Abstract

Wind is an alternative source of renewable energy following the current surge in energy demand globally. This is attributed to the worldwide call for the alleviation of the use of fossil fuel sources due to climate change. However, the larger part of the global coverage experiences low wind speed, inhibiting the application of medium and large wind turbines in harvesting wind energy with a return on investment. This leads to an increase in the application of small wind turbines. This study focused on studying the Savonius wind turbine, which is one of the potential candidates for harnessing wind energy efficiently in low wind speed areas. The study aimed to analyze the aerodynamic performance of a two-stage Savonius wind turbine using the Computational Fluid Dynamic (CFD) method by varying the phase shift angles (PSA) and tip speed ratio (TSR). The lower and upper rotors were designed such that the phase shift angles varied were 45⁰, 60⁰, 75⁰ and 90⁰. A Shear Stress Transport turbulence model SST k-omega with a steady-state method was used to analyze the influence of PSA and TSR on the performance of a two-stage Savonius wind turbine. The findings of this study indicated that the Savonius wind turbine with a PSA of 45⁰ had the highest torque coefficient of 0.3654 at a TSR of 0.8 and a wind speed of 4m/s. Hence, phase shift angles significantly influence the performance of a two-stage Savonius wind turbine in low wind speed applications.

1. Introduction

Recently, the human population has exponentially grown, leading to a high demand for domestic and industrial energy consumption. A large amount of energy is currently generated from fossil sources, which negatively impact climate change, such as global warming, rise in temperature, and unpredictable rainfall patterns. Some authors ¹ suggest that this is caused by the emission of greenhouse gases. In the long run, this advocates for the use of alternative energy sources, mainly renewable energy, such as hydro, tide, solar, biomass, geothermal, and wind. These sources have drawn a lot of attention from governments, private industries, and the research sector.

Wind energy is abundantly available and considered the least costly renewable energy source ². In relation to this, the popularity of wind energy has immensely grown in the last two decades, with countries such as China, the US, and Germany taking the lead in harvest of wind energy ³. Wind turbine blades and wind vanes are known devices that convert kinetic energy in moving air to useful mechanical energy before changing it to electric power or other forms of consumable energy. The wind turbines are grouped based on the orientation of the rotational axis with reference to the ground surface. The two types of wind turbines are vertical axis wind turbines (VAWTs) and horizontal axis wind turbines (HAWTs). The HAWTs turbines’ rotational axis is horizontal to the ground, while the VAWTs turbines’ rotational axis is perpendicular to the ground.

Savonius wind turbines are VAWTs mainly used in electricity production and water pumping. One of the benefits brought in by the Savonius wind turbine is that it can operate under low wind speed, and this is attributed to its popularity in application to areas with low wind ⁴. The turbine works best at low tip speed ratios (TSR) of between 0.6 and 0.8 ^{5, 6}, which contributes to their noiselessness, making them more acceptable in residential, urban, and rural areas. Additionally, these turbines have a high self-starting capability and can operate in turbulent wind conditions, which are mainly experienced in urban areas ⁷. However, the fundamental flaw in these turbines' performance is their low efficiency and low power generation compared to other turbines ⁴. Additionally, the turbine produces negative torque within the ranges of 135⁰ and 165⁰ as well as between 315⁰ and 345^{0 8}.

These flaws have been the epitome of research, with various studies focusing on specific parameters that affect the turbine's performance, including the aspect ratio, overlapping ratio, end plate, number of blades, number of stages, blade material, and other augmentation geometric properties such as the use of smart blades, guide plates, and blade shape. Multi-stage turbines are viable in reducing negative torque, as evidenced by ^{9, 10}.

A comparison between a conventional and a two-stage turbine indicated that the latter performed better ¹¹. The conventional turbine, in this case, is referred to as a single-stage Savonius wind turbine, which is illustrated in Figure 1. In addition, a comparison between single-stage and two-stage Savonius wind turbines from various research conducted in helical turbines, hydrokinetic and elliptic turbines identified that the latter performs better ^{8, 12, 13}.

