# Effect of Blade Diameter on the Performance of Horizontal-Axis Ocean Current Turbine

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

_{m}value is about 0.24 J at a tip-speed ratio (TSR) of 0.8 at a constant speed of 0.7 m/s. From 1 TSR onward, a further decrease occurs in the power coefficient. That point indicates the optimum velocity at which maximum power exists. The pressure contour shows that maximum dynamic pressure exists at the convex side of the advancing blade. The value obtained at that place is −348 Pa for case 1. When the dynamic pressure increases, the power also increases. The same trend is observed for case 2 and case 3, with the same value of optimum TSR = 0.8.

## 1. Introduction

_{p}of the turbine by 80% [26]. A higher-pressure differential ratio was achieved by a decrease in negative torque value on the blade. The ratio obtained between the approaching and returning blade led to a high torque and eventually higher power coefficient. The power coefficient was also enhanced by lowering the depth of the submersion of the turbine. The turbine’s overall efficiency was also noted to increase [27].

## 2. Theory

#### 2.1. CFD Description

_{x}, G

_{y}, G

_{z}) represents body acceleration and (${f}_{x},{f}_{y},{f}_{z})$ represents the viscous acceleration in the respective direction (x, y, z). The velocity in the x, y, and z-direction is represented by u, v, and w, respectively, where A

_{x}, A

_{y}, and A

_{z}show the area vector in the x, y, and z-directions, repectively. The density of the water is $\rho $, R

_{sur}is the source term for density, and t is time.

#### 2.2. Standard k-ε Turbulence Model

^{−3}. In this case, the Y + value is 30, which determines that the k-epsilon model is suitable.

_{k}is used to produce turbulent kinetic energy caused by the gradient velocity; N

_{b}expresses the turbulent K.E, which results in the courtesy of buoyancy; D

_{M}is the subsidy of fluctuating dilation to dissipation. x

_{i}is the coordinate of the ith direction, µ is the viscosity, σk and σε are the turbulent Prandtl numbers, C$\mu $ is a constant, and its value is 0.09. The value of C$\mu $ came from the number of iterations for a wide range of turbulent flows [21,29].

#### 2.3. Performance of Equation

_{m}represents the torque coefficient; Q is the torque extracted from the numerical simulation; A

_{s}is the turbine’s swept area, whose value is 0.665 m

^{2}(A = H*D); r is the radius of the rotor.

_{p}represents the power coefficient.

## 3. Numerical Setup

#### 3.1. Geometry Modeling

#### 3.2. Meshing

_{m}value for different refinement levels. The refinement level indicates a stable value as the mesh size decreases. Such a process has been practiced in advanced structures too [13,30].

## 4. Result and Discussion

#### 4.1. Velocity and Pressure Contour

_{p}for each design can be calculated. As the pressure contour plot of all cases shows, the side static pressure decreases from upstream to the turbine downstream. The color scheme shows that pressure decreases from 331 Pa to −663 Pa for case 1 in Figure 8. For the remaining cases, the same trend is observed. At the downstream side of the blade, negative static pressure exists. The negative static pressure indicates a higher velocity. Higher velocity results in the rotation of the turbine. The same trend follows for Case 2 and Case 3, as shown in Figure 9 and Figure 10, respectively.

#### 4.2. Comparison of Torque and Power Curve

^{−3}, and a maximum value of torque of 8.49 J is achieved for TSR 0.6. Torque is directly proportional to power. From the numerical values given in Table 3 and the plots in Figure 14 and Figure 15, the highest value of C

_{m}is achieved to be 0.225 J, 0.2 J, and 0.24 J, at a tip speed ratio of 1. From the results, it is clear that Case 3 has the highest C

_{m}performance value. Hydrokinetic turbines are used due to the higher smoothness and stability compared to a wind turbine, but achieving an efficiency above 35% from the hydrokinetic turbine is difficult. For low heads, this type of turbine design should be used for ocean power with low heads that are less stressful. In a techno-economic analysis, using a hydrokinetic turbine independent of the river has not been of much economic benefit, but if one of the generators is responsible for synchronization or a hybrid system, it can be costly and profitable [21].

