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Department of Ocean System Engineering, Jeju National University, Jeju 63243, Korea

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Received: 01 December 2023 Accepted: 19 February 2024 Published: 23 February 2024

© 2024 by the authors; licensee SCIEPublish, SCISCAN co. Ltd. This article is an open access article distributed under the CC BY license (https://creativecommons.org/licenses/by/4.0/).

ABSTRACT:
Despite that ocean current energy is one of the promising sources of electricity produced in the ocean, the development of ocean current energy is far behind compared to other ocean energy due to the low efficiency and high cost of installation and maintenance. Among many converting devices, the Savonius turbine has been proven to be effective and competitive in harnessing ocean current energy. The primary purpose of the present study is to search for the optimum shape of a Savonius rotor based on CFD simulation (Star-CCM+). A Savonius turbine composed of two rotating cup-shaped rotors is selected as a numerical model. We focus on the effect of two geometry parameters such as the overlap and gap ratio on the power coefficient. Throughout the parametric study, the shape of a Savonius rotor affects the power performance, and two geometry parameters with an overlap ratio of 0.15 and a gap ratio of −0.03 are found to be the optimum design. It demonstrates stable performance within the wide TSR (Tip Speed Ratio) range of 0.6 to 1.6, with the maximum power coefficient *C*_{p} of 0.34 achieved at a TSR of 0.8. According to the numerical results based on the new CFD model, the presence of a bottom wall does not significantly affect the performance of a Savonius turbine. It means that the present unbounded CFD model can be acceptable in the initial design stage for the determination of the geometry parameters of a Savonius turbine.

