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

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  • 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
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    References listed on IDEAS

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    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.
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    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).

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