The effect of multi-stage modification on the performance of Savonius water turbines under the horizontal axis condition

Abstract Indonesia has the abundant potential of hydropower but not yet processed optimally, which intensely depends on fossil fuel. Hydropower installed in Indonesia is only 11,272 MW, from the estimated potential approximately 94,476 MW. This data shows that 89% of the hydropower potential in Indonesia has not been processed. One of the present efforts to utilize this resource is addressed to develop the Savonius water turbine. Conventional water Savonius turbines have a comprehensible structure and easy to be applied. However, the turbines produce relatively small power, which requires further assessment to improve its performance. The current study is performed by considering geometric changes on the water Savonius turbine to observe their effect on power characteristics. Considered changes are made on the number of stages, and the angle between stages, specifically a single-stage, two-stage 0°, Two-stage 90°, three-stage 0°, and three Stage 120°. The research was carried out by designing simulation model using ANSYS software with CFX Solver. Water speed is determined to 0.8 m/s, while plates with 110 mm in diameter and 110 mm in height are incorporated as rotor configuration. Based on this study, it can be concluded that the addition of the stage affected improving the performance of the Savonius water turbine, where the multi-stage turbine experienced an increment compared to conventional water turbines. The interesting tendency was found on the two-stage rotors with angle of 0° which produced a smaller Cpmax compared to the conventional water Savonius turbines.


Introduction
An average increase in electrical energy consumption by 4.7% and production by 11.8% in the last three years in Indonesia. Electricity consumption is dominated by the household, business, and industrial sectors. The National Power Plant is supplied by 61% of coal power plants [1]. However, the energy source has decreased every year. An-other energy source that has great potential in Indonesia is Hydropower. Hydro energy and micro-mini hydro have a potential of 76% compared to other energy sources [2]. The development of a water turbine is one of the efforts to process water energy into electricity. Research on hydro turbines has been carried out such as screw-type at small hydropower plants [3]. In general, turbines are divided into horizontal axis and the vertical axis in this study using a horizontal axis Savonius type turbine. In the 1920s, Savonius published the results of carried out tests on his rotor design. They are operating in both wind and water. In the case of water, the test was carried out in the river flow, tidal waters and sea waves [4].
Research has been conducted on Savonius type turbines, especially on the vertical axis and wind turbines. Research on the effect of the overlap ratio has been carried out on vertical wind turbines. The study was conducted in an overlap ratio of 0 to 0.3. The results of the study show that the overlap ratio of 0 produces the highest Cpmax [5]. In another study regarding the overlap ratio that has been carried out on horizontal axis water turbines, it shows that Cpmax is obtained in 0.3 overlaps. The Cpmax produced in the study was 0.19 at TSR 0.79 [6]. Other research is about performance with the addition deflector variation. From this study it was found that the addition of the deflector increased the coefficient of power (Cp) by 50% [7]. The change of shape of blade becomes a helix shape, and the addition of deflector has been tested to the water Savonius turbine on the vertical axis. The study resulted in an increase in Cpmax from 0.125 to 0.14 [8]. Research on Savonius wind turbines with number of blades 2 and 3 was car-ried out and resulted that the Savonius wind turbines with two blades produced higher Cpmax compared to wind turbines with three blades [9]. In general, research on Savonius turbine development is about modifying the number of blades and Shape of blade which is carried out either in simulation or experiment [10]. Collaboration of the mentioned methods is very effective as results of experimental works can be expanded by numerical approach, and vice versa, which this research stage is taken as benchmarking in computational fluid dynamic [11][12][13][14][15] and finite element method [16][17][18][19][20].
This research was carried out using a Savonius type turbine on the horizontal axis. Since Savonius has a simple structure that is easy to modify and can operate at low speeds, Savonius has a lower efficiency than other types, so research still needs to be done to improve its performance [21]. This study aims to determine the effect of the number of stage on the performance of Savonius water turbines with cconsidered changes on the number of stages, precisely a single-stage, two-stage 0 ∘ , two-stage 90 ∘ , three-stage 0 ∘ , and three stage 120 ∘ .

Data Reduction and Model Geometry
Turbine performance always uses the relationship between the coefficient of power and the Tip Speed Ratio function. So the results of the research that has been carried out through simulation, then processed using equa- where U is the free flow velocity, ρ is the water density, A is the Area of the Rotor, T is the torque, ω is the angular velocity, C t is Coefficient torque and Cp is the Power coefficient [22]. This study was carried out using the Savonius rotor on the horizontal axis. The research has been done with variation single-stage, two-stage 0 ∘ , two-stage 90 ∘ , three-stage 0 ∘ , and three Stage 120 ∘ . The dimensions for each rotor are shown in Table 1. The number of rotors tested is five rotors. Description dimension on the geometry of the rotor shown in Figures 1 and 2. Figure 2 shows the top projection of single-stage rotors, two-stage 0 ∘ , and three-stage 0 ∘ . Research conducted using the aspect ratio (D / H) of 1 and the overlap ratio of 0. Table 1 shows that D is the endplate diameter, d is the rotor diameter, H is the rotor height, h is the stage height of the rotor, and T is the thickness.

Methodology
The research was carried out in 3D simulation using Ansys software with cfx solver. The research was conducted with the pre-research and research stages. Performed on prestudy phase is to make 3D design, validate, mesh independence study. The second stage determines boundary conditions, meshing, and running simulations. Validation was carried out on Roy et al. [23]. Validation was carried out at the position of TSR 0.74 where Cpmax was reached. Cp at 0.65 TSR obtained from the simulation was 0.252, wherein the mentioned study, it was 0.252. The data shows a 2.35% error rate. Benchmark has shown in Figure 3.
Mesh independence study needs to be done in simulation research. By conducting mesh independence of our research can obtain a number of elements that are effective in the simulation process. Mesh independence study is done by adding cells [24]. Data from the mesh independence study process are shown in Figure 4 which the  graph shows the relationship between the numbers of elements with a torque value. The graph shows that the most effective mesh has meshed with the number of elements 1,883,498. The number of elements in the mesh was chosen because there is no significant change in the torque value when the number of elements adds more.