Keywords:
Savonius turbine; Overlap ratio; Gap ratio; Power coefficient; CFD

In the modern days, electricity has become an indispensable element of daily life. However, a significant portion of electricity is still generated from fossil fuels such as coal, oil, and gas, giving rise to serious environmental problems like global warming, which in turn leads to severe floods and droughts worldwide [1]. Therefore, to prevent the earth from being hotter, governments and researchers must develop renewable clean energy as an alternative to fossil fuels. Solar, hydropower, wind, biomass, geothermal, and ocean energy belong to renewable and clean energy. The electricity produced from hydropower, solar, wind, and geothermal are currently used in several countries. But, despite the potential of ocean energy, challenges remain in the research and development of efﬁcient energy converting devices, assessment of environmental impact, and establishment of policies and regulations. Even though the commercialization of ocean energy is way slower compared to other renewable energy sources, ocean energy will allow millions of homes to be powered soon [2].
Ocean energy exists in the forms of wind, wave, ocean/tidal current, and thermal and salinity gradients. It is estimated that this potential ranges from 20,000 to 80,000 terawatt-hours (TWh) of electricity annually, which is 100–400% of current global demand. Ocean energy development lags significantly in technical maturity when compared to other renewable sources like onshore wind and solar. However, as has been demonstrated in the case of the development of onshore wind and solar energy, the difficulty of ocean energy development will be overcome. Also, economic feasibility will be greatly increased by investment, innovation, and installation of prototypes. Recently, most of the researchers focused on ocean/tidal current energy owing to uniformity. As a conversion system from the kinetic energy inherent in water movement to mechanical energy, a variety of turbines connected to the generator are essentially used. The hydrokinetic turbine suitable for ocean/tidal current converter must be designed considering the following: initial installation cost, maintenance fee, efficiency, and working even at low-velocity conditions. Turbines may be classiﬁed as horizontal-axis turbines (HATs) and vertical-axis turbines (VATs) [3]. When considering the installation site, an appropriate type of turbine need to be selected.
A Savonius rotor rotates due to the drag force exerted by the moving fluid. These crossflow systems are not highly efficient, primarily because the difference in the drag forces between the two curved surfaces is available to turn the rotor. The concave surface captures the moving fluid, inducing more drag than the convex surface. Even though a Savonius rotor shows low efﬁciency, it has the advantage that it can self-start in low-speed flow conditions [4]. Efﬁciency has been improved further by using more elaborate developed design tools, recently. Regarding the Savonius rotor, much research has been conducted to improve its performance, such as the aspect ratio (AR) [5,6], overlap ratio (OR) [6,7], number of blades [5,8,9], blade shape, addition of end plate, and rotor angle. Although studies on the Savonius rotor working in water are scarce, they show that the hydrokinetic Savonius rotor can produce greater energy than the aerodynamic Savonius rotor [10].
Nakajima et al. (2008) tested the environmentally sustainable Savonius hydraulic turbine. They evaluated the effect of two parameters such as the clearance ratio and rotation direction of the Savonius rotor. Here the clearance ratio means the gap distance between the rotor and the bottom surface divided by a turbine diameter. According to their research, a turbine shows the best performance when a turbine rotates counterclockwise, and the clearance ratio is greater than 0.73. They showed that the variation of the flow field around the rotor due to the clearance ratio affected its performance [11].
In addition, the adjustment of the separation gap between two rotors can have a significant impact on the rotor’s performance. This separation gap accelerated the fluid flow from the concave side of the advancing rotor to the returning rotor, thereby reducing negative torque. The separation gap can be subdivided by two key parameters, such as the overlap ratio and gap ratio. According to the related studies, it was reported that the optimum overlap ratio was within the range of 0.15–0.30 [12]. Most studies focused mainly on the overlap ratio, on the other hand, the effect of the gap ratio on the efficiency of the Savonius rotor was not reported much.
Ushiyama and Nagai (1988) conducted experiments on a conventional Savonius wind turbine with two cup-shaped rotors with five different gap ratios. They observed that the gap ratio of −0.05 yielded the best performance among them. Also, it was found that an increase in the gap ratio between the two rotors led to a decrease in the torque coefficient throughout intensive experiments. They recommended that it is advisable to give a small negative gap ratio to the Savonius rotor [13].
Kerikous and Thevenin (2019) carried out the numerical calculations using Star-CCM++ and in-house optimization code (OPAL++) was used to search for the optimum overlap ratio (OR) and gap ratio (GR) on the Savonius hydrokinetic turbine. Within a variation range of OR and GR from 0 to 0.42, the optimum range of OR is between 0.12–0.21, and the optimum GR is around 0.033 [14]. Their study only focused on the positive gap ratio. Hence, the negative gap ratio on a Savonius hydrokinetic turbine is still in the veil and requires additional research.
The present study assesses the performance of the Savonius hydrokinetic rotor by investigating the power coefficient in the combination of overlap ratio and gap ratio, including positive and negative gap ratio. The computational fluid dynamics (CFD) simulation was conducted with an unbounded model, in which symmetric conditions at the top and bottom boundary are imposed. It helps to reduce the simulation time, but the influence of the adjacent boundaries such as the bottom wall and free surface on the turbine’s performance need to be investigated. Therefore, a new CFD model with a non-slip condition at the bottom wall is examined to verify the effect of the bottom wall on the performance of a Savonius turbine. The SST k-ω turbulent mode with Reynolds-Averaged Navier-Stokes (RANS) formulations is employed for CFD simulation. The Savonius turbine consists of two cup-shaped rotors. Notably, the present study focuses on the comprehensive investigation of the effect of a variety of overlap ratios and gap ratios on the hydrodynamic performance of the Savonius turbine in uniform flow. The present paper is organized into four sections. Section 2 presents the key design parameters affecting the power of a Savonius rotor. Section 3 demonstrates the mesh generation and the computational domain setup. Section 4 shows the validation of the present CFD model through the comparison of Nakajima’s experiment, and the detailed results and discussion on the effects of the overlap ratio and gap ratio on the hydrodynamic performance of a Savonius rotor. Section 5 summarizes the main conclusions drawn from the present study.

