Re = 104-106

Shyy et al. [147] evaluated the aerodynamics between the chord Reynolds number of 7.5 x 104 and 2 x 106, using the XFOIL code [96], for two conventional airfoils – NACA 0012 and CLARK-Y – and two low Reynolds number airfoils: S1223 [148] and an airfoil modified from S1223, which is called UF (see Fig. 2.22). Figures 2.23 and 2.24 show the power index, cL/2/Cd, and lift-to-drag ratio, CL/CD, plots at three Reynolds numbers: 7.5 x 104 , 3 x 105, and 2 x 106. It is noted that for steady-state flight, the power required for maintaining a fixed-wing vehicle in the air is

(2-20)

where P and W are the required power and vehicle weight, respectively. For all air­foils, the CL/CD ratio exhibits a clear Reynolds number dependency. For Reynolds numbers varying between 7.5 x 104 and 1 x 106, CL/CD changes by a factor of 1-3 for the airfoils tested. Except for the UF airfoil, which is very thin, the range of the AoA within which aerodynamics is satisfactory becomes narrower as the Reynolds num­ber decreases. Clearly, the camber is important. NACA 0012, with 0 percent camber, and CLARK-Y with 3.5 percent camber, yield a less satisfactory performance under all three Reynolds numbers. S1223 and UF, both with 8.89 percent camber, perform better.

Finally, NACA 0012, CLARK-Y, and S1223 all have maximum thickness of about 0.12c. The UF airfoil, in contrast, is considerably thinner, with a maximum thickness of 0.06c. It is interesting to compare the Reynolds number effect. At the Reynolds number Re = 2 x 106, S1223 and UF airfoil have comparable peak per­formances in terms of cL/2/Cd and CL/CD; however, S1223 exhibits a wider range of acceptable AoAs. At the Reynolds number Re = 7.5 x 104, the situation is quite different. UF, the thinner airfoil with identical camber, exhibits a substantially bet­ter aerodynamic performance while maintaining a comparable range of acceptable AoAs. This is consistent with the finding of Okamoto et al. [139] discussed previously.

Murphy and Hu [149] experimentally measured the aerodynamic characteristics of a bio-inspired corrugated airfoil compared with a smooth-surfaced airfoil and a flat plate at the chord Reynolds numbers of 5.8 x 104 and 1.25 x 105. Their measurement result revealed that the corrugated airfoil has better performance in providing higher lift and preventing large-scale flow separation and airfoil stall at low Reynolds num­bers (<105) than the smooth-surfaced airfoil and the flat plate, as shown in Figures 2.25 and 2.26. However, the corrugated airfoil was found to have higher drag coef­ficients compared to those of the smooth-surfaced airfoil and the flat plate at low

120

CJCD

80
40
0

Figure 2.24. CL/CD against AoA plots for the four airfoils [147]. —, the Reynolds number,

Re = 7.5 x 104; —, the Reynolds number, Re = 3 x 105; ……. , the Reynolds number, Re =

2 x 106.

AoAs (<8°). The corrugated airfoil is less sensitive to the variation in the Reynolds number. Furthermore, as shown in Figure 2.26 Murphy and Hu’s [149] flow measure­ment suggested that the protruding corrugation corners would act as boundary-layer trips to promote the transition of the boundary layer from laminar to turbulent while remaining “attached” to the envelope profile of the high-speed streamlines.