Investigation of Performance Enhancements of Savonius Wind Turbines through Additional Designs

Abstract

This study examines the literature on improving the low performance of Savonius wind turbines, which are a type of vertical axis wind turbine. The literature studies on improving the performance of Savonius turbines have been summarized into two categories: interior structural design and exterior additional design. Due to the extensive nature of studies focusing on interior design changes, this research primarily focuses on performance studies related to exterior design modifications of Savonius wind turbines, particularly in recent years. This study aimed to provide a comprehensive examination of these performance studies and contribute to the existing literature by presenting a systematic reference on this issue. To achieve this objective, a thorough review of turbine exterior design studies has been conducted. The focus was on determining the percentage increase in power coefficient achieved by turbines with exterior design modifications compared to the classical turbine versions. Here, it has been determined that the power coefficient values of Savonius wind turbines can reach approximately 0.400 through interior design changes. However, with the implementation of additional exterior design modifications, these power coefficient values can be further increased to around 0.520. Thus, within the scope of this study, it has been determined that the turbine power coefficients show a fairly good increase with exterior design techniques compared to interior design techniques.

1. Introduction

To harness the potential of wind energy, which is a clean energy source, and meet the growing energy demands, extensive research has been conducted and continues to be pursued in the field of wind turbines [1,2,3]. Wind turbines are divided into two main classes according to the axis of rotation: horizontal-axis and vertical-axis wind turbines. The Savonius type wind turbine is also one of the vertical-axis wind turbine types. The Savonius wind turbines have lower performance than horizontal-axis wind turbines. However, due to their lower cost and simpler construction compared to horizontal axis wind turbines, Savonius wind turbines have a much lower cost and simpler construction than horizontal axis wind turbines are particularly suitable for meeting personal energy needs in both rural and urban areas.

Savonius wind turbines have a simple shape obtained by cutting a cylinder in half in the middle and shifting its axes symmetrically, as shown in Figure 1. As can be seen in the figure, one part of the cylinder forms the concave blade, and the other part forms the convex blade. Since the torque on the concave blade is greater than the torque on the convex blade, the turbine starts to rotate in the direction of the incoming wind. Since Savonius wind turbines can receive wind from all directions during operation, there is also no need for an additional system to rotate the Savonius wind turbines against the wind.

Due to the fact that the turbine blades of the vertical axis Savonius wind turbine produce both negative and positive torque during operation, they have a lower power coefficient (C_p) than the horizontal axis turbines. Given the advantages of Savonius wind turbines, such as low cost and simple construction, there has been ongoing development and innovation in order to enhance their low power coefficients. Numerous innovative designs have been and continue to be developed to maximize the potential benefits of these turbines [4,5,6,7]. In this study, these innovative designs have been collected in two main design groups: interior designs containing structural design changes on the Savonius wind turbine and exterior designs containing assemblies or modifications added to the outside of the turbine without any changes in the structure of the classical Savonius wind turbine. As shown in Figure 2, the regions where these design modifications or changes are made are called the interior design and exterior design regions. Within the scope of this study, the design changes in the interior and exterior design regions of the Savonius wind turbine have been taken separately.

In the interior designs of Savonius wind turbines, structural design changes within the turbine structure, such as the turbine blade shape, number of blades, blade overlap ratio, blade end plate, and number of stages, are discussed. In the exterior design of Savonius wind turbines, additional external modifications have been handled without making any structural changes within the turbine, thereby preserving its classical form. The basic steps of this study are shown in Figure 3. In this context, Savonius wind turbines and basic aerodynamic equations have been introduced. The obtained literature studies have been examined by classifying them as interior and exterior design. The aerodynamic performance data obtained from these studies have been compared and evaluated [8].

In this study, the effects of interior and exterior design changes made in Savonius wind turbines on turbine performances have been examined comparatively. Given the extensive literature on performance studies obtained through interior design changes, this study focuses primarily on the comprehensive coverage of performance studies related to exterior design modifications of Savonius wind turbines. This is particularly important considering the recent advancements in this field. Thus, the studies conducted to improve the low performance of the Savonius wind turbine have been examined, and they have been aimed at contributing to the literature by providing a systematic reference within the scope of this topic.

