Experimental and analytical investigation into lift prediction on large trailing edge flaps

Abstract

The present work aims to demonstrate the relationship between circulation production and force production on rapidly maneuvering wings using experimental measurements and two forms of low order modeling: an empirical model based on Lamb’s point vortex impulse theory and an analytical model stemming from classical airfoil theory. Experiments were performed on a 50%-chord trailing-edge flap deflecting with a linear motion profile. Both flap-down (0° − δf) and flap-up (δf − 0°) motions were examined, where δf = 20° or 40°. All cases were run at a Reynolds number of Re ∼ O(104), corresponding to convective times on the order of the free stream or faster, with the fore element of the wing fixed at zero incidence. Time-resolved circulation measurements confirmed that bound circulation on the wing equated to circulation shed into the wake from the trailing edge for the duration of flap deflection. A two-vortex model matched well with the experimental results, regardless of whether the plate experienced fully attached or massively separated flow. An analytical model based only on flap kinematics showed an equivalence between its time-dependent quantities proportional to the motion rate (δ̇,δ̈) and those proportional to the circulation rate (Γ̇) in the empirical model. Agreement between force measurements and both low order models emphasizes the need for future investigation into the direct relationship between force and circulation production.