Nishino, Takafumi2016-11-012016-11-012016-10-03Takafumi Nishino, Two-scale momentum theory for very large wind farms, Journal of Physics: Conference Series 753, 2016, Article number 0320541742-6588http://dx.doi.org/10.1088/1742-6596/753/3/032054http://dspace.lib.cranfield.ac.uk/handle/1826/10917A 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 Cf0 is 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/Cf0 increases 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.enAttribution 3.0 UnportedAttribution 3.0 Unportedhttps://creativecommons.org/licenses/by/3.0/Article