2. Designs and Method

The first theoretical study on wind turbines was conducted by Albert Betz in 1919 [9]. The Betz limit is the maximum theoretical efficiency that can be achieved by a wind turbine. Here, the wind turbine is considered ideal. This ideal wind turbine model is placed in a moving atmosphere. Assuming that air is incompressible, the continuity condition can be written as in Equation (1).

$$A_1{V}_1=AV=A_2{V}_2$$

(1)

where $V_1$ is the wind speed at a considerable distance upwind, where it is not affected by the turbine. $V_2$ is the wind speed far from the turbine, downwind. $A_1$ is the upstream air flow cross-sectional area in front of the turbine of the air flow passing through the rotor, and $A_2$ is the downstream air flow cross-sectional area. $V$ is the wind speed actually passing through the turbine and assumed to be uniform over the whole area A swept by the blades. The force exerted on the wind turbine by the wind is given by Euler’s theorem in Equation (2).

$$F=\rho AV\left(V_1-V_2\right)$$

(2)

where $\rho$ is the density of the air. Thus, the power absorbed by the turbine blades is given in Equation (3).

$$P=FV=\rho A{V}^2\left(V_1-V_2\right)$$

(3)

This energy is taken from the kinetic energy of the wind. The variation of the kinetic energy from upstream to downstream is given in Equation (4).

$$\mathsf{\Delta }ke=\frac{1}{2}\rho AV\left(V_1^2-V_2^2\right)$$

(4)

By equalizing the expressions P and $\mathsf{\Delta }ke$, the ideal turbine speed is determined, and the ideal turbine power is found as in Equation (5).

$$P_{ideal}=\frac{8}{27}\rho A{V}_1^3$$

(5)

The maximum power value that can be converted from the air flow with the help of a turbine is found by the ratio value given in Equation (6).

$$\frac{P_{ideal}}{k{e}_{air}}=\frac{16}{27}=0.5926$$

(6)

The theoretical maximum efficiency value for wind turbines, known as the Betz limit, is calculated at 59.26%. In real-world applications, the actual efficiency of wind turbines is far below the Betz limit. This is particularly true when the system efficiency of components such as wind turbine gears, generators, and power transmission systems is considered. The performance of wind turbines is determined by their torque and power coefficients. The torque coefficient (C_t) is determined by the ratio of the torque obtained from the turbine to the torque obtained by the wind. The power coefficient (C_p) is determined by the ratio of the power obtained from the turbine to the power obtained by the wind.

2.1. Savonius Wind Turbine Aerodynamics

Figure 4 shows the dimensions of the classical Savonius wind turbine. As seen in the figure, d is the turbine blade diameter, e is the overlap distance, and D is the turbine diameter.

Figure 5 shows the wind forces and velocity vectors on the blades of the Savonius wind turbine. In a situation where the wind speed is V and the turbine blade speed is v, the power and performance values occurring in the Savonius wind turbine are found from the forces generated on the blade [10].

The force occurring on the turbine blade is expressed by Equation (7).

$$F=\frac{1}{2}c\rho A{V}^2$$

(7)

where $\rho$ is the density of the air, c is the drag coefficient, and A is the projection swept area of the turbine. The value of the swept area A is expressed in Equation (8). Here, H is the turbine height.

$$A=DH=\left(2d-e\right)H$$

(8)

Turbine power is equal to the product of the aerodynamic force generated on the blades and the speed. The force on the blade rotating in the direction of the wind $\left(V-v\right)$ and the force on the blade rotating against the wind direction occur under the influence of $\left(V+v\right)$. The forces on the concave and convex surfaces of the turbine are expressed by Equations (9) and (10), where $c_1$ is the drag coefficient of the concave surface and $c_2$ is the convex surface [11].

$$P^{+}=\frac{1}{2}\rho A\left[c_1{\left(V-v\right)}^2\right]v$$

(9)

$$P^{-}=\frac{1}{2}\rho A\left[c_2{\left(V+v\right)}^2\right]v$$

(10)

The total power of the turbine is transformed into a relation as in Equation (12) by using Equation (11).

$$P_T=P^{+}-P^{-}$$

(11)

$$P_T=\frac{1}{2}\rho Av\left[B{V}^2-G2Vv+B{v}^2\right]$$

(12)

where $B=\left(c_1-c_2\right)$ and $G=\left(c_1+c_2\right)$. To obtain optimum power under a constant wind speed, the derivative taken with respect to the blade speed $v$ must be equal to zero. Accordingly, $v$ turbine speed is found as in Equation (13).

$$v_{1,2}=\frac{2GV\pm V\sqrt{4G^2-3B^2}}{3B}$$

(13)

