Coupled aero-structural shape and topology optimization of HAWT rotor blades

A wind turbine rotor should capture as much wind power as possible. However, the more energy extracted from the wind, the larger the aerodynamic forces induced on the rotor blades, which thus requires a stronger blade structure. Consequently, one of the challenges during the design of an optimal rotor blade is to find the right balance between its aerodynamic performance and its structural behavior. This contribution presents a coupled multi-objective shape and topology optimization framework for the aero-structural design of Horizontal-Axis Wind Turbine (HAWT) rotor blades. It aims at optimizing simultaneously the blade outer shape and the interior layout from aerodynamic and structural requirements. Accordingly, a multi-objective optimization model is developed, based on the weighted sum method, in which the rotor power coefficient and the blade structural compliance are considered as two sub-objectives. In order to limit the computational demand, the power coefficient and structural compliance are efficiently evaluated via the Blade Element Momentum (BEM) and beam Finite Element Method (FEM) models, respectively. The shape design variables are characterized by the control point locations of Non-Uniform Rational B-Splines (NURBS) that govern the blade geometry. The topology design variables are represented by the relative densities assigned to the finite elements modeling the blade cross-sections, as common for the Simplified Isotropic Material with Penalization (SIMP) method. The coupled optimization model is solved by sequentially performing shape and topology optimizations with different weighting factors for the sub-objectives. In order to further improve the computational efficiency of the optimization model, the sensitivities for shape and topology optimization are derived in closed form, and incorporated within a gradient-based optimization algorithm. The presented optimization framework is used to optimize the National Renewable Energy Laboratory (NREL) 5MW wind turbine rotor blades. The optimized design of the rotor blades achieves a higher power coefficient and a lower structural compliance than the reference design, which clearly indicates the practical applicability of the coupled optimization framework.