# Research on the Hydrodynamic Performance of a Horizontal-Axis Tidal Current Turbine with Symmetrical Airfoil Blades Based on Swept-Back Models

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## Abstract

**:**

## 1. Introduction

## 2. Backward Swept Blade Design

#### 2.1. Initial Model

#### 2.2. Swept Model

#### 2.3. 3D Model

## 3. Numerical Simulation

#### 3.1. Meshing

#### 3.2. Mesh Independence Analysis

#### 3.3. Calculation and Post-Processing

^{−3}to converge.

## 4. Analysis of Simulation Results

#### 4.1. Starting Torque

#### 4.2. Energy Efficiency Analysis

#### 4.3. Load Analysis

## 5. Experimental Verification

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Spanwise Position (r/R) | Radius r/mm | Chord Length c/mm | Airfoils |
---|---|---|---|

0.09 | 14.94 | − | − |

0.15 | 24.90 | − | circle with radius 10 |

0.20 | 33.20 | 33.44 | NACA0030 |

0.27 | 44.82 | 45.54 | NACA0018 |

0.35 | 58.10 | 43.51 | NACA0018 |

0.40 | 66.40 | 41.49 | NACA0015 |

0.47 | 78.02 | 39.46 | NACA0015 |

0.53 | 87.98 | 37.44 | NACA0015 |

0.60 | 99.60 | 35.42 | NACA0015 |

0.66 | 109.56 | 33.39 | NACA0015 |

0.73 | 121.18 | 31.37 | NACA0012 |

0.79 | 131.14 | 29.34 | NACA0012 |

0.86 | 142.76 | 27.32 | NACA0012 |

0.93 | 154.38 | 25.30 | NACA0012 |

1 | 166.00 | 23.32 | NACA0012 |

Model Type | Offset Equation |
---|---|

1 | ${z}_{offset}=\frac{\left({r}_{\mathrm{r}}-{r}_{start}\right)\left(R\times {P}_{\mathrm{s}}\right)/\left(R-{r}_{start}\right)}{{M}^{\left(\left(1-{P}_{\mathrm{r}}\right)\left(1-{P}_{rstart}\right)/{P}_{\mathrm{r}}\right)}}$ (Kaya 2018) |

2 | ${z}_{offset}=-a\frac{{r}_{r}}{R}+b{\left(\frac{{r}_{r}}{R}\right)}^{2}$ (Hansen 2011) |

3 | ${z}_{offset}=d{\left(\frac{{r}_{r}-{r}_{\mathrm{start}}}{R-{r}_{\mathrm{start}}}\right)}^{\gamma}$ (Larwood 2014) |

Spanwise Position (r/R) | Offset/mm | ||
---|---|---|---|

Model 1 | Model 2 | Model 3 | |

0.09 | 0 | 0 | 0 |

0.15 | 0 | 0 | 0 |

0.20 | 0 | 0 | 0 |

0.27 | 0 | 0 | 0 |

0.35 | 0 | 0.00100 | 0 |

0.40 | 0.649622 | 0.50880 | 0.0982 |

0.47 | 1.843385 | 1.43280 | 0.5657 |

0.53 | 3.082826 | 2.42280 | 1.2729 |

0.60 | 4.728119 | 3.80880 | 2.4556 |

0.66 | 6.277070 | 5.19470 | 3.7757 |

0.73 | 8.214997 | 7.04260 | 5.6734 |

0.79 | 9.968596 | 8.82440 | 7.6065 |

0.86 | 12.10352 | 11.1342 | 10.2193 |

0.93 | 14.31841 | 13.6927 | 13.2171 |

1 | 16.60000 | 16.6000 | 16.6000 |

Scheme | Number of Nodes | Total Number of Grids | Power Coefficient |
---|---|---|---|

1 | 497,198 | 2,068,095 | 0.2527 |

2 | 659,907 | 3,060,727 | 0.2537 |

3 | 889,314 | 4,972,207 | 0.2486 |

4 | 1,000,141 | 5,035,295 | 0.2898 |

5 | 1,639,727 | 7,848,863 | 0.2899 |

Velocity(m/s) | Starting Torque/N.m | ||
---|---|---|---|

Model 1 | Model 2 | Model 3 | |

0.2 | 0.0055851 | 0.0056708 (+1.53%) | 0.0055949 (+0.18%) |

0.3 | 0.0126293 | 0.0126649 (+0.28%) | 0.0126492 (+0.16%) |

0.4 | 0.0225441 | 0.0226049 (+0.27%) | 0.0225837 (+0.18%) |

0.5 | 0.0353502 | 0.0354231 (+0.21%) | 0.0354115 (+0.17%) |

TSR | Power Coefficient | ||
---|---|---|---|

Model 1 | Model 2 | Model 3 | |

2 | 0.05498 | 0.05424 (−1.35%) | 0.05341 (−2.86%) |

3 | 0.16236 | 0.15923 (−1.93%) | 0.16284 (+0.3%) |

4 | 0.2527 | 0.25514 (+0.96%) | 0.25534 (+1.00%) |

5 | 0.21838 | 0.22091 (+1.20%) | 0.22151 (+1.40%) |

6 | 0.10393 | 0.10739 (+3.22%) | 0.1096 (+5.17%) |

TSR | Thrust Coefficient | ||
---|---|---|---|

Model 1 | Model 2 | Model 3 | |

2 | 0.43441 | 0.43453 (+0.03%) | 0.43299 (−0.33%) |

3 | 0.64484 | 0.63774 (−1.1%) | 0.64689 (+0.32%) |

4 | 0.73239 | 0.73574 (+0.457%) | 0.73575 (+0.459%) |

5 | 0.75227 | 0.75575 (+0.46%) | 0.75702 (+0.63%) |

6 | 0.72829 | 0.73242 (+0.57%) | 0.73610 (+1.07%) |

7 | 0.68359 | 0.69225 (+1.27%) | 0.69507 (+1.68%) |

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**MDPI and ACS Style**

Yan, Y.-T.; Xu, S.-M.; Liu, C.; Zhang, X.; Chen, J.-M.; Zhang, X.-M.; Dong, Y.-J.
Research on the Hydrodynamic Performance of a Horizontal-Axis Tidal Current Turbine with Symmetrical Airfoil Blades Based on Swept-Back Models. *J. Mar. Sci. Eng.* **2022**, *10*, 1515.
https://doi.org/10.3390/jmse10101515

**AMA Style**

Yan Y-T, Xu S-M, Liu C, Zhang X, Chen J-M, Zhang X-M, Dong Y-J.
Research on the Hydrodynamic Performance of a Horizontal-Axis Tidal Current Turbine with Symmetrical Airfoil Blades Based on Swept-Back Models. *Journal of Marine Science and Engineering*. 2022; 10(10):1515.
https://doi.org/10.3390/jmse10101515

**Chicago/Turabian Style**

Yan, Yu-Ting, Shi-Ming Xu, Cong Liu, Xiao Zhang, Jian-Mei Chen, Xue-Ming Zhang, and Yong-Jun Dong.
2022. "Research on the Hydrodynamic Performance of a Horizontal-Axis Tidal Current Turbine with Symmetrical Airfoil Blades Based on Swept-Back Models" *Journal of Marine Science and Engineering* 10, no. 10: 1515.
https://doi.org/10.3390/jmse10101515