A numerical analysis to evaluate Betz's Law for vertical axis wind turbines

Abstract

The upper limit for the energy conversion rate of horizontal axis wind turbines (HAWT) is known as the Betz limit. Often this limit is also applied to vertical axis wind turbines (VAWT). However, a literature review reveals that early analytical and recent numerical approaches predicted values for the maximum power output of VAWTs close to or even higher than the Betz limit. Thus, it can be questioned whether the application of Betz's Law to VAWTs is justified.To answer this question, the current approach combines a free vortex model with a 2D inviscid panel code to represent the flow field of a generic VAWT. To ensure the validity of the model, an active blade pitch control system is used to avoid flow separation. An optimal pitch curve avoiding flow separation is determined for one specific turbine configuration by applying an evolutionary algorithm. The analysis yields a net power output that is slightly (≈6%) above the Betz limit. Besides the numerical result of an increased energy conversion rate, especially the identification of two physical power increasing mechanisms shows, that the application of Betz's Law to VAWTs is not justified.