## 5 Results of the Mathematical Model  
Figures 13 and 14 show contour plots of static pressure, allowing us to understand the physics of flow in Darrieus rotors. For the wind wheel, the blades were considered as moving blades. At a flow velocity of 3 m/s, the obtained results are a three-dimensional contour plot of the static pressure distribution around the vertical axis of the wind turbine (VAWT). The figures show the static pressure distribution and aerodynamic interaction of a wind turbine with and without plates. In the first figure, (a) the use of plates leads to a more pronounced pressure gradient: high-pressure zones are concentrated at the leading edges of the blades located in the windward zone, which increases the lift. However, this also causes increased vortex formation behind the structure, which increases the turbulent wake and can affect the aerodynamic efficiency. In the second figure, (b) where there are no plates, the pressure distribution is more uniform, and the turbulence intensity is lower, which helps to reduce vortex losses and increase the stability of the structure. However, in this case, the lift can be reduced due to a less pronounced pressure gradient. Thus, the plates increase the aerodynamic effect on the blades but, at the same time, increase  
Figure 14: Static pressure contours around a wind turbine (top view). Figure 13: Static pressure contours around the wind wheel. turbulence, while their absence provides a more stable pressure distribution and reduces vortex losses. The data highlight the aerodynamic design features that are important for optimizing turbine performance. The provided Figures 15 and 16 illustrate the distribution of velocity vectors around a three-bladed wind wheel based on mathematical modeling, as modeled in the Ansys program. The presented visualization demonstrates the distribution of velocity vectors around a wind turbine with asymmetric blades, as created in ANSYS. The first figure, (a) shows the velocity field around the wind turbine structure with plates, where clear zones of air flow acceleration are visible along the surfaces of the blades and plates. The smooth velocity lines indicate the minimization of turbulence zones on the leeward side of the structure. The second figure, (b) shows the velocity field around a wind turbine without plates. Here, vortex formations behind the blades are clearly visible, caused by the increase in resistance in the leeward zone. The absence of plates leads to a more pronounced flow disturbance, which affects the overall aerodynamic efficiency of the plant. Comparison of the curves shows that adding plates to the wind wheel design improves the flow characteristics, reduces the turbulent wake zone, and increases the rotation efficiency. At the same time, the wind wheel without plates demonstrates an unstable flow, characterized by increased turbulence and a decrease in the power factor with an increase in the air flow speed. These features emphasize the efficiency of the wind wheel design in creating lift and ensuring aerodynamic stability in various azimuthal positions. Figure 16: Fields of distribution of velocity vectors in the plane around the wind wheel (top view). Figure 15: Fields of distribution of velocity vectors in the plane around the wind wheel. For a more accurate assessment of the aerodynamic efficiency of the design, the power factor \(C_{p}\) was used, which is calculated using the following formula:  
\[C_{p}=\frac{N_{r}-N_{c}}{N_{\omega f}} \tag{12}\]  
where \(N_{c}=mM_{c}\omega_{c}\) is the blade rotation power; \(m\) is the number of blades; \(M_{c}\)--is the force acting on the blades during their rotation; \(\omega_{c}\)--is the angular velocity arising from the blade rotation, \(N_{\omega f}\)--is the wind power, and \(N_{r}\)--is the rotor power. Figure 17 below shows the change in the power factor \(C_{p}\) depending on the tip speed ratio (TSR).