The power is optimal when the convex surface has the least effect on the rotation of the Savonius wind turbine. This situation can be created by directing the wind coming to the turbine only to the concave blade in the exterior designs of Savonius wind turbines. Therefore, $c_2=0$ should be taken. Then $B=c_1-c_2$ becomes $B=c_1$ and $G=c_1+c_2$ becomes $G=c_1$. Accordingly, if the $B$ and $G$ coefficients are replaced in Equation (7) and the equation is rearranged, the optimum speeds of the turbine are obtained as ${\nu }_1=\frac{1}{3}V, {\nu }_2=V$. For ${\nu }_2=V$, the turbine must rotate at the same speed as the wind speed, and power cannot be produced in this case. Therefore, $v_{opt}=v_1=\frac{1}{3}V$ for optimum turbine power. Thus, the optimum total turbine power is obtained as in Equation (14).

$$P_T=\frac{2}{27}\rho A{c}_1{V}^3$$

(14)

In Savonius wind turbines without exterior design, both the drag coefficients $c_1$ and $c_2$ are considered. For example, if $c_1=3c_2$ is taken, $B=2c_2$ and $G=4c_2.$ Accordingly, if the $B$ and $G$ coefficients are substituted in Equation (13), the optimum speed of the turbine will be approximately $v_{opt}=\frac{1}{6}V$. The power coefficient of the Savonius wind turbine is calculated in Equation (15).

$$C_p=\frac{P_T}{P_W}$$

(15)

where $P_W$ is the power from the wind. Additionally, $P_W=\frac{1}{2}\rho A{V}^3$.

The performance of a Savonius turbine can be calculated using the power coefficient, as defined in Equation (16), when the torque produced in the turbine and the angular velocity of the turbine are known. The tip speed ratio (λ) given in Equation (17) is used to calculate the tip speed ratio of the turbine. Here, T: torque, U: turbine tip speed, and ω: angular velocity.

$$C_p=\frac{2T\omega }{\rho A{V}^3}$$

(16)

$$\lambda =\frac{U}{V}=\frac{\omega D}{2V}$$

(17)

In the literature, the performance status of the Savonius wind turbine has been examined through two main groups of studies. One group focuses on making structural design changes to the turbine itself, while the other group explores the performance status by incorporating external designs around the turbine while still maintaining the turbine’s original design. The power coefficients indicating the turbine performances as reflected by the data reported in those studies have been compared with each other. At the same time, the percentages of increase in power coefficients obtained with interior and exterior design models have been determined and compared with those of classical versions with two blades.

2.2. Exterior Design Studies

In general, the aim of the external design studies is to enhance the performance of the turbine by increasing the positive torque and reducing the negative torque. This is achieved through the implementation of various exterior design assemblies. In particular, external design (e.d.) changes implemented on the outside of the turbine without any structural changes to the classical Savonius wind turbine structure have been discussed in the present study [4,5]. In general, the effects of changing the geometrical parameters of external designs on turbine performance have been examined. The maximum power coefficients with optimized geometric parameters of external designs have been determined. Thus, the effects of external design changes alone on turbine performance have been analyzed.

The maximum power coefficient values of the two-bladed classical Savonius wind turbines, which have been carried out in the literature in recent years with and without external design, are given in

Table 1. (a) Power coefficient values of two-bladed Savonius wind turbines with and without exterior design (e.d.). (b) Power coefficient values of two-bladed Savonius wind turbines with and without exterior design (e.d.).

(a)
E.d. No	Reference	Study Type	Exterior Design Name	Cp without e.d.	Cp with e.d.	Exterior Design
1	Irabu and Roy [4]	Experimental	Guide-box tunnel	0.225	0.276
2	Deda Altan et al. [5]	Experimental	Curtain arrangement	0.160	0.380
3	Mohamed et al. [19]	Validated numerical Optimization	Shielding obstacle	0.170	0.258
4	Tartuferi et al. [20]	Experimental Numerical	Conveyor-deflector curtain system	0.250	0.300
5	El-Askary et al. [21]	Validated numerical	Guide plates design	0.190	0.520
6	Kalluvila and Sreejith [22]	Experimental Numerical	Guide blade arrangement	0.180	0.280
7	Mohammadi et al. [23]	Validated numerical	Nozzle design	0.130	0.363
8	Layeghmand et al. [25]	Validated numerical	Airfoil-shaped deflector	0.237	0.313
(b)
E.d. No	Reference	Study Type	Exterior Design Name	Cp without e.d.	Cp with e.d.	Exterior Design
9	Yuwono et al. [26]	Experimental	Circular cylinder	0.178	0.200
10	Nimvari et al. [27]	Validated numerical	Porous deflector	0.249	0.274
11	Yahya et al. [28]	Experimental	Guide vane	0.017	0.028
12	Hesami et al. [24]	Validated numerical	Wind-lens	0.167	0.210
13	Hesami et al. [24]	Validated numerical	Wind-lens (with a dual turbine)	0.167	0.358
14	Fatahian et al. [29]	Validated numerical	Nanofiber-based deflector	0.250	0.272
15	Marinic-Kragic et al. [30]	Validated numerical Optimization	Deflector blades	0.240	0.350
16	Tian et al. [31]	Validated numerical	Passive deflector	0.250	0.313

