Conceptual errors in actuator disc theory and Betz’s law for wind turbines

Zhang, Zhengji

doi:10.3390/en15165902

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-26476

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Conceptual errors in actuator disc theory and Betz’s law for wind turbines
Authors:	Zhang, Zhengji
et. al:	No
DOI:	10.3390/en15165902 10.21256/zhaw-26476
Published in:	Energies
Volume(Issue):	15
Issue:	16
Page(s):	5902
Issue Date:	2022
Publisher / Ed. Institution:	MDPI
ISSN:	1996-1073
Language:	English
Subjects:	Wind turbine; Betz’s law; Froude-Rankine theorem; Actuator disc
Subject (DDC):	620: Engineering
Abstract:	This paper started with the explanation of the conditions for using the momentum equation and with the presentation of the actuator disc theory. Focusing on the flow model used in actuator disk theory, both the Froude-Rankine theorem and Betz’s law have been examined. It has been found that the Froude-Rankine theorem is not justified because a stream-tube that is used as the control volume does not really exist (pseudo stream-tube). The theorem is also not justified because an unfounded velocity (v2) is used to connect the thrust of the actuator disc with the total power loss. Two flaws have been identified in Betz’s law. First, the use of both the unjustified Froude-Rankine theorem and the incorrect flow model totally violates the condition of determining the thrust of the actuator disc using the momentum equation. Second, the unfounded velocity (v2) from the Froude-Rankine theorem is misinterpreted and used for the volumetric flow rate through the actuator disc. These two main flaws lead to diverse computational contradictions and paradoxes, particularly when considering the case of an impermeable circular disc. The flaws in Betz’s law become evident when the law is applied to a rectangular actuator plate of infinite length. The possible solution for the actuator disc flow has been presented. This includes the additional consideration of energy dissipation in the flow downstream of the actuator disc, similar to the method used to calculate the Borda-Carnot shock loss.
URI:	https://digitalcollection.zhaw.ch/handle/11475/26476
Fulltext version:	Published version
License (according to publishing contract):	CC BY 4.0: Attribution 4.0 International
Departement:	School of Engineering
Organisational Unit:	Institute of Energy Systems and Fluid Engineering (IEFE)
Appears in collections:	Publikationen School of Engineering

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Zhang, Z. (2022). Conceptual errors in actuator disc theory and Betz’s law for wind turbines. Energies, 15(16), 5902. https://doi.org/10.3390/en15165902

Zhang, Z. (2022) ‘Conceptual errors in actuator disc theory and Betz’s law for wind turbines’, Energies, 15(16), p. 5902. Available at: https://doi.org/10.3390/en15165902.

Z. Zhang, “Conceptual errors in actuator disc theory and Betz’s law for wind turbines,” Energies, vol. 15, no. 16, p. 5902, 2022, doi: 10.3390/en15165902.

ZHANG, Zhengji, 2022. Conceptual errors in actuator disc theory and Betz’s law for wind turbines. Energies. 2022. Bd. 15, Nr. 16, S. 5902. DOI 10.3390/en15165902

Zhang, Zhengji. 2022. “Conceptual Errors in Actuator Disc Theory and Betz’s Law for Wind Turbines.” Energies 15 (16): 5902. https://doi.org/10.3390/en15165902.

Zhang, Zhengji. “Conceptual Errors in Actuator Disc Theory and Betz’s Law for Wind Turbines.” Energies, vol. 15, no. 16, 2022, p. 5902, https://doi.org/10.3390/en15165902.