Nonlinear blade element-momentum analysis of Betz-Goldstein rotors

D.H. Wood and V.L. Okulov

Renewable Energy, 2017, vol. 107, issue C, 542-549

Abstract: Blade element-momentum theory is a fundamental tool of wind turbine aerodynamics but several of its basic assumptions are not easily examined. By applying the theory to ideal Betz-Goldstein (BG) rotors, two important aspects of the theory are investigated. We prove for the first time that Glauert's inclusion of the tip loss factor in the angular and axial momentum equations is exact for BG rotors. Then we derive, also for the first time, the nonlinear contributions to the angular momentum balance when the rotor has a finite number of blades. The most important nonlinearity is the induced azimuthal velocity of the blades combined with that of the trailing vorticitiy. The derivation follows the recent formulation for the tip loss factor (F) by Wood et al. [1] in terms of the azimuthal variations in the induced velocities due to the trailing vortices. Nonlinearity is potentially important when F differs from unity. For a three-bladed BG rotor with the tip speed ratio (λ) varying from 0 to 15, we show that the nonlinear angular momentum peaks at 12% of the blade element torque when λ is in the range 0.8≤λ≤1.5. As λ increases above 1.5, the nonlinear terms reduce in importance. Nonlinearities also arise in the axial momentum equation but are more difficult to analyze. An approximate treatment of them suggests similar behaviour to the nonlinear angular momentum terms, but those in the axial momentum equation arise purely from the trailing vortices.

Keywords: Wind turbine; Tip loss; Blade element analysis; Nonlinear contributions (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960148117301131
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:renene:v:107:y:2017:i:c:p:542-549

DOI: 10.1016/j.renene.2017.02.027

Access Statistics for this article

Renewable Energy is currently edited by Soteris A. Kalogirou and Paul Christodoulides

More articles in Renewable Energy from Elsevier
Bibliographic data for series maintained by Catherine Liu ().