a,b. Considering that only one study [12] was available on this subject before the year 2000, the focus of the analysis was primarily on the studies conducted since the year 2000. Among these studies, Irabu and Roy [4] placed a guide-box tunnel assembly around the Savonius turbine to improve its output power. They experimentally determined the design configuration that provided the best performance by experimenting with different area ratios between the inlet and outlet of the guide-box tunnel assembly. Deda Altan et al. [5] designed a curtain assembly to improve the low performance levels of conventional Savonius wind turbines. They determined the turbine’s performance by conducting experimental tests with and without curtains. The curtain arrangement was designed specifically to prevent negative torque on the convex blade of the turbine. In addition, their study was supported by numerical analysis, and the findings were analyzed statically and dynamically in detail [13]. When further studies in this field were examined in the literature, it was also determined that other studies were conducted in line with this idea [14,15,16,17,18]. To improve the performance of Savonius turbines, Mohamed et al. [19] installed a shielding obstacle to eliminate the effect of negative torque on the rotating blade. They determined the best position and angle of this shielding obstacle for both two-blade and three-blade Savonius wind turbines by mathematical optimization in order to obtain the maximum power coefficient. Tartuferi et al. [20] improved the aerodynamic performance of Savonius wind turbines with a conveyor-deflector curtain system that is self-steered according to the wind direction. The device is self-oriented according to the wind direction due to the shape of the curtain system. El-Askary et al. [21] aimed to harvest wind energy to improve the performance of Savonius wind turbines. In line with that goal, they controlled the wind direction with a guide plate design. With the top plate of that guide plate design, the wind is directed to the concave side of the blade of the Savonius wind turbine, which is rotating downwind. Negative torque on the Savonius wind turbine is prevented by the center section of the guide plate design. With the bottom plate of the guide plate design, the wind is directed to the concave side of the upwind blade of the turbine. Thus, positive torque is generated on both blades of the turbine. In their experimental and numerical study, Kalluvila and Sreejith [22] focused on improving turbine efficiency by placing guide blade arrangements around a Savonius wind turbine. It was stated that with this peripherally placed assembly, the Savonius wind turbine could maintain its ability to receive incoming wind from all directions. Mohammadi et al. [23] placed a nozzle design in front of a vertical-axis Savonius wind turbine to improve its performance. With the nozzle design, they tried to direct the wind to the turbine blade rotating in the direction of the wind and prevent it from going to the turbine blade rotating against the wind. Hesami et al. [24] investigated variations in the low-power performance of single and twin Savonius wind turbines by accelerating the wind coming into the turbine with an external design called a wind lens. The optimum wind lens was determined by analyzing turbine performance values with different geometric parameters of the wind lens. Layeghmand et al. [25] proposed an airfoil-shaped deflector exterior design to be placed in front of Savonius wind turbines to improve performance. Yuwono et al. [26] experimentally investigated the effect of such a cylinder design on the performance of Savonius wind turbines by placing a circular cylinder in front of the turbine blade and rotating it against the wind coming into the turbine. In their study, Nimvari et al. [27] proposed a porous deflector in front of a classical Savonius wind turbine to improve its performance. This porous deflector was intended to improve turbine performance by minimizing the effects of the complex flow region behind the conventional non-porous solid deflector. Yahya et al. [28] placed an additional guide vane assembly around a Savonius wind turbine to improve low turbine performances. Fatahian et al. [29] placed a nanofiber-based deflector in front of a turbine to achieve the best performance of Savonius wind turbines. Marinic-Kragic et al. [30] used a certain number of fixed blade deflectors around a Savonius wind turbine to increase its efficiency. The number of blades in the fixed deflector was determined as a result of optimization according to power coefficient values as turbine performance indicators. Tian et al. [31] designed a passive deflector that can self-position according to the direction of the wind. The efficiency of the Savonius wind turbine was improved by the passive deflector’s ability to passively adjust its position with a change in wind direction. As seen in Table 1a,b, the power coefficients of Savonius wind turbines without exterior design have been obtained at different values between 0.016 and 0.250. It has been determined that these power coefficients have been increased in the range of 0.028 to 0.520 with the addition of exterior design without changing the Savonius wind turbines themselves. As seen from Table 1a,b, it has been determined that the best power coefficient with external design has been obtained with guide plate design number five.

