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Application of extended vortex theory for blade element analysis of horizontal-axis wind turbines

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  • Wood, D.H.

Abstract

Vortex theory is used in blade element analysis (BEA) of wind turbines to account for the finite number of blades, N, usually in terms of Prandtl's “tip loss function”, F. Wood et al. [13] calculated alternative “trailing vorticity functions” using helical vortex theory. F was found to be inaccurate over the entire blade at low tip speed ratio and in error near the hub at any tip speed ratio. Further, the trailing vorticity function is not constrained to be less than unity as is F. Wood & Okulov [19] analyzed the nonlinear terms in the streamtube equations for angular and axial momentum and found an accurate way of including these in BEA. This paper describes the use of the trailing vorticity functions, which can be different in the axial and azimuthal directions, in an otherwise standard blade element analyses. Comparison is made to wind tunnel tests of model rotors and to calculations using F. There is only a small difference in the calculated power and thrust coefficients. The present calculations show higher induced axial velocities in the tip and hub regions and it is suggested that the trailing vorticity functions can be used in situations where F cannot.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:renene:v:121:y:2018:i:c:p:188-194
    DOI: 10.1016/j.renene.2017.12.085
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    References listed on IDEAS

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    1. 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.
    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.
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    Cited by:

    1. 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.
    2. Widad Yossri & Samah Ben Ayed & Abdessattar Abdelkefi, 2023. "High-Fidelity Modeling and Investigation on Blade Shape and Twist Angle Effects on the Efficiency of Small-Scale Wind Turbines," Energies, MDPI, vol. 16(8), pages 1-26, April.
    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.

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