Review of Speciﬁc Performance Parameters of Vertical Wind Turbine Rotors Based on the SAVONIUS Type

: Increasing energy demand and environmental regulations around the world provide an adequate framework for developing methods of obtaining energy from renewable sources. Wind force is a resource with a high potential through which green energy can be obtained with no negative impact on the environment. Different turbine typologies have been developed, which can convert the wind force into mechanical and electrical energy through turbine rotational motion. Starting from the classic vertical-axis SAVONIUS rotor model, other models have been designed, which, according to the numerical studies and experimental test results, show higher performance parameters in operation. Such models present speciﬁc rotor blade geometries to achieve better operational results in terms of shaft torque and generated power. There are multiple research results from numerical analysis on virtual models or experimental tests that use rotor models in different constructive conﬁgurations aiming to improve operation performance. These research activities are related to the rotor blade number, the aspect and overlap ratio values, the blade proﬁle geometry modiﬁcation, the use of end plates connected to the rotor blades, curtain mounting solutions for directing the air ﬂow on the active blade alone, and rotor constructive variants with deformable blades during operation. Some of the results obtained from the mentioned research activities are shown in this review for special rotor conﬁgurations whose performance results in terms of torque or power values are compared to the classical SAVONIUS model.


Introduction
Wind power has been used since ancient times by humans to obtain mechanical energy, but today wind energy is used to provide electricity where there are favorable conditions for power plant installation. The operation principle of these energy conversion plants is based on the rotor, with blades capable to take over the atmospheric air flow rates at a certain height level.
The horizontal-axis wind turbine (HAWT) with rotors operating on the lift type model offers better performance results in terms of torque and power. The vertical-axis wind turbine (VAWT) with drag-type rotor models provides lower performance values, but they benefit from constructive cost advantages, an easy starting possibility, and operation at lower wind velocities [1][2][3][4].
The SAVONIUS rotor type represents a simple constructive variant that can be achieved with low costs, characterized by lower power coefficient (CP) values compared to horizontal-axis rotor types [5][6][7][8]. By comparison, the horizontal-axis turbine's rotor reaches 45% CP values, and the DARRIEUS vertical-axis rotor type reaches CP values up to 35%, whereas the classical SAVONIUS rotor with a 15% CP is located far behind but can compensate with other features related to its simple construction, low production cost, independence of wind direction, as well as good starting torque at low wind velocity values [9][10][11][12][13][14].

The Betz Limit Considered for the Wind Turbine Operation
Specific performance parameters in terms of the torque coefficient (CT) or the power coefficient evaluate wind turbine operation. The maximum power coefficient values that can be obtained by a wind turbine were identified based on the wind velocity values considered before (upstream) and after the rotor blade area (downstream). The wind velocity after passing the turbine rotor is considered much lower, and in ideal conditions it should be at one third of the initial velocity. Decreasing the air circulation velocity would lead to a limitation of the turbine rotor efficiency due to the air flow braking, which continues to move after passing the turbine rotor. The air viscosity and pressure losses at the blade level as well as the turbulences created by the rotor blades were also considered. The wind turbine's maximum efficiency value theory was presented by the German engineer Albert Betz in 1919 and is applicable to both horizontal-and vertical-axis turbines.
Energies 2021, 14, 1962 3 of 23 In Figure 1, the rotor and air enclosure are schematically presented with the diagram of upstream and downstream velocity modification [60]. The ideal wind turbine model that is placed within the air stream path, as shown in Figure 1, was considered. The turbine rotor area is S, and the air speed is v [60].
The maximum power value that can be converted from the air current with the help of a turbine rotor is the ratio 16 27 = 0.5925 = 59.25 % , which is the Betz limit or the Betz coefficient. Power values are obtained according to the rotor diameter square and the air circulation velocity cube. Under normal conditions, in which the losses inevitably occur in the turbine rotor operation, it is considered that 35-40% of the total available wind power is converted by the wind turbine rotor. It should be emphasized that any turbine rotor that is placed in the air stream path tends to change the downstream speed values, which means converting the wind energy to a certain value given by its constructive and functional principle. The maximum percentage energy conversion would mean stopping the air flow or zero downstream speed, which is not possible [60].

