Analysis of small-aspect-ratio lifting surfaces in extreme curved-ground effect

作者：Wang Q X^*

来源：IMA Journal of Applied Mathematics, 2011, 76(4): 514-523.

DOI：10.1093/imamat/hxq051

• extreme ground effect
• potential flow theory
• small-aspect-ratio lifting surfaces
• matched asymptotic expansion

This paper extends Newman's (1982, Analysis of small-lifting-ratio lifting surfaces in ground effect. J. Fluid Mech., 117, 305) analysis for a small-aspect-ratio lifting surface moving in very close proximity to a rigid plane surface to one near a curved surface. In this 3D problem, the variation of the velocity along the chord is much smaller than in the transverse cross section, while the flow in the gap beneath the wing is dominant over that above it. At first order, the problem reduces to flow in the gap, which can be represented through a simple non-linear solution. The solution has different boundary conditions at the leading and trailing edges of the wing, where the mean normal velocity on the upper surface and lower surface of the wing is inward and outward of the gap, respectively. Calculations for a delta wing reveal that the changeover point between the leading and trailing edges tends to move forward (backward) when the wing moves over convex (concave) ground. If the angle of attack is positive (negative), a lift (attraction) force acts on the wing. The magnitude of the lift or attraction increases (decreases) when the wing moves over convex (concave) ground. When a wing at a positive angle of attack and its rear part is over curved ground, the lift increases (decreases) significantly for convex (concave) ground because the curved-ground effect is strengthened by a shift in the changeover point. The pressure centre shifts slightly forward when the fore part of the wing is over convex ground. It shifts backward at a much larger amplitude when the rear part of the wing is over convex ground. The similar but reverse trends are observed when the wing moves over concave ground.

• 出版日期2011-8