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Direct calculation of wind turbine tip loss

Author

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  • Wood, D.H.
  • Okulov, V.L.
  • Bhattacharjee, D.

Abstract

The usual method to account for a finite number of blades in blade element calculations of wind turbine performance is through a tip loss factor. Most analyses use the tip loss approximation due to Prandtl which is easily and cheaply calculated but is known to be inaccurate at low tip speed ratio. We develop three methods for the direct calculation of the tip loss. The first is the computationally expensive calculation of the velocities induced by the helicoidal wake which requires the evaluation of infinite sums of products of Bessel functions. The second uses the asymptotic evaluation of those sums by Kawada. The third uses the approximation due to Okulov which avoids the sums altogether. These methods are compared to the tip loss determined independently and exactly for an ideal three-bladed rotor at tip speed ratios between zero and 15. Kawada's asymptotic approximation and Okulov's equations are preferable to the Prandtl factor at all tip speed ratios, with the Okulov equations being generally more accurate. In particular the tip loss factor exceeds unity near the axis of rotation by a large amount at all tip speed ratios, which Prandtl's factor cannot reproduce. Neither the Kawada nor the Okulov equations impose a large computational burden on a blade element program.

Suggested Citation

  • Wood, D.H. & Okulov, V.L. & Bhattacharjee, D., 2016. "Direct calculation of wind turbine tip loss," Renewable Energy, Elsevier, vol. 95(C), pages 269-276.
  • Handle: RePEc:eee:renene:v:95:y:2016:i:c:p:269-276
    DOI: 10.1016/j.renene.2016.04.017
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    Cited by:

    1. Wood, D.H., 2018. "Application of extended vortex theory for blade element analysis of horizontal-axis wind turbines," Renewable Energy, Elsevier, vol. 121(C), pages 188-194.
    2. Wood, D.H. & Okulov, V.L., 2017. "Nonlinear blade element-momentum analysis of Betz-Goldstein rotors," Renewable Energy, Elsevier, vol. 107(C), pages 542-549.
    3. Hércules Araújo Oliveira & José Gomes de Matos & Luiz Antonio de Souza Ribeiro & Osvaldo Ronald Saavedra & Jerson Rogério Pinheiro Vaz, 2023. "Assessment of Correction Methods Applied to BEMT for Predicting Performance of Horizontal-Axis Wind Turbines," Sustainability, MDPI, vol. 15(8), pages 1-26, April.
    4. Jinming Wu & Yingxue Yao & Dongke Sun & Zhonghua Ni & Malin Göteman, 2019. "Numerical and Experimental Study of the Solo Duck Wave Energy Converter," Energies, MDPI, vol. 12(10), pages 1-19, May.
    5. Vaz, Jerson R.P. & Okulov, Valery L. & Wood, David H., 2021. "Finite blade functions and blade element optimization for diffuser-augmented wind turbines," Renewable Energy, Elsevier, vol. 165(P1), pages 812-822.
    6. David Wood, 2021. "Wake Expansion and the Finite Blade Functions for Horizontal-Axis Wind Turbines," Energies, MDPI, vol. 14(22), pages 1-12, November.
    7. Dai, Juchuan & Li, Mimi & Chen, Huanguo & He, Tao & Zhang, Fan, 2022. "Progress and challenges on blade load research of large-scale wind turbines," Renewable Energy, Elsevier, vol. 196(C), pages 482-496.

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