Flapping dynamics of an inverted flag with different shapes in a uniform flow

The flapping motion of an inverted flag with different shapes in a uniform flow was simulated using an immersed boundary method. The shapes of the flag were distinguished by the shape ratio (S=W_T / W_L) defined as the ratio of the trailing edge width (W_T) to the leading edge width (W_L). To investigate the effects of the shape ratio on the dynamics of the inverted flag, the peak-to-peak amplitude (A/L) and the Strouhal number (St) were analyzed as a function of the bending rigidity (0.1 ≤ γ ≤ 0.3) and the shape ratio (0.5 ≤ S ≤ 2). The vortical structures behind the inverted flag were visualized by the Q-criterion to examine the vortex dynamics. The hydrodynamic forces exerted on the flag were explored to reveal the correlation between the kinematics of the inverted flag and the vortex formation during a flapping period. Finally, we estimated the strain energy (E_s) stored on the inverted flag and the conversion ratio (R) of the flow kinetic energy to the strain energy.