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 (phi) and pitching amplitude (alpha(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 degrees to 360 degrees at three different pitching amplitudes, that is, 30 degrees, 45 degrees and 60 degrees, was studied. Our experimental results revealed that the largest lift and lift/drag ratio were achieved under the condition of advanced pitching (phi > 90 degrees). However, further increasing phi beyond a certain value would not enhance the average lift any more. In contrast, the delayed pitching (phi < 90 degrees) would cause the average lift to decrease and generally the averaged drag to increase, compared to the normal pitching (phi = 90 degrees), 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 phi 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.