# Optimization of Small Horizontal Axis Wind Turbines Based on Aerodynamic, Steady-State, and Dynamic Analyses

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## Abstract

**:**

## 1. Introduction

## 2. Structural Analysis and Design of the Blade

#### 2.1. Wind Turbine Blade Design

#### 2.2. Blade’s Material and Lay-Up Sequence

#### 2.3. Finite Element Analysis of Steady-State Problem

#### 2.4. Boundary Conditions

#### 2.5. FE Modeling of Wind Blade

#### 2.6. The FE Formulation

## 3. Results and Discussions

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

c | Chord length |

${C}_{P}$ | Power coefficient |

$Re$ | Reynolds number |

${U}_{rel}$ | Relative velocity |

${U}_{design}$ | Design wind speed |

r | Local radius |

R | Wind turbine radius |

${C}_{l,design}$ | Design lift coefficient |

$B$ | Number of blades |

${F}_{T}$ | Tangential load |

${F}_{N}$ | Normal load |

$\left\{F\right\}$ | Load vector |

$\left\{u\right\}$ | Displacement vectors |

[K] | Stiffness matrix |

[M] | Mass matrix |

$\left\{\ddot{u}\right\}$ | Acceleration |

[A] | dynamic matrix |

[I] | Identity matrix |

X | eigenvector |

$E$ | Young’s modulus |

Greek symbols | |

$\theta $ | Twist angel |

$\left\{\varnothing \right\}$ | Reynolds or turbulent stress |

$\mu $ | viscosity |

$\omega $ | angular natural frequency |

$\rho $ | Air density |

${\mathsf{\alpha}}_{opt}$ | Optimal angel of attack |

${\lambda}_{r}$ | Local speed ratio |

${\lambda}_{0}$ | Design tip speed ratio |

$\phi $ | Relative angle |

$\Omega $ | Rotational speed |

Superscripts | |

WWEA | World wind energy association |

GWEC | Global wind energy council |

AEP | Annual energy production |

FEM | Finite element method |

UD | Unidirectional |

BEM | blade element momentum |

AoA | Angle of Attack |

DOF | degrees of freedom |

HAWT | Horizontal axis wind turbine |

CFD | computational fluid dynamics |

## References

- Rosato, M.A. Small Wind Turbines for Electricity and Irrigation: Design and Construction; CRC Press: New York, NY, USA, 2018. [Google Scholar]
- WWEA. World Wind Energy Association. Available online: https://wwindea.org/information-2/statistics-news/ (accessed on 24 March 2022).
- Rašuo, B.P.; Bengin, A.Č. Optimization of wind farm layout. FME Trans.
**2010**, 38, 107–114. [Google Scholar] - Norouzi, N.; Bozorgian, A. A Wind-Thermal System Design Based on an Energetic and Exergetic Approch. Iran. J. Chem. Chem. Eng.
**2022**. [Google Scholar] [CrossRef] - Win, S.Y.; Thianwiboon, M. Parametric optimization of NACA 4412 airfoil in ground effect using full factorial design of experiment. Eng. J.
**2021**, 25, 9–19. [Google Scholar] - Mousavi, S.M.; Shafiei, N.; Dadvand, A. Numerical simulation of subsonic turbulent flow over NACA0012 airfoil: Evaluation of turbulence models. Sigma J. Eng. Nat. Sci.
**2017**, 35, 133–155. [Google Scholar] - Garcia-Ribeiro, D.; Flores-Mezarina, J.A.; Bravo-Mosquera, P.D.; Cerón-Muñoz, H.D. Parametric CFD analysis of the taper ratio effects of a winglet on the performance of a Horizontal Axis Wind Turbine. Sustain. Energy Technol. Assess.
**2021**, 47, 101489. [Google Scholar] [CrossRef] - Bai, C.-J.; Wang, W.-C. Review of computational and experimental approaches to analysis of aerodynamic performance in horizontal-axis wind turbines (HAWTs). Renew. Sustain. Energy Rev.
**2016**, 63, 506–519. [Google Scholar] [CrossRef] - Maizi, M.; Mohamed, M.; Dizene, R.; Mihoubi, M. Noise reduction of a horizontal wind turbine using different blade shapes. Renew. Energy
**2018**, 117, 242–256. [Google Scholar] [CrossRef] - Kaya, M.N.; Kose, F.; Ingham, D.; Ma, L.; Pourkashanian, M. Aerodynamic performance of a horizontal axis wind turbine with forward and backward swept blades. J. Wind. Eng. Ind. Aerodyn.
**2018**, 176, 166–173. [Google Scholar] [CrossRef] [Green Version] - Parezanovic, V.; Rasuo, B.; Adzic, M. Design of airfoils for wind turbine blades. In Proceedings of the French-Serbian European Summer University: Renewable Energy Sources and Environment-Multidisciplinary Aspect, Vrnjacka Banja, Serbia, 17–24 October 2006. [Google Scholar]
- Song, F.; Ni, Y.; Tan, Z. Optimization design, modeling and dynamic analysis for composite wind turbine blade. Procedia Eng.