Just as exterior designs have improved the performance of two-bladed Savonius wind turbines, exterior designs have also been developed to improve the performance of three-bladed Savonius wind turbines, and their effects have been investigated. The maximum power coefficient values of three-bladed Savonius wind turbines with and without exterior design changes are given in

Table 2. Power coefficient values of three-bladed Savonius wind turbines with and without exterior design (e.d.).

E.d. No	Reference	Study Type	Exterior Design Name	Cp without e.d.	Cp with e.d.	Exterior Design
1	Irabu and Roy [4]	Experimental	Guide-box tunnel	0.160	0.240
2	Mohamed et al. [19]	Validated numerical Optimization	Shielding obstacle	0.151	0.212
3	Yao et al. [32]	Numerical Experimental	Tower cowling	0.200	0.480
4	Manganhar et al. [33]	Experimental	Rotor house	0.125	0.218

. When the design models in Table 1 and Table 2 are compared in terms of power coefficient, it has been determined that the power coefficients of two-bladed turbines are generally higher than those of three-bladed turbines. Here, it has been seen that power production is higher with the flow reaching the blade surfaces of two-bladed turbines more than three-bladed turbines [4,19]. Therefore, it is thought that the power performances are lower in the three-bladed turbine since the solidity’s effect is higher than that of the two-bladed turbine.

2.3. Interior Design Studies

Scientists and researchers have been actively involved in developing new interior designs for Savonius wind turbines through numerical and experimental methods. They have focused on optimizing the effects of different geometrical parameters to enhance turbine performance. Ongoing research aims to further improve the efficiency of Savonius wind turbines. As shown in Figure 6, different design parameters such as the number of blades, blade type, blade overlap ratio, turbine aspect ratio, and blade end plate have been considered as interior design parameters in the literature studies. At the same time, these structural designs have been investigated in combination.

Details of the maximum power coefficients of Savonius wind turbines without and with interior design changes in terms of blade profile shape are given in

Table 3. Power coefficients of Savonius wind turbines with and without interior design (i.d.) in terms of blade profile (blade shape).

I.d. No	Reference	Study Type	Interior Design Name	Cp without i.d.	Cp with i.d.
1	Zhou and Rempfer [6]	Compared numerical	Bach-type	0.189	0.264
2	Kacprzak et al. [34]	Compared numerical	Bach-type	0.155	0.180
3	Kacprzak et al. [34]	Compared numerical	Elliptical blade	0.155	0.170
4	Mao and Tian [35]	Validated numerical	Blade arc angle	0.262	0.284
5	Alom and Saha [36]	Experimental Numerical	Vented elliptical blade	0.112	0.146
6	Alom and Saha [36]	Experimental Numerical	Non-vented elliptical blade	0.112	0.134
7	Ramadan et al. [37]	Experimental Numerical Genetic algorithm	S-shaped optimum blade design	0.140	0.280
8	El-Askary et al. [38]	Experimental Numerical	Twisted modified design	0.140	0.220
9	Damak et al. [39]	Experimental Numerical	Helical Bach design	0.180	0.200
10	Zemamou et al. [40]	Validated numerical Optimization Taguchi method	Bezier curved blade	0.270	0.350
11	Ramarajan and Jayavel [41]	Validated numerical	Three-fourth modified blade	0.230	0.250

.

Details of the maximum power coefficients of Savonius wind turbines without and with interior design changes in terms of blade attachment and blade surface geometry of the blade profile are given in

Table 4. Power coefficients of Savonius wind turbines with and without interior design (i.d.) in terms of blade profile (blade attachment and blade surface geometry).

I.d. No	Reference	Study Type	Interior Design Name	Cp without i.d.	Cp with i.d.
12	Sharma and Sharma [42]	Validated numerical	Multiple quarter blades	0.208	0.227
13	Deda Altan et al. [43]	Experimental Numerical	Additional design	0.099	0.119
14	Sharma and Sharma [44]	Validated numerical	Multiple miniature blades	0.192	0.213
15	Tian et al. [45]	Validated numerical Optimization	Optimal design	0.247	0.258
16	Ostos et al. [46]	Validated numerical	Two-quarters conventional blade	0.214	0.252
17	Haddad et al. [47]	Validated numerical	Additional inner blade	0.196	0.243
18	Gallo et al. [48]	Experimental Numerical	Multi-blade geometry	0.195	0.295
19	Al Absi et al. [49]	Experimental Numerical	Zigzag surface blade	0.260	0.292

.

