# Fluid–Structure Interaction Modeling of Structural Loads and Fatigue Life Analysis of Tidal Stream Turbine

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## Abstract

**:**

## 1. Introduction

_{p}) and thrust coefficient (C

_{t}) are small, but the effects on wake are large. Ahmadi et al. [13] and others studied the evolution of the wake characteristics of horizontal-axis tidal-energy turbines experimentally, followed by numerical simulations of the flow field, using a combination of Large Eddy Simulation (LES) and Augmented Lagrangian Method (ALM) to partition the turbine wake into different regions, suggesting that to study the characteristics of the turbine wake, it is necessary to understand the variation of flow characteristics in the transition zone.

## 2. Basic Theory

## 3. Computational Model

#### 3.1. Numerical Calculation Model

#### 3.2. Grid-Independence Verification

_{p}and C

_{t}values quickly decrease from 4.5 to 6 million grids, and then asymptote with numbers over 6 million. The maximum deformation and stress increases with grid reduction and converges with sizes less than 4 mm. Consequently, using a grid size of 3 mm for the solid and 6 million grids for the fluid saves computational resource without sacrificing accuracy level (<0.1%). The bidirectional fluid–solid coupling simulation was conducted by a computer with 32-cores AMD CPU. The final computation time for each case is 132 h.

#### 3.3. Model Test Validation

_{p}= 0.332–0.345. In general, the FSI simulations deviate more from the measurements than the CFD’s do due to the non-optimal initial twist blade angle and deformation consideration; however, the error is less than 4.01% for the contemplated study’s range (TSR = 3.64–4.32).

## 4. Results Analysis

#### 4.1. Hydrodynamic Performance of Blades

#### 4.2. Blade Structural Stress Analysis

#### 4.3. Blade-Fatigue-Life Analysis

## 5. Conclusions

- (1)
- The difference between the calculated hydraulic turbine power coefficients with and without fluid–structure coupling conditions is not significant, and the deformation of the blade under the bidirectional fluid–structure coupling calculation will have a certain impact on the pressure difference on the blade’s surface.
- (2)
- As a cantilever beam structure, the blade has its maximum stress concentrated in the root of the leaf, and its maximum deformation is located near the tip of the leaf. The change of water depth has little influence on the stress and deformation of the blade, but the change of rotation speed has the most significant influence on it. The blade will be subjected to abrupt load when it is first started, and the increase of rotation speed will increase the abrupt load.
- (3)
- The fatigue-life prediction of the blade of the tidal-energy turbine was carried out. Similar to the blade stress variation, the lower safety factor of the blade is located near the root of the blade, and the blade’s rotation-speed variation has a more significant effect than water depth. The number of stress cycles of the blade at different rotational speeds is within the safety range.
- (4)
- During the design process of the blade, not only the hydraulic performance but also the strength of the blade situation should be taken into consideration.
- (5)
- These results represent an excellent initial step toward the wider use of the coupled fluid structure model due to high computational accuracy and resource efficiency; and toward further testing in more complex situations, such as incoming waves and currents, and floating turbine systems.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Mesh division and constraint setting of solid domain model: (

**a**) mesh of solid domain and (

**b**) constraints on solid domain.

**Figure 7.**Pressure distribution of different blade sections: (

**a**) span = 20%, (

**b**) span = 40%, (

**c**) span = 50%, (

**d**) span = 60%, (

**e**) span = 70%, and (

**f**) span = 80%.

**Figure 13.**Blade safety factor at different water depths: (

**a**) water depth of 0.48 m, (

**b**) water depth of 0.6 m, and (

**c**) water depth of 0.72 m.

**Figure 14.**Blade safety factor at different rotational speeds: (

**a**) 92.69 r/min, (

**b**) 100 r/min, (

**c**) 102.11 r/min, and (

**d**) 110.01 r/min.

Material | Density (kg·m^{−3}) | Young’s Modulus (Pa) | Poisson’s Ratio |
---|---|---|---|

Aluminum 6061 | 2750 | 7e + 10 | 0.33 |

Segmentation Scheme | Grid Size (mm) | Number of Grids | Maximum Deformation (m) | Maximum Stress (MPa) |
---|---|---|---|---|

1 | 6 | 4187 | 0.012049 | 979.2 |

2 | 5 | 6409 | 0.012191 | 984.68 |

3 | 4 | 9616 | 0.012376 | 1122.3 |

4 | 3 | 15,337 | 0.012614 | 1307.5 |

5 | 2 | 43,382 | 0.012691 | 1337 |

Rotational Speed (r/min) | Average Stress (MPa) | Average Deformation (mm) |
---|---|---|

92.69 | 0.339 | 0.543 |

100 | 0.361 | 0.550 |

102.11 | 0.364 | 0.551 |

110.007 | 0.38 | 0.544 |

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**MDPI and ACS Style**

Zhang, Y.; Liu, Z.; Li, C.; Wang, X.; Zheng, Y.; Zhang, Z.; Fernandez-Rodriguez, E.; Mahfoud, R.J.
Fluid–Structure Interaction Modeling of Structural Loads and Fatigue Life Analysis of Tidal Stream Turbine. *Mathematics* **2022**, *10*, 3674.
https://doi.org/10.3390/math10193674

**AMA Style**

Zhang Y, Liu Z, Li C, Wang X, Zheng Y, Zhang Z, Fernandez-Rodriguez E, Mahfoud RJ.
Fluid–Structure Interaction Modeling of Structural Loads and Fatigue Life Analysis of Tidal Stream Turbine. *Mathematics*. 2022; 10(19):3674.
https://doi.org/10.3390/math10193674

**Chicago/Turabian Style**

Zhang, Yuquan, Zhiqiang Liu, Chengyi Li, Xuemei Wang, Yuan Zheng, Zhi Zhang, Emmanuel Fernandez-Rodriguez, and Rabea Jamil Mahfoud.
2022. "Fluid–Structure Interaction Modeling of Structural Loads and Fatigue Life Analysis of Tidal Stream Turbine" *Mathematics* 10, no. 19: 3674.
https://doi.org/10.3390/math10193674