# Occurrence of orbital cylinder motion for flow around freely vibrating circular cylinder in uniform stream

## Description

In this study flow around a freely vibrating circular cylinder in two-degrees-of-freedom is investigated using two-dimensional numerical approach. The equations of motion, the continuity and the pressure Poisson equations are solved for incompressible constant property Newtonian fluid using the finite difference method. Systematic computations are carried out to investigate the effect of the natural frequency fN of the cylinder on the oscillation amplitudes and aerodynamic force coefficients. The mass ratio and the structural damping coefficient values are fixed at m*=10 and ζ=0, respectively. In addition to the typical distorted figure-eight motion, a raindrop-shaped path is also found whose range widens with increasing fN. Within this range the streamwise oscillation amplitude reaches higher values compared to figure-eight motions and the curves shift upwards with increasing fN. Different vortex structures belong to each cylinder path: 2S or C(2S) modes are observed for distorted figure-eight and P+S mode is found for raindrop-shaped trajectories. The time-mean values of lift jump abruptly between two solutions. Pre- and post-jump analysis reveals that these solutions are mirror images of each other. The root-mean-square (rms) values of lift plotted against U*St shift upwards in the raindrop-shaped motion range and downwards in the figure-eight motion range, while the rms of drag shifts to higher values in both regimes with increasing fN. Chaotic cylinder paths are observed when increasing the natural frequency over a critical value.