Constructive and Functional Parameters of the Vertical-Axis Rotor Model
The SAVONIUS rotor constructive solution has two or more blades positioned along the central axis to take over part of the main air stream in which they are positioned. There are many blade types with different section shapes placed at a different distance from the rotor central axis, known as the blade gap. Figure 2 presents the principal design parameters for the SAVONIUS rotor model [61][62][63][64][65].   Rotor height (H r ) 3.
Rotor area A r = D r · H r 4.
End plate diameter D p
Blade gap b g 8.
Aspect ratio a = H r D r

9.
Overlap ratio The functional parameters are represented by the total available wind power, (N W ), the angular velocity provided at the rotor shaft, (ω r ), the ratio between the wind speed and the blade ration speed, (TSR), the rotor torque, (T r ), the air pressure coefficient (CP), the torque coefficient, and the power coefficient corresponding to each constructive type of turbine rotor used. Table 2 presents these functional parameters characteristic of any type of turbine rotor with a vertical-axis as well as the characteristic relation for each parameter [61][62][63][64][65]. Table 2. Functional parameters for vertical-axis wind turbine rotors [61][62][63][64][65].
Pressure coefficient

6.
Torque coefficient The power coefficient as it is presented by Ragheb M et al. is defined as the ratio between the amount of power converted by the wind turbine rotor (P t ) relative to the available power within the air stream (P a ) [61][62][63][64][65].

The Influence of Blade Number on Rotor Performance
The rotor blade number has an influence in obtaining the specific performance parameters at different wind speeds. Regarding the optimum rotor blade number, numerous studies have been made, and their results indicate that the two-blade rotor has the best values in terms of torque and power coefficients compared to the three-blade rotor, as shown by the results obtained by M. Ali who performed wind tunnel experiments on rotor models in different blade number configurations [66].
The obtained results for the two rotor models with two and three blades in terms of torque and power coefficients depending on the TSR are presented. The wind velocity values inside the wind tunnel were measured in the range of 2-6 m/s. The blades of semicircular shape with a diameter of 100 mm and a height of 200 mm were mounted in a configuration of two and three blades, being fixed with end plates at both ends with a diameter of 210 mm and a thickness of 1.59 mm [66].
The torque and power coefficient results are presented in Figures 3 and 4.   Comparable results regarding the SAVONIUS rotor performance have also been presented by U.K Saha et al. They studied the rotor behavior with two and three blades of semicircular and elliptical shapes at different air velocities (6-11 m/s) within the wind tunnel to highlight the differences in operation. The values obtained are presented in terms of CP for rotor models in single, double, and triple configurations of the rotor ( Figure 5) [67][68][69][70][71].  The obtained results are presented in Table 3 for each analyzed case. Additionally, with the idea of optimizing the rotor performance, U.K Saha et al. presented a solution to improve the initial configuration of the experimentally tested model by including valves at the rotor blades that allow air flow on the idle blade, with the aim of reducing negative torque values. This system was tested on the three-blade rotor model, and the results indicate an increase in CP just above the level recorded by the two-blade  Table 4. The performance of the single and double stage rotor was also studied by Mahmoud et al., and experiments were performed on the two-blade rotor with an overlap ratio of 0. The obtained results emphasize the specific power values at the rotor blade depending on the wind velocity ( Figure 6) [72]. Rotor models with different numbers of blades were also analyzed by Wenehenubun et al. who carried out experimental research on SAVONIUS rotor models with two, three, and four blades ( Figure 7) built with an overlap ratio of 0.15, an aspect ratio of 1, and end plates whose diameter exceeded the rotor blades' diameter by 10% [73]. The rotor diameter and height were 370 mm, and the blades' thickness was 2 mm. The experiments were performed in the wind tunnel with wind speeds in the range of 1-10 m/s. According to the experimental results obtained, the four-blade rotor had the highest CP value at a TSR of 0.37 or wind speed of 6 m/s. After this value, the four-blade rotor had a decreasing rotational speed, which affected its energy efficiency. The three-blade rotor had better performance than the four-blade rotor at wind speeds between 7 and 10 m/s, an interval in which it recorded better power values than the analyzed models [73].

Aspect Ratio Effect on Rotor Performance
The SAVONIUS rotor performance is significantly influenced by the ratio between the rotor height and the diameter or aspect ratio. Experimental results obtained from testing rotor models with different aspect ratio values are presented.
Mahmoud et al. experimentally tested rotor models with different geometries in terms of aspect ratio with values of 0.5, 1, 2, 4, and 5, with and without end plates mounted. The experiments were performed in a wind tunnel with a diameter of 49 cm at air speeds in the range of 0-13 m/s measured at the tunnel exit. The rotor blades were made of plastic (PVC) with diameters of 0.08, 0.1, 0.2, and 0.3 m, and the attached end plates were made of 2.5 mm thick wood with a 10% larger diameter than the rotor diameter [72]. The presented experimental results obtained for different rotor aspect ratios showed an increase in CP values with increasing aspect ratio values ( Figure 8).

