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A Novel Analytical Wake Model with a Cosine-Shaped Velocity Deficit

State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
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Energies 2020, 13(13), 3353; https://doi.org/10.3390/en13133353
Received: 24 May 2020 / Revised: 19 June 2020 / Accepted: 26 June 2020 / Published: 30 June 2020
(This article belongs to the Collection Wind Turbines)
A novel analytical model is proposed and validated in this paper to predict the velocity deficit in the wake downwind of a wind turbine. The model is derived by employing mass and momentum conservation and assuming a cosine-shaped distribution for the velocity deficit. In this model, a modified wake growth rate rather than a constant one is chosen to take into account the effects of the ambient turbulence and the mechanical turbulence generated. The model was tested against field observations, wind-tunnel measurements in different thrust operations and high-resolution large-eddy simulations (LES) for two aerodynamic roughness lengths. It was found that the normalized velocity deficit predicted by the proposed model shows good agreement with experimental and numerical data in terms of shape and magnitude in the far wake region ( x / d 0 > 3 ). Based on the proposed model, predictions from multiple views and at different locations are demonstrated to show the spatial distribution of streamwise velocity downwind of a wind turbine. The result shows that the model is suitable for predicting streamwise velocity fields and thus could provide some references for the selection of wind turbine spacing. View Full-Text
Keywords: analytical wake model; cosine-shaped velocity deficit; mass and momentum conservation; velocity prediction analytical wake model; cosine-shaped velocity deficit; mass and momentum conservation; velocity prediction
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Zhang, Z.; Huang, P.; Sun, H. A Novel Analytical Wake Model with a Cosine-Shaped Velocity Deficit. Energies 2020, 13, 3353.

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