Improved Understanding of Aerodynamic Damping Through the Hilbert Transform

Abstract

The equation of motion used to derive the aerodynamic damping coefficient for a single-degree-of-freedom airfoil oscillating in pitch about its quarter-chord is rewritten in analytic signal form through application of the Hilbert transform. The results yield a mathematical framework that can be used to estimate the aerodynamic damping coefficient throughout the entire pitch cycle. The analysis is then applied to experimental data from attached, light, and deep dynamic stall conditions at freestream Mach numbers ranging from 0.2 to 0.6 and Reynolds numbers up to . The Hilbert-transform-based approach is used to demonstrate that the cycle-integrated aerodynamic damping coefficient masks the physics underlying the stabilizing and destabilizing mechanisms of the dynamic stall process. In particular, conditions that exhibit positive cycle-integrated aerodynamic damping may include time intervals of negative aerodynamic damping during the pitch cycle.