Note on the limitations of the Theodorsen and Sears functions

Abstract

Two transfer functions for the unsteady lift response of an airfoil under attached flow conditions are experimentally investigated: the Theodorsen function for an airfoil oscillating in a constant free stream and the Sears function for a steady airfoil encountering a sinusoidal vertical gust. A two-dimensional airfoil with a Clark Y profile is submitted to two different unsteady excitations of distinct frequencies: a pitching oscillation around the leading edge and a sinusoidal vertical gust. The reduced frequency of the perturbation is in the range of $0.025<k<0.3$ and the Reynolds number of the undisturbed flow is in the range of $120\,000<\mathit{Re}<300\,000$. While the Theodorsen function is found to be a good estimator for the unsteady lift at moderate mean angles of attack, the Sears function does not capture the experimental transfer functions in frequency dependence or in limiting values. A second-order model provided by Atassi (J. Fluid Mech., vol. 141, 1984, pp. 109–122) agrees well with the experimental transfer function.