Airfoil longitudinal gust response in separated vs. attached flows

Abstract

Airfoil aerodynamic loads are expected to have quasi-steady, linear dependence on the history of input disturbances, provided that small-amplitude bounds are observed. We explore this assertion for the problem of periodic sinusoidal streamwise gusts, by comparing experiments on nominally 2D airfoils in temporally sinusoidal modulation of freestream speed in a wind tunnel vs. sinusoidal displacement of the airfoil in constant freestream in a water tunnel. In the wind tunnel, there is a streamwise unsteady pressure gradient causing a buoyancy force, while in the water tunnel one must subtract the inertial load of the test article. Both experiments have an added-mass contribution to aerodynamic force. Within measurement resolution, lift and drag, fluctuating and mean, were in good agreement between the two facilities. For incidence angle below static stall, small-disturbance theory was found to be in good agreement with measured lift history, regardless of oscillation frequency. The circulatory component of fluctuating drag was found to be independent of oscillation frequency. For larger incidence angles, there is marked departure between the measured lift history and that predicted from Greenberg's formula. Flow visualization shows coupling between bluff-body shedding and motion-induced shedding, identifiable with lift cancellation or augmentation, depending on the reduced frequency. Isolating the buoyancy effect in the wind tunnel and dynamic tares in the water tunnel, and theoretical calculation of apparent-mass in both cases, we arrive at good agreement in measured circulatory contribution between the two experiments whether the flow is attached or separated substantiating the linear superposition of the various constituents to total lift and drag, and supporting the idea that aerodynamic gust response can legitimately be studied in a steady freestream by oscillating the test article.