Reaching the betz limit experimentally and numerically

Document Type: Research Paper


1 College of Mechanical Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

2 Waterloo Institute for Sustainable Energy (WISE), University of Waterloo, Waterloo, ON, N2L 3G1, Canada



The Betz theory expresses that no horizontal axis wind turbine can extract more than 16/27 (59.3%) of the kinetic energy of the wind. The factor 16/27 (0.593) is known as the Betz limit. Horizontal Axis wind turbine designers try to improve the power performance to reach the Betz limit. Modern operational wind turbines achieve at peak 75% to 80% of the Betz limit. In 1919, Albert Betz used an analytical method to derive the Betz limit. He derived momentum equations of an Actuator Disc (AD) in the stream. In this research, an experimental and a numerical setup based on the Actuator Disc (AD) have been designed and tested to reach the Betz limit. A Plexiglass screen with the porosity of 0.5 mimics the wind turbine rotor. For the numerical study, a 2D flow filed is considered. The results of both experimental and numerical methods agree well with the analytical results of the Betz theory. From the experimental and numerical results, the relative errors in comparison with the Betz limit (which is 16/27) are 0.16% and 1.27%, respectively. The small amount of errors shows the possibility of reaching the Betz limit using either experimental or numerical methods. This approach can be used for modeling ideal wind turbines, ideal rotating devices or ideal wind farms either numerically or experimentally and gives the maximum possible power extractions; thus, any improvement to the performance of a system can be made by this method.


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