Center for Turbulence Research Proceedings of the Summer Program 2012 241 Robust optimization for windmill airfoil design under variable wind conditions By H. Tachikawa†, D. Schiavazzi‡, T. Arima† AND G. Iaccarino Robust design of windmill airfoils is carried out in the presence of uncertain envi- ronmental conditions. The formulation follows a multi-objective optimization approach, where the mean aerodynamic performance is maximized while sensitivity to changes in wind conditions is kept to a minimum. Due to the complex nature of the physical pro- cesses involved, a non-intrusive collocation approach is used to quantify uncertainties, coupled with a RANS solver for the fluid flow. A robust design optimization frame- work is thus assembled, where Genetic Algorithms are used to iteratively evolve section parameters toward optimal designs. Expectations and variances are computed with a Smolyak sparse grid approach combined with nested Clenshaw-Curtis quadrature, lead- ing to a minimization of the number of deterministic solutions needed. The results show the potential applicability of the proposed methodology to the robust design of industrial devices. 1. Introduction Wind power generation, the production of electric power by conversion of wind energy into propeller rotation, is increasingly seen as an attractive energy source. The ability to achieve high conversion efficiency under changing wind conditions is crucial to this technology. The velocity triangle of a windmill airfoil section illustrated in Figure 1 shows how the change in wind velocity V a results in changes in the angle of attack and inflow velocity relative to the airfoil section. Under such conditions, optimization should guarantee a stable performance while maximizing the rotation thrust or, in other words, should be formulated as a robust process. However, due to the significant computational cost associated with traditional Monte Carlo-like strategies used in conjunction with CFD simulations, design optimization is often carried out for specific environmental conditions. The objective of this study is twofold: (a) To investigate and show the increase in computational cost involved in the transi- tion from traditional to robust optimization for windmill airfoil section profiles and (b) To explore efficient optimization methods. 2. Problem formulation Two optimization problems are analyzed in the present study. The first approach is using a traditional optimization strategy where no variation of inflow wind conditions is considered. It is formulated as a single objective optimization, maximizing a measure of aerodynamic efficiency, i.e., the lift to drag coefficient ratio C L /C D . Robust optimization is successively investigated, where disturbances in the inflow angle † Honda R&D Co., Ltd, 1-4-1 Chuo,Wako-shi, Saitama 351-1093 Japan ‡ Department of Mathematics, University of Padua, Italy