Effects of Using the End Plates Attached to the Rotor
The experiments carried out by Mahmoud et al. also aimed at the effect given by the end plates mounted on the wind turbine's rotor. The results obtained are better in terms of the CP for the rotor with mounted end plates, justified by the fact that the end plates' presence has the role of increasing the air volume that presses directly on the active rotor blade ( Figure 9) [72].  The obtained results are presented for the rotor with two blades in the version with end plates and without end plates. The differences were obvious in terms of the mechanical power recorded at the rotor shaft depending on different values of air flow used in the experiment.

Overlap Ratio Effect on Rotor Performance
In the operation of the SAVONIUS vertical-axis turbine rotor, the overlap ratio is a parameter that has an influence on the rotor's operating performance values, according to the experimental results obtained by various researchers. The overlap ratio is a parameter expressed according to the value of the blade diameter, the diameter of the rotor shaft, as well as the distance of the blade placement within the rotor.

Blade Profile Optimization for Improved Performance in Operation
Starting from the classic SAVONIUS model, whose blades are of semicircular profile, many research activities have been carried out to obtain improved performance values for different innovative blade profile concepts. Such experimental activities were performed by Roy and Saha [68][69][70][71], who analyzed the SAVONIUS model with semicircular blades, a model with semi-elliptical blades, the Benesh model [74][75][76][77][78][79][80][81], the modified Bach model [82][83][84], as well as a newly proposed variant with the idea of comparing the results obtained by each rotor model separately. The schematic presentation of the analyzed rotor models is presented in Figure 11. The experiments were performed for several values of the Reynolds number (Re) in the range of Re = 6 × 10 4 ÷ 1.5 × 10 5 , starting with a wind velocity value of 6 m/s to determine the torque, power, and static torque coefficients at the analyzed rotor model level.
The results show the specific values recorded, highlighting the functional characteristics for each type of rotor. The best results were obtained by the rotor model proposed by Roy and Saha, which obtained the best values in terms of the power coefficient at different tip speed ratio values as a function of the Reynolds number ( Figure 12). It was followed by the Bach modified model and the Benesh model.  Figure 13) [85]. The results showed that for the slots positioned near the blade root the rotor had better performance at low tip speed ratios and offered a higher starting torque value ( Figure 13). Figure 13. The slotted rotor model analyzed [85].
The special profile with slotted blades can provide operation performance improvement compared with the classical blade profile in a standard configuration registered at a low rotational motion ( Figure 14).

Rotor Performance Improvement Using Curtaining Method
Altan et al. brought performance improvements by modifying the rotor assembly, which was materialized by adding a curtain that aims to close the area corresponding to the inactive blade to avoid the negative torque that acts towards stopping the rotor in operation ( Figure 15) [86]. The rotor of different curtain placement configurations was tested in the wind tunnel and the performances were compared to those of a conventional rotor. Based on the obtained results, the power coefficient increased by approximately 38.5% because of the optimal installation of the rotor curtain, corresponding to the angles α = 45 • ; β = 15 • (Figure 15) [86]. The curtain installation ensures the best rotor performance values only in case of lower wind speeds, and, for the experimental results, this was highlighted at wind values of 7 m/s Re = 1.5 · 10 5 . For higher wind speeds of 10 to 13 m/s, no improved values in the rotor's energy performance were recorded. The CP value of 38% represents an optimized value, and, for the same rotor type (classic SAVONIUS) without a curtain, the CP value of 16% was obtained. Thus, the curtain's role for obtaining higher CP values justified by airflow capture area enhancement was approximately two times higher than in the classic rotor construction. This offers the active rotor blade the possibility to receive considerably higher air flow rates, thus obtaining improved pressure values on the active rotor blade.
The experimental research was initially performed on the rotor model without a curtain, then three types of curtains were tested with walls of a small length (curtain one), an intermediate length (curtain two), and the longest length (curtain three). The obtained results highlight the advantage of using curtains to direct the air flow rates on the active blade, through the higher power coefficient values obtained ( Figure 16) [86].

