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An Analytical Model for Wind Turbine Wakes under Pressure Gradient

Author

Listed:
  • Arslan Salim Dar

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

  • Fernando Porté-Agel

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

Abstract

In this study, we present an analytical modeling framework for wind turbine wakes under an arbitrary pressure gradient imposed by the base flow. The model is based on the conservation of the streamwise momentum and self-similarity of the wake velocity deficit. It builds on the model proposed by Shamsoddin and Porté-Agel, which only accounted for the imposed pressure gradient in the far wake. The effect of the imposed pressure gradient on the near wake velocity is estimated by using Bernoulli’s equation. Using the estimated near wake velocity as the starting point, the model then solves an ordinary differential equation to compute the streamwise evolution of the maximum velocity deficit in the turbine far wake. The model is validated against experimental data of wind turbine wakes on escarpments of varying geometries. In addition, a comparison is performed with a pressure gradient model which only accounts for the imposed pressure gradient in the far wake, and with a model that does not account for any imposed pressure gradient. The new model is observed to agree well with the experimental data, and it outperforms the other two models tested in the study for all escarpment cases.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:15:p:5345-:d:869768
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Lopez, Daniel & Kuo, Jim & Li, Ni, 2019. "A novel wake model for yawed wind turbines," Energy, Elsevier, vol. 178(C), pages 158-167.
    4. 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.
    5. Brogna, Roberto & Feng, Ju & Sørensen, Jens Nørkær & Shen, Wen Zhong & Porté-Agel, Fernando, 2020. "A new wake model and comparison of eight algorithms for layout optimization of wind farms in complex terrain," Applied Energy, Elsevier, vol. 259(C).
    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. Bastankhah, Majid & Porté-Agel, Fernando, 2014. "A new analytical model for wind-turbine wakes," Renewable Energy, Elsevier, vol. 70(C), pages 116-123.
    8. Hoon Hwangbo & Andrew L. Johnson & Yu Ding, 2018. "Spline model for wake effect analysis: Characteristics of a single wake and its impacts on wind turbine power generation," IISE Transactions, Taylor & Francis Journals, vol. 50(2), pages 112-125, February.
    9. 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).
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    Cited by:

    1. Davide Astolfi & Fabrizio De Caro & Alfredo Vaccaro, 2023. "Characterizing the Wake Effects on Wind Power Generator Operation by Data-Driven Techniques," Energies, MDPI, vol. 16(15), pages 1-19, August.
    2. Zygmunt Szczerba & Piotr Szczerba & Kamil Szczerba & Marek Szumski & Krzysztof Pytel, 2023. "Wind Tunnel Experimental Study on the Efficiency of Vertical-Axis Wind Turbines via Analysis of Blade Pitch Angle Influence," Energies, MDPI, vol. 16(13), pages 1-21, June.
    3. Zhang, Ziyu & Huang, Peng & Bitsuamlak, Girma & Cao, Shuyang, 2024. "Large-eddy simulation of upwind-hill effects on wind-turbine wakes and power performance," Energy, Elsevier, vol. 294(C).
    4. Dara Vahidi & Fernando Porté-Agel, 2022. "A New Streamwise Scaling for Wind Turbine Wake Modeling in the Atmospheric Boundary Layer," Energies, MDPI, vol. 15(24), pages 1-18, December.
    5. Sudip Basack & Shantanu Dutta & Dipasri Saha, 2022. "Installation and Performance Study of a Vertical-Axis Wind Turbine Prototype Model," Sustainability, MDPI, vol. 14(23), pages 1-29, December.

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