Details of the maximum power coefficients of Savonius wind turbines without and with interior design changes for different designs and approaches to the blade profile are given in

Table 5. Power coefficients of Savonius wind turbines with and without interior design (i.d) in terms of blade profile (different design and approach).

I.d. No	Reference	Study Type	Interior Design Name	Cp without i.d.	Cp with i.d.
20	Roy and Saha [50]	Experimental Numerical	Newly developed blade	0.230	0.310
21	Tian et al. [51]	Validated numerical	Fullness of the blade	0.232	0.257
22	Roy and Ducoin [52]	Validated numerical	New blade design with moment arms	0.280	0.370
23	Zhang et al. [53]	Validated numerical Optimization	Optimal design	0.247	0.262
24	Chan et al. [54]	Numerical Genetic algorithm	Optimized blade	0.169	0.225
25	Marinic-Kragic et al. [55]	Validated numerical Optimization Genetic algorithm	Flexible-blade	0.220	0.238
26	Sobczak et al. [56]	Validated numerical	Deformable blade	0.210	0.400
27	Lajnef et al. [57]	Experimental Numerical	Novel delta-bladed	0.124	0.142
28	Imeni et al. [58]	Validated numerical	Airfoil-shaped blade	0.229	0.259

. As can be seen from this table, many blade profile models other than the classical blade shape have been designed and analyzed in terms of performance.

Details of the maximum power coefficients of Savonius wind turbines with interior design changes in terms of the number of blades are given in

Table 6. Power coefficients of Savonius wind turbines with and without interior design in terms of the number of blades.

I.d. No	Reference	Study Type	Interior Design Name	Cp without i.d.	Cp with i.d.
1	Ramadan et al. [37]	Experimental Numerical Genetic algorithm	3 blades	0.140	0.110

. When studies in the literature on this subject are examined, it has been seen that the number of blades negatively affects the performance of Savonius wind turbines [59,60]. It has also been seen in these studies that the power coefficients of two-blade turbines are higher than those of three-blade turbines.

Details of the maximum power coefficients of Savonius wind turbines with and without interior design changes in terms of turbine design ratios are given in

Table 7. Power coefficients of Savonius wind turbines with and without interior design in terms of turbine design ratios.

I.d. No	Reference	Study Type	Design Remarks	Cp without i.d.	Cp with i.d.
1	Kamoji et al. [65]	Experimental	Overlap ratio = 0 Aspect ratio = 0.7 Blade arc angle = 124° Blade shape factor (p/q) = 0.2 End plate ratio = 1.1	0.175	0.210
2	Akwa et al. [66]	Validated numerical	Overlap ratio (0–0.6) Overlap ratio = 0.15	0.200	0.316
3	Nasef et al. [64]	Experimental Numerical	Overlap ratios; 0, 0.15, 0.2, 0.3, 0.5 (Max. Overlap ratio = 0.15)	0.170	0.210
4	Mohammadi et al. [67]	Validated numerical Optimization Genetic algorithm Artificial neural network	Overlap ratio = 0.159 Aspect ratio = 0.89	0.196	0.222

. In the first studies with Savonius wind turbines, the effect of turbine design ratios on turbine performance has been investigated [61,62,63]. Specifically, in terms of blade overlap ratios, it has been found that classical Savonius turbines with overlapping blades have better initial characteristics compared to non-overlapping blades [64].

The maximum power coefficients of Savonius wind turbines with and without interior design changes in terms of the use of end plates are given in

Table 8. Power coefficients of Savonius wind turbines with and without interior design in terms of end plates.

I.d. No	Reference	Study Type	Design Remarks	Cp without i.d.	Cp with i.d.
1	Jeon et al. [70]	Experimental	Helical Savonius	0.060	0.082
2	Premkumar et al. [72]	Experimental	Helical Savonius	0.042	0.054
3	Goodarzi and Salimi [73]	Validated numerical	Conventional Savonius Quarter-spherical end-plate, Semi-circular end-plate, Circular end-plate	0.047	0.163

. One of the simplest methods for improving the aerodynamic performance of conventional Savonius turbines is the utilization of blade tip end plates [68,69,70]. The optimum diameter (D₀) of the blade end plates has been determined as a 1.1D turbine rotation diameter [65,71].

The maximum power coefficients of Savonius wind turbines with and without interior design changes in terms of the number of stages and related details are given in

Table 9. Power coefficients of Savonius wind turbines with and without interior design in terms of the number of stages.

