## 3 Results and Discussion  
The present work employs dimensionless parameters to analyze the results. Since the turbines analyzed are scale models of real turbines, a dimensionless analysis allows a comparison with turbines of different sizes and in different wind conditions. TSR is the ratio between of the blade tip tangential velocity and the wind speed, calculated using Equation (4):  
\[\text{TSR}=\frac{\text{blade tip }\tan\text{gential velocity}}{\text{wind speed}}=\frac{\omega\text{R}}{\text{V}} \tag{4}\]  
where \(\omega\) is the rotational speed of the rotor, R is the rotor radius, and V is the wind speed. Figure 5: Boundary conditions. Figure 6: (**a**) Wind tunnel used for the measurements; (**b**) turbine inside the test section. \(\rm C_{m}\) is the torque coefficient, defined as follows:  
\[\rm C_{m}=\frac{M}{0.25\rho SV^{2}\phi_{t}} \tag{5}\]  
where M is the torque, \(0.5\rho V^{2}\) the kinetic energy per unit volume of the incoming flow and S the cross-section area, given by \(\rm S=\phi_{t}H\). \(\rm C_{p}\) is the power coefficient. It expresses which fraction of the power in the wind is being extracted by the turbine, as shown in Equation (6):  
\[\rm C_{p}=\frac{P}{0.5\rho SV^{3}}=C_{m}TSR \tag{6}\]  
where P is the shaft power. This should be the power on the shaft, but since the objective of this study is to compare the performance of the Fibonacci rotor against the Savonius rotor, for this case P has been taken as output power (electrical power obtained), taking into account that the losses by friction and electrical are practically the same in both cases  
Figure 7 shows the average power coefficients against the TSR for the Fibonacci I, Fibonacci II, and Savonius configurations. Both numerical and experimental results are shown in this figure. Since the Fibonacci II configuration lead to lower TSR than Savonius, it was not considered experimentally. The main difference between Fibonacci I and Fibonacci II is that the former places the lower arc in the end of the blade, Figure 4a, as indicated by the results obtained by other authors, Figure 1.  
As can be seen in Figure 7, there is a peak value for each curve and the power coefficient increases with TSR up to a certain point after which it drops down as the TSR further increases. Both the experimental and numerical results show the superiority of the Fibonacci I turbine over the Savonius one. Particularly, the maximum power coefficients for Fibonacci I and Savonius were 0.1129 and 0.0986, respectively, for the CFD analysis, which means a 14.5% improvement of Fibonacci I over Savonius. Regarding the experimental results, the maximum power coefficients for Fibonacci I and Savonius were 0.1106 and 0.0943, respectively, which means a 17.6% improvement of Fibonacci I over Savonius. Several reasons are responsible for the discrepancies between the numerical and experimental results shown in Figure 7. The mechanical losses in the generator, bearings, transmission, electrical losses in the generator, and the blockage effect do not allow for the experimental reproduction of the CFD data. Regarding CFD, the k-\(\epsilon\) turbulence model does not provide accurate results near the wall [29]. DNS (Direct Numerical Simulation) or LES (Large Eddy Simulation) would provide more accurate results but with a considerably  
Figure 7: Power coefficients against TSR for Fibonacci I, Fibonacci II, and Savonius configurations. higher computational cost. CFD is not an exact science, and the mesh generation and discretization processes induce inevitable numerical errors. Another source of error in the numerical model is the length of the domain. A larger length should provide a better characterization of the wake behind the turbine. Despite the discrepancies between numerical and experimental results, both procedures demonstrate the superiority of Fibonacci over Savonius, which is the goal of the present work. Figure 8 shows the power coefficient as a function of the azimuth angle for several TSR values. This figure was obtained through the CFD model.