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A two-dimensional Jensen model with a Gaussian-shaped velocity deficit

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  • Ge, Mingwei
  • Wu, Ying
  • Liu, Yongqian
  • Yang, Xiang I.A.

Abstract

The one-dimensional (1D) Jensen model is probably the most often used model for engineering analysis of wind turbine wakes. Identifying a more realistic shape function for the near and far wakes behind a wind turbine and incorporating the identified shape function into a wake model can significantly improve the accuracy of wake modelling. The conventional approach is to first solve the 1D Jensen model and subsequently redistribute the wake using a specified shape function. The above procedure conserves mass globally and is useful in wake modelling. However, it needs to solve a top-hat wake using Jensen model first, which inevitably violates the local mass conservation. In this work, we propose a two-dimensional (2D) wake model that conserves mass locally and globally. The model is a direct extension of Jensen model, and the wake decay rate is the only model parameter. In addition, by accounting for the pressure recovery region, which is often neglected in wake models, the present model can provide accurate prediction of the velocity deficit behind a wind turbine. The present model is compared with the high-fidelity simulations, wind-tunnel measurements, and field observations. A reasonably good agreement is found between the model and the validation data.

Suggested Citation

  • Ge, Mingwei & Wu, Ying & Liu, Yongqian & Yang, Xiang I.A., 2019. "A two-dimensional Jensen model with a Gaussian-shaped velocity deficit," Renewable Energy, Elsevier, vol. 141(C), pages 46-56.
    • Handle: RePEc:eee:renene:v:141:y:2019:i:c:p:46-56
    DOI: 10.1016/j.renene.2019.03.127
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    References listed on IDEAS

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    Cited by:

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    6. Carl R. Shapiro & Genevieve M. Starke & Charles Meneveau & Dennice F. Gayme, 2019. "A Wake Modeling Paradigm for Wind Farm Design and Control," Energies, MDPI, vol. 12(15), pages 1-19, August.
    7. 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).
    8. Wang, Tengyuan & Cai, Chang & Wang, Xinbao & Wang, Zekun & Chen, Yewen & Song, Juanjuan & Xu, Jianzhong & Zhang, Yuning & Li, Qingan, 2023. "A new Gaussian analytical wake model validated by wind tunnel experiment and LiDAR field measurements under different turbulent flow," Energy, Elsevier, vol. 271(C).
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    14. Li, Li & Huang, Zhi & Ge, Mingwei & Zhang, Qiying, 2022. "A novel three-dimensional analytical model of the added streamwise turbulence intensity for wind-turbine wakes," Energy, Elsevier, vol. 238(PB).
    15. Ge, Mingwei & Zhang, Shuaibin & Meng, Hang & Ma, Hongliang, 2020. "Study on interaction between the wind-turbine wake and the urban district model by large eddy simulation," Renewable Energy, Elsevier, vol. 157(C), pages 941-950.
    16. He, Ruiyang & Sun, Haiying & Gao, Xiaoxia & Yang, Hongxing, 2022. "Wind tunnel tests for wind turbines: A state-of-the-art review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 166(C).
    17. He, Ruiyang & Yang, Hongxing & Sun, Haiying & Gao, Xiaoxia, 2021. "A novel three-dimensional wake model based on anisotropic Gaussian distribution for wind turbine wakes," Applied Energy, Elsevier, vol. 296(C).
    18. Niebuhr, C.M. & Schmidt, S. & van Dijk, M. & Smith, L. & Neary, V.S., 2022. "A review of commercial numerical modelling approaches for axial hydrokinetic turbine wake analysis in channel flow," Renewable and Sustainable Energy Reviews, Elsevier, vol. 158(C).
    19. 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.
    20. Zhou, Huanyu & Qiu, Yingning & Feng, Yanhui & Liu, Jing, 2022. "Power prediction of wind turbine in the wake using hybrid physical process and machine learning models," Renewable Energy, Elsevier, vol. 198(C), pages 568-586.
    21. Jianhua Xu & Zhonghua Han & Xiaochao Yan & Wenping Song, 2019. "Design Optimization of a Multi-Megawatt Wind Turbine Blade with the NPU-MWA Airfoil Family," Energies, MDPI, vol. 12(17), pages 1-24, August.
    22. Ge, Mingwei & Gayme, Dennice F. & Meneveau, Charles, 2021. "Large-eddy simulation of wind turbines immersed in the wake of a cube-shaped building," Renewable Energy, Elsevier, vol. 163(C), pages 1063-1077.

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