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A new analytical model for wind turbine wakes based on Monin-Obukhov similarity theory

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  • Cheng, Yu
  • Zhang, Mingming
  • Zhang, Ziliang
  • Xu, Jianzhong

Abstract

The wake flow behind a wind turbine induces a significant slowdown of wind velocity, leading to a great loss of power generation for the turbines located in the downstream region. Hence it is very important to predict the velocity in an efficient way. To satisfy this requirement, we propose a simple analytical wake model based on the Monin-Obukhov similarity theory. The new model adopts a Gaussian function and takes surface roughness length and Obukhov length into account for the first time. Then the model is validated from the following three aspects. Firstly, compared with experimental and numerical data, it is shown that the model can present a satisfactory prediction of the ambient turbulence intensities in three spatial directions and the wake expansion parameters. In addition, wind velocity deficits in the wake calculated by the model are compared with the LES data and the Lidar measurements. The results indicate that there is a good agreement with the referenced data. Finally, wake expansion parameters and wind velocity deficits are estimated for three atmospheric stabilities and compared with high resolution LES results. Even though some predicting errors exist in near wakes and for low incoming turbulence intensities, acceptable results are achieved in most of the regions of the wake. Overall speaking, roughness length and atmospheric stability have a great impact on ambient turbulence intensity, which significantly influences the velocity recovery speed in the wind turbine wake.

Suggested Citation

  • Cheng, Yu & Zhang, Mingming & Zhang, Ziliang & Xu, Jianzhong, 2019. "A new analytical model for wind turbine wakes based on Monin-Obukhov similarity theory," Applied Energy, Elsevier, vol. 239(C), pages 96-106.
    • Handle: RePEc:eee:appene:v:239:y:2019:i:c:p:96-106
    DOI: 10.1016/j.apenergy.2019.01.225
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    1. Li, Qing'an & Murata, Junsuke & Endo, Masayuki & Maeda, Takao & Kamada, Yasunari, 2016. "Experimental and numerical investigation of the effect of turbulent inflow on a Horizontal Axis Wind Turbine (Part I: Power performance)," Energy, Elsevier, vol. 113(C), pages 713-722.
    2. Li, Qing'an & Murata, Junsuke & Endo, Masayuki & Maeda, Takao & Kamada, Yasunari, 2016. "Experimental and numerical investigation of the effect of turbulent inflow on a Horizontal Axis Wind Turbine (part II: Wake characteristics)," Energy, Elsevier, vol. 113(C), pages 1304-1315.
    3. Feng, Ju & Shen, Wen Zhong, 2017. "Design optimization of offshore wind farms with multiple types of wind turbines," Applied Energy, Elsevier, vol. 205(C), pages 1283-1297.
    4. Gao, Xiaoxia & Yang, Hongxing & Lu, Lin, 2016. "Optimization of wind turbine layout position in a wind farm using a newly-developed two-dimensional wake model," Applied Energy, Elsevier, vol. 174(C), pages 192-200.
    5. Archer, Cristina L. & Vasel-Be-Hagh, Ahmadreza & Yan, Chi & Wu, Sicheng & Pan, Yang & Brodie, Joseph F. & Maguire, A. Eoghan, 2018. "Review and evaluation of wake loss models for wind energy applications," Applied Energy, Elsevier, vol. 226(C), pages 1187-1207.
    6. Bastankhah, Majid & Porté-Agel, Fernando, 2014. "A new analytical model for wind-turbine wakes," Renewable Energy, Elsevier, vol. 70(C), pages 116-123.
    7. Song, Dongran & Fan, Xinyu & Yang, Jian & Liu, Anfeng & Chen, Sifan & Joo, Young Hoon, 2018. "Power extraction efficiency optimization of horizontal-axis wind turbines through optimizing control parameters of yaw control systems using an intelligent method," Applied Energy, Elsevier, vol. 224(C), pages 267-279.
    8. Sun, Haiying & Yang, Hongxing, 2018. "Study on an innovative three-dimensional wind turbine wake model," Applied Energy, Elsevier, vol. 226(C), pages 483-493.
    9. Amin Niayifar & Fernando Porté-Agel, 2016. "Analytical Modeling of Wind Farms: A New Approach for Power Prediction," Energies, MDPI, vol. 9(9), pages 1-13, September.
    10. Li, Qing'an & Maeda, Takao & Kamada, Yasunari & Hiromori, Yuto, 2018. "Investigation of wake characteristic of a 30 kW rated power Horizontal Axis Wind Turbine with wake model and field measurement," Applied Energy, Elsevier, vol. 225(C), pages 1190-1204.
    11. Guirguis, David & Romero, David A. & Amon, Cristina H., 2017. "Gradient-based multidisciplinary design of wind farms with continuous-variable formulations," Applied Energy, Elsevier, vol. 197(C), pages 279-291.
    12. Ge, Mingwei & Wu, Ying & Liu, Yongqian & Li, Qi, 2019. "A two-dimensional model based on the expansion of physical wake boundary for wind-turbine wakes," Applied Energy, Elsevier, vol. 233, pages 975-984.
    13. Kuo, Jim Y.J. & Romero, David A. & Beck, J. Christopher & Amon, Cristina H., 2016. "Wind farm layout optimization on complex terrains – Integrating a CFD wake model with mixed-integer programming," Applied Energy, Elsevier, vol. 178(C), pages 404-414.
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    Cited by:

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    15. Gao, Xiaoxia & Li, Bingbing & Wang, Tengyuan & Sun, Haiying & Yang, Hongxing & Li, Yonghua & Wang, Yu & Zhao, Fei, 2020. "Investigation and validation of 3D wake model for horizontal-axis wind turbines based on filed measurements," Applied Energy, Elsevier, vol. 260(C).
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