Drag reduction by flapping a flexible filament behind a stationary cylinder

Abstract

The hydrodynamic mechanism of drag reduction by flapping a flexible filament behind a stationary cylinder was explored using the penalty immersed boundary method. The effects of the filament length, bending rigidity, pitching amplitude, and frequency on drag reduction were systematically examined. We analyzed the underlying mechanism of drag reduction in detail by examining flapping modes, wake patterns, pressure distributions, and flapping dynamics of the flapping filament. The flapping motion of the flexible filament is determined by the combined effect of forcing parameters and the surrounding flow. Three distinct flapping modes are observed when the aforementioned parameters are varied: an oscillation mode, an undulation mode, and a vortex-dominated mode. The oscillation and undulation modes are more beneficial to drag reduction than the vortex-dominated mode. In the oscillation mode, drag reduction is mainly realized by the high thrust generated by the filament overwhelming the increased form drag of the cylinder caused by the trailing edge vortex. A flexible filament flapping in the oscillation mode generates thrust more efficiently. In the undulation mode, a long filament reduces the form drag of the cylinder and generates relatively low thrust, showing a similar drag reduction as a short oscillating filament. In the vortex-dominated mode, the thrust of the filament is very low because of the weakened trailing edge vortex, yielding a weakened drag reduction effect.