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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Aerodynamics and rotor design' taking place on Wednesday, 12 March 2014 at 09:00-10:30. The meet-the-authors will take place in the poster area.

Carlo Luigi Bottasso Technische Universitaet Muenchen, Germany
Carlo Luigi Bottasso (1) F P Alessandro Croce (2) Francesco Grasso (3) Luca Sartori (2)
(1) Technische Universitaet Muenchen, Garching b. München, Germany (2) Politecnico di Milano, Milano, Italy (3) ECN, Petten, The Netherlands

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Free-form aero-structural optimization of rotor blades


The design of rotor blades for wind turbines is a highly multidisciplinary activity, which involves the determination of the aerodynamic shape of the blade, the choice of materials and the sizing of all structural members. The design must satisfy a possibly large number of constraints, which account for various effects such as noise, structural integrity, manufacturability, transportability, etc. In general, aim of the design is the minimization of the cost of energy, with the simultaneous satisfaction of all constraints.


Given the complexity of the blade design problem, it is important to develop automated methodologies that can deliver high quality solutions and that can help in the full exploration of the design space with minimal assumptions. This is becoming of prominent importance as the next-generation of very large machines is being investigated for the exploitation of both on and off-shore resources.
At present, blade design is typically conducted by the following iterative process: 1) a collection of existing suitable airfoils is selected, 2) the blade chord, twist, pre-bend/cone and possibly sweep are defined, 3) materials are chosen and the blade structural members are sized. Iterations are conducted among these design steps, until all constraints are satisfied and an optimal configuration has been achieved.
The current approach used for designing rotor blades limits the exploration of the design space to a set of pre-assumed airfoils. As the airfoil shape has a strong influence on the aerodynamic performance but also on the structural sizing, such limitation hinders a full exploration of the design space. For example, selecting or not flatback airfoils in a certain region of the blade, one can profoundly alter the thickness of the spar caps and/or the necessary mechanical material properties, with consequent coupled effects on performance, loads, weight, cost of material and manufacturing, etc., all items eventually participating in the definition of the cost of energy. To overcome such limitations, the present work describes an integrated aero-structural approach that aims at a real full free-form optimization of rotor blades.

Main body of abstract

Objective of this work is the definition of a new blade design procedure, whereby airfoils are designed together with the rest of the blade, resulting in a general and flexible tool that achieves a more complete exploration of the design space. Another scope of this new tool is to relieve the designer from a priori choices. With reference to the example mentioned above, by this methods flatbacks should automatically emerge as part of the solution if they represent optimal choices in certain parts of the blade, without requiring the designer to make this choice a priori. The idea of simultaneously designing airfoils and rotor was previously described in Ref. [1], although limitedly to the sole aerodynamic optimization of the blade; that idea is here generalized to the aero-structural design problem.

The design problem is cast as a constrained optimization of the cost of energy, following Refs. [2,3]. The rotor aerodynamic model is based on a classical BEM approach, the airfoil flow model on the formulation of Refs. [4,5], while the structural model uses a beam approximation of the blade coupled to a semi-monocoque cross-sectional model.
The design unknowns include the span-wise airfoil shapes, chord and twist distributions, and spar-cap thickness; such quantities are discretized assuming suitable shape functions based on Bezier curves and their associated discrete nodal parameters. For simplicity of implementation, at this stage the design assumes fixed and given skin and shear web thicknesses, as well as a straight axis and a fixed cone angle. Again for simplicity and to reduce the computational cost, the present analysis does not consider the effects of fatigue, and it assumes ultimate loads due storm conditions. These limitations will be removed in a continuation of the present effort using the more complete formulation of Ref. [2], which closely follows accepted certification guidelines.
The optimization cost function is based on the NREL LCOE model of Ref. [6], while the design constraints include maximum tip deflection, placement of first flap natural frequency, and not to be exceeded allowables in the spar caps.
At each instantiation of the design parameters, the aerodynamic characteristics at various spanwise stations are estimated using the Xfoil code, and extrapolated to ±180 deg using the Viterna method. These aerodynamic coefficients are then used for the definition of a lifting line BEM approach, completing the aerodynamic description of the model. The aerodynamic model is then coupled to a structural beam model, whose stiffness and mass characteristics are computed for the current values of design parameters based on the cross sectional model and the local material properties. The resulting complete aeroelastic model of the rotor is then used for the necessary simulations required for the evaluation of the contributing terms of the cost function and constraints.

