Three-dimensionality in the flow of an elastically mounted circular cylinder with two-degree-of-freedom vortex-induced-vibrations

The study numerically investigates the three-dimensionality in the flow and two-degree-of-freedom (2DOF) vortex-induced-vibrations (VIV) characteristics of an elastically mounted circular cylinder. The cylinder is allowed to vibrate in both streamwise and transverse directions. A low value of mass-ratio (m*=2.546) with the zero-damping coefficient (ζ=0) is taken for the simulations. The primary aim is to understand the vortex shedding behind the cylinder and the transition characteristics of the wake-flow from two-dimensional (2D) to three-dimensional (3D). The Reynolds number (Re) is varied from 150 (fully 2D flow) to 1000 (fully 3D flow), which lies inside the laminar range. The reduced velocity (Ur) is varied 2≤Ur≤17, which covers all three major VIV branches [initial branch (IB), upper branch (UB), and the lower branch (LB)]. The oscillating cylinder sweeps the figure-eight trajectory. Two branches (IB, LB) and three branches (IB, UB, LB) amplitude responses are obtained for the low and high Re values, respectively. The wake behind the cylinder with 2DOF VIV undergoes the mode-C transition of 2D to 3D flow as opposed to the direct mode-B transition observed for transverse only VIV in the literature. The critical Re range of the 2D to 3D transition for the 2DOF VIV cylinder at a reduced velocity of 6 is around 250, less than the 1DOF VIV. Also, this range varies with the variation in m* and the streamwise to transverse oscillation frequency ratio (f*). A λz−Re map (where λz represents the spanwise wavelength of the streamwise vortices) is proposed for the 2DOF VIV, highlighting different modes of transition obtained for combinations of f* and Re.