# Performance Improvement of a Drag Hydrokinetic Turbine

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## Abstract

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## 1. Introduction

_{p max}= 0.31) than the three-blade Savonius rotor. The same conclusion was found with numerical simulations by Zhao et al. [10], who worked on a 180° twist Savonius rotor. Zheng et al. [11] also carried out a numerical study for a modified Savonius rotor with four, five and six blades. They found that the maximum power coefficient is equal to 27.14%, 28.493% and 30.864%, respectively. According to Kamoji et al. [8] and Hayashi et al. [12], a single stage Savonius rotor is more efficient than two and three stage Savonius rotors at the same Reynolds number. The blade shape is another parameter that has been studied to find the optimum form which gives best performances [13,14]. Driss et al. [15] studied the effect of a bucket arc angle on an unconventional Savonius rotor. A novel two-bladed turbine proposed by Roy et al. [16] was tested in the lab and its power and torque coefficients were compared with standard semi elliptic, semi-circular, bach and benesh blade shapes. An important gain of 19.2%, 34.8%, 3.3% and 6.9%, respectively, is obtained. A combined elliptical and conventional Savonius rotor was investigated by Hassan et al. [17], obtaining an improvement of 35.9%.

## 2. Materials and Methods

#### 2.1. Experimental Test Rig

^{−1}, a width of 0.6 m and a height of 0.5 m (Figure 2b). A Pitot tube is used to measure the water flow velocity upstream the rotor.

#### 2.2. Savonius Rotor Physical Model

#### 2.3. Experimental Apparatus

_{T}) and power coefficient (C

_{P}), by measuring the load applied on the rotor shaft along with its rotational speed. It consists of four rectangular plates acting as a supporting structure which houses the Savonius rotor. The rotation of the rotor shaft is conducted by two ball bearings which are mounted at the top and at the bottom of the metallic structure.

_{T}), the power coefficient (C

_{P}) and the Tip Speed Ratio (TSR), were expressed by the following equations:

- T
_{r}: The dynamic torque, - ω: The angular velocity,
- ρ: The water density,
- A: The area of the rotor blade,
- V
_{∞}: The water flow velocity, - R: The radius of the rotor.

- F
_{r}: The force applied on the rotor shaft, - r
_{p}: The radius of the pulley, - r
_{n}: The radius of the nylon string, - M: The mass loaded on the weighing pan,
- m: The spring balance load reading.

## 3. Numerical Procedures

- $\overline{{u}_{i}}$: The averaged velocity,
- $\overline{p}$: The averaged pressure,
- $\upsilon $: The kinematic viscosity,
- ${\tau}_{ij}$: The specific Reynolds Stress tensor.

#### 3.1. Computation Domain and Boundary Conditions

^{−1}is set as b.c. at the front face of the 3D computational domain, and the outlet boundary condition is set in the rear front [28,29]. For the side and bottom faces of the domain, a slip boundary condition is applied in order to reduce the lateral boundary effect of the experimental channel. The top surface of the domain is assumed as a symmetry boundary condition. It is assumed that the turbine operates at the proper depth in order to reduce the surface effect, and free surface effects are neglected in the simulation. At the vanes of the Savonius rotor, a no-slip moving walls condition is imposed. Turbulence intensity and viscosity are, respectively, set equal to 5% and 10% for both inlet and outlet.

#### 3.2. Meshing

#### 3.3. Deflector System

## 4. Experimental Results and Validation

^{−1}. The performance characteristics such as C

_{P}and C

_{T}are calculated experimentally using a rope type dynamometer. The C

_{T}and C

_{P}are plotted versus TSR, as shown in Figure 8.

_{T}equal to zero, could be evaluated. The maximum rotational speed is equal to 119 rpm. The increase in the braking torque on the rotor shaft raises the C

_{T}at the cost of a reduction in the rotational speed and in TSR, up to a maximum value. Further reduction in the TSR leads to a quick increase in C

_{T}. The maximum C

_{T}is equal to 0.25 at TSR = 0.54. For the variation of C

_{P}versus TSR, it has been observed that C

_{P}follows the same behavior as C

_{T}, but attains the maximum value of 0.14 at a larger TSR, equal to 0.69. Table 3 shows the systematic error for the different experimental apparatus which are used in this work.

_{T}with respect to TSR. However, from 910,000 to 1.4 million, the change in C

_{T}is negligible. Therefore, the fine mesh is assumed as the best grid level for the present simulation to optimize the computational time.

