*4.2. Mesh Creation and Choice*

Wind turbine blades, under operation, are mainly subjected to bending and torsion. To capture these phenomena correctly, proper structural mesh must be prepared. The analyzed blade is a sweepable body, making it possible to only use solid hexahedron elements instead of tetrahedrons. The body was meshed using ANSYS Solid 185 elements with eight nodes with three degrees of freedom at each node (translations in all directions). Moreover, the body is going to be subjected to bending, which means that at least three elements through the thickness are necessary to capture the stresses properly. For the mesh convergence study, four meshes are prepared—the mesh operations and sizings are as follows (see Figure 9):


**Figure 9.** Mesh operations on the blade.

Four meshes under inspection are denoted as I, II, III, and IV. First, three meshes differ only by means of the sizing of elements. In mesh IV, additionally, the bias in the length of the blade direction is applied. The mesh parameters for these densities are presented in Table 4. The cross-sections of the blades for meshes II, III, and IV are the same. The comparison of these cross-sections with a cross-section of the mesh I is presented in Figure 10.


**Table 4.** Mesh sizing.

<sup>1</sup> In mesh IV, a bias is applied in order to increase the number of elements near the fixing point.

**Figure 10.** Comparison of blade grids in cross-sections in meshes (**a**) II, III, IV, and (**b**) I.

Mesh convergence study has been performed for maximal thrust case (wind speed equal to 12 m/s and *TSR* = 5). The criteria for investigating these three meshes are as follows:


**Figure 11.** Blade tip deflection δ (in mm).

**Figure 12.** Map of equivalent (von Mises) stresses appearing in the blade σ*max* (in MPa).

**Figure 13.** Control line passing through the leading and trailing edge of the blades for determining blade tip twist.

The last parameter, which is the twist of the blade due to deformation (in addition to the design section twist), must be quantified manually by means of comparing coordinates of the nodes before and after deformation. It is determined for the blade tip, as the highest angular deformations of the blade appear there. Coordinates of the leading edge node with coordinates of the mid-node at the trailing edge are being extracted from the software and twist in blade-tip cross-section plane is being calculated.

Based on the coordinates of points A and B, a twisting of the blade tip is determined. A line is traced through points at the blade tip leading edge (A) and trailing edge (B). The angle of inclination of this line with respect to the rotor plane of rotation may be computed using simple mathematical transformations, both before and after the deformation. A difference between these two values, Δβ, is a measure of the deformation twist angle of the blade due to deformation.

A summary of all three examined parameters is shown in Table 5. It is visible that all mesh densities are providing the results, which are in agreement with each other in terms of the deformations—both total deflections and deformation twist angles are comparable to each other for all structural meshes (the relative difference is not higher than 2%). The situation is similar when talking about the convergence of the value of allowable stress—the relative differences between two diverging results are not exceeding the value of 2%.