The paper explores the capabilities of the novel proposed formulation, by designing rotors up to 10 MW. In the present abstract, we limit the discussion to a 2MW wind turbine with a rotor diameter of about 92 meters. The blade was initially sized using five symmetric airfoils, with thicknesses ranging between 18 and 40%; assuming these frozen airfoils, an optimization was run to determine the rest of the configuration, resulting in the associated chord, twist and spar cap thickness distributions.
This initial configuration was then let evolve using the proposed free-form optimization strategy. The free-form optimized shape resulted in a 6% reduction of the LCOE, with a 4.3% reduction in blade weight and a 7.4% increase in AEP with respect to the initial configuration.
Although these rather dramatic improvements are largely due to the very rough initial configuration that used only symmetric airfoils, it is interesting to look at the free-form optimized result. A view of the resulting blade is shown in Figure 1, showing the natural emergence of thick flatbacks at the inner spanwise stations, as well as a general (fully expected) positive cambering of all airfoils from their initial symmetric shapes.

Figure 1. Three-dimensional view of the free-form optimized blade, with detail of thick trailing edge and flatback airfoils in the inner span stations.


The present work has presented a new approach to the aero-structural optimization of wind turbine rotor blades. The method is based on the simultaneous design of the airfoils, together with the rest of the aerodynamic and structural parameters of the blade. The procedure results in a general and flexible free-form optimization, which does not require a priori assumptions on the most appropriate collection of airfoils.
The design procedure is formulated as a constrained optimization. Design parameters are computed by minimizing a LCOE model, subjected to constraints that translate desired characteristics in the solution. The numerical optimization is based on an efficient sequential quadratic programming approach.
Results dealing with the optimization of rotor blades of multi-MW machines have shown that the procedure can reliably converge to convincing blade configurations. When starting from simple symmetric airfoils, the optimal solution exhibits the expected emergence of positively cambered airfoils. In some cases, as shown in this abstract, results have also shown the natural emergence of flatbacks in the inner span portion of the blade, as seen on many modern large wind turbine blades.
The current implementation has mainly aimed at the proof of the proposed concept, by using a simplified implementation with only a limited set of design parameters, constraints and design load cases. Based on the very encouraging results observed here, the method will be expanded in order to increase its generality and applicability. The final implementation should allow for a more complete structural sizing, considering all relevant structural members and a full set of extreme and fatigue loading conditions; furthermore, the blade shape design parameters should also include sweep and prebend/cone.

The present work is supported in part by the FP7 INNWIND project.

Learning objectives
- General understanding of the aero-structural optimization of rotor blades
- Design of wind turbines based on LCOE minimization
- Free-form optimization, and its advantages with respect to a priori choices made by the designer
- Necessity of tools for the full exploration of vast design spaces

[1] L. Sartori, F. Grasso, C.L. Bottasso, A. Croce, `Integration of Airfoil Design During the Design of New Blades', ICOWES2013, International Conference on Aerodynamics of Offshore Wind Energy Systems and Wakes, Lyngby, Denmark, June 17-19, 2013.
[2] C.L. Bottasso, F. Campagnolo, A. Croce, S. Dilli, F. Gualdoni, M.B. Nielsen, `Structural Optimization of Wind Turbine Rotor Blades by Multi-Level Sectional/Multibody/3DFEM Analysis', Multibody System Dynamics, doi:10.1007/s11044-013-9394-3, 2013.
[3] C.L. Bottasso, A. Croce, F. Campagnolo, `Multi-Disciplinary Constrained Optimization of Wind Turbines', Multibody System Dynamics, 27:21-53, doi:10.1007/s11044-011-9271-x, 2012.
[4] M. Drela, `XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils', Conference on Low Reynolds Number Airfoil Aerodynamics, University of Notre Dame, June 1989.
[5] M. Drela, `XFOIL 6.94 User Guide', MIT Aero & Astro, Dec 2001.
[6] L. Fingersh, M. Hand, A. Laxson, `Wind Turbine Design Cost and Scaling Model', Technical Report NREL/TP-500-40566, December 2006.