2025-02-21 ペンシルベニア州立大学 (PennState)
＜関連情報＞
- https://www.psu.edu/news/engineering/story/student-refines-100-year-old-math-problem-expanding-wind-energy-possibilities
- https://wes.copernicus.org/articles/10/451/2025/
Glauertの最適ローターディスクの再考-変分方程式の解と推力および曲げモーメント係数の厳密積分 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
Wind Energy Science Published:21 Feb 2025
DOI:https://doi.org/10.5194/wes-10-451-2025
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 for λ→∞. 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, and its validity is discussed in the context of other works since Glauert.