The Performance of an Ice Wind Turbine Rotor Compared to the Classic SAVONIUS Model
An innovative rotor model was presented by a startup in Iceland in 2012. It represents a SAVONIUS -type rotor model modified in terms of blade geometry ( Figure 17). Figure 17. The Ice Wind rotor assembly and geometry for three and four blades [87,88]. Research on this model had been started to establish the efficiency of this innovative geometric shape rotor type. Using numerical methods, Aymane et al. showed that the three-blade Ice Wind rotor achieves better results in terms of shaft torque, depending on the rotor blades' orientation. Thus, for the ice wind rotor with a blade orientation of 30 degrees, a value of 0.035 Nm was registered, whereas for the classic SAVONIUS model, a value of 0.012 Nm was obtained for 5 m/s wind velocity [87,88]. Analyzing the second position of the rotor (90 degrees), the results were 0.34 Nm for the ice wind rotor and 0.15 for the classic SAVONIUS model. Figure 18 presents the angular rotor positions according to wind direction. Figure 18. The Ice Wind rotor best fit the configuration for CFD analysis [87,88].
Going further to experimental testing in the wind tunnel, the ice wind model and the SAVONIUS Classic model were analyzed. Aspects related to the construction of the two rotor models are presented with the observation that the ice wind model was easier to achieve than the SAVONIUS model. The final weight of the two experimental models was 1035.55 g for the ice wind model and 936.6 g for the SAVONIUS model. The tests were performed at wind speeds of 2, 3, and 4 m/s, and the results are presented in terms of torque values (Table 5) [87]. The results obtained show that the ice wind rotor model generated 19% more torque compared to the classic SAVONIUS model for the same material type and the same blade surface area [87]. Based on the torque values (Figure 19), the power coefficient values of the two rotor models can be calculated according to the wind speed. Calculations were made for hypothetical aluminum rotor models and models used in the experiment. The CP values corresponding to the rotor models with aluminum blades are presented in Table 6, while the graphical representation is shown in Figure 20.  The average power coefficient values were 34.26% for ice wind rotor and 26.68% for the classic SAVONIUS rotor [87]. For the rotor models used in the experiment, the  Table 7, and the graphical diagram is presented in Figure 21.  The average power coefficient values were 34.26% for ice wind rotor and 26.68 the classic SAVONIUS rotor [87]. For the rotor models used in the experiment, the p coefficient values are presented in Table 7, and the graphical diagram is present Figure 21.  The average power coefficient values were 0.44% for the ice wind model and 0 for the classic SAVONIUS model [87]. There were obvious large differences betwee hypothetical aluminum models and those used in the experiment, which induces the of inaccuracy in obtained results. The CP ratio is what is interesting in this case, and the authors concluded that the ice wind model was 28.4% more efficient than the c SAVONIUS model for the same type of material and the same blade surface area.
The results obtained by Mansour et al. from numerical analyses performed ANSYS Fluent on 3D models of the ice wind and the classic SAVONIUS rotor highlight the better values obtained by the ice wind model at higher wind speeds The average power coefficient values were 0.44% for the ice wind model and 0.34% for the classic SAVONIUS model [87]. There were obvious large differences between the hypothetical aluminum models and those used in the experiment, which induces the idea of inaccuracy in obtained results. The CP ratio is what is interesting in this case, and here the authors concluded that the ice wind model was 28.4% more efficient than the classic SAVONIUS model for the same type of material and the same blade surface area.
The results obtained by Mansour et al. from numerical analyses performed with AN-SYS Fluent on 3D models of the ice wind and the classic SAVONIUS rotor also highlight the better values obtained by the ice wind model at higher wind speeds (15.8 m/s), obtaining static torque values of 0.055 (ice wind rotor) and 0.052 (SAVONIUS rotor) [87].

