Vortex-induced vibration for an isolated circular cylinder under the wake interference of an oscillating airfoil: Part II. Single degree of freedom

The vortex-induced vibration behind an isolated cylinder under the wake interference of an oscillating airfoil at different oscillating frequencies and amplitudes have been studied numerically. Our previous research [11] mainly focused on the two degree of freedom vibration problem, several types of the phase portraits of the displacement have been newly found, including the "half -8″ and “cone-net” types as reduced velocity increases. At present, we have continued the research to the single degree of freedom vibration, the corresponding results had been found that under the wake of the free steady flow, as the reduced velocity increases, the phase portraits displacements of the single degree of freedom vibrating cylinder will begin to rotate counterclockwise from the first and third quadrants to the second and fourth quadrants in a Cartesian coordinate system. Under the wake of the oscillating airfoil, the single bending curve and the single closed orbit (double “8-shape” like) of the displacements are newly found in the drag and thrust producing cases respectively. Except this, the two triplets of vortices have also been newly found in the pair and single plus pair wakes at each cycle. The vorticity dynamics behind the vibrating cylinder together with the corresponding force variations have also been obtained computationally and analyzed in details.