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A momentum explanation for the unsatisfactory Betz model prediction in highly loaded wind turbines

Authors

  • D. P. Georgiou,

    Corresponding author
    1. Department of Mechanical Engineering and Aeronautics, Thermal Engines Lab., University of Patras, Rion-Patras, Greece
    • Department of Mechanical Engineering and Aeronautics, Thermal Engines Lab., University of Patras, Rion-Patras, 26500, Greece
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  • N. G. Theodoropoulos

    1. Department of Mechanical Engineering and Aeronautics, Thermal Engines Lab., University of Patras, Rion-Patras, Greece
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Abstract

The present study attempts to provide a direct explanation for the strong deviation between the predictions of the well-known Betz model and the actual results for the performance of highly loaded wind turbines. The new model accounts for the inner and outer stream interaction (momentum and energy transfers) by reformulating the relevant one-dimensional flow equations. This results in a very good prediction of the experimentally measured CT = f(a) relationship in ‘windmilling propeller’ tests. It is shown that although the maximum power coefficient is near that predicted by Betz, for rotor loadings beyond the ‘optimum’ point, this drops sharply (instead of remaining steady, near the CP = 0.5 value). Further analysis shows that the main contributor for this ‘efficiency’ degradation is the reduction in the mass flux through the turbine rotor, apparently because of the wake vortices that block its passage in the inner section. Copyright © 2010 John Wiley & Sons, Ltd.

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