Glauert's optimum rotor disk revisited – a calculus of variations solution and exact integrals for thrust and bending moment coefficients
Year: 2025
Type: article
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.
Source: Wind energy science
Authors: Divya Tyagi, Sven Schmitz
Institution: Pennsylvania State University
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,132
Funder: Pennsylvania State University
OpenAlex ID: W4407830356