In the ocean current with speed *U*, the power across a cross-sectional area (*A*) can be expressed by the following equation.
where *ρ* is the sea water density (=1024 kg/m^{3}).
A fraction of the ocean energy that passes through the energy conversion system can be extracted [14] for electricity. This ratio of the extracted power to input power is called as power coefficient, *C*_{P}, and can be expressed as:
where *P*_{E} which is the mechanical power extracted through the conversion system is expressed by:
where *Q* is the torque (Nm) and *ω* the angular velocity of a rotor, and *N* is the revolution-per-minute (RPM).
The power coefficient is closely dependent on the tip speed ratio (TSR), which is defined by the ratio of the speed of the tips of the rotor to the undisturbed current speed *U*. Given a rotor radius of *R*, the TSR (*λ*) can be expressed as:
Besides the power coefficient, the torque coefficient (*C*_{t}) is also an important parameter in determining the performance of the Savonius rotor:
The numerical rotor model as shown in Figure 1 is the same as an experimental model adopted by Nakajima et al. [11]. The specification of a rotor model is listed in Table 1.
Two key parameters affecting the rotor’s performance are the overlap ratio and the gap ratio (Figure 2). The overlap ratio (OR) is defined as the ratio of the overlap distance (*e*) to the diameter (*D*_{B}) of a rotor as follows:
On the other hand, the gap ratio (GR) is the ratio of the gap distance (*s*) to the diameter of a rotor.

```latex
P_I=\frac{1}{2} ρAU^3
```

```latex
C_P=\frac{P_E}{P_I} =\frac{P_E}{0.5ρAU^3}
```

```latex
P_E=Qω=\frac{2πNQ}{60}
```

```latex
λ=\frac{ωR}{U}
```

```latex
C_t=\frac{Q}{Q_I}=\frac{Q}{0.5ρAU^2 R}
```

```latex
\text{OR}=\frac{e}{D_B}
```

```latex
\text{GR}=\frac{s}{D_B}
```

In this study, we performed a comprehensive parameter study on the shape of a Savonius rotor, focusing on nondimensional parameters such as gap ratio and overlap ratio. From this investigation, several key conclusions have been drawn:
1. The findings obtained from CFD simulations show the Savonius rotor with an overlap ratio of 0.15 achieves a peak efficiency of 0.334 at a TSR of 0.8, while an overlap ratio of 0.3 exhibits stable behavior across the TSR range of 0.6 to 1.6.
2. Regarding the gap ratio, the negative gap ratio demonstrates slightly higher power coefficients at a lower TSR range showing a sudden drop in a high range of TSR, whereas the positive gap ratio provides a wider operational range without a sudden decline.
3. The separation gap (gap ratio and overlap ratio) of a Savonius rotor affects the patterns of wake vorticity downstream behind the rotor and the rotor tip vortex. The performance of a Savonius rotor depends on the characteristics of these vortices, which cause unfavorable energy dissipation.
4. From the parametric study with two parameters such as the gap and overlap ratio, a Savonius rotor with an overlap ratio of 0.15 and a gap ratio of −0.03 is proved to be an optimum shape. A Savonius rotor designed from this combination demonstrates stable performance within the wide TSR range of 0.6 to 1.6, together with a highest power coefficient of 0.34 achieved at a TSR of 0.8.
5. The effect of the bottom wall on the performance of a Savonius turbine is also investigated. The maximum power coefficient is achieved at Cr/DR of 1.7 in the low TSR region less than 1.0. However, the bottom wall with different gap distances follows the trend of an unbounded model, without significant quantitative difference. It indicates clearly that the unbounded CFD model is acceptable in the preliminary design stage.

The researcher uses this opportunity to express our appreciation to NIIED (National Institute for International Education) sponsored by Korean Ministry of Education.

M.A.R.: Conceptualization, Formal Analysis, Writing – Original Draft Preparation. A.G.: Investigation, Writing – Review & Editing. I.H.C.: Supervision, Writing – Review & Editing.

Not applicable.

Not applicable.

This research received no external funding.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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