Numerical Investigation of Inner Blade Effects on the Conventional Savonius Rotor with External Overlap

The Savonius wind turbine is considered as one of the best vertical axis wind turbines for harvesting the kinetic energy from the wind in the urban areas, due to magnificent features such as high starting torque, low construction and maintenance costs, simple design, and self-starting ability especially at low wind speed. However, the conventional style of the Savonius rotor suffers from low efficiency. Consequently, modifying the configuration of the rotor may be an appropriate solution for providing electricity to the communities with no access to the power grid. Thus, this study aims to enhance the performance of the conventional Savonius rotor with an external overlap by adding an inner blade to the rotor configuration. Hence, a comparison study between five new arrangements against the conventional rotor in terms of power coefficient (Cp) and torque coefficient (Ct) is performed through a two-dimensional simulation by using ANSYS Fluent 19.2. The k-ε/Realizable turbulence model is employed in the simulation. Results conclude that inner blade with an angle of 120° increases the power coefficient by 41%, 39%, and 7% at tip speed ratio (TSR) = 0.7, 0.6, and 0.5, respectively.


INTRODUCTION
The rapid energy consumption, population growth, consumption of traditional energy sources, and the environmental issues are pushing most of the world countries to the efficient use of clean and renewable energy sources. In recent years, electricity production from renewable sources has been increased as being clean and available [1]. Amongst the renewable sources, wind energy has turned into a favourite source of Due to the main feature of the Savonius rotor, self-starting, studies have been conducted on the Savonius rotor as a starter for the other types of the VAWTs which suffered from low starting performance. Sahim et al. [8] have suggested the combine between Savonius and Darrieus rotors which will give better performance at low wind speeds. Torque coefficient (Ct) was evaluated for various Tip Speed Ratio (TSR) with different values of turbine diameter. A hybrid Savonius-Darrieus wind turbine to improve the starting performance was performed by Liang et al. [9]. Enhancement for the torque coefficient, power coefficient (Cp), and self-starting capability at different radius ratio and attachment angles for different TSR was reached. In the same way, ed-Dı̂n Fertahi et al. [10] performed a study on the Savonius-Darrieus hybrid wind turbine to estimate the effect of blade's angular position on the self-start ability over various ranges of TSR. An integration of a Savonius rotor and H-rotor in order to make the system completely self-starting and enhance the power performance was carried out by Bhuyan and Biswas [11]. Ghosh et al. [12] performed a three-dimensional simulation using Computational Fluid Dynamic (CFD) model in order to study the aerodynamics of the three-bladed Darrieus Savonius rotor. Authors conclude that such a hybrid system is recommended for wind power conversion due to the improvement in the performance at low wind speeds.
Overall the literature, the main negative of the Savonius rotor was the low efficiency, this is mainly due to the negative torque which generates on the returning blade with the convex side [13,14]. Many aerodynamic improvements have been accomplished on Savonius wind turbine in recent decades by researchers as the performance of the traditional turbine is low [15].
Influence of different parameters on the efficiency of Savonius wind turbine was investigated in the previous studies such as number of stages, overlap ratio, aspect ratio, number of blades, and use of accessories such as end plates and power augmentation devices. Two-stage Savonius turbine performs better than the single-stage turbine in terms of static torque [16]. Low values of overlap ratio enhance the performance of the Savonius rotor as reported in many studies [17,18]. Using high values of aspect ratio is recommended to increase the angular velocity of the rotor and so improve the coefficient of power [19,20]. Three bladed rotors reduce the performance compares to the two-bladed rotors [21,22]. The extracted power from the Savonius rotor can be improved by preventing air leakage from the concave side to the external airflow by using end plates [23]. The performance of the Savonius rotor can be improved by utilizing power augmentation devices such as deflector plates and windshields. Deflector plates are placed in front of the returning blades in order to reduce wind resistance [24]. Moreover, they enhance the self-starting capability with a net positive static torque [25]. However, although the Savonius rotor was invented in 1922, the research related to this turbine is still of a genuine interest in the last decade. The current increasing research on the vertical turbines could mainly be imputed to the recent discoveries that small-scale vertical turbines could be more appropriate and operate more effectively in low wind speed regions [26]. Given that it offers sundry features over its counterpart horizontal turbine in terms of capability to perform very well in highly turbulent and low wind speed regions. Additionally, the noise caused by the rotation of blades is low due to the lower spinning speed and the simple design [27].
While there are various effective techniques to harvest wind energy, many researchers are trying to enhance the performance of the Savonius rotor in terms of Cp by optimizing the shape of blades or adding power augmentations like wind deflectors.
The design of the Savonius rotor needs to be the focuses of development in order to enhance the generated torque by the wind rotor. Thus, there should be research on the Savonius rotor in relation to the addition of inner blade in order to enhance the performance of the turbine. Therefore, in this study, a new blade configuration of Savonius rotor having an inner blade with external overlap is proposed. One of the advantages of this new configuration is more energy could be captured from the wind compared to the conventional Savonius rotor. The study has been conducted with the assist of numerical simulations performed using ANSYS Fluent. The study has been conducted with the assist of numerical simulations performed using ANSYS Fluent.

