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Aerodynamic optimization of wind turbine rotors using a blade element momentum method with corrections for wake rotation and expansion


Mads Døssing, Division of Wind Energy, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, PO Box 49, Frederiksborgvej 399, DK-4000 Roskilde, Denmark.



The blade element momentum (BEM) method is widely used for calculating the quasi-steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (math formula), and more accurate solutions can now be obtained in the blade root and tip sections. It is expected that this will lead to small changes in optimum blade designs. In this work, math formula has been implemented, and the spanwise load distribution has been optimized to find the highest possible power production. For comparison, optimizations have been carried out using BEM as well. Validation of math formula shows good agreement with the flow calculated using an advanced actuator disk method. The maximum power was found at a tip speed ratio of 7 using math formula, and this is lower than the optimum tip speed ratio of 8 found for BEM. The difference is primarily caused by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using math formula, it is possible to obtain a 5% reduction in flap bending moment when compared with BEM. In short, math formula allows fast aerodynamic calculations and optimizations with a much higher degree of accuracy than the traditional BEM model. Copyright © 2011 John Wiley & Sons, Ltd.