_{P}with TSR for different numerical simulations, which seems to be in good agreement with the experimental data. The average error value is about 4.6%. Thus, the numerical model is appropriate for predicting the impact of the deflector system on both hydrodynamic and performance parameters of the Savonius rotor.

## 5. Numerical Results

#### 5.1. Velocity Distribution

^{−1}, as set in the boundary conditions for all studied cases. Without a deflector, the presence of a slowing zone of the water velocity upstream the rotor has been noted. In fact, the Savonius rotor is considered as a barrier in front of the flowing water. When the rotor starts to rotate, different important zones are developed, i.e., a high-velocity zone and a wake zone. In fact, it has been observed that a high velocity zone is developed at the tip of the returning vane. In addition, cyclical high flow velocity zones have been noticed near the wake zone of the flow velocity created downstream the rotor. This fact could be explained by the increase in the flow speed after passing the wake zone. By installing a deflector upstream the rotor, a noticeable increase in the peak value of the flow velocity has been observed. Indeed, this peak value has been noted at the tip of the returning vane for all deflector designs. The improvement of the flow velocity near the rotor vanes could be explained by the enhancement of the rotational speed of the Savonius rotor due to the large water volume absorbed by the deflector plates. The maximum magnitude velocity is V = 1.71 m·s

^{−1}, V = 1.75 m·s

^{−1}, V = 1.80 m·s

^{−1}, V = 1.97 m·s

^{−1}and V = 2.12 m·s

^{−1}for the configuration without a deflector, α = 15°, α = 20°, α = 25° and α = 30°, respectively. Comparing the different distributions, it could be confirmed that the different deflector designs affect the flow velocity around the rotor.

^{−1}(Figure 12a). A deceleration is observed in Figure 12b,c, which corresponds to the area around the rotor. From Figure 12b and for an interval ranging from y = −0.1 m to y = 0 m and corresponding to the area in front of the concave side of the advancing blade, the velocity of the water directed to the concave side increases with the use of the deflector system compared to that without deflector. For an interval ranging from y = 0 m to y = 0.1 m and corresponding to the area in front of the convex side of the returning blade, the velocity of the water directed to the convex returning blade decreases with the use of deflector systems compared to that without a deflector. Indeed, the role of the deflector system mentioned before is confirmed. Downstream, while moving away from the rotor, the velocity starts to increase (Figure 12d). This increment characterizes the wake zone, which gradually disappears with the increase in the downstream distance, and this behavior is enhanced by the increment of the deflection angle. Comparing all configurations, it turns out that the addition of the deflector system positively affects the flow filed around the Savonius rotor in terms of velocity magnitude. The increment of the deflection angle, based on these findings, improves the predicted net torque. The highest increment is obtained for a deflection angle equal to α = 30°.

#### 5.2. Total Pressure

_{pr}) shown in Figure 14 is plotted along the y coordinate with incoming water in the x direction. As it is depicted in Figure 14a, positive values of the y coordinate correspond to the convex side of the returning blade and negative values correspond to the concave side of the advancing blade. From Figure 14b, the highest-pressure coefficient on the concave side of the advancing blade is obtained for α = 30°, corresponding to C

_{pr}= 0.33 against the value C

_{pr}= 0.2 obtained without a deflector. Therefore, a higher positive drag is obtained for α = 30°. From Figure 14c, the pressure coefficient on the convex side of the returning blade decreases with the increase in the deflection angle. Its lowest value is computed for α = 30°, corresponding to C

_{pr}= 2.07 against the value C

_{pr}= 0.31 obtained without a deflector. Therefore, a lesser negative drag is obtained. Thus, the highest total drag is obtained with a deflection angle of α = 30°.

#### 5.3. Turbulent Kinetic Energy

#### 5.4. Turbulence Eddy Dissipation

#### 5.5. Turbulent Viscosity

#### 5.6. Turbulent Intensity

#### 5.7. Performance Characteristics

_{T}= 0.20 for the configuration without a deflector to C

_{T}= 0.23 for α = 30°. Thus, a significant improvement in the predicted net torque is obtained. This fact is justified by the reduction in the negative drag force by preventing the convex returning blade from the incoming water and the increase in the positive drag force by redirecting the water flow to the concave advancing blade.

_{p,max}= 0.163 at a tip speed ratio TSR= 0.81. For the configuration without a deflector, the maximum power coefficient is equal to C

_{p,max}= 0.143 at a tip speed ratio TSR = 0.7. Thus, we numerically confirm an improvement in C

_{P}by 14%.

