The complementary Betz Theory

Getting More Out of the Wind: Extending Betz's Law to Multiple Turbines

The Betz law places a fundamental limit on the amount of power that can be extracted by a wind turbine for a fixed area wind column. This manuscript extends the original Betz Law derivation to a "multi-turbine" approach.

超越Betz理论-阻塞、尾流混合和Turbulence

Beyond the Betz Theory - Blockage, Wake Mixing and Turbulence

本文综述了近年来有关船用流体动力（MHK）涡轮机极限效率的分析模型，重点讨论了阻塞（局部和全局流道）和尾流混合的重要性。还讨论了充分发展的紊流明渠水流发电的效率。这些问题主要涉及潮汐涡轮机阵列的设计/优化;然而，其中一些也与风力机相关。

风力涡轮机效率极限高于兰彻斯特（贝茨）极限

A Wind Turbine Efficiency Limit Higher than the Lanchester (Betz) Limit

该研究提出风力涡轮机效率极限高于传统贝茨极限，通过分析流体力学方程推导出新的效率上限为78%。

Beating Betz's Law: A larger fundamental upper bound for wind energy harvesting

Betz's law, purportedly, says an ideal wind harvester cannot extract more than 16/27 ($\sim$59\%) of the wind energy. As the law's derivation relies on momentum and energy conservation with incompressible flow and not the physical mechanism coupling the wind-field to the extraction of work it is ubiquitously regarded as a "universal" upper bound on efficiency, as inclusion of mechanics, aerodynamics and thermodynamics are presumed to worsen this upper bound. Here we show that when unneeded assumptions in the Betz's law derivation are relaxed a higher bound of 2/3 ($\sim$67\%) can be achieved. …

Two-scale momentum theory for very large wind farms

A new theoretical approach is proposed to predict a practical upper limit to the efficiency of a very large wind farm. The new theory suggests that the efficiency of ideal turbines in an ideal very large wind farm depends primarily on a non-dimensional parameter $λ/C_{f0}$, where $λ$ is the ratio of the rotor swept area to the land area (for each turbine) and $C_{f0}$ is a natural friction coefficient observed before constructing the farm. When $λ/C_{f0}$ approaches to zero, the new theory goes back to the classical actuator disc theory, yielding the well-known Betz limit. When $λ/C_{f0}$ incr…

垂直轴风力机近尾流动力学的直接数值模拟

Direct Numerical Simulation of Vertical-Axis Wind Turbine Near-Wake Dynamics

通过高保真直接数值模拟，研究了叶片数对垂直轴风力机近尾流中动态失速涡演化的影响，发现叶片-涡相互作用加速涡破裂并促进尾流向钝体动力学过渡。