Note on the limitations of the Theodorsen and Sears functions. (7th December 2016) - Cordes, Ulrike; Kampers, G.; Meißner, T.; Tropea, C.; Peinke, J.; Hölling, M.
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<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.