IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v13y2020i5p1078-d326815.html
   My bibliography  Save this article

Wind Turbine Performance in Very Large Wind Farms: Betz Analysis Revisited

Author

Listed:
  • Jacob R. West

    (Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA)

  • Sanjiva K. Lele

    (Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
    Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA)

Abstract

The theoretical limit for wind turbine performance, the so-called Betz limit, arises from an inviscid, irrotational analysis of the streamtube around an actuator disk. In a wind farm in the atmospheric boundary layer, the physics are considerably more complex, encompassing shear, turbulent transport, and wakes from other turbines. In this study, the mean flow streamtube around a wind turbine in a wind farm is investigated with large eddy simulations of a periodic array of actuator disks in half-channel flow at a range of turbine thrust coefficients. Momentum and mean kinetic energy budgets are presented, connecting the energy budget for an individual turbine to the wind farm performance as a whole. It is noted that boundary layer turbulence plays a key role in wake recovery and energy conversion when considering the entire wind farm. The wind farm power coefficient is maximized when the work done by Reynolds stress on the periphery of the streamtube is maximized, although some mean kinetic energy is also dissipated into turbulence. This results in an optimal value of thrust coefficient lower than the traditional Betz result. The simulation results are used to evaluate Nishino’s model of infinite wind farms, and design trade-offs described by it are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:5:p:1078-:d:326815
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/13/5/1078/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/13/5/1078/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cortina, G. & Sharma, V. & Torres, R. & Calaf, M., 2020. "Mean kinetic energy distribution in finite-size wind farms: A function of turbines’ arrangement," Renewable Energy, Elsevier, vol. 148(C), pages 585-599.
    2. Fernando Porté-Agel & Yu-Ting Wu & Chang-Hung Chen, 2013. "A Numerical Study of the Effects of Wind Direction on Turbine Wakes and Power Losses in a Large Wind Farm," Energies, MDPI, vol. 6(10), pages 1-17, October.
    3. Claire VerHulst & Charles Meneveau, 2015. "Altering Kinetic Energy Entrainment in Large Eddy Simulations of Large Wind Farms Using Unconventional Wind Turbine Actuator Forcing," Energies, MDPI, vol. 8(1), pages 1-17, January.
    4. 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.
    5. Yu-Ting Wu & Fernando Porté-Agel, 2012. "Atmospheric Turbulence Effects on Wind-Turbine Wakes: An LES Study," Energies, MDPI, vol. 5(12), pages 1-23, December.
    6. Wim Munters & Johan Meyers, 2018. "Dynamic Strategies for Yaw and Induction Control of Wind Farms Based on Large-Eddy Simulation and Optimization," Energies, MDPI, vol. 11(1), pages 1-32, January.
    7. 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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rafał Figaj & Maciej Żołądek & Wojciech Goryl, 2020. "Dynamic Simulation and Energy Economic Analysis of a Household Hybrid Ground-Solar-Wind System Using TRNSYS Software," Energies, MDPI, vol. 13(14), pages 1-27, July.
    2. Kelan Patel & Thomas D. Dunstan & Takafumi Nishino, 2021. "Time-Dependent Upper Limits to the Performance of Large Wind Farms Due to Mesoscale Atmospheric Response," Energies, MDPI, vol. 14(19), pages 1-16, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. 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.
    4. Pankaj K. Jha & Earl P. N. Duque & Jessica L. Bashioum & Sven Schmitz, 2015. "Unraveling the Mysteries of Turbulence Transport in a Wind Farm," Energies, MDPI, vol. 8(7), pages 1-29, June.
    5. Deepu Dilip & Fernando Porté-Agel, 2017. "Wind Turbine Wake Mitigation through Blade Pitch Offset," Energies, MDPI, vol. 10(6), pages 1-17, May.
    6. 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.
    7. Zhang, Huan & Ge, Mingwei & Liu, Yongqian & Yang, Xiang I.A., 2021. "A new coupled model for the equivalent roughness heights of wind farms," Renewable Energy, Elsevier, vol. 171(C), pages 34-46.
    8. Nicolas Kirchner-Bossi & Fernando Porté-Agel, 2018. "Realistic Wind Farm Layout Optimization through Genetic Algorithms Using a Gaussian Wake Model," Energies, MDPI, vol. 11(12), pages 1-26, November.
    9. Nicolas Kirchner-Bossi & Fernando Porté-Agel, 2021. "Wind Farm Area Shape Optimization Using Newly Developed Multi-Objective Evolutionary Algorithms," Energies, MDPI, vol. 14(14), pages 1-25, July.
    10. Daniel Houck & Edwin A. Cowen, 2022. "Power and Flow Analysis of Axial Induction Control in an Array of Model-Scale Wind Turbines," Energies, MDPI, vol. 15(15), pages 1-27, July.
    11. Bastankhah, Majid & Porté-Agel, Fernando, 2014. "A new analytical model for wind-turbine wakes," Renewable Energy, Elsevier, vol. 70(C), pages 116-123.
    12. 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).
    13. Li, Li & Wang, Bing & Ge, Mingwei & Huang, Zhi & Li, Xintao & Liu, Yongqian, 2023. "A novel superposition method for streamwise turbulence intensity of wind-turbine wakes," Energy, Elsevier, vol. 276(C).
    14. Yang, Haoze & Ge, Mingwei & Abkar, Mahdi & Yang, Xiang I.A., 2022. "Large-eddy simulation study of wind turbine array above swell sea," Energy, Elsevier, vol. 256(C).
    15. 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.
    16. Jim Kuo & Kevin Pan & Ni Li & He Shen, 2020. "Wind Farm Yaw Optimization via Random Search Algorithm," Energies, MDPI, vol. 13(4), pages 1-15, February.
    17. 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.
    18. Mou Lin & Fernando Porté-Agel, 2019. "Large-Eddy Simulation of Yawed Wind-Turbine Wakes: Comparisons with Wind Tunnel Measurements and Analytical Wake Models," Energies, MDPI, vol. 12(23), pages 1-18, November.
    19. Fan, Xiantao & Ge, Mingwei & Tan, Wei & Li, Qi, 2021. "Impacts of coexisting buildings and trees on the performance of rooftop wind turbines: An idealized numerical study," Renewable Energy, Elsevier, vol. 177(C), pages 164-180.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:13:y:2020:i:5:p:1078-:d:326815. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.