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Energies 2018, 11(1), 93;

On the Evolution of the Integral Time Scale within Wind Farms

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210024, China
Mechanical Science and Engineering, University of Illinois, Urbana, IL 61801, USA
Aerospace Engineering, University of Illinois, Urbana, IL 61801, USA
Civil and Environmental Engineering, University of Illinois, Urbana, IL 61801, USA
Author to whom correspondence should be addressed.
Received: 27 November 2017 / Revised: 19 December 2017 / Accepted: 28 December 2017 / Published: 2 January 2018
(This article belongs to the Collection Wind Turbines)
Full-Text   |   PDF [1531 KB, uploaded 2 January 2018]   |  


A wind-tunnel investigation was carried out to characterize the spatial distribution of the integral time scale ( T u ) within, and in the vicinity of, two model wind farms. The turbine arrays were placed over a rough wall and operated under high turbulence. The two layouts consisted of aligned units distinguished only by the streamwise spacing ( Δ x T ) between the devices, set at five and ten rotor diameters d T (or S x = Δ x T / d T = 5 and 10). They shared the same spanwise spacing between turbines of 2.5 d T ; this resulted in arrays of 8 × 3 and 5 × 3 horizontal-axis turbines. Hotwire anemometry was used to characterize the instantaneous velocity at various vertical and transverse locations along the central column of the wind farms. Results show that T u was modulated by the wind farm layout. It was significantly reduced within the wind farms and right above them, where the internal boundary layer develops. The undisturbed levels above the wind farms were recovered only at ≈ d T / 2 above the top tip. This quantity appeared to reach adjusted values starting the fifth row of turbines in the S x = 5 wind farm, and earlier in the S x = 10 counterpart. Within the adjusted zone, the distribution of T u at hub height exhibited a negligible growth in the S x = 5 case; whereas it underwent a mild growth in the S x = 10 wind farm. In addition, the flow impinging the inner turbines exhibited T u / T i n c u < 1 , where T i n c u is the integral time scale of the overall incoming flow. Specifically, T u β T i n c u at z = z h u b , where β < 1 within standard layouts of wind farms, in particular β 0.5 and 0.7 for S x = 5 and 10. View Full-Text
Keywords: integral time scale; wake; wind turbine; wind farm integral time scale; wake; wind turbine; wind farm

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Liu, H.; Hayat, I.; Jin, Y.; Chamorro, L.P. On the Evolution of the Integral Time Scale within Wind Farms. Energies 2018, 11, 93.

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