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Reaching the betz limit experimentally and numerically

机译：通过实验和数值达到贝兹极限

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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.
机译：贝兹理论表示，没有水平轴风力涡轮机可以提取超过16/27（59.3％）的风动能。系数16/27（0.593）被称为贝兹极限。水平轴风力涡轮机设计人员试图提高功率性能以达到Betz极限。现代可操作的风力涡轮机的峰值达到了Betz极限的75％至80％。 1919年，阿尔伯特·贝兹（Albert Betz）使用一种分析方法得出贝兹极限。他推导了流中致动器盘（AD）的动量方程。在这项研究中，已经设计并测试了基于执行器盘（AD）的实验和数值设置，以达到Betz极限。孔隙率为0.5的有机玻璃屏风模仿了风轮机转子。对于数值研究，考虑了二维流场。实验和数值方法的结果都与贝兹理论的分析结果非常吻合。从实验和数值结果来看，与贝兹极限（16/27）相比的相对误差分别为0.16％和1.27％。少量的误差表明使用实验或数值方法都可以达到贝兹极限。这种方法可用于在数值上或实验上对理想的风力涡轮机，理想的旋转设备或理想的风场进行建模，并能最大程度地提取功率。因此，可以通过此方法对系统性能进行任何改进。

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