Performance Aspects of a Deformable Blade Turbine Rotor Model
An innovative perspective regarding the rotor construction solution, which introduces a blade-variable geometry during operation, has been presented by Sobczak et al. [89]. The turbine model was based on the SAVONIUS concept with blade-variable geometry ( Figure 22). The rotor blades made of elastic material were continuously deformed during the rotor revolution to increase the advancing blade positive torque and to decrease the returning blade negative torque value. By means of numerical analyses performed on a virtual model, the power coefficient values recorded for the maximum values of the blade deformation during rotor operation are presented. Numerical analysis on the virtual rotor model shows the results in terms of a power coefficient value over 0.30 registered for the 10% eccentricity magnitude and 0.39 for the highest magnitude value. The obtained results correspond to a 90% improvement in comparison to a 0.21 CP for the classical SAVONIUS profile [89]. The main rotor movement angular positions and blade deformation in relation to wind direction and eccentricity are shown in Figure 23.  The optimal eccentricity position was the 105-degree area for all eccentricity values. The obtained power coefficient values for both rotor model types are presented in Table 8. The obtained values provide an increase of 37%, 66%, and 90% compared with the classical SAVONIUS model. The disadvantages of misaligning the rotor eccentricity were also highlighted. For this rotor model, a mechanism for positioning the rotor in relation to the wind direction action must be considered as the key factor in the optimal operation of this rotor type.
A special rotor blade configuration method is meant to increase the rotor efficiency by adjusting the blade radius being obtained with an increase in rotor efficiency by about 18% according to the results obtained by 2D numerical analysis [90,91].
The air circulation velocity was the key parameter in the operation of these devices and must be considered with the upstream, inside, and downstream conditions to obtain optimum performance results. Thus, the numerical studies performed highlight the main flow patterns in the rotor vicinity area meant to establish exactly the working conditions in which this type of rotor must operate [92][93][94][95][96]. A novel model of wind turbine was presented by Doerffer et al. with a constructive solution involving twin rotors showing an efficiency of above 20% corresponding to wind velocity [97]. Following the operating performance increase, the twisted blade rotor model was analyzed, and the results show an improved performance of 20-25% at the optimal TSR compared to the conventional SAVONIUS rotor [98,99].
Regarding the placement of wind turbines with the SAVONIUS improved rotor, the possibilities of mounting on the structure of buildings was analyzed to capitalize the existing air stream at a certain elevation. Most studies revealed that the air stream behavior around a building at the upper edge is of great wind energy potential. The effect is even more intense when the building is taller and when the wind direction is perpendicular to the building facade. For example, in a five-story building, the wind velocity increases by 1.2 times at the windward edge. The wind velocity increment at the building edge is ranged between 10-30%, while the turbulence intensity increases considerably. This fact is not an inconvenience for SAVONIUS turbines, since it has been demonstrated that, at increased turbulence, the separation of the boundary layer takes place on the lower side of the rotor-returning blade, thereby reducing the negative torque.
High turbulent flow areas create more frequent and stronger air stream fluctuations, but, because of a long SAVONIUS rotor (high aspect ratio), the inertial rotation can be maintained for the turbine without relevant variations. Additionally, it has been demonstrated that, because of blade tips, aerodynamic losses are reduced in SAVONIUS turbines with high aspect ratios [100].
For the building edge mounting position of the turbine, the wind angle has been emphasized as the most significant parameter influencing rotor performance. Smaller turbine gap values also improve turbine performance [101].

Conclusions
Starting from the SAVONIUS rotor model, multiple improvements have been made over time that ensure an efficient operation of the latest generation of rotor models with performance values that can be considered for energy production based on wind force in smaller units of low power.
The analysis of the experimental results obtained by various research teams in the last period highlights the characteristics that an innovative rotor model can have, built in terms of the knowledge acquired from the obtained results.
The main features that should be considered are related to the fact that: • the two-blade rotor has the best values in terms of coefficients of torque and power, compared to the three-blade rotor; • good results in terms of the power coefficient were registered by a rotor with four blades (0.37 CP) but for wind velocities of 6 m/s. After this value, the rotational speed was reduced, which affects its energy efficiency; • regarding the rotor constructive configuration, better results in terms of the power coefficient were obtained by the double rotor having the semicircular blade profile (0.29 CP) and the twisted angle (12.5 degrees) blade profile with 0.31 CP. The double rotor with valves added presented CP values of 0.31 for the semicircular blade profile and 0.32 for the twisted angle blade profile; • regarding the rotor aspect ratio based on the experimental obtained results, it is clear that there is an increase in the CP for higher aspect ratio values; • better results are obtained in terms of the CP from the experimental work for twobladed rotors with mounted end plates, ensuring the effect of increasing the air volume acting directly on the rotor active blade; • the overlap ratio also influenced rotor performance based on the obtained results, highlighting the better power values obtained for tested rotor models with a lower overlap ratio; • regarding the blade profile, the obtained results from the experiments made by Roy and Saha found that an innovative blade profile obtained better power coefficient values compared with the Bach modified profile, the Benesh profile, the semi-elliptic model, and the SAVONIUS model; • a curtain construction solution, which added a curtain to the rotor assembly, gave an improvement in rotor performance. With this solution, the rotor acquired an improvement in the power coefficient up to 38.5% for optimal installation and a wind velocity of 7 m/s. This curtain solution can be used for wind velocities up to 13 m/s. After this value, the performance parameter improvement is no longer available.
• the improved rotor geometry of the ice wind type offered improved behavior in terms of the static torque and the power coefficient compared to the classic SAVO-NIUS model. • an innovative rotor model with deformable blades proposed by Sobczak et al. showed improved performance values in terms of the power coefficient, which exceeded 0.3 and almost reached 0.4 for the highest eccentricity position. This concept needs an additional mechanism for blade deformation and wind direction positioning, which can consume a part of the turbine-provided energy; • the use of SAVONIUS -type turbines may be applicable to buildings located within urban areas to convert wind energy.