Free vibrations of a cylinder: 3-D computations at Re=1000

Vortex-induced vibrations of a circular cylinder of low non-dimensional mass ( m ⁎ = 10.0 ) are investigated at Re=1000. A stabilized space–time finite element formulation is utilized to solve the incompressible flow equations in primitive variables in three dimensions. Computations are carried out for reduced velocities in the range 4.2 ≤ U ⁎ ≤ 6.2 for, both, increasing and, decreasing U⁎. Three branches are identified for the cylinder response: initial, upper and lower. The cylinder response and force coefficients exhibit beats in the initial branch. The initial–upper branch transition is hysteretic. The maximum amplitude of transverse oscillations is 0.7D. This value is larger than that observed in the laminar regime and smaller than that reported earlier for large Re. Intermittency is observed in the transition between upper and lower branches. During the transition, the fraction of time spent by the cylinder in lower branch increases with U⁎. Soft-lock-in is observed on the upper branch. Although the frequency of vortex shedding and the cylinder vibration match, they are different than the natural frequency of the spring-mass system. The mode of vortex shedding is 2S on the initial branch while it is 2P along the lower branch. Perhaps, for the first time, 2S mode of vortex shedding is found along the upper branch. This is confirmed via investigation of phase difference between the lift and cylinder response.