Flow Past Large and Moderate Aspect Ratio Wings

In this chapter we will study 3-D steady flows past finite wings of large and moderate aspect ratios. The wing geometrical parameters have been defined in Chap. 1 with wing aspect ratio given by AR = b2/S, where b is the wing span from tip to tip and S is the projected surface area of the wing onto the x, y plane, the x-axis being aligned and in the direction of the incoming flow in the plane of symmetry of the wing, the y-axis being along the right wing and the z-axis completing the direct orthonormal coordinate system. For a rectangular wing, this reduces to AR = b/c, where c is the constant chord. The assumption of a large aspect ratio wing will contribute to a major simplification which consists in neglecting geometric influence in the y-direction compared to the other directions, in other words

д д d

« , (6.1) dy dx dz

which corresponds to the so-called strip theory. Large aspect ratio lifting elements make for the wings of commercial aircraft, glider, helicopter and wind turbine blades. Such a fundamental geometrical aspect has ramifications not only for aerodynamics, but also for structures with the beam theory. Aspect ratio varies widely:

• AR ~ 35 for high performance sailplanes

• AR = 7 — 2 for commercial airplanes

• AR = 4 — 5 for transport jets

• AR ~ 2 for supersonic jets

Note that AR > 7 will be considered high aspect ratio and AR < 4 low aspect ratio (Fig. 6.1).

© Springer Science+Business Media Dordrecht 2015

J. J. Chattot and M. M. Hafez, Theoretical and Applied Aerodynamics,

DOI 10.1007/978-94-017-9825-9_6

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