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

Author

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  • Ziyu Zhang

    (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China)

  • Peng Huang

    (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China)

  • Haocheng Sun

    (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China)

Abstract

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.

Suggested Citation

  • Ziyu Zhang & Peng Huang & Haocheng Sun, 2020. "A Novel Analytical Wake Model with a Cosine-Shaped Velocity Deficit," Energies, MDPI, vol. 13(13), pages 1-20, June.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:13:p:3353-:d:378758
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    References listed on IDEAS

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    Cited by:

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    2. Ling, Ziyan & Zhao, Zhenzhou & Liu, Yige & Liu, Huiwen & Ali, Kashif & Liu, Yan & Wen, Yifan & Wang, Dingding & Li, Shijun & Su, Chunhao, 2024. "Multi-objective layout optimization for wind farms based on non-uniformly distributed turbulence and a new three-dimensional multiple wake model," Renewable Energy, Elsevier, vol. 227(C).
    3. Zhang, Ziyu & Huang, Peng, 2023. "Prediction of multiple-wake velocity and wind power using a cosine-shaped wake model," Renewable Energy, Elsevier, vol. 219(P1).
    4. Jirarote Buranarote & Yutaka Hara & Masaru Furukawa & Yoshifumi Jodai, 2022. "Method to Predict Outputs of Two-Dimensional VAWT Rotors by Using Wake Model Mimicking the CFD-Created Flow Field," Energies, MDPI, vol. 15(14), pages 1-29, July.
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    6. Tian, Linlin & Song, Yilei & Xiao, Pengcheng & Zhao, Ning & Shen, Wenzhong & Zhu, Chunling, 2022. "A new three-dimensional analytical model for wind turbine wake turbulence intensity predictions," Renewable Energy, Elsevier, vol. 189(C), pages 762-776.

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