Optimization & Automatic Design of Fluid-Dynamical Systems: Towards Optimal Shapes for Wind Turbine Blades

Martin Bünner

NTB, Institute for Computational Engineering


Despite the fact that size and power of current and next-generation wind turbines has risen tremendously, there remain important fundamental questions unresolved: What are optimal blade shapes for wind turbines? Here, we consider an optimal shape problem (OSP) for 2D-airfoils, with objectives in lift force and drag force for angles of attack between -10° and +10°. Since, in recent years, many approaches to solve OSPs have been proposed, we compare several approaches in detail: (a) map OSP to an unconstrained optimization problem: (a1) Nelder-Mead method, (a2) Quasi-Newton-method, (b) map OSP to a constrained optimization problem: (b1) SQP-method. As a first result, the solution methods (a1)-(a2) are not suitable to solve the OSP, since there are too many objective functions. As
a second result, the solution method (b1) is well suited to solve the OSP. On the basis of (b1), we will present optimal air foils for wind turbines which are optimized for (i) low-to-medium wind velocities, and (ii) medium-to-high wind velocities. Finally we present the “NTB CFD Automatic Design Toolbox”, which is a user-friendly toolbox for practitioners to solve CFD optimal shape problems. It allows CFD engineers to enjoy the benefits of high-end solution-techniques, like SQP-methods, without having to deeply dive into the intricacies of modern optimization theory.