I.d. No	Reference	Study Type	Design Remarks	Cp without i.d.	Cp with i.d.
1	Saha et al. [79]	Experimental	Single-, two- and three-stage (max. two-stage) Semicircular and twisted blade (max. twisted blade) Two and three bladed (max. two-bladed)	0.150	0.310
2	Mrigua et al. [80]	Numerical	Elliptical-bladed multistage (one, two, three-stage) (max. two-stage)	0.130	0.195
3	Saad et al. [81]	Numerical	Multi-stage turbines with twisted blades (a) single-stage, (b) two-stage, (c) three-stage, (d) four-stage (max. four-stage)	0.223	0.261

. Conventional Savonius turbines have fluctuating torque variation, with negative torque at certain turbine angles. To improve the turbine torque characteristics, staged Savonius turbines have also been proposed. However, it has been determined that the increase in the power coefficient is less than that of single-stage turbines [74,75,76,77,78].

3. Results and Discussions

The power coefficients of Savonius wind turbines obtained from the literature in classical, exterior design change, and interior design change cases have been analyzed in graphs. At the same time, the percentage increase in the power coefficients has also been compared in order to evaluate the best performance improvements of Savonius wind turbines according to interior or exterior design changes. Percentage increases in the power coefficient have been calculated according to values for classical Savonius wind turbines. The power coefficients and the corresponding increase percentages of classical two-bladed Savonius wind turbines, with and without exterior design, are presented in Figure 7. The values are extracted from Table 1a,b. Here, the focus has been primarily on studies published after the year 2000. As can be seen from the figure, the power coefficients of Savonius wind turbines without exterior design have been obtained at different values between 0.016 and 0.250. It has been determined that these power coefficients have been increased in the range of 0.028 to 0.520 with the addition of exterior design without changing the Savonius wind turbines themselves. In order to compare the efficiency of external design changes for these turbines, percentage power factor increases have been calculated. It has been determined that the highest increase has been obtained with the exterior design named “nozzle design” with number 7, and the lowest increase has been obtained with the exterior design named “nanofiber-based deflector” with number 14. As can be seen from the figure, the exterior designs that provide power coefficient increases of more than 100% have been determined as “nozzle design number 7,” “guide plate design number 5,” “curtain arrangement number 2,” and “wind lens number 13,” respectively.

A comparison of the power coefficients of three-blade Savonius wind turbines with and without exterior design changes is shown in Figure 8. The values here are based on Table 2. As can be seen from the figure, power coefficients between 0.125 and 0.200 have been obtained with Savonius turbines without exterior design changes. Maximum power coefficients between 0.212 and 0.480 have also been obtained by Savonius turbines with exterior design changes. As can be seen from this figure, the lowest power coefficient increase of 40% has been obtained with the exterior design named “shielding obstacle number 2.” The highest power coefficient increase has also been obtained with the exterior design named “tower cowling number 3,” with 140%.

It has been determined that the maximum power coefficient increase in the two-bladed Savonius wind turbine is around 180% with the nozzle exterior design and around 140% with the three-bladed turbine with the tower cowling exterior design. It has been found that the power coefficient values of the classical Savonius turbine, with or without exterior design, are lower than those of the two-bladed turbine due to the solidity effect of its three blades. Although the power coefficients of the Savonius wind turbine with the exterior design are higher than those of the classic turbine, these designs can destroy the Savonius wind turbine’s ability to take the wind from all directions. For this reason, an extra direction sensor mechanism is needed for turbines with exterior designs. At the same time, large exterior design additions such as nozzle, curtain, and guide plate designs may cause a wind-blocking effect during the collective use of turbines such as wind farms, which may cause a decrease in the power performance of these designs. Therefore, it is thought that these designs will be much more efficient in meeting personal electrical needs, such as in rural areas or on the roofs of buildings.

The power coefficients of the blade profile of Savonius wind turbines with and without interior design changes in terms of blade shape are shown in Figure 9. The power coefficient values here are based on the studies listed in Table 3. Among the Savonius wind turbines with interior design changes, the maximum power coefficient of 0.350 has been obtained with “Bezier curved blade number 10.” The maximum power coefficients for these Savonius wind turbines without interior design changes have been obtained in studies #4 and #10. The highest power coefficient increase has been obtained with the interior design named “S-shaped optimum blade design number 7” at 100%. The lowest power coefficient increase has been obtained with the interior design named “blade arc angle number 4.” When other power coefficient increases are analyzed, it has been determined that the increase has been approximately 23% on average.

