IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v14y2021i22p7653-d680205.html
   My bibliography  Save this article

Wake Expansion and the Finite Blade Functions for Horizontal-Axis Wind Turbines

Author

Listed:
  • David Wood

    (Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada)

Abstract

This paper considers the effect of wake expansion on the finite blade functions in blade element/momentum theory for horizontal-axis wind turbines. For any velocity component, the function is the ratio of the streamtube average to that at the blade elements. In most cases, the functions are set by the trailing vorticity only and Prandtl’s tip loss factor can be a reasonable approximation to the axial and circumferential functions at sufficiently high tip speed ratio. Nevertheless, important cases like coned or swept rotors or shrouded turbines involve more complex blade functions than provided by the tip loss factor or its recent modifications. Even in the presence of significant wake expansion, the functions derived from the exact solution for the flow due to constant pitch and radius helical vortices provide accurate estimates for the axial and circumferential blade functions. Modifying the vortex pitch in response to the expansion improves the accuracy of the latter. The modified functions are more accurate than the tip loss factor for the test cases at high tip speed ratio that are studied here. The radial velocity is important for expanding flow as it has the magnitude of the induced axial velocity near the edge of the rotor. It is shown that the resulting angle of the flow to the axial direction is small even with significant expansion, as long is the tip speed ratio is high. This means that blade element theory does not have account for the effective blade sweep due to the radial velocity. Further, the circumferential variation of the radial velocity is lower than of the other components.

Suggested Citation

  • David Wood, 2021. "Wake Expansion and the Finite Blade Functions for Horizontal-Axis Wind Turbines," Energies, MDPI, vol. 14(22), pages 1-12, November.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:22:p:7653-:d:680205
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/14/22/7653/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/14/22/7653/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    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. Kiran Siddappaji & Mark Turner, 2022. "Improved Prediction of Aerodynamic Loss Propagation as Entropy Rise in Wind Turbines Using Multifidelity Analysis," Energies, MDPI, vol. 15(11), pages 1-44, May.

    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. Silva, Paulo A.S.F. & Tsoutsanis, Panagiotis & Vaz, Jerson R.P. & Macias, Marianela M., 2024. "A comprehensive CFD investigation of tip vortex trajectory in shrouded wind turbines using compressible RANS solver," Energy, Elsevier, vol. 294(C).
    2. 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.
    3. Miriam L. A. Gemaque & Jerson R. P. Vaz & Osvaldo R. Saavedra, 2022. "Optimization of Hydrokinetic Swept Blades," Sustainability, MDPI, vol. 14(21), pages 1-13, October.
    4. Jerson R. P. Vaz & Adry K. F. de Lima & Erb F. Lins, 2023. "Assessment of a Diffuser-Augmented Hydrokinetic Turbine Designed for Harnessing the Flow Energy Downstream of Dams," Sustainability, MDPI, vol. 15(9), pages 1-15, May.
    5. Dogru, Safak & Yilmaz, Oktay, 2024. "Extensive design and aerodynamic performance investigation of diffuser augmented wind turbine (DAWT) guided by generalized actuator disc theory," Renewable and Sustainable Energy Reviews, Elsevier, vol. 192(C).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Yilmaz, Oktay, 2023. "Low-speed, low induction multi-blade rotor for energy efficient small wind turbines," Energy, Elsevier, vol. 282(C).

    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:14:y:2021:i:22:p:7653-:d:680205. 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.