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An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes

Author

Listed:
  • Mahdi Abkar

    (Department of Engineering, Aarhus University, 8000 Aarhus C, Denmark)

  • Jens Nørkær Sørensen

    (Department of Wind Energy, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark)

  • Fernando Porté-Agel

    (Wind Engineering and Renewable Energy Laboratory, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland)

Abstract

In this study, an analytical wake model for predicting the mean velocity field downstream of a wind turbine under veering incoming wind is systematically derived and validated. The new model, which is an extended version of the one introduced by Bastankhah and Porté-Agel, is based upon the application of mass conservation and momentum theorem and considering a skewed Gaussian distribution for the wake velocity deficit. Particularly, using a skewed (instead of axisymmetric) Gaussian shape allows accounting for the lateral shear in the incoming wind induced by the Coriolis force. This analytical wake model requires only the wake expansion rate as an input parameter to predict the mean wake flow downstream. The performance of the proposed model is assessed using the large-eddy simulation (LES) data of a full-scale wind turbine wake under the stably stratified condition. The results show that the proposed model is capable of predicting the skewed structure of the wake downwind of the turbine, and its prediction for the wake velocity deficit is in good agreement with the high-fidelity simulation data.

Suggested Citation

  • Mahdi Abkar & Jens Nørkær Sørensen & Fernando Porté-Agel, 2018. "An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes," Energies, MDPI, vol. 11(7), pages 1-10, July.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:7:p:1838-:d:157777
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    References listed on IDEAS

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    1. Wu, Yu-Ting & Porté-Agel, Fernando, 2015. "Modeling turbine wakes and power losses within a wind farm using LES: An application to the Horns Rev offshore wind farm," Renewable Energy, Elsevier, vol. 75(C), pages 945-955.
    2. 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.
    3. Mahdi Abkar & Fernando Porté-Agel, 2013. "The Effect of Free-Atmosphere Stratification on Boundary-Layer Flow and Power Output from Very Large Wind Farms," Energies, MDPI, vol. 6(5), pages 1-24, April.
    4. Bastankhah, Majid & Porté-Agel, Fernando, 2014. "A new analytical model for wind-turbine wakes," Renewable Energy, Elsevier, vol. 70(C), pages 116-123.
    5. Abkar, Mahdi & Porté-Agel, Fernando, 2014. "Mean and turbulent kinetic energy budgets inside and above very large wind farms under conventionally-neutral condition," Renewable Energy, Elsevier, vol. 70(C), pages 142-152.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Mahdi Abkar, 2018. "Theoretical Modeling of Vertical-Axis Wind Turbine Wakes," Energies, MDPI, vol. 12(1), pages 1-10, December.
    2. Emmanuvel Joseph Aju & Dhanush Bhamitipadi Suresh & Yaqing Jin, 2020. "The Influence of Winglet Pitching on the Performance of a Model Wind Turbine: Aerodynamic Loads, Rotating Speed, and Wake Statistics," Energies, MDPI, vol. 13(19), pages 1-15, October.
    3. Kale, Baris & Buckingham, Sophia & van Beeck, Jeroen & Cuerva-Tejero, Alvaro, 2022. "Implementation of a generalized actuator disk model into WRF v4.3: A validation study for a real-scale wind turbine," Renewable Energy, Elsevier, vol. 197(C), pages 810-827.
    4. Xiong, Xue-Lu & Lyu, Pin & Chen, Wen-Li & Li, Hui, 2020. "Self-similarity in the wake of a semi-submersible offshore wind turbine considering the interaction with the wake of supporting platform," Renewable Energy, Elsevier, vol. 156(C), pages 328-341.
    5. Posa, Antonio, 2022. "Wake characterization of paired cross-flow turbines," Renewable Energy, Elsevier, vol. 196(C), pages 1064-1094.
    6. Esmail Mahmoodi & Mohammad Khezri & Arash Ebrahimi & Uwe Ritschel & Leonardo P. Chamorro & Ali Khanjari, 2023. "A Simple Model for Wake-Induced Aerodynamic Interaction of Wind Turbines," Energies, MDPI, vol. 16(15), pages 1-13, July.
    7. Michael F. Howland & John O. Dabiri, 2020. "Influence of Wake Model Superposition and Secondary Steering on Model-Based Wake Steering Control with SCADA Data Assimilation," Energies, MDPI, vol. 14(1), pages 1-20, December.
    8. Mohammadreza Mohammadi & Majid Bastankhah & Paul Fleming & Matthew Churchfield & Ervin Bossanyi & Lars Landberg & Renzo Ruisi, 2022. "Curled-Skewed Wakes behind Yawed Wind Turbines Subject to Veered Inflow," Energies, MDPI, vol. 15(23), pages 1-16, December.
    9. Syed Ahmed Kabir, Ijaz Fazil & Safiyullah, Ferozkhan & Ng, E.Y.K. & Tam, Vivian W.Y., 2020. "New analytical wake models based on artificial intelligence and rivalling the benchmark full-rotor CFD predictions under both uniform and ABL inflows," Energy, Elsevier, vol. 193(C).
    10. Feng, Dachuan & Li, Larry K.B. & Gupta, Vikrant & Wan, Minping, 2022. "Componentwise influence of upstream turbulence on the far-wake dynamics of wind turbines," Renewable Energy, Elsevier, vol. 200(C), pages 1081-1091.
    11. Dar, Arslan Salim & Porté-Agel, Fernando, 2022. "Wind turbine wakes on escarpments: A wind-tunnel study," Renewable Energy, Elsevier, vol. 181(C), pages 1258-1275.
    12. Arslan Salim Dar & Fernando Porté-Agel, 2022. "An Analytical Model for Wind Turbine Wakes under Pressure Gradient," Energies, MDPI, vol. 15(15), pages 1-13, July.

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