Description of the Structural Model

subjected to high wind speeds. The authors observe that a good agreement with measured data can be obtained following the extension method proposed by Lindenburg [75]. In addition, in order to obtain accurate rotor sectional lift characteristics, and hence accurate power prediction (in particular in the stalled region), bi-dimensional airfoil data need to be corrected for the three-dimensional inboard stall delay eects [76]. In fact, due to rotation, the boundary layer is subjected to Coriolis and centrifugal forces which alter the bi-dimensional airfoil characteristics [77]. Accordingly, the boundary layer is less thick and more stable compared to the non-rotational state [75], enhancing the performance of the blades, particularly in their innermost portion. To take into account these eects, the correction on the lift and drag coecients proposed by Lindenburg [75] is hereby considered.

5.2.1 BEM Code Validation

The adopted BEM code is validated against experimental data of the AOC 15/50 wind turbine installed at NREL's National Wind Technology Center (NWTC) in Colorado [65]. All the numerical simulations are conduced considering a constant rotor angular speed of 65 rpm for a range of wind velocities between 5 m/s and 20 m/s. Air density is set to 1.225 kg/m³and the dynamic viscosity to 1.78 P a·s. The polar curves for the S814, S812 and S813 airfoils are obtained using RFoil for a constant Reynolds number of 10⁶ and extended up to 90^◦ using the Lindenburg method [75]. The generator eciency is assumed constant and equal to 89.4% (from: [68]). Figure 5.3 shows a comparison between the power curve at sea level air density and the numerical simulations. The numerical power curve at low velocities presents an overestimation of the wind turbine performances. This is probably caused by the inertia of the wind turbine in the start-up phase; the cut-in speed is indeed 4.8 m/s and the inertia of the blades (that are starting to moving) could inuence the experimental measurement at low velocities.

A remarkable agreement can be observed up to a wind velocity of 18 m/s, where a deep stall condition is experienced by the blades. However, this portion of the power curve can be neglected for the scope of the present analysis and the accuracy of the prediction can be therefore considered acceptable.

5.3 Description of the Structural Model

The FEM model adopted for the present optimization is built using SHELL 181 elements to simulate the composite skin of the blade; such element can reproduce the behaviour of the layered structures by specifying the sequence of layers, the thickness and the orientation of each single lamina and the adopted material.

As shown in Figure 5.4, each element is composed of 4 nodes and has 6 degrees of freedom at each

Figure 5.3: Experimental and numerical power production as a function of the wind speed for the AOC 15/50 wind turbine

node: translations in the nodal x, y and z directions and rotations about the nodal x, y and z axes.

A free mesh topology and a quad shape of the elements are adopted to discretize each surface of the model. A medium dimension of the surface elements of 20 mm is imposed; a representation of the mesh in the root area is shown in Figure 5.5.

Figure 5.4: Shell 181 conguration

The layup schedule of the model blade is assumed by the Sandia report [66] and summarized in Table 5.3. A Layup number is assigned to every area of the blade where the layup changes. The graphic representation of the dierent layup distribution along the blade is shown in Figure 5.2. Number 11 represents the spar ange layers, overlapped to the central ones from 3 to 6 and number 12 represents the Spar Web.

The adopted materials are some varieties of Glass Reinforced Polyester (GRP): all the lamina are

5.3  Description of the Structural Model

Figure 5.5: A detail of the adopted in mesh in the root area A130 DB120 Balsa Wood

(0^◦) (±45^◦)

EL=EX [MPa] 31700 26200 187

ET=EY [MPa] 7580 6550 61

EZ=EZ [MPa] 7580 6550 4070

ν_LT = νXY [-] 0.32 0.39 0.67 νT Z = νY Z [-] 0.32 0.35 0.01 νLZ = νXZ [-] 0.32 0.32 0.02 GLT=GXY [MPa] 3450 4140 20.3 GT Z=GY Z [MPa] 3100 3720 150 GLZ=GXZ [MPa] 3100 3720 220

ρ [kg/m³] 1714 1714 153

t [mm] 0.571 0.203 9.530

Table 5.4: Structural properties of the materials adopted in the AOC 15/50 blade

composed by E-glass bres embedded in a polymer matrix. The layup is modelled as orthotropic in a given layer with two of the principal material axes in the plane of the shell, as can be seen from the material parameters listed in Table 5.4. Dierent materials are adopted for the layers with dierent orientations of the bres. The 0^◦ layups are made by A130, while DB120 is used for the ±45^◦ ply layups. In order to minimize the probability of buckling, the balsa wood is adopted as a ller in the sandwich layup of the trailing edge (zone 9).

A rigid constraint is applied to the root area of the blade: the three spatial displacements and the three rotations are xed for the nodes belonging to the surface. The mechanical loads for the structural model are obtained by an interpolation of the aerodynamic forces computed from the BEM model.

The validation of the structural model is obtained by comparing the results of a FEM analysis to the same results provided in the AOC 15/50 Sandia report [66]. The apwise, edgewise and torsional

rigidities of the blade (treated as a cantilever beam) with a xed load applied at its tip are computed and compared with experimental results. The detailed description of the validation procedure is provided in [54] and is not reported here again for brevity's sake.