TURBULENCE MODEL
The realizable k-ε turbulence model was employed in the simulation which has two equations [28]. The main features of this model include enhanced performance inflow with recirculation and a strong pressure gradient. The transport equation for and in the model are given as Mohamed et al. [29]: where μt is the eddy viscosity, σk and σε are diffusion constants of the model, = max *0.43, 0 012 3 , 4 = , = 5 2 7 7 , Gk and Gb are the generation of turbulent kinetic energy due to the mean velocity gradient and the buoyancy, respectively, YM is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, and Sk and Sε are the user-defined functions. The employed values of constants in the computations are shown in Table 1.

NUMERICAL METHODS
ANSYS is a CFD software for analyzing simple and complex geometries, steady and transient problems. It can predict the aerodynamics of wind turbines whether in two-dimensions or in three-dimensions whereby the analysis starts by generating the CAD geometry and end up with post-processing of the results.
For the present study, a two-dimensional simulation was adopted utilizing ANSYS Fluent 19.2 software. Fluid flow around turbine geometries can be solved in efficient and realistic simulation using Fluent whereby the generated result can give a comprehensive study without any costs [30]. Consequently, a transient 2D simulation was selected in ANSYS Fluent 19.2 to obtain a steady solution from the initial boundary conditions.

Geometry configuration
A comparison study between the conventional Savonius rotor with an external overlap of e = 0.02 m against the novel configuration of the rotor was carried out. In Figure 2 and Figure 3, a top view of the conventional and novel configurations rotors are shown, and their detailed dimensions are listed in Table 2. The conventional blade was taken with a fixed diameter of d = 0.188 m. The diameter of the inner blade was di = 0.144 m. In addition, the inner blade arc angle was changed between the values (180-100) by a step of 20 degrees in each time. Abraham et al. [31] have reported that the end plates increase the performance of the Savonius rotor. Additionally, authors like Plourde et al. [32] and Fujisawa and Gotoh [33] have assured as optimum an end plates diameter of De = 1.1D to enhance the rotor performance. Consequently, end plates, De = 0.4862 m was taken for all tested turbines. The shaft diameter was taken 0.03 m. Previous studies showed a lack of consensus about the optimum value of overlap ratio. Savonius rotor with an internal overlap ratio between their blades shows a better performance in their starting [15]. On the other hand, studies such as Driss et al. [34] have determined that the external overlap between the blades decreases the performance of the conventional rotor. Thus, the current study aims to increase the performance of the rotor with an external overlap.

