FIGURE 3 Three cross sections of hindwing and the
microstructure of the first groove on the leading edge. (a) The H.
axyridis hindwing and sampling positions from P1 to P3; The
microstructure of the first leading edge groove on P1 (b), P2 (c) and P3
(d). DS is dorsal side and VS is ventral side.
3.2 | Cl andCd analysis and
interpretation
Figure 4 shows the changes of Cl andCd at different flapping frequency for the three
CA models during one flapping cycle. In previous studies (Yang et al.,
2015; Truong et al., 2013), the flapping frequency of the ladybird was
usually set in the range between 55 Hz and 75 Hz. Here, the frequencies
were set at 55 Hz, 65 Hz and 75 Hz. The graphs show
first the downstroke and upstroke
after that.
As shown in Figure 4 (a-c), theCl tends to rise in the first half of the
downstroke and decrease in the second half, and then decreases further
during the first half of the upstroke and rises again during the second
half. The higher the frequency, the higher the lift coefficient. The
results are related to the veins distribution of models (Figure 1b and
1c). Because the veins distribution decides the corrugated shape. A
leading edge vortex (LEV) appears to be crucial for lift development
during the downstroke, causing more air to be deflected downwards, hence
producing more lift, as was also shown in Hawkmoth hovering flight (Yang
et al., 2021). Simulations of Hawkmoth hovering show that about two
thirds of the lift is associated with the LEV (Willmott et al., 1995).
The average Cl and Cd are
shown in Table 2. It shows that the average Cl of
each model increases gradually with the increase of flapping frequency.
The increment of AP1, AP2, and AP3 reached 33.99%, 13.61% and 67.35%,
respectively.
From Figure 4(d-f), the change of Cd is shown
during this flapping cycle. The first drag peak is caused mainly by the
falling off of the LEV and the delayed stall phenomenon (Addo-Akoto et
al., 2019). The second drag peak is caused mainly by the wake effect
when the upstroke is about to end (Sujoy et al., 2012). The wake effect
hardly changes with an increase in frequency, the second force peak is
almost constant. As the frequency increases, the averageCd of these models increases first with frequency
and then decreases at even higher frequency; the highest drag values
were obtained at 65 Hz.