CFD-based curved tip shape design for wind turbine blades

This work presents a high-fidelity shape optimization framework based on computational fluid dynamics (CFD). The presented work is the first comprehensive curved tip shape study of a wind turbine rotor to date using a direct CFD-based approach. Preceding the study is a thorough literature survey particularly focused on wind turbine blade tips in order to place the present work in its context. Then follows a comprehensive analysis to quantify mesh dependency and to present needed mesh modifications ensuring a deep convergence of the flow field at each design iteration. The presented modifications allow the framework to produce up to six-digit-accurate finite difference gradients which are verified using the machine-accurate Complex-Step method. The accurate gradients result in a tightly converged design optimization problem in which the studied problem is to maximize power using 12 design variables while satisfying constraints on geometry, as well as on the bending moment at 90 % blade length. The optimized shape has about 1 % r/R blade extension, 2 % r/R flapwise displacement, and slightly below 2 % r/R edgewise displacement resulting in a 1.12 % increase in power. Importantly, the inboard part of the tip is de-loaded using twist and chord design variables as the blade is extended, ensuring that the baseline steady-state loads are not exceeded. For both analysis and optimization an industrial-scale mesh resolution of above 14×106 cells is used, which underlines the maturity of the framework.