Investigation of two degrees of freedom on vortex-induced vibration under the wake interference of an oscillating airfoil

The vortex formation and shedding process behind an isolated cylinder under the wake interference of an oscillating airfoil at different oscillating frequencies and amplitudes have been studied numerically. The “2S” and “P+S” mode are found in the drag-producing von Kármán vortex wake and thrust-producing inverted von Kármán vortex wake, respectively. For the “2P” case, the pairs of vortices with different sizes are laterally parallel to each other. For the “2P+2S” case, the merged single vortices do not appear between the vortex pairs, but they only emerge after every two pairs of vortices. For the two-degree of freedom (2-DOF) VIV in the wake of the steady flow, seven types of the phase portraits of the displacement shapes are observed. In the range of small reduced velocity (V_r<5), the body trajectories are mainly characterized by an “8-shape” with some differences in phase. At the peak amplitude, the body trajectories have changed into two shapes: i.e., the half “8-shape” (initial stage) and the crescent-shape (final stage). When V_r=6, the body trajectories have also shown to have two shapes: i.e., the “8-shape” (initial stage) and the half “8-shape” (final stage). When V_r arrives at the low branch (V_r>7), the body trajectories will become irregularly shaped like a cone-net.