Effect of Three-Dimensional Geometry on Harmonic Gust–Airfoil Interaction

Abstract

Two-dimensional (2-D) strip-theory modeling of unsteady gust–airfoil interaction is standard practice in many industrial applications, but the limits of applicability of 2-D unsteady flow modeling on three-dimensional (3-D) wing and rotor geometries are not well understood. This paper investigates the effects of 3-D geometry features (such as finite span, taper, sweep, and rotation) on the unsteady lift response to gusts and the flow-physical differences between 2-D and 3-D geometries in unsteady flow. A frequency-domain inviscid vortex lattice model is validated and used for the 3-D analysis. The results are compared to unsteady transfer functions from 2-D linear analytic theory (for example, Theodorsen and Sears functions). The study agrees with previous research findings that 3-D effects are most significant at low reduced frequencies and low aspect ratios, as well as near the wing tips. The driving cause of 3-D response is shown to be the wake vorticity: both streamwise and spanwise components of unsteady wake vorticity must be modeled. The study concludes by investigating whether unsteady response of more complex 3-D wing and rotor geometries can be represented by the response of a rectangular wing. The results indicate that this is possible for tapered wings and rotating blades, but not for swept wings.