A study by ¹⁴ revealed that a two-stage turbine with two blades performs better in terms of torque and power efficiency at a TSR of 0.6 than a two-stage turbine with either three or four blades. Investigation done numerically showed that the torque decreases with an increase in TSR ¹⁴. Additionally, for all the turbines tested, the power output and power coefficient initially increased with an increase in TSR up to a peak of between 0.6 and 0.8 and later decreased with an increase in TSR ¹⁴. An experimental and numerical study by ¹⁵ on a two-stage Savonius wind turbine, with the turbine being tilted at different angle positions. Their findings indicated that the torque coefficient (C_T) decreased with an increase in tip speed ratio (TSR).

Further, ¹⁶ investigated the aerodynamic performance of a two-stage Savonius wind turbine with twisted blades, and they concluded that the modifications of geometric parameters improved the overall performance of the turbine. However, these changes are lineated with complexing the structure of a Savonius turbine, and making it costly to maintain compared to the conventional two-stage Savonius wind turbine.

Various studies on multi-stage Savonius wind turbines have been numerically done using computational fluid dynamics (CFD). Numerical studies are used to verify and validate proposed wind turbine design concepts before building physical prototypes ^{18, 19}. This allows innovative blade features and configurations to be evaluated efficiently through computational analysis. From the relevant literature reviewed, most studies focused on the comparison between single-stage and two-stage Savonius turbines. It revealed that the performance of the Savonius wind turbine depends on geometric parameters, positioning, and orientation of the blades. In conclusion, the reviewed literature calls for the design of an innovative turbine that can guarantee maximum power generation. This study, therefore, seeks to analyze how phase shift angles ranging between 45⁰ and 90⁰ affect the performance of a two-stage wind turbine.

2. Methodology

All simulations were carried out using ANSYS version 2022 installed on a system having parallel processing with 8 core Intel ® i7-4510 u with 16 GB RAM.

The Savonius wind turbine under this study has two rotors, one on the lower stage and the other one on the upper stage, such that the two are superimposed on each other, which is then referred to as a two-stage Savonius wind turbine as shown in Figure 2. Both rotors have similar shapes, and all geometrical dimensions are the same for both lower and upper rotors. They are also aligned with the same orientation. The geometric dimensions of this wind turbine are tabulated in Table 1. This two-stage Savonius wind turbine is taken as the original wind turbine, and it is used to benchmark the findings obtained from this study.

The orientation of the upper rotor was laterally rotated within angular angles ranging between 45⁰ and 90⁰. The shifting angular angle interval was kept at 15^o, and it is referred to as the phase shift angle (PSA) in this study. The various rotors are shown in Figures 3 and 4 below, both in 2D and 3D.

The endplates (D_e) used have a circular profile where their diameters are kept constant and 1.1 of the rotor diameter (D). Each stage rotor created had its own endplates before being superimposed to form a two-stage turbine. The aspect ratio for each stage is 1, and the whole turbine is 2, as recommended by ¹⁶. The overlapping ratio (s/d) for all the tested rotors is set at 0.16. All the rotors have a constant sweep area (A), where A = DH.

The domain consists of stator domain and rotating domain as shown in Figure 5. The domains are separated using a sliding interface, ensuring the flow field continuity around the rotor. The measurements of domains are taken in multiples of the rotor diameter (D), where the measurements of the stator domain are 60D X 40D X 20D. The distance of the turbine center (0, 0, 0) to the inlet is 15D following recommendations by ¹⁹, which is in the brackets of a safe minimum distance to the inlet and avoids overestimation of the results. The distance to the outlet was set at 45D, which leads to a uniform outlet pressure coefficient. The diameter of the rotating domain was set at 1.5D. Overall, the size of the computational domain is maintained large enough to eliminate the effect of its boundaries on the performance of the rotor.

In the present study, the fluid domain was discretized into small computational cells comprising unstructured tetrahedron elements. The stationary zone was meshed using the coarse elements, while the rotating domain and the turbine took up the finer mesh elements. The mesh generation process started with the edges, followed by faces and later body sizing to emulate the bottom-to-top strategy, and Figures 6 and 7 below show the mesh resolution. The quality of the elements was evaluated in terms of orthogonality quality and skewness. The quality of these elements was found to be in the range of 0 – 0.38 and 0.63 – 1.0 in terms of skewness and orthogonal quality, respectively. The mesh sizes were deemed of satisfactory quality with guaranteed reasonable accuracy, according to ²⁰. A mesh sensitivity test was conducted by considering six different mesh sizes on the stator domain, rotating domain, and blade surface. Refinement of the mesh was emphasized around the rotating domain and the blade surfaces.

