Flapping dynamics of an inverted flag in a uniform flow

• The simulation was computed using the immersed boundary method.
• An inverted flag has many advantages for energy harvesting system.
• A biased-straight mode was observed.
• The peak-to-peak amplitude showed a plateau in the flapping mode.
• Various vortical structures were presented during the flapping sequences.

The flapping motions of an inverted flag in a uniform flow were simulated using the immersed boundary method. The strain energy of the inverted flag was used as an indicator of the energy harvesting system efficiency. The flapping dynamics of and vortical structures around the inverted flag were examined in terms of the bending rigidity (γ  ) and the Reynolds number (Re). Three flapping motion modes were observed: a deflected mode, a flapping mode, and a straight mode. A mode intermediate between the flapping mode and the straight mode was identified, the biased mode. The vortical structures in the wake were characterized by three modes: a vortex pair; a vortex pair with a single vortex, and two vortex pairs, during half of the flapping period. The maximum mean strain energy (ES)(ES) was obtained when the vortical structures behind the inverted flag formed a vortex pair during the flapping mode.