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International Journal of Rotating Machinery
Volume 2012, Article ID 476908, 7 pages
Research Article

The Circulation Distribution on the Lifting Line for a Given Extracted Power

1Research Unit of Mechanics and Energetic (URME), National Engineering School of Tunis, 1002 Tunis, Tunisia
2Laboratory of Applied Physics (LPA), Faculty of Sciences of Sfax, 3038 Sfax, Tunisia
3Department of Physics, Faculty of Sciences, University of Buea, Buea, Cameroon

Received 28 April 2011; Revised 1 August 2011; Accepted 19 October 2011

Academic Editor: Paolo Pennacchi

Copyright © 2012 Ali Helali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Presently, there exist few numerical methods which treat the inverse problem for the determination of the geometry of wind turbine blades. In this work, authors intend to solve the inverse optimum project for horizontal axis wind turbine in which the selection of the circulation distribution is obtained by resolving two variational problems: the first consists in sorting the circulation distribution on the lifting line, which, for a given power extracted by the wind turbine, minimizes the loses due to the induced velocity. In the second, the optimal circulation distribution is selected such that the kinetic energy of the wind downstream of the rotor disc is minimum, when the energy extracted by the wind turbine for one rotating period is imposed. A code has been developed which incorporates the real pitch of the helicoidal vortex wake. Very promising results have been obtained: the circulation distribution for a given extracted power and the chord lengths distribution law along the blade span.