IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v12y2019i2p320-d199362.html
   My bibliography  Save this article

Non-Empirical BEM Corrections Relating to Angular and Axial Momentum Conservation

Author

Listed:
  • Søren Hjort

    (Volu Ventis ApS, Ferskvandscentret, 8600 Silkeborg, Denmark)

Abstract

The Blade-Element Momentum (BEM) model for Horizontal-Axis Wind Turbines (HAWTs), although extremely useful, is known to be approximate due to model formulation insufficiencies, for which add-ons and corrections have been formulated over the past many decades. Scrutiny of the axial and azimuthal momentum conservation properties reveals momentum simplifications and absence of momentum sources not included in momentum theory underlying the standard BEM. One aspect relates to azimuthal momentum conservation, the wake swirl. This correction can be expressed analytically. Another aspect relates to axial momentum conservation, the wake expansion. This correction is not analytically quantifiable. The latter correction term is therefore quantified from postprocessing a large number of axisymmetric Actuator Disk (AD) Navier-Stokes computations with systematic variation of disk loading and tip-speed ratio. The new momentum correction terms are then included in the BEM model, and results benchmarked against references. The corrected BEM is derived by re-visiting the governing equations. For a disk represented by a constant-circulation set of blades, the corrected BEM contains no approximation to the underlying conservation laws. The study contributes by bridging the gap between BEM and the axisymmetric AD method for all disk load levels and tip speed ratios relevant for a wind turbine. The wake swirl correction leads to higher power efficiency at lower tip-speed ratios. The wake expansion correction causes a redistribution of the potential for power extraction, which increases on the inner part of the rotor and decreases on the outer part of the rotor. The overall rotor-averaged value of Betz limit is unaffected by the new corrections, but exceeding Betz locally on the inner- and mid-section of the rotor is shown to be possible. The two corrections significantly improve the axi-symmetric static BEM modelling accuracy for the radial distributions as well as for the rotor-integrated quantities, by reducing errors, approximately one order of magnitude. The relevance of these corrections for modern multi-MW rotors is quantified and discussed.

Suggested Citation

  • Søren Hjort, 2019. "Non-Empirical BEM Corrections Relating to Angular and Axial Momentum Conservation," Energies, MDPI, vol. 12(2), pages 1-28, January.
    • Handle: RePEc:gam:jeners:v:12:y:2019:i:2:p:320-:d:199362
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/12/2/320/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/12/2/320/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Søren Hjort & Helgi Larsen, 2015. "Rotor Design for Diffuser Augmented Wind Turbines," Energies, MDPI, vol. 8(10), pages 1-39, September.
    2. Søren Hjort & Helgi Larsen, 2014. "A Multi-Element Diffuser Augmented Wind Turbine," Energies, MDPI, vol. 7(5), pages 1-26, May.
    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. Subbulakshmi, A. & Verma, Mohit & Keerthana, M. & Sasmal, Saptarshi & Harikrishna, P. & Kapuria, Santosh, 2022. "Recent advances in experimental and numerical methods for dynamic analysis of floating offshore wind turbines — An integrated review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 164(C).

    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. Keramat Siavash, Nemat & Najafi, G. & Tavakkoli Hashjin, Teymour & Ghobadian, Barat & Mahmoodi, Esmail, 2020. "Mathematical modeling of a horizontal axis shrouded wind turbine," Renewable Energy, Elsevier, vol. 146(C), pages 856-866.
    2. 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).
    3. Rezek, Thiago J. & Camacho, Ramiro G.R. & Manzanares-Filho, Nelson, 2023. "A novel methodology for the design of diffuser-augmented hydrokinetic rotors," Renewable Energy, Elsevier, vol. 210(C), pages 524-539.
    4. Sorribes-Palmer, F. & Sanz-Andres, A. & Ayuso, L. & Sant, R. & Franchini, S., 2017. "Mixed CFD-1D wind turbine diffuser design optimization," Renewable Energy, Elsevier, vol. 105(C), pages 386-399.
    5. Anbarsooz, M. & Amiri, M., 2022. "Towards enhancing the wind energy potential at the built environment: Geometry effects of two adjacent buildings," Energy, Elsevier, vol. 239(PD).
    6. Mauro, S. & Brusca, S. & Lanzafame, R. & Messina, M., 2019. "CFD modeling of a ducted Savonius wind turbine for the evaluation of the blockage effects on rotor performance," Renewable Energy, Elsevier, vol. 141(C), pages 28-39.
    7. Søren Hjort & Helgi Larsen, 2015. "Rotor Design for Diffuser Augmented Wind Turbines," Energies, MDPI, vol. 8(10), pages 1-39, September.
    8. Bontempo, R. & Manna, M., 2020. "Diffuser augmented wind turbines: Review and assessment of theoretical models," Applied Energy, Elsevier, vol. 280(C).
    9. Avallone, Francesco & Ragni, Daniele & Casalino, Damiano, 2020. "On the effect of the tip-clearance ratio on the aeroacoustics of a diffuser-augmented wind turbine," Renewable Energy, Elsevier, vol. 152(C), pages 1317-1327.

    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:12:y:2019:i:2:p:320-:d:199362. 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.