A vortex model for forces and moments on low-aspect-ratio wings in side-slip with experimental validation

Abstract

This paper studies low-aspect-ratio (A) rectangular wings at high incidence and in side-slip. The main objective is to incorporate the effects of high angle of attack and side-slip into a simplified vortex model for the forces and moments. Experiments are also performed and are used to validate assumptions made in the model. The model asymptotes to the potential flow result of classical aerodynamics for an infinite aspect ratio. The A → 0 limit of a rectangular wing is considered with slender body theory, where the side-edge vortices merge into a vortex doublet. Hence, the velocity fields transition from being dominated by a spanwise vorticity monopole (A ≤ 1) to a streamwise vorticity dipole (A ∼ 1). We theoretically derive a spanwise loading distribution that is parabolic instead of elliptic, and this physically represents the additional circulation around the wing that is associated with reattached flow. This is a fundamental feature of wings with a broad-facing leading edge. The experimental measurements of the spanwise circulation closely approximate a parabolic distribution. The vortex model yields very agreeable comparison with direct measurement of the lift and drag, and the roll moment prediction is acceptable for A ≤ 1 prior to the roll stall angle and up to side-slip angles of 20°.