is observed in the lift fluctuation increases with f*. The correlation decreases in the lock-in range and reaches its minimum value around the transition region between the lock-in and post-lock-in ranges. Three vortex shedding modes (2S, P + S and 2P) appear in the present simulation. A dominant P + S mode is associated with the oblique figure-eight trajectories. Variation of vortex shedding flows along the cylinder is observed leading to the poor correlation of the sectional lift forces.