This study considered appropriate boundary conditions as they are necessary to obtain comprehensive results. In relation to this, the left and right boundary were assigned as inlet and outlet, where the inlet velocity was maintained at 4 m/s with a turbulent viscosity ratio and intensity of 10% and 5%, respectively. The inlet boundary was placed upstream of the rotor such that there was negligible effect on the inlet velocity profile. The outlet was assigned a pressure-based boundary condition, the gauge pressure was assigned zero, and a turbulence intensity of 1%. The surface of the blades is considered a rotatory wall and is assigned a no-slip boundary condition. The upper, lower, and lateral sides were assigned symmetry boundary conditions, such that the velocity normal to these sides was zero. The blades rotated at speeds corresponding to TSR values. As the wind turbine operated in an open atmosphere, the working fluid of the rotors under consideration was taken as air with a density of 1.225 kg/m³ and a dynamic viscosity of 1.7894 × 10⁻⁵ Ns/m².

Computational Fluid Dynamics (CFD) method was used to perform all the simulations involved in this study. The methodology approach was borrowed from ²¹. All the geometries and computational domains were developed using ANSYS Design Modeler, then they were subdivided into small finite volumes using ANSYS Mechanical mesh program. The computations were carried out using ANSYS Fluent. The finite volume method (FVM) was used in conjunction with the Reynolds Average Navier-Stoke (RANS) method, which was applied to solve and compute all the governing equations.

From Literature ^{16, 22, 23} SST model, which combines the superior elements of and turbulence models was selected as a closure to the governing equations. The first model is utilized in the inner part of the boundary layer. The SST then switches to the standard in the core region of the flow, which is the wake region of the boundary layer and free shear layers. Another advantage that sets the SST model apart is the eddy viscosity formulation, which is modified to take into account the effect of turbulent shear stress transportation, which is fundamental in predicting severe adverse pressure gradient flows.

The governing equations of the model are expressed as follows;

(1)

(2)

where , and are the mean flow velocity components, density and pressure, respectively, is the Cartesian coordinate and t is time. For the case of rotating reference the centrifugal and Coriolis are incorporated in the specific body force and is the time-averaged viscous stress tensor components.

The closure SST is expressed as shown in Eq. 3 and 4 below,

(3)

(4)

where k is turbulent kinetic energy, S is the invariant measure of the strain rate, is 0.856,

A Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm was used to decouple velocity and pressure in a segregated manner. The convergence criterion of the x, y, and z velocities, k, and omega residuals was set at 10^-5 apart from the residual for the continuity equation, which was set at 10^-4.

3. Results and Discussion

The primary parameters in this study are power coefficient, TSR and torque coefficient calculated using Eq. 5, 6 and 7.

(5)

(6)

(7)

Where, , , , , A, R, V, u are power available, power generated at the rotor, torque generated by the rotor, torque available, area swept by rotor, radius of the rotor and free stream velocity and tip speed of the rotor, respectively.

Table 2 shows the amount of torque obtained for the six sets of mesh generated to determine the mesh size that strikes the balance between accuracy and computational rate. Figure 8 illustrates the performance of meshes with varying element sizes.

The results show that coarse elements resulted in poor performance compared to fine meshes. There was minimal torque difference for the mesh in case serial No. 4 as compared to obtained torque in mesh serial No. 5. In terms of mesh convergence, stability and computational rate, the mesh at serial No 4. was deemed satisfactory and it was selected for this study.

To validate the methodology adopted for simulation in this study, the first step was to attempt to replicate experimental data borrowed from ²⁴, who used a conventional Savonius wind turbine having a gap width ratio of 0, aspect ratio of 1, and operating at Reynolds number 4.32 x 10⁵. The results obtained from the CFD simulation were compared with the experimental data since the developed model emulates the same geometric designs as the experiment. The comparison of the results is shown in Figure 9 below.

From the results obtained and from Figure 9 above, the CFD results are in good agreement with the experimental data, where the mean absolute error is 6.974%, which was acceptable. These results also validated using the SST turbulence model for the rest of the simulation. The deviation between experimental and CFD results could be due to inaccurate precision of the model geometry, material properties, and difficulty in quantifying and propagating uncertainties ²⁵.