The power coefficients of the blade profile of Savonius wind turbines with and without interior design changes obtained from the studies in Table 4 in terms of blade attachment and blade surface geometry are shown in Figure 10. When power coefficient increases are examined in terms of the blade attachment and blade surface geometry of the blade profile, it has been observed that increases are made in the range of 10% to 20% in general. The best power coefficient increase has been found to be about 51% with interior design #18 using a multi-blade geometry. It has been determined that the power coefficient increases by about 18% on average with internal designs made with a blade attachment or surface geometry.

A comparison of the power coefficients of the blade profile of Savonius wind turbines with and without interior design changes for different designs and approaches is shown in Figure 11. For the power coefficients here, the studies listed in Table 5 have been used. As can be seen in this figure, the highest power coefficient is approximately 0.400 with “deformable blade interior design number 26.” With the same interior design, the best power coefficient increase has also been achieved at about 90%. The lowest power coefficient increase has been found to be about 6% with the interior design named “optimal design number 23.” It has been found that an average improvement of about 27% in the power coefficient can be achieved with blade profile changes in terms of different designs and approaches.

The power coefficients of Savonius wind turbines with interior design changes and turbine design ratios are shown in Figure 12. The studies listed in Table 7 have been used for the values here. As can be seen from the figure, it has been determined that the improvements in the power coefficient are in the range of 13% to 58%, and the average is around 28%. It has been found that the best power coefficient value is obtained with “internal design conditions number 2.”

Figure 13 illustrates a comparison of the power coefficients of Savonius wind turbines with the interior design incorporating an end plate, as presented in Table 8. As can be seen from the figure, the power coefficient improvements in the helical Savonius wind turbines with interior design numbers 1 and 2 have been found to be around 30% on average. On the other hand, it has been determined that the power coefficient of the classical Savonius turbine with the interior design number 3 has been improved by around 244%. The power coefficient of the classical Savonius turbine with interior design #3 has been found to be very low, at about 0.04 in the case without an end plate and about 0.16 in the case with an end plate.

Figure 14 presents a comparison of the power coefficients of Savonius wind turbines with interior design changes based on the number of stages, as indicated in Table 9. As can be seen from the figure, the power coefficients of Savonius wind turbines without interior design have been obtained at different values between 0.13 and 0.22. It has been found that these power coefficients increase within the range of 0.19 to 0.31 for Savonius wind turbines with interior design changes. The interior design of Savonius wind turbine number 1 showed the highest power coefficient increase of 105%, while interior design number 3 exhibited the lowest power coefficient increase of 17%.

Increases in power coefficient above 100% in Savonius wind turbines with interior design have been achieved by designs made with blade shape, end plate, and a number of stages. Since the design changes made in this way take place in the structure of the turbine, the turbine maintains its ability to receive the wind from all directions. At the same time, it can be used collectively, as in wind farms, since there are no exterior design additions.

4. Conclusions

In this study, we examined literature studies aiming to increase the low-power performance of Savonius turbines, which are one of the most popular vertical-axis wind turbines made in recent years. These studies were categorized into two groups: interior designs and exterior designs. Thus, a systematic reference for Savonius wind turbines, which have been of great interest in recent years, has been presented with this study.

According to this study:

• It has been determined that the turbine’s performance can be increased by structural design changes on the Savonius wind turbine as well as with the assemblies added to the outside of the turbine without making any changes to the turbine.
• It has been determined that the power coefficient values of Savonius wind turbines have been increased up to 0.400 levels with interior design changes.
• It has been determined that the power coefficient values of Savonius wind turbines with exterior designs have been increased up to 0.520 levels.
• According to the studies reviewed in this study, the average power coefficient increases in Savonius wind turbines are around 33% for interior design modifications and around 64% for exterior design modifications. This indicates that the impact of exterior designs on the power coefficient of Savonius wind turbines is greater compared to interior design.
• It has been determined that the Savonius wind turbine’s ability to receive wind from all directions has been reduced or destroyed due to exterior design additions. An additional wind direction sensor mechanism can be used to regain this ability. In the case of turbines with interior designs, there is no need for an additional sensor mechanism as the ability of the turbine to receive wind from all directions is preserved.
• The inclusion of exterior design additions and additional equipment, such as direction sensors, in turbines with exterior design results in additional manufacturing and cost compared to turbines with interior design.
• Turbines with exterior design additions occupy a larger space compared to turbines with interior design, which can lead to a wind blockage effect in collective uses such as wind farms. Therefore, for meeting personal energy needs, especially in rural areas, it is more efficient to utilize turbines with exterior designs.

In conclusion, the studies reviewed in the literature play a crucial role in improving the low performance of Savonius wind turbines. For future performance studies, it is recommended to explore different interior design parameters and evaluate the impact of various exterior designs on Savonius wind turbines.