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Note on the limitations of the Theodorsen and Sears functions

Published online by Cambridge University Press:  07 December 2016

Ulrike Cordes ,
G. Kampers ,
T. Meißner ,
C. Tropea ,
J. Peinke  and
M. Hölling
Ulrike Cordes*
Affiliation:
Institute for Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Flughafenstraße 19, 64347 Griesheim, Germany
G. Kampers
Affiliation:
ForWind, Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany
T. Meißner
Affiliation:
Institute for Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Flughafenstraße 19, 64347 Griesheim, Germany
C. Tropea
Affiliation:
Institute for Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Flughafenstraße 19, 64347 Griesheim, Germany
J. Peinke
Affiliation:
ForWind, Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany
M. Hölling
Affiliation:
ForWind, Institute of Physics, University of Oldenburg, 26111 Oldenburg, Germany
*
†Email address for correspondence: cordes@sla.tu-darmstadt.de
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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.

JFM classification

Aerodynamics: Aerodynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , R1
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Copyright
© 2016 Cambridge University Press 

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References

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