About a century ago, two different rotor models were proposed by Joukowsky (1912–1918) and Betz (1919). Both models were based on assumptions regarding the vortex structures of the wake and its induction on the rotor plane. However, due to complications of formulating the wake behavior into actual guidelines for the aerodynamic design of the rotor geometry, the models have until now not been used to design actual industrial wind turbine rotors. In this article, we propose a technique to solve analytically the induction problem of the two models, which enables the design of wind turbine rotors. We briefly present the theory behind the two rotor models, and show how this theory can be exploited to make actual designs of rotor planforms, i.e. chord- and twist-distributions. The designs are for three-bladed rotors optimized for different tip speed ratios and analyzed by comparing their performance to results using blade-element/momentum technique and lifting line theory.

大约一个世纪前，Joukowsky (1912-1918) 和 Betz (1919) 提出了两种不同的转子模型。两种模型都基于关于尾流涡结构及其在转子平面上的感应的假设。然而，由于将尾流行为公式化为转子几何形状的空气动力学设计的实际指南的复杂性，这些模型直到现在还没有用于设计实际的工业风力涡轮机转子。在本文中，我们提出了一种技术来分析解决这两个模型的感应问题，从而能够设计风力涡轮机转子。我们简要介绍了两种转子模型背后的理论，并展示了如何利用该理论来进行转子平面形状的实际设计，即弦分布和扭曲分布。