## 3 Results and Discussion  
To simulate the operation of the Darrieus rotor and calculate its energy characteristics, a mathematical model was developed using the finite element method. The geometry was created at the software CATIA P3V5 (Mechanical Design). The calculations and simulations were made at the software ANSYS 14.5, ANSYS Fluent. At the first stage, the geometry of the NACA 0021 blade was created. To construct the model of the Darrieus rotor blades, in the CATIA program, the geometric points of the edges were calculated using the known models of the blade profiles. The model was used as a base profile naca0021-il, which has the next parameters: Max thickness 21% at 30% chord, Max camber 0% at 0% chord. Profile characteristics are shown in the Figure 3.  
Figure 3: Profile characteristics of the naca0021-il. The naca0021-il profile points were transferred to the CATIA program and a sketch of the Darrieus rotor blade was created (Figure 4). Then, this blade was transformed into a full-fledged geometric copy of the rotor (Figure 5). The next step was to set additional geometry elements in the form of geometric contours of boundary conditions, which were necessary for performing subsequent calculations in ANSYS and ANSYS FLUENT software. Figure 6 shows an image of the final version of the geometry of the simulated Darrieus rotor with a given geometry of all boundary conditions, including three main boundaries: the area remote from the rotor (for approximate modeling of the environment--meshes with large elements), the area near the rotor (for more accurate modeling of the environment around the rotor we used meshes with middle elements), and the area around the rotor blades (for accurate modeling of the environment and the flow of the wind flow along the geometry of the blade we used meshes with small elements). Figure 4: Sketch of the Darrieus rotor blade in CATIA. Figure 5: Sketch of the Darrieus rotor blades in CATIA. The mesh was generated in ANSYS Mesh using the proximity and curvature advanced size function. The mesh is shown on the Figure 7.  
The results of the simulation of the velocities are shown in Figure 8a,b. Figure 6: Sketch of the Darrieus rotor blades in CATIA. Figure 7: Mesh of the model. As a result of the simulation, the characteristic of the utilization factor (Cp) from the peripheral speed was obtained and presented in Figure 8. From the presented characteristics, it follows that the maximum value of the utilization factor is 0.345, which can be assumed as a small value with the respect to the number of model assumptions. As a result, it is necessary to carry out work aimed at increasing this indicator by changing the geometry parameters of the wind turbine rotor and the use of other technical design improvements. The work planned in the subsequent stages of work under this grant will be aimed at solving these problems. Figure 9 shows the flow velocity diagram in the cross section of a wind turbine with a diameter of 2 m, obtained because of the simulation at a wind speed of 10 m/s using the finite volume method. Figure 8: Results of the simulation (velocities): (**a**) simulation results and (**b**) enlarged view of the simulation model. During modeling, the dependence of the coefficient of use of wind energy \(C_{p}\) at different angles of installation of the rotor blades was determined. The results obtained are shown in the summary graph (Figure 10), from which it follows that the maximum value of the wind energy utilization factor \(C_{p}\) is achieved when setting the blade angle \(\varphi=3.8^{\circ}\), while the design value of this angle, regulated by the manufacturer, is \(7.8^{\circ}\). Thus, the simulation showed that initially the wind turbine was operating at limited capacity. An experimental study was also carried out, the purpose of which was to verify the results obtained from digital simulations.