Flutter analysis of a flexibly supported wing

Abstract

Flutter is a dynamic aeroelastic phenomenon. Current aeroelastic theoretical models have some issues with the parameters related to the outcomes of wing flutter speed analysis. The typical trend in applying static derivatives in estimating wing flutter speed is one of the factors for the inconsistency. This study aimed to establish dynamically measured derivatives with comparisons to conventional static derivatives in predicting the wing flutter speed by using aeroelastic stiffness and damping equation. A free oscillation wind tunnel test rig was designed to measure the dynamic derivatives of rigid wings with flexible mounting at root simulated within a reduced frequency, Km range from 0.04 to 0.40 under subsonic incompressible flow. The dynamically measured aerodynamic stability derivatives were determined from oscillation frequencies and amplitude decay of the wind-off and wind-on time response history. Four rectangular 3D wing models with NACA 0010, NACA 0012, NACA 0014 and NACA 0018 aerofoil configurations were tested. Each wing model has a wingspan of 0.36m and chord length of 0.16m with an aspect ratio of 4.5. The aerodynamic loads model with the dynamic derivatives was applied into the aeroelastic equation of motion to solve the flutter speed via eigenvalue solution. It was found that the (CLa)Dynamic and (CMa) Dynamic were 10%-40% higher than (CLa)Static and (CMa)Static for all the wing models. However, the differences between the dynamically and statically measured derivatives reduced by 12% for CLa and 7% for CMa as the thickness-to-chord ratio of the wing model increased. The measured (CLa + CLa)Dynamic increases when aerofoil thickness-to-chord ratio increases. Besides, less fluctuations in (CLa + CLa)Dynamic was seen for Km<0.10 and the measured (CMa + CMa)Dynamic was reduced as Km increased, with insignificant differences for all wing models. The predicted wing flutter speeds with dynamic derivatives are two times less than the estimations with Theodorsen model and 20% higher than the estimations with Scanlan model. These show that the dynamically measured derivatives have improved the wing flutter speed analysis for optimisation.