Note on the limitations of the Theodorsen and Sears functions. (7th December 2016)

• Record Type: Journal Article
• Authors: Cordes, Ulrike; Kampers, G.; Meißner, T.; Tropea, C.; Peinke, J.; Hölling, M.
• Is Part Of: Journal of fluid mechanics. Volume 811(2017)
• Publication Date: 2016-12-07
• Subjects: aerodynamics; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.780
• Languages: English
• ISSNs: 0022-1120

Abstract

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.