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The Effect of Free-Atmosphere Stratification on Boundary-Layer Flow and Power Output from Very Large Wind Farms

Author

Listed:
  • Mahdi Abkar

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

  • Fernando Porté-Agel

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

Abstract

Large-eddy simulation is used to study the influence of free-atmosphere stratification on the structure of atmospheric boundary-layer flow inside and above very large wind farms, as well as the power extracted by the wind turbines. In the simulations, tuning-free Lagrangian scale-dependent dynamic models are used to model the subgrid-scale turbulent fluxes, while the turbine-induced forces are parameterized with an actuator-disk model. It is shown that for a given surface cover (with and without turbines) thermal stratification of the free atmosphere reduces the entrainment from the flow above compared with the unstratified case, leading to lower boundary-layer depth. Due to the fact that in very large wind farms vertical energy transport associated with turbulence is the only source of kinetic energy, lower entrainment leads to lower power production by the wind turbines. In particular, for the wind-turbine arrangements considered in the present work, the power output from the wind farms is reduced by about 35% when the potential temperature lapse rate in the free atmosphere increases from 1 to 10 K/km (within the range of values typically observed in the atmosphere). Moreover, it is shown that the presence of the turbines has significant effect on the growth of the boundary layer. Inspired by the obtained results, a simple one-dimensional model is developed to account for the effect of free-atmosphere stability on the mean flow and the power output from very large wind farms.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:6:y:2013:i:5:p:2338-2361:d:25365
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    Citations

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    Cited by:

    1. 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.
    2. Ka Ling Wu & Fernando Porté-Agel, 2017. "Flow Adjustment Inside and Around Large Finite-Size Wind Farms," Energies, MDPI, vol. 10(12), pages 1-23, December.
    3. Souaiby, Marwa & Porté-Agel, Fernando, 2024. "An improved analytical framework for flow prediction inside and downstream of wind farms," Renewable Energy, Elsevier, vol. 225(C).
    4. Susumu Takakuwa & Takanori Uchida, 2022. "Improvement of Airflow Simulation by Refining the Inflow Wind Direction and Applying Atmospheric Stability for Onshore and Offshore Wind Farms Affected by Topography," Energies, MDPI, vol. 15(14), pages 1-27, July.
    5. Meyer Forsting, Alexander R. & Navarro Diaz, Gonzalo P. & Segalini, Antonio & Andersen, Søren J. & Ivanell, Stefan, 2023. "On the accuracy of predicting wind-farm blockage," Renewable Energy, Elsevier, vol. 214(C), pages 114-129.
    6. Jacob R. West & Sanjiva K. Lele, 2020. "Wind Turbine Performance in Very Large Wind Farms: Betz Analysis Revisited," Energies, MDPI, vol. 13(5), pages 1-25, March.
    7. Jay P. Goit & Wim Munters & Johan Meyers, 2016. "Optimal Coordinated Control of Power Extraction in LES of a Wind Farm with Entrance Effects," Energies, MDPI, vol. 9(1), pages 1-20, January.
    8. Barlas, Emre & Wu, Ka Ling & Zhu, Wei Jun & Porté-Agel, Fernando & Shen, Wen Zhong, 2018. "Variability of wind turbine noise over a diurnal cycle," Renewable Energy, Elsevier, vol. 126(C), pages 791-800.
    9. Jens Nørkær Sørensen & Gunner Christian Larsen, 2021. "A Minimalistic Prediction Model to Determine Energy Production and Costs of Offshore Wind Farms," Energies, MDPI, vol. 14(2), pages 1-27, January.
    10. Rafael V. Rodrigues & Corinne Lengsfeld, 2019. "Development of a Computational System to Improve Wind Farm Layout, Part II: Wind Turbine Wakes Interaction," Energies, MDPI, vol. 12(7), pages 1-27, April.
    11. Amiri, Mojtaba Maali & Shadman, Milad & Estefen, Segen F., 2024. "A review of physical and numerical modeling techniques for horizontal-axis wind turbine wakes," Renewable and Sustainable Energy Reviews, Elsevier, vol. 193(C).
    12. 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.
    13. Tristan Revaz & Fernando Porté-Agel, 2021. "Large-Eddy Simulation of Wind Turbine Flows: A New Evaluation of Actuator Disk Models," Energies, MDPI, vol. 14(13), pages 1-22, June.
    14. Takanori Uchida & Susumu Takakuwa, 2020. "Numerical Investigation of Stable Stratification Effects on Wind Resource Assessment in Complex Terrain," Energies, MDPI, vol. 13(24), pages 1-32, December.
    15. Deepu Dilip & Fernando Porté-Agel, 2017. "Wind Turbine Wake Mitigation through Blade Pitch Offset," Energies, MDPI, vol. 10(6), pages 1-17, May.
    16. Kevin A. Adkins & Adrian Sescu, 2022. "Wind Farms and Humidity," Energies, MDPI, vol. 15(7), pages 1-15, April.
    17. 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.

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