Numerical simulation of a freely vibrating circular cylinder with different natural frequencies

This paper deals with the numerical simulation of low-Reynolds-number flow around a freely vibrating circular cylinder in two-degrees-of-freedom. The governing equations are written in a non-inertial system fixed to the moving cylinder and solved using finite difference method. The natural frequency of the cylinder is chosen to be constant, agreeing with the vortex-shedding frequency for a stationary cylinder at Reynolds number Re0. Systematic computations are carried out for Re0 = 80, 100, 140 and 180 keeping the mass ratio and structural damping coefficient at m* = 10 and ζ = 0. The effect of Re0 on the root-mean-square (rms) values of cylinder displacements and drag coefficients is analyzed. Plotting the data set belonging to different Re0 values against U*St0 makes comparison easier. Local extreme values are found in the rms of streamwise displacement and drag coefficient in the range U*St0 = 0.4-0.65. In the vicinity of U*St0 = 0.5 the rms of drag approaches zero and the phase angle between the x component of the motion and drag changes abruptly from 0° to 180°. The pressure drag coefficient seems to be responsible for the sudden change. The cylinder follows a distorted figure-eight path in most cases investigated and its orientation changes from clockwise to counterclockwise orbit at around U*St0 = 0.5.