## 6. Conclusions

_{∞}= 0.86 m·s

^{−1}. In addition, a deflector system was suggested and four deflector designs were numerically tested to examine their influence on the efficiency of the Savonius rotor. Computational investigations were conducted by means of the CFD code ANSYS FLUENT 17.0. The main outputs of this paper are summarized as follows:

- The rotational speed of the Savonius rotor reaches a peak value of 119 rpm.
- The maximum experimental power coefficient C
_{p max}= 0.14 is reached at a tip speed ratio equal to TSR = 0.69. - From the numerical results, it has been confirmed that the performance parameters of the Savonius rotor are improved with the use of the upstream deflector.
- The most performant configuration over the different studied cases gives an improvement of 14% in the power coefficient.
- The proposed deflector system affects the flow characteristics around the Savonius rotor.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{1ε} | constant of the k-ε turbulence model, dimensionless |

c | vane chord, m |

D | Savonius turbine diameter, m |

G_{k} | production term of turbulence, kg·m^{−1}·s^{−3} |

H | Savonius turbine height, m |

k | turbulent kinetic energy, m^{2}·s^{−2} |

$\overline{p}$ | average pressure, Pa |

R | Savonius turbine radius, m |

s | turbine shaft diameter, m |

T_{r} | turbine torque, N·m |

t | time, s |

u_{j} | velocity components, m·s^{−1} |

${u}_{i}^{\prime}$ | fluctuating velocity components, m·s^{−1} |

V_{∞} | flow velocity, m·s^{−1} |

x_{i} | Cartesian coordinate, m |

x | Cartesian coordinate, m |

y | Cartesian coordinate, m |

z | Cartesian coordinate, m |

ε | dissipation rate of the turbulent kinetic energy, W·kg^{−1} |

μ | dynamic viscosity, Pa·s |

μ_{t} | turbulent viscosity, Pa·s |

ρ | density, kg·m^{−3} |

ω | turbine rotational speed, rad·s^{−1} |

TSR | tip-speed ratio, dimensionless |

σ_{k} | constant of the k-ε turbulence model, dimensionless |

σ_{ε} | constant of the k-ε turbulence model, dimensionless |

ψ | Savonius turbine vane twist angle, ° |

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**Figure 1.**Geometrical parameters of Savonius rotor [12].

Parameter | Value |
---|---|

Rotor diameter (D) | 160 mm |

Rotor height (H) | 200 mm |

End plate diameter (De) | 165 mm |

Shaft diameter (s) | 20 mm |

Number of blades | 2 |

Blade chord (d) | 90 mm |

Blade thickness | 2 mm |

Blade twist angle (ψ) | 90° |

Configuration | H (mm) | L1 (mm) | L2 (mm) | L3 (mm) | Ra (mm) | β (°) | γ (°) |
---|---|---|---|---|---|---|---|

α = 15° | 200 | 115 | 100 | 110 | 110 | 20 | 35 |

α = 20° | 200 | 115 | 100 | 110 | 110 | 20 | 35 |

α = 25° | 200 | 115 | 100 | 110 | 110 | 20 | 35 |

α = 30° | 200 | 115 | 100 | 110 | 110 | 20 | 35 |

Experimental Apparatus | Systematical Error |
---|---|

Pitot tube | 1% |

Electrical balance | 2% |

Non-contact digital tachometer | 3% |

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**MDPI and ACS Style**

Mosbahi, M.; Lajnef, M.; Derbel, M.; Mosbahi, B.; Aricò, C.; Sinagra, M.; Driss, Z.
Performance Improvement of a Drag Hydrokinetic Turbine. *Water* **2021**, *13*, 273.
https://doi.org/10.3390/w13030273

**AMA Style**

Mosbahi M, Lajnef M, Derbel M, Mosbahi B, Aricò C, Sinagra M, Driss Z.
Performance Improvement of a Drag Hydrokinetic Turbine. *Water*. 2021; 13(3):273.
https://doi.org/10.3390/w13030273

**Chicago/Turabian Style**

Mosbahi, Mabrouk, Mariem Lajnef, Mouna Derbel, Bouzid Mosbahi, Costanza Aricò, Marco Sinagra, and Zied Driss.
2021. "Performance Improvement of a Drag Hydrokinetic Turbine" *Water* 13, no. 3: 273.
https://doi.org/10.3390/w13030273