## 5 Conclusions  
In this research, the optimal proportions of the secondary element of a multi-element geometry in a Savonius rotor with a split Bach type blade profile without an intermediate shaft were numerically determined. The results showed that every factor analyzed had a statistically significant effect on the power coefficient in the experimental domain studied. Likewise, it was observed that there is a great interaction between the factors that determine the distance between the elements of the blade. The optimal dimensions obtained for said profile are 96.81, 17.43, and 9.4 in percentage values of the rotor diameter, for the parameters \(O\), \(P\), and \(Q\), respectively.  
Although the full factorial experimental design had greater acceptance within the purposes of this research, the face-centered central composite design allowed the rotor performance to be modeled with great adjustment, saving a third of the number of treatments.  
The conventional semicircular profile rotor established as a reference, presented a \(C_{P}\) of 0.195 in a flow close to a Reynolds number of \(6\times 10^{4}\) and a blockage ratio of 2%. Likewise, the geometry with the split Bach type profile without secondary elements allows reaching a \(C_{P}\) of 0.2661. In turn, the rotor with the multi-element profile optimized using the response surface methodology presented a \(C_{P}\) of 0.2948, under the same conditions, which represents an increase of 51.2% and 10.8% in performance, respectively.  
It was determined that the secondary element favors the performance during much of the advancing phase of the blade, when it receives the flow directly. In the last part of this phase and in the first half of the returning phase, a loss in performance is generated mainly due to the greater resistance that the additional surface implies. During the second half of the returning phase, there are no significant differences, which may be due to a slight increase in performance that allows to counteract the additional resistance.  
Figure 25: Velocity contour graphs for the split Bach profile (**left**) and the multi-blade Bach profile (**right**) at a rotor azimuth angle (\(\theta\)) of 185\({}^{\circ}\) and a \(TSR\) of 1.0996.  
Likewise, the rotors with conventional semicircular, split Bach, and multi-blade Bach profiles were experimentally studied using a wind tunnel under the same conditions established in the simulations. The numerical results used for verification were obtained from the simulation of computational replicas from the experimental setup of each rotor, considering the three-dimensionality and the degrees of freedom of the system. The difference between the results of the multi-blade Bach profile and the split Bach profile was found to be approximately half the difference between the latter and the conventional semicircular profile, both in the numerical and experimental approach.  
Conceptualization, L.A.G.; methodology, L.A.G. and F.A.O.; software, L.A.G. and F.A.O.; investigation, L.A.G.; resources, F.A.O.; data curation, E.L.C. and E.G.F.; writing--original draft preparation, L.A.G.; writing--review and editing, L.A.G., E.L.C. and E.G.F.; supervision, E.L.C. and E.G.F.; project administration, E.G.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.  
The authors gratefully acknowledge the financial support provided by the Colombia Scientific Program within the framework of the call Ecosistema Cientifico (Contract number FP44842-218-2018).  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} FFD & full factorial experimental design \\ FCC & face-centered central composite design \\ TSR & tip speed ratio \\ PWM & pulse width modulation \\ MAMSL & meters above mean sea Level \\
6-DOF & six degrees of freedom \\ \end{tabular}