Two-scale momentum theory for very large wind farms

The Science of Making Torque from Wind

Nishino, Takafumi^1

Centre for Offshore Renewable Energy Engineering, Cranfield University, Cranfield, Bedfordshire

MK43 0AL, United Kingdom^1

关键词: Actuator disc;    Array configurations;    Friction coefficients;    Maximum power;    Momentum theory;    Non-dimensional parameters;    Power densities;    Theoretical approach;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/753/3/032054/pdf
DOI  :  10.1088/1742-6596/753/3/032054

来源: IOP

【 摘 要 】

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/Cf0, where λ is the ratio of the rotor swept area to the land area (for each turbine) and Cf0is a natural friction coefficient observed before constructing the farm. When X/Cf approaches to zero, the new theory goes back to the classical actuator disc theory, yielding the well-known Betz limit. When λ/Cf0increases to a large value, the maximum power coefficient of each turbine reduces whilst a normalised power density of the farm increases asymptotically to an upper limit. A CFD analysis of an infinitely large wind farm with 'aligned' and 'displaced' array configurations is also presented to validate a key assumption used in the new theory.