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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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.
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    Cited by:

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