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Unsteady Tip Vortices
A low AR wing is susceptible to rolling instabilities (wobbling). This problem is particularly important in view of the strong gust effect on MAVs. Tang and Zhu [167] investigated the aerodynamic characteristic of a low AR wing. The wing has an elliptic planform, using the E-174 airfoil with an AR of 1.33. Based on the maximum chord length, the Reynolds number is 1 x 104. Through numerical simulation and flow visualization in a water tunnel, they found that TiVs are unsteady in sizes and strengths when the AoA is larger than 11°. Figure 2.47a-c, on the right side of the figure, shows the positions of the TiVs at an AoA of 25° in the vertical plane (Trefftz plane) at three time instants. As time evolves, the left and right TiVs change their sizes and strengths. The asymmetric flow causes unequal drag between the two sides of the wing, which produces a yawing moment; the asymmetric flow also causes uneven lift, resulting in a rolling instability.
From the numerical results, they suggested that this unstable phenomenon is caused by the interaction between the secondary vortical flows and the TiVs. The separated vortical flows are on the upper surface of the wing. The schematic diagram on the left of Figure 2.47 shows that, as the wing incidence progressively increases from 5°, substantial time dependency of the TiVs is observed. At the AoA = 5°, the position of the separated vortical flow is around the trailing edge. As the incidence
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Figure 2.47. Left: Schematic of the dynamics of tip vortices (viewed above the wing, secondary vortices are above the upper surface of the wing). Right: tip vortices streamlines in vertical planes (Trefftz plane) at about 0.5c behind trailing edge at the AoA of 25°, at three nondimensional times (based on the free-stream velocity and maximum chord length): (a) t = 42, (b) t = 54, and (c) t = 62 (viewed from aft). From Tang and Zhu [167]. |
increases, the separating flow moves toward the leading edge. When the incidence reaches 15° or higher, the separating flows above the wing interact with the TiVs, causing them to become substantially unsteady. To date, MAV flight tests have not reported such rolling instabilities as a major barrier. This is apparently because the airfoil shapes used for MAV flyers are much thinner and do not induce as many separating flows above the wing surface. Nevertheless, the issue of unsteady TiVs needs to be investigated in the MAV design and flight test process.
