Wind Energy Science
Wind Energy Science
WES
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https://doi.org/10.5194/wes-2024-111
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-2024-111
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
Preprints
30 Sep 2024
 | 30 Sep 2024
Status: a revised version of this preprint is currently under review for the journal WES.

Glauert's Optimum Rotor Disk Revisited – A Calculus of Variations Solution and Exact Integrals for Thrust and Bending Moment Coefficients

Divya Tyagi and Sven Schmitz

Abstract. The present work is an amendment to Glauert's optimum rotor disk solution for the maximum power coefficient, CPmax, as a function of tip speed ratio, λ. First, an alternate mathematical approach is pursued towards the optimization problem by means of calculus of variations. Secondly, analytical solutions for thrust and bending moment coefficients, CT and CBe, are derived, where an interesting characteristic is revealed pertaining to their asymptotic behavior. In addition, the limit case of the non-rotating actuator disk for λ → 0 is shown for all three performance coefficients by repeated use of L'Hôpital's theorem.

How to cite. Tyagi, D. and Schmitz, S.: Glauert's Optimum Rotor Disk Revisited – A Calculus of Variations Solution and Exact Integrals for Thrust and Bending Moment Coefficients, Wind Energ. Sci. Discuss. [preprint], https://doi.org/10.5194/wes-2024-111, in review, 2024.
Received: 03 Sep 2024 – Discussion started: 30 Sep 2024
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Divya Tyagi and Sven Schmitz

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Divya Tyagi and Sven Schmitz
Divya Tyagi and Sven Schmitz

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Short summary
This paper adds to the literature on rotor disk theory by solving the century-old problem with a different mathematical approach. The classical results are recovered, while also adding expressions and asymptotic limits for performance coefficients that were not included in the original theory. This work adds to classical rotor disk theory as a valuable contribution to research and teaching in wind turbine aerodynamics.
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