# Aerostructural Design Optimization of Wind Turbine Blades

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions, as suggested by the Intergovernmental Panel on Climate Change (IPCC) [1].

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Baseline Wind Turbine Blades

#### 3.2. Aerostructural Optimization Framework

#### 3.3. RANS-Based Turbulent Simulation

^{2}/s

^{2}, 0.2 m

^{2}/s

^{3}, 5 × 10

^{−5}m

^{2}/s, 12.24 s

^{−1}, and 5 × 10

^{−5}m

^{2}/s, respectively. The inlet velocity of the fluid is 7 m/s, and the blade has a rotational velocity of 72 rpm. The initial values for the boundary conditions are calculated based on the turbulence free-stream boundary conditions.

#### 3.4. Structural Model

#### 3.5. Discrete Adjoint Derivative Computation

- (1)
- Figuring out the partial derivatives ${\left[\partial f/\partial \omega \right]}^{T}$ and ${\left[\partial R/\partial \omega \right]}^{T}$
- (2)
- The adjoint vector $\psi $ in the linear Equation (13) solution.
- (3)
- The method of computing the partial derivatives $\partial f/\partial x$ and $\partial R/\partial x$.
- (4)
- Calculate the total derivative $df/dx$ using Equation (15).

#### 3.6. Aerostructural Coupling

#### 3.7. Baseline Geometry Configuration for Aerostructural Optimization

## 4. Mesh Convergence and Validation

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Blade geometry [33].

**Figure 5.**(

**a**) Spherical volume mesh; (

**b**) hyperbolic expansion layer; (

**c**) aerodynamic surface mesh; (

**d**) structural mesh; (

**e**) FFD points for aerodynamic optimization; (

**f**) structural design variables (in terms of panels with random colors).

**Figure 6.**Comparison of the pressure coefficients (Cp) from level 2 mesh and NREL experimental data.

**Figure 7.**(

**a**) Pressure on the blade on the aerodynamic side (Pa); (

**b**) stress on the structural side (Pa).

**Figure 8.**(

**a**) Cp comparisons before and after the optimization in terms of 30%, 63%, and 95% spanwise section; (

**b**) shape changes in the cross-section profiles accordingly.

Boundary Conditions | Blade | Inout |
---|---|---|

Epsilon | epsilonWallFunction | inletOutlet |

Nut | nutUSpaldingWallFunction | fixedValue |

nuTilda | fixedValue | inletOutlet |

K | kqRWallFunction | inletOutlet |

Omega | omegaWallFunction | inletOutlet |

P | zeroGradient | fixedValue |

U | fixedValue | inletOutlet |

**Table 2.**Mesh convergence by comparing the torque result from simulation against experimental value.

Mesh# | L0 | L1 | L2 | NREL Exp. |
---|---|---|---|---|

Mesh type | Fine mesh | Medium mesh | Course mesh | - |

Cells (million) | 25.3 | 10.12 | 2.53 | - |

Torque (Nm) | 743.2 | 705.1 | 678.4 | 785 |

Error (%) | 5.35 | 10.19 | 13.63 | - |

HPC Workstation | CPU Time (hours) | ||
---|---|---|---|

Model | Intel^{®} Xeon(R) CPU E5-2699 v4 @ 2.20GHz | CFD with L0 | 7.5 |

Processors | 88 | CFD with L | 5.3 |

RAM | 503.8GB | CFD with L2 | 2.1 |

OS | Ubuntu | Optimization with L2 | 33 |

Aerostructural Optimization | ||
---|---|---|

Aerodynamic Optimization | Structural Optimization | |

Objective function | Torque | Mass |

Design variables | Blade shape in terms of FFD points | Panel thickness |

Constraints | Volume and thickness | Panel thickness and von Mises stress |

Quantity of the design variables | 240 FFD points | 60 panels |

Optimization by percentage | ↑ 6.78% | ↓ 4.22% |

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**MDPI and ACS Style**

Batay, S.; Baidullayeva, A.; Zhao, Y.; Wei, D.; Baigarina, A.; Sarsenov, E.; Shabdan, Y.
Aerostructural Design Optimization of Wind Turbine Blades. *Processes* **2024**, *12*, 22.
https://doi.org/10.3390/pr12010022

**AMA Style**

Batay S, Baidullayeva A, Zhao Y, Wei D, Baigarina A, Sarsenov E, Shabdan Y.
Aerostructural Design Optimization of Wind Turbine Blades. *Processes*. 2024; 12(1):22.
https://doi.org/10.3390/pr12010022

**Chicago/Turabian Style**

Batay, Sagidolla, Aigerim Baidullayeva, Yong Zhao, Dongming Wei, Akerke Baigarina, Erkhan Sarsenov, and Yerkin Shabdan.
2024. "Aerostructural Design Optimization of Wind Turbine Blades" *Processes* 12, no. 1: 22.
https://doi.org/10.3390/pr12010022