Plots of swirling strength combined with velocity vector at the wingspan of 0
The minimum distance between the leading edges of the two wings at 0
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Figure 12. 75R created by the flapping-wing system with the clap-and-fling effect (case A) and without the clap-and-fling effect (case B). LEV, leading edge vortex; TEV, trailing edge vortex; DW, downwash; IoA, influx of air; UW, upwash.
The minimum distance between the leading edges of the two wings at 0
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Figure 11 shows the snapshots of the swirling strengths and velocity vectors located at 0.25R of the two wings. In case A, when the wings approached each other to the end of the upstroke (t/T = 0.96–1.00), strong leading edge vortices (LEVs) and weak trailing edge vortices (TEVs) that remained attached to the wings were formed. 25R was approximately 0.5c in case A. The wings rotated about their leading edges to complete the clap of the wings at t/T = 1.02. At this period of time, the wing chords were nearly parallel but were not in contact with each other. As the wings drew closer to each other from the leading edge to the trailing edge, a downwash developed between the two trailing edges. Then, the wings rotated about their trailing edges to move away from each other (t/T = 1.04–1.12, fling phase). During this, the LEVs and TEVs were shed and diffused quickly. Subsequently, new weak LEVs and strong TEVs formed and grew in strength (t/T = 1.08–1.12). As the wings separated from the leading edge to the trailing edge, the airflow rushed into the opening gaps between the leading edges as well as between the trailing edges (t/T = 1.12). However, the downwash continued to be present beneath the gap between the trailing edges during the fling phase. In case B, strong LEVs and weak TEVs were formed when the wings approached each other from t/T = 0.96 to t/T = 1.02. The wings rotated for the next stroke and the vortices were diffused from the leading edges and the trailing edges of the wings (t/T = 1.04). These characteristics of the airflow were similar to those in case A at the corresponding non-dimensional time period. However, the downwash in case B was not clearly developed in the gap between the 
trailing edges as that in case A. New LEVs formed and developed when the wings moved apart from each other during the next stroke. Nevertheless, the formed LEVs were weaker than the TEVs in strength (t/T = 1.08–1.12). The influx of airflow (IoA) in case B, unlike that in case A, was not clearly distinguished when the wings moved away.
The swirling strengths and velocity vectors at 0.75R are plotted in figure 12. In case A, LEVs and TEVs were formed when the wings approached each other (t/T = 0.96–1.00). 75R was approximately 0.25c. The wings rotated as the leading edges moved apart for the next cycle while the trailing edges came closer (t/T = 1.02). At this rotation, the vortices were shed from the tips of the wings (leading edges and trailing edges), and new LEVs were generated due to the rotation. When the wings came close to clap, a strong downwash was formed and expelled through the gap between the trailing edges of the wings. The wings commenced the fling when the trailing edges moved apart following the leading edges (t/T = 1.04–1.12). The motion of each wing broke and divided the previous shed LEV into two parts. A part was shed and rolled upward, and the other part remained attached to the wing surface (t/T = 1.04). The new LEVs were formed and partly shed (these shed vortices subsequently diffused) at a time (t/T = 1.04) prior to that when their strength increased (t/T = 1.08–1.12). Only a part of the air rushed into the opening gap when the wings separated (at t/T = 1.04) due to the presence of the LEVs shed in the previous stroke. The previously shed LEVs diffused rapidly and the airflow began to invade the opening gap at t/T = 1.04–1.12. During this time, the TEVs were formed and eventually diffused due to the presence of the mirror wings. Most of the TEVs were mutually exterminated, and therefore the Wagner effect was reduced . It should be noted that the strong downwash between the TEVs shed in the previous stroke appeared throughout the fling period. The airflow structures in case B (non-clap-and-fling case) were quite similar to those in case A for the same instant in time, with the exception of a few major differences. First, the downwash formed but was not clear when the wings approached and separated from each other (case B, t/T = 0.96–1.12). As the wings moved away from each other, the IoA in the opening gap was from both the leading edges and also from the trailing edges between the wings due to the presence of trailing edge circulation. Additionally, the motion of the previous shed TEVs in this case was slower than that in case A (t/T = 1.04–1.12). Hence, the presence of the downwash when the wings drew close to each other and then moved apart in case A (the case with the clap-and-fling effect), was the main source of the augmented vertical force. Furthermore, the IoA in the low-pressure region between the wings from the leading edges also significantly contributed to enhance the vertical force.
