Drag reduction by flapping a pair of flexible filaments behind a cylinder

The hydrodynamic mechanism of drag reduction by flapping a pair of flexible filaments behind a cylinder was explored using the penalty immersed boundary method. The effects of the phase difference between two filaments, the attachment height, and the flapping amplitude on drag reduction were examined. The flapping filaments weaken the vortex shedding via the destructive interaction between the vortices with the opposite signal. The clapping (out-of-phase) flexible filaments experience a lower friction drag and reduce a form drag of the cylinder, showing a better drag reduction than the snaking (in-phase) flexible filaments and the clapping rigid filaments. A minimum drag is obtained at an appropriate attachment height and flapping amplitude that avoid collision of the filaments and weaken the shear-layer-filaments interaction. The effectiveness ratio of the clapping filaments is higher than that of the snaking filaments. Energy saving can be achieved by avoiding the shear layer-filament interaction at a low flapping amplitude, whereas the filaments can further reduce the drag with greater energy consumption at an appropriate flapping amplitude. In addition, the total drag decreases with increasing Reynolds number, accompanied by a transition of the wake pattern from the 2S mode to the P + S mode.