Numerical Model
Simulations are carried out using mesh with the tetrahedral method and using inflation on the rotor wall. The results of the mesh are shown in Figures 5 and 6. The figure shows the mesh method used and mesh size. Meshing for rotary domains and domain stationaries is done separately. Figure 5 shows the mesh on the rotary domain, and Figure 6 shows the mesh on the stationary domain. In this study, CFX software has been used for computing. Using this software, all rotor designs have been analyzed. Numerical research is possibly done using numerical methods of one dimensional [25] or three-dimensional [26]. Equation of momentum, turbulent kinetic energy has been solved numerically using the software, where the governing equation is shown in Equations 4-7.
Continuity Equation: X-Momentum: where ρ is the density, t is the time, u, v, and w are the velocities in three coordinates of Cartesian, and x, y, and z are the Cartesian coordinates. The simulation domain consists of two domains, namely the stationary domain and the rotary domain [27]. A rotary domain is a rotating domain, and this domain consists of parts of the wall rotor, front interface, interface, and rear interface. The rotary domain is shown in Figure 7a The Stationery domain is non-rotating. This domain consists of six parts. These parts are the front interface, interface, rear interface, inlet, wall, and outlet. The stationary domain is shown in Figure 6b The rotary domain and stationary domain are connected by the interface section. The overall schematic simulation is shown in Figure 8. An inflation with a 1.2 growth rate and level of 5 was using. the small thickness of the cells in the boundary layer of the blades from the first small layer aim to smooth transition using the y ≤ 1 value highly recommended for turbulent models [28].     Table 2. Density (kg/m 3 ) 1,000 5.

Results and Discussion
The performance of the Savonius hydrokinetic turbine having the variable number of stages on rotor has been investigated numerically in velocity of 0.8 m/s at TSR interval 0.4-1. From the simulation process, the pressure contours and velocity contours of each design are obtained. Also, the torque value is obtained so that Cp can be obtained from each design. Simulation has convergence at residual target 10 −4 . Coefficient power (Cp) and coefficient torque (C t ) generated by the Single Stage Rotor at TSR intervals of 0.3-0.9 are shown on the graph Figure 9. Cp continues to increase at TSR < 0.6 and decrease at TSR > 0.6. The resulting Cpmax is 0.1 at TSR 0.7. C tmax is obtained at 0.2 at TSR 0.3. Where Cpmax and C tmax are not on the same TSR. Figure 10 shows the Cp and C t generated by the twostage Rotor 90 ∘ . Cp increases at TSR <0.7 then decreases at TSR > 0.7. The resulting Cpmax is 0.18 at TSR 0.8. C t increases at TSR <0.5 C t values increase, whereas at TSR > 0.5 C t values decrease. C tmax is obtained at 0.29 on TSR 0.5. The Cp and C t produced by the two-stage 0 ∘ rotors are shown in Figure 11. The graph shows that the Cpmax is 0.058 at TSR 0.4. C tmax was reached at 0.158 at TSR 0.3. For this rotor, the same as the previous rotor, where Cpmax and C tmax are not on the same TSR.
Cp and C t generated by the Rotor three Stage 120 ∘ stage at TSR intervals of 0.4-1.1 are shown in Figure 12. Cp continues to increase at TSR < 0.9 and decrease at TSR > 0.9. The resulting Cpmax was 0.197 at TSR 0.9. C tmax was obtained at 0.249 at TSR 0.7. Where Cpmax and C tmax are not on the same TSR. Figure 13 shows the Cp and C t produced by Rotor threestage 0 ∘ . Cp increases at TSR < 0.4 then decreases at TSR > 0.4. The resulting Cpmax was 0.048 at TSR 0.4. C t increases at TSR < 0.4 C t values increase, whereas at TSR > 0.4 C t values decrease. C tmax is obtained at 0.12 at TSR 0.4. Where TSR for Cpmax is the same as TSR for C tmax .
Besides producing Cp and C t values, this simulation produces output in the form of pressure contours, velocity contours, and streamlines. The pressure contours for each type of rotor are shown in Figure 14. The velocity contour is shown in Figure 15, and the velocity vector is shown in Figure 16. By studying pressure contours around models with different numbers of stage (Figures 14 and 15), there is a slight difference in pressure distribution in the blade with the same position. Where pressure is seen around the upper blade, more rotors with more stages have greater pressure. This is due to the area of the blade in multistage rotors smaller than the single-stage rotors. Figure 16 shows the vector of velocity streamlines at single-stage, two-stage, and three-stage.

Conclusions
The simulation of three different types of Savonius rotors has been carried out by involving single-stage and twostage. The results of this study conclude that the modification of the Rotor three-stage 120 ∘ has the highest coefficient of power maximum (Cpmax) value compared to another Rotor. The Cpmax Rotor three-stage 120 ∘ is reached at 0.197, Rotor two-stage 90 ∘ is reached at 0.178, and the single-stage Cpmax is reached at 0.1. On two-stage and three-stage 0 ∘ rotors, Cpmax is lower than a single-stage, two-stage 0 ∘ is reached at 0.058 and Three-stage 0 ∘ at 0.048. Therefore, the three-stage 120 ∘ rotor is proofed as an alternative design which can improve the performance of water turbine Savonius, especially utilize water resources to produce renewable energy. From this simulation research we get a picture of the velocity and pressure distribution that can be used as a reference for experimental studies and the development of the next rotor design.