Computational domain and boundary conditions
It is necessary to mention that the two-dimensional simulation can predict the performance of the rotor with high accuracy [35]. Moreover, the cross-section of the rotor is the same along it height which means that we can neglect the flow in the vertical axis which is also equivalent to the three-dimension simulation for the rotors with end plates [36,37]. Consequently, since this study focuses more on some key modeling details rather than waiting for three-dimension complex geometries to be solved, a two-dimensional modeling is selected.
In order to build a suitable computational domain for a wind turbine modelling, two conditions must be followed: firstly, the dimensions have to be large enough in a way that the domain walls have no effect on the airfield and secondly, the domain must not be extremely large in order to reach the optimal solution by using the computational resources in an effective way. The simulation domain, mainly, consists of two sub-domains: a moving domain and a stationary domain. The moving domain is where the rotor will start moving in a certain rotational speed, whereas, the stationary domain contains the flowing air and represents the wind tunnel. Therefore, the dimensions of the simulation domain must be extended at least 10 times the rotor diameter to avoid the influence of the boundary conditions on the results [38].
The computational domain utilized in this study is shown in Figure 4. The circular region with moving mesh has a dimension of 1.1D. The center of the shaft is placed at a distance of 5D from both upper and lower sides. These two subdomains are parted by a defined interface. At the inlet, a constant wind speed U of 9 m/s was used. The outlet of the domain was set as a pressure outlet. Stationary walls at the top and bottom of the domain and blade wall are set to no-slip condition. Rotor angular speed is set to five degrees/step to minimize the simulation time. The air stream was turbulent flow with 2.69 × 10 5 Reynolds number (Re).
Pressure-based transition simulation is used in the general setting of fluent solver. For pressure-velocity coupling, the SIMPLE algorithm is adopted since the solver was set to a transient pressure-based. The spatial discretization of the conservative equations is treated with a second-order upwind scheme.

Meshing considerations
The moving sub-domain was meshed using unstructured mesh whereas a refinement was applied to the interface between the two sub-domains to enhance the adaptation of the rotor geometry. The boundary layer effect can be defined in the ANSYS software as the inflation on the rotor blades which take into consideration the energy loss due to the friction. In addition to the fine mesh around the blades, y + factor should be taken into consideration, this factor estimates the thickness of the first inflation layer. According to Yu and Thé [39], y + represents the proportion between turbulent and laminar effects in a cell. The desirable value of y + factor is around 1 [40], this value gives more accurate solution nearby the boundary layer. The non-dimensional factor can be calculated using the following equation: where ρ [kg/m 3 ] is the air density, Ut [m/s] is the friction velocity, y is the thickness of the first boundary layer on the blades and μ [kg/ms] is the dynamic viscosity. The friction velocity can be obtained using the following equation: In the beginning, a mesh convergence test was carried out through various grids in order to make the solution independent of the grid size. Coarse, medium and fine meshes were generated using mechanical mesh in ANSYS software. To validate the mesh selection, a model proposed by Hayashi et al. [41] was created and simulated, grid sizes were taken as listed in Table 3. To assure the convergence of the solution, the solver time step was set to cover ten full rotations. Validation results are illustrated in Figure 5. The average percentage of error is less than 7% for both medium and fine mesh when it compared to the experimental results of Hayashi et al. [41]. The medium grid was adopted for this study in order to reduce the simulation time. Including the air resistance around the shaft, an inflation of 25 layers with a 1.1 growth rate was applied around both of blades and the shaft in order to keep the y + values around one. For the current study, the mesh that used in the validation process will be applied to the new geometries as shown in Figure 6.

Performance parameters
The performance of wind turbines can be expressed in a dimensionless form. For a certain wind speed, Cp, Ct and TSR are effective indicators to evaluate the performance of the turbine. For a particular configuration of Savonius rotor, these parameters are [42]: where R is the radius of the turbine, ω is the angular velocity of the rotor, A is the swept area of the rotor (A = H × D), with H the height of the rotor and T is the average torque.

RESULTS AND DISCUSSION
ANSYS FLUENT 19.2 employed for the simulation purpose, all the experimental data relating to this research were used from Hayashi et al. [41] for the validation. Different values of TSR (0.4, 0.5, 0.6, and 0.7) were used to determine the Cp of the rotor. The results in Figure 5 show that the percentage of error is less than 7% and prove the reliability of the current simulation. From the past few decades, different efficiency enhancement studies on Savonius wind turbines were carried by varying some design parameters such as number of blades and overlap ratio, however, until yet none research has been carried on the effect of the inner blade with various blade arc angles on the rotor. Moreover, previous studies were concluded that the external overlap could reduce the performance of the rotor. On such concept basis, the novel configuration along with an inner blade and external overlap is investigated and compared with the conventional rotor.