## 5. Conclusions

_{m}value of about 0.24 J. The turbine is located at the center of the outer domain. Our study concludes that the tip speed ratio increases the power coefficient from 1 TSR, further decreasing the power coefficient. This point indicates an optimum velocity at which the maximum power exists. In the future, the increase in efficiency can be made possible by optimizing the aspect ratio. The present study only considers the variation in the inner diameter of the rotor. Future work will include the deflector and end plates of the blade. According to our research, the Savonius turbine improves with the deflector and end plates; however, the present turbine also operates on a similar drag mechanism.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations and Symbols

CFD | Computational Fluid Dynamics |

HAOCT | Horizontal-Axis Ocean Current Turbine |

VAOCT | Vertical-Axis Ocean Current Turbine |

OCT | Ocean Current Turbine |

TSR | Tip Speed Ratio |

N_{k} | Production term of turbulent kinetic energy because of the gradient of mean velocity |

N_{b} | The turbulent kinetic energy due to buoyancy |

DM | Contribution of fluctuating dilation to the all-inclusive dissipation rate |

x_{i} | Coordinate in the ith direction |

$\mu $ | Dynamic viscosity |

${\mu}_{t}$ | Turbulent dynamic viscosity |

${\sigma}_{k}$, ${\sigma}_{\epsilon}$ | Turbulent Prandtl numbers for ‘k’ and ‘$\epsilon $’ respectively, have a value of 0.39. |

A_{x}, A_{y}, A_{z} | Areas in the direction x, y, z, respectively |

u, v, w | Velocities in the x, y, z-direction, respectively |

A1ε, A2ε, A3ε | Model constants |

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**Figure 15.**Variation in the power coefficient against Tip Speed Ratio (TSR) of different cases compared to the numerical data [21].

Refinement Level | No of Mesh Cell | Torque |
---|---|---|

1 | 912,375 | 7.265479 |

2 | 1,097,000 | 8.768413 |

3 | 1,164,860 | 9.669196 |

4 | 1,456,978 | 9.671234 |

Velocity (m/s) | Tip Speed Ratio (TSR) | Angular Velocity (Rad/s) |
---|---|---|

0.7 | 0.6 | 0.885 |

0.7 | 0.8 | 1.17 |

0.7 | 1 | 1.474 |

0.7 | 1.2 | 1.768 |

**Table 3.**Comparative values of C

_{m}and C

_{p}for different blade designs at different Tip Speed Ratios (TSRs).

Tip Speed Ratio | Case 1 | Case 2 | Case 3 | Published Numerical Results [21] | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Torque | C_{m} | C_{p} | Torque | C_{m} | C_{p} | Torque | C_{m} | C_{p} | ||

0.6 | 8.4964 | 0.11 | 0.066 | 9.48659 | 0.1228 | 0.0736918 | 9.66793538 | 0.12516 | 0.0751 | 0.08 |

0.8 | 12.1227 | 0.15694 | 0.12556 | 13.5881 | 0.1759 | 0.1407367 | 14.9248751 | 0.19322 | 0.1545 | 0.17 |

1 | 17.4458 | 0.22586 | 0.225866 | 15.448 | 0.2 | 0.2 | 18.2490398 | 0.23626 | 0.23626 | 0.185 |

1.2 | 11.586 | 0.15 | 0.18 | 12.3584 | 0.16 | 0.192 | 13.517 | 0.175 | 0.21 | 0.17 |

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**MDPI and ACS Style**

Ahmed Zaib, M.; Waqar, A.; Abbas, S.; Badshah, S.; Ahmad, S.; Amjad, M.; Rahimian Koloor, S.S.; Eldessouki, M.
Effect of Blade Diameter on the Performance of Horizontal-Axis Ocean Current Turbine. *Energies* **2022**, *15*, 5323.
https://doi.org/10.3390/en15155323

**AMA Style**

Ahmed Zaib M, Waqar A, Abbas S, Badshah S, Ahmad S, Amjad M, Rahimian Koloor SS, Eldessouki M.
Effect of Blade Diameter on the Performance of Horizontal-Axis Ocean Current Turbine. *Energies*. 2022; 15(15):5323.
https://doi.org/10.3390/en15155323

**Chicago/Turabian Style**

Ahmed Zaib, Mansoor, Arbaz Waqar, Shoukat Abbas, Saeed Badshah, Sajjad Ahmad, Muhammad Amjad, Seyed Saeid Rahimian Koloor, and Mohamed Eldessouki.
2022. "Effect of Blade Diameter on the Performance of Horizontal-Axis Ocean Current Turbine" *Energies* 15, no. 15: 5323.
https://doi.org/10.3390/en15155323