# Leading-Edge Vortex Characteristics of Low-Aspect-Ratio Sweptback Plates at Low Reynolds Number
## 3 Results and Discussion
At \(\beta=36\) deg (Figure 9c), the LEV trace appeared at a smaller \(\alpha\) of 5 deg, meaning that the spanwise flow here would be sufficient to roll up a chordwise inflow. At \(\alpha=10\) deg, the line of separation was connected to the bottommost point of the right side; this was maintained until \(\alpha=20\) deg. The LEV was gradually developed with increasing \(\alpha\), encroaching the attached flow region between the LEV and TiV on the left side. This TiV was also grown to the attached flow region. At \(\alpha=30\) deg, the LEV and TiV were bonded to each other across the line of reattachment. The LEV covered the model plate across the wingspan, except for a small region where the TiV was placed on the right edge. This structure is quite similar to that on a revolving/flapping wing [31], as well as that on a non-sender delta wing [25; 32; 33]. Figure 8: Maximum C\({}_{\rm L,cw}\) with respect to \(\beta\). Figure 7: Lift coefficients based on the chordwise component of the freestream C\({}_{\rm L,cw}\). (**a**) AR = 2.03; (**b**) AR = 3.13; (**c**) AR = 4.50. Figure 10 exhibits the surface streamlines near the stall \(\alpha\) at \(\beta=36\) deg. Before the stall (\(\alpha=25\) deg), the three AR plates resulted in an identical LEV structure except for the scale along the spanwise direction. TiVs on the left side also had a similar size, and the attached flows settled in between the LEVs and the TiVs. The line of separation  
Figure 3:0 Surface oil-flow pattern on the AR = 3.13 plate. (a) \(\beta=0\) deg; (b) \(\beta=24\) deg; (c) \(\beta=36\) deg. on the AR = 2.03 plate was considerably stepped back to the trailing edge at \(\alpha\) = 30 deg (Figure 10a), reminding us of a lifted-off LEV on a revolving/flapping wing [15; 16; 17; 18]. At \(\alpha\) = 32 deg, the trace of the LEV was only observed near the trailing edge, but it was still distributed in most of the span. The LEV at AR = 3.13 also covered most of the span at the same \(\alpha\) (the final row in Figure 10b), but the LEV was less deformed than that of AR = 2.03. The line of separation at \(\alpha\) = 32 deg begun from \(\sim\)0.4\(\alpha\) at the inboard region, and gradually developed up to \(\sim\)0.62\(\alpha\) until it was bent by the TiV on the right side. The LEV at AR = 4.50 (Figure 10c) also left a similar oil-flow pattern. The LEV was shortly extended to the right side so as to give a small region for the attached flow even at \(\alpha\) = 32 deg. However, the relatively short LEV eventually left a considerable outboard region where the unsteady wake shedding appeared. Note that the LEVs at AR = 2.03 and 3.13 (Figure 10a,b) fully covered the suction side without an outboard wake region on the right side. Note also that the two LEVs at AR = 3.13 (Figure 10b) and at AR = 4.50 (Figure 10c) covered up the surface approximately three times the chord along the wingspan. These characteristics remind us of the previous studies on a revolving/flapping wing, which showed a conical LEV system in an inboard quasi-steady region that takes approximately three chords from the root [18]. A concept of 'radial stall limit' for the LEV on a revolving wing, where the limit found as r/c < 4 [15], also seems to have consistency with the LEVs in this study. These all do not only indicate identical characteristics between the two different LEVs as mentioned before, but also imply that the similar concept to characterize an LEV will be adoptable to an LEV on a sweptback plate. Based on the line of separation at AR = 4.50, a critical length of the LEV of a sweptback plate could be determined as \(b/c\approx 3.1\), at least at this Reynolds number. Such a resemblance between the two LEVs further gives us another explanation for stall characteristics at AR = 2.03. [PERSON] et al. [16] found an excessive flux running to the  
Figure 3:1 Surface oil-flow pattern near stall \(\alpha\) at \(\beta\) = 36 deg. (**a**) AR = 2.03; (**b**) AR = 3.13; (**c**) AR = 4.50.  
wingtip around an LEV on a flapping wing at AR \(<\) 3.