Power coefficient comparison
The operation of the Savonius wind rotor depends on the lift and drag forces acting on the blades. Factors like blade angle and blade shape can vary the amount of these forces. Thus, each rotor configuration has its own power coefficient. For that, the Cp of the conventional rotor and the novel configuration rotor was investigated and compared. The results were analysed and plotted in Figure 7, where Cp is a function of TSR. It can be clearly seen from Figure 7 that model 3 with inner blade arc angle of 120° shows the best performance in terms of Cp followed by model 1 with inner blade angle of 160°. Model 3 at the design points (TSR = 0.5, 0.6, 0.7) shows an enhanced percentage of 7%, 39%, 41%, respectively. On the other hand, model 1 shows an improvement of 11% and 26.7% at TSR 0.6 and 0.7, respectively. Such enhancements can be related to the pressure drop and rise on the convex and concave side of the rotor respectively. Furthermore, the other models scenarios exhibit slightly lower Cp values than the conventional rotor for most of TSR values. Besides, it is also observed that the values of Cp for models 1 and 2 are highly declined at low TSR values. Finally, the "main configuration" shows a slightly higher Cp value (2%) than the conventional rotor at TSR = 0.4. Figure 8 illustrates  The instantaneous Ct at TSRs = 0.5 and 0.7 are illustrated in Figure 9 and Figure 10 for all simulated rotors. It is clear that the instantaneous Ct of the rotor with 120° inner blade at TSR = 0.5 is increased mostly in the region between 100° and 210° angle of rotation due to the low pressure near the blade tip. Later, this low pressure influences the Ct values to be decreased in the region between 35° and 95°. However, at high considered TSR = 0.7, the rotor showed an improvement in terms of Ct at all the regions. Besides, it is also observed from the figures that the maximum torque values were generated close to (90° and 270°) for all configurations at TSR = 0.5, and (105°, 290°) for configurations at TSR = 0.7. On the other hand, the lowest generated torque occurred around (30° and 180°) at TSR = 0.5 and around (20°, 190°) at TSR = 0.7. Furthermore, it was observed that at high TSR (0.7) the tested rotors experienced negative torque values whereas at low TSR

Velocity and pressure analysis
Pressure and velocity contours for all tested rotors at TSR of 0.7 are shown in Figure 11 and Figure 12, respectively. The 9 th rotation of the rotor is selected for high accuracy. Angels of rotation (0°, 105°, and 190°) were adopted to analyse the behaviour of pressure and velocity contours. Winds around the rotor start moving with a rotational speed due to the spin of the rotor. This circular motion of the wind contributes to reduce the velocity of the incoming wind on the returning blade which usually affects the performance of the rotor due to the generated resistance between the blade surface and the incoming air. A high-pressure value is noticed on the convex side of the returning blade due to low-velocity around the blade. In contrast, low-pressure zones are much noticed at the tip of the advancing blade which the wind velocity is the maximum. For a better view of the low wind speed zone wind, streamlines are shown in Figure 13. It is clearly shown that the inner blade changed the size and shape of the zone. Savonius rotors spin due to the pressure drag force on the rotors. This force differs with the angle of attack of the blades. Based on that, blades expose their various geometries to the wind stream. Thus, each configuration has its own drag force coefficient. Consequently, the average torque of the rotor changes with the change of blade position as well as with the rotational speed. Inside the inner blade of the concave side of the returning blade, there is a blue spot which represents a low wind velocity at that point. This may be due to the dragging effects. It is also noticed that the shape of this zone was changed with the change of the blade arc angle. Referring to Figure 11e at θ = 0° and 190°, high-pressure region is noticed on the convex side of the returning blade more than the other models, and low-pressure region is noticed near the tip of the advancing blade less than the other tested models. This provides evidence that the pressure difference in model 3 is higher than the other models. Thus, the generated torque and power from the rotor in model 3 is higher.