The torque coefficient of all turbines with varying phase-shift angles was compared, and the results are shown in Figure 10 below.

The turbine with a phase shift of 45⁰ has the highest torque coefficient of 0.3654, while the turbine with a PSA of 90⁰ has the lowest C_T of 0.2499. All the turbines had the highest C_T at a TSR of 0.2 where the C_T was 0.3654, 0.3164, 0.2706 and 0.2499 for turbines with PSAs of 45⁰, 60⁰, 75⁰, and 90⁰_, respectively. The torque coefficient for all the turbines decreased with increasing TSR, such that the least C_T occurred at a TSR of 1.2, with the lowest Cm being 0.0081 for a turbine with a PSA of 90⁰. This observation of a decreasing C_T with an increasing TSR on Savonius turbines was also noted by various researchers, including ^{14, 15}. The lowest C_T for other turbines were 0.0215, 0.0122 and 0.0098 for turbines with PSAs 45⁰, 60⁰ and 75⁰_, respectively.

At low TSR, the wind speed is much higher relative to the speed of the rotating blades. This creates a higher drag force on the concave side of the Savonius rotor blades as they push against the wind. This drag force is what creates the torque on the shaft. As TSR increases, the relative velocity between the wind and the blades decreases, reducing the torque, in turn reducing the torque coefficient. Compared to the rest of the turbines, for the PSA-45⁰ turbines, the blades are positioned such that the advancing blade begins to capture the wind energy more effectively right after the previous blade has passed its peak torque position. This synchronization ensures a more continuous and smoother torque generation, minimizing the torque dips that can occur between blade transitions.

The power coefficients for all the turbines are graphically represented in Figure 11 below. The turbine with PSA 45⁰ performed the best, with a power coefficient of 0.1923 at a TSR of 0.8. Two of the turbines with PSAs 45⁰ and 90⁰, had their best performance at a TSR of 0.8, with the highest Cp of the latter being 0.1434. For the turbine with a PSA of 45⁰ there is a minimal angular displacement or phase shift between the lower and upper stage compared to other turbines tested. This allows for a more continuous and smooth interaction with the wind, reducing the amount of turbulent flow and leading to more consistent aerodynamic forces on the blades.

The rest of the turbines with PSAs 60⁰ and 75⁰ had their best performance at TSR 0.6, where the Cps were 0.1613 and 0.1419, respectively. The turbine with PSA 75⁰ had the lowest performance compared to other turbines, with a discrepancy of 15.08% from the highest Cp recorded. The Cps for all the turbines increased with an increasing TSR until at certain points, 0.6 and 0.8, before decreasing with increasing TSR, a case also observed by ^{5, 26}.

The power coefficient of a wind turbine increases with increasing tip speed ratio up to an optimal point in this study, 0.6 and 0.8, due to improved aerodynamic efficiency and reduced flow separation. Beyond this optimal TSR, the power coefficient starts to decrease because of increased drag forces, unfavorable angle of attack, and mechanical limitations.

Figure 12 and Figure 13 show the contours for all turbines for the upper and lower rotor.

From Bernoulli’s principle, velocity and pressure are inversely proportional, and this is evident from velocity and pressure contours shown in Figure 12 and Figure 13 for both the lower and upper stage rotors. Significant changes in velocity and pressure contours on the upper-stage rotors were caused by changes in phase shift angles. The turbine with PSA 45⁰ had a higher pressure gradient when compared to all the turbines studied, hence, its high performance.

4. Conclusion

A series of numerical simulations were conducted to investigate the impact of phase shift angles (45⁰, 60⁰, 75^0, and 90⁰) on the performance of a two-stage Savonius wind turbine using (CFD). The analysis employed ANSYS software and the SST k-ω turbulence model. The results revealed a significant influence of phase shift angle on the turbine's power and torque coefficients, which are key metrics for wind energy conversion efficiency. The configuration with a phase shift angle of 45° achieved the highest Cp and C_T values of 0.19 and 0.3654. The turbine with a phase shift angle of 75° resulted in the lowest Cp of 0.1419 at its peak TSR of 0.6. The observed trends can be attributed to the interaction between the blade profiles of the two stages at different phase shifts. These findings highlight the importance of optimizing phase shift angle for maximizing the power output of two-stage Savonius wind turbines.

References