Effects of pitching phase angle and amplitude on a two-dimensional flapping wing in hovering mode

This paper reports on a fundamental investigation of the effects of pitching phase angle (ϕ) and pitching amplitude (α_A) on the aerodynamics of a two-dimensional (2D) flapping wing executing simple harmonic motion in hovering mode. A force sensor and digital particle image velocimetry were employed to obtain the time-dependent aerodynamic forces acting on the wing and the associated flow structures, respectively. Pitching phase angle ranging from 0° to 360° at three different pitching amplitudes, that is, 30°, 45° and 60°, was studied. Our experimental results revealed that the largest lift and lift/drag ratio were achieved under the condition of advanced pitching (ϕ > 90°). However, further increasing ϕ beyond a certain value would not enhance the average lift any more. In contrast, the delayed pitching (ϕ < 90°) would cause the average lift to decrease and generally the averaged drag to increase, compared to the normal pitching (ϕ = 90°), overall reducing the lift/drag ratio greatly. Our experimental results also supported the findings of Lua et al. (J Exp Fluids 51:177–195, 2011) that there are two kinds of wing–wake interactions, and they can either enhance or reduce lift on the wing depending on the wing motion and the timing of the reverse stroke. Our results show that wing–wake interaction of the first kind normally has an adverse effect on lift generation when the wing is undergoing delayed pitching but has a positive effect on the lift when the wing is undergoing advanced pitching motion. When the ϕ became larger, the second kind of wing–wake interaction, that is, sliding of the leading edge vortex under the wing, will cause the concurrent fall in lift and drag.