Four-Winged Flapping Flyer in Forward Flight - Selected Topics of Computational and Experimental Fluid Mechanics - page 150

(a) (b)

(c)

Fig. 7 Time series of the y -position of the leading and trailing edges of both wings for f = 23Hz

and a ˕ =

. ˀ ʳ

0and b 1 3 . The leading-edge-trailing-edge phase lag is shown schematically. In

˕ = ʳ 1 = ʳ 2 ≡ ʳ

the .The y -axis is rendered dimensionless using A , the peak-to-peak

amplitude swept by the leading edge at mid-chord. c Trailing-edge-leading-edge phase lag

0 case,

ʳ for

different forewing-hindwing phase lags. The two different markers correspond to the forewing ʳ 1

( ) and hindwing ʳ

2 (

)

4 Discussion

Before discussing the effect of the forewing-hindwing phase lag we start with a
comment on the role of the flapping frequency. The existence of an optimal flapping
frequency for the present setup (as is evident in Fig. 3 ) is related to the effect of
wing compliance on the propulsive performance of the flapping wings, a question
that has been widely discussed in the literature (Shyy et al. 2010 ; Spagnolie et al.
2010 ; Masoud andAlexeev 2010 ; Thiria andGodoy-Diana 2010 ; Ramananarivo et al.
2011 ; Kang et al. 2011 ). For flexible wings flapping in air, where the mass ratio of
the wing with respect to the surrounding fluid is high, the main bending motor is the
wing inertia (Daniel and Combes 2002 ; Thiria and Godoy-Diana 2010 ). Increasing
the flapping frequency leads to an increased deformation of the wing, which is useful
in terms of propulsive performance up to a certain point where the effective lifting
surface is diminished and thrust production drops (Ramananarivo et al. 2011 ). An
interesting point is that the optimal frequency f opt that can be estimated by inspection
of Fig. 3 is different depending on whether one considers maximum cruising speed