# Leading-Edge Vortex Characteristics of Low-Aspect-Ratio Sweptback Plates at Low Reynolds Number
## 3 Results and Discussion
The increment in the \(\rm C_{L,LEV}\) even appeared at AR = 2.03, implying that the plateau of the \(\rm C_{L,max}\) at AR = 2.30 at \(\rm\beta\)\(<\) 30 deg in Figure 6a originally resulted from the LEV that compensated a gradual loss in the lift force with increasing \(\rm\beta\) (refer to the black dashed line in Figure 6a for the loss in the lift force). At \(\rm\beta\)\(>\) 36 deg. The \(\rm C_{L,LEV}\) of the AR = 3.13 plate resulted in higher values. This suggests that an LEV would be most effective at an AR of approximately three with a sufficient sweptback angle. All the \(\rm C_{L,LEV}\) then decreased at \(\rm\beta\)\(>\) 45 deg, where the spanwise component of the freestream is larger than the chordwise one. The \(\rm C_{L,LEV}\) gradually reduced from this point; the \(\rm C_{L,LEV}\) will eventually approach zero with increasing \(\rm\beta\) as the frontal area of the model plates approach zero. According to [PERSON] and [PERSON] (2016) and [PERSON] et al. (2017), two TiVs at a sufficient a induce massive downwash covering up to the midspan at an AR of approximately two and below. This implies that the flow over the AR = 2.03 plate was stabilized by two TiVs, and the \(\rm C_{L,max}\) at AR = 2.03 was achieved by the two strong TiVs at \(\rm\beta\) = 0 deg already. Developing an LEV with increasing \(\rm\beta\) at AR = 2.03, therefore, could not be effective to obtain an additional lift, because the Kutta condition at the trailing edge, which is expected as a result of the LEV attachment, was already achieved by the two TiVs (refer to [PERSON] and [PERSON] (2018) for the LEV system of a flapping plate in detail). This suggests that from this AR, supplying a spanwise flow using a sweptback angle for a lower AR plate would not be beneficial for lift production. Figure 6: The maximum \(\rm C_{L}\) and the contribution of the leading-edge vortex. (**a**) The maximum lift coefficients \(\rm C_{L,max}\) with respect to \(\rm\beta\); (**b**) The contribution of the leading-edge vortex \(\rm C_{L,LEV}\) with respect to \(\rm\beta\). At AR = 3.13 and AR = 4.50, the TiVs at \(\beta\) = 0 deg could not cover the midspan region as [PERSON] et al. [7] revealed. The flow in the midspan region would show similar behavior to that of a two-dimensional airfoil at higher \(\alpha\), i.e., unsteady vortex shedding. Here, introducing the spanwise flow by increasing \(\beta\) would develop an LEV and gradually increase the \(\text{C}_{\text{L,max}}\) as shown in Figure 6a. The relatively wider inboard region of the AR = 4.50 plate would result in both the lowest \(\text{C}_{\text{L,max}}\) at \(\beta\) = 0 deg and the rapid rate of growth of the \(\text{C}_{\text{L,max}}\) with the slightly extended LEV (as discussed later). This manner, i.e., increasing \(\beta\) to develop an LEV and to enhance a lift, however, seems to need at least a certain higher \(\beta\) because there were also slight losses in the lift at \(\beta\) = 6 deg at the two higher ARs (Figure 6a). The \(\text{C}_{\text{L,LEV}}\) at \(\beta\) = 6 deg at the two ARs remained near zero (Figure 6b),, also implying an insiginifcant LEV contribution. Another interesting feature is the superior lift production and the largest LEV contribution of the AR = 3.13 plate at \(\beta\) > 36 deg. Considering that the LEV system would be fully developed at such a higher \(\beta\), it can be interpreted that an AR near three might be an optimal value for the lift enhancement of a sweptback plate. Note that a stable LEV attachment on a revolving/flapping wing solely appeared in an inboard limited region from the wingroot in the previous studies (r/c < 4.0 in ref. [15]; r/c \(\approx\) 3.0 in ref. [18]). Note also that a revolving/flapping wing with an AR of around three results in the maximum lift production and reasonable efficiency [16; 18].