Abstract

Wind energy is one of the main factors in the future transition to renewable energies. Hence, it is important to understand how much work can be extracted from the kinetic energy of the wind. Understanding these constraints is important for setting correct strategic goals in wind power research and industry. The current standard opinion is that the limits on the efficiency of work-extraction are provided by the Betz (or more precisely, the Lanchester–Betz–Joukowsky) model, which states that only 59% of the kinetic energy can be extracted. Here we reexamine the Betz model and scrutinize its main assumptions. We detect several serious inconsistencies, some of which were already noted in the literature, and others are new. Altogether, the Betz model does not bound from above (or from below) the efficiency of wind engines. These conclusions corroborate the point expressed recently that the maximal work-extraction efficiency of a wind engine is not a universal number but it depends on the parameters of the engine.

中文翻译：

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重新检查贝兹风力发动机的极限

摘要

风能是未来向可再生能源过渡的主要因素之一。因此，重要的是要了解可以从风的动能中提取多少功。了解这些约束对于在风电研究和行业中设定正确的战略目标很重要。当前的标准意见是，工作提取效率的限制是由Betz模型（或更准确地说，是Lanchester-Betz-Joukowsky模型）提供的，该模型指出只能提取59％的动能。在这里，我们重新审查了Betz模型并仔细研究了其主要假设。我们发现了一些严重的不一致之处，其中一些已经在文献中指出，而另一些则是新出现的。总体而言，贝茨模型并未从上方（或从下方）限制风力发动机的效率。