**2011**, 16, 369–375. [Google Scholar] [CrossRef] [Green Version] - Lipian, M.; Czapski, P.; Obidowski, D. Fluid–structure interaction numerical analysis of a small, urban wind turbine blade. Energies
**2020**, 13, 1832. [Google Scholar] [CrossRef] - Boudounit, H.; Tarfaoui, M.; Saifaoui, D.; Nachtane, M. Structural analysis of offshore wind turbine blades using finite element method. Wind Eng.
**2020**, 44, 168–180. [Google Scholar] [CrossRef] - Wu, W.H.; Young, W.B. Structural analysis and design of the composite wind turbine blade. Appl. Compos. Mater.
**2012**, 19, 247–257. [Google Scholar] [CrossRef] - Pourrajabian, A.; Afshar, P.A.N.; Ahmadizadeh, M.; Wood, D. Aero-structural design and optimization of a small wind turbine blade. Renew. Energy
**2016**, 87, 837–848. [Google Scholar] [CrossRef] - Tüfekci, M.; Genel, Ö.E.; Tatar, A.; Tüfekci, E. Dynamic Analysis of Composite Wind Turbine Blades as Beams: An Analytical and Numerical Study. Vibration
**2021**, 4, 1–15. [Google Scholar] [CrossRef] - Navadeh, N.; Goroshko, I.; Zhuk, Y.; Etminan Moghadam, F.; Soleiman Fallah, A. Finite Element Analysis of Wind Turbine Blade Vibrations. Vibration
**2021**, 4, 310–322. [Google Scholar] [CrossRef] - Lagdani, O.; Tarfaoui, M.; Nachtane, M.; Trihi, M.; Laaouidi, H. Modal analysis of an iced offshore composite wind turbine blade. Wind Eng.
**2022**, 46, 134–149. [Google Scholar] [CrossRef] - Puterbaugh, M.; Beyene, A. Parametric dependence of a morphing wind turbine blade on material elasticity. Energy
**2011**, 36, 466–474. [Google Scholar] [CrossRef] - Alkhabbaz, A.; Yang, H.-S.; Weerakoon, A.S.; Lee, Y.-H. A novel linearization approach of chord and twist angle distribution for 10 kW horizontal axis wind turbine. Renew. Energy
**2021**, 178, 1398–1420. [Google Scholar] [CrossRef] - Gupta, M.K.; Subbarao, P. Design and Performance Analysis of Hydrokinetic Turbine with Aerodynamic Stall Model. In Advances in Thermofluids and Renewable Energy; Springer: Singapore, 2021; pp. 221–231. [Google Scholar]
- Marten, D.; Wendler, J. QBlade Guidelines v0.6; TU Berlin: Berlin, Germany, 2013. [Google Scholar]
- Zhou, S.; Wu, X. Fatigue life prediction of composite laminates by fatigue master curves. J. Mater. Res.
**2019**, 8, 6094–6105. [Google Scholar] [CrossRef] - Gao, X.; Yuan, L.; Fu, Y.; Yao, X.; Yang, H. Prediction of mechanical properties on 3D braided composites with void defects. Compos. Part B Eng.
**2020**, 197, 108164. [Google Scholar] [CrossRef] - Pagano, A. Aerodynamic Analyses of Tiltrotor Morphing Blades. In Morphing Wing Technologies; Elsevier: Amsterdam, The Netherlands, 2018; pp. 799–839. [Google Scholar] [CrossRef]
- Zuheir, S.; Abdullah, O.I.; Al-Maliki, M. Stress and vibration analyses of the wind turbine blade (A NREL 5MW). J. Mech. Eng. Res. Dev.
**2019**, 42, 14–19. [Google Scholar] [CrossRef] - Garinis, D.; Dinulović, M.; Rašuo, B. Dynamic analysis of modified composite helicopter blade. FME Trans.
**2012**, 40, 63–68. [Google Scholar] - Abdullah, O.I. A finite element analysis for the damaged rotating composite blade. Al-Khwarizmi Eng. J.
**2011**, 7, 56–75. [Google Scholar] - Miau, J.-J.; Li, S.-R.; Tsai, Z.-X.; Van Phung, M.; Lin, S.-Y. On the aerodynamic flow around a cyclist model at the hoods position. J. Vis.
**2019**, 23, 35–47. [Google Scholar] [CrossRef] [Green Version] - Abdullah, O. Vibration analysis of rotating pre-twisted cantilever plate by using the finite element method. J. Eng.
**2009**, 15, 3492–3505. [Google Scholar]

**Figure 10.**Distribution of Von Mises stresses of (

**a**) carbon/epoxy, (

**b**) E-glass/epoxy, and (

**c**) Braided composite.

**Figure 13.**Distributions of (

**a**) the density, (

**b**) longitudinal stiffness, (

**c**) Flapwise Stiffness, and (

**d**) Edgewise Stiffness along the blade.

**Figure 15.**The first 6th mode shape of Carbon/Epoxy material. (

**a**) 1st mode. (

**b**) 2nd mode. (

**c**) 3rd mode. (

**d**) 4th mode. (

**e**) 5th mode. (

**f**) 6th mode.

**Figure 16.**The first 6th mode shape of Braided composite material. (

**a**) 1st mode. (

**b**) 2nd mode. (

**c**) 3rd mode. (

**d**) 4th mode. (

**e**) 5th mode. (

**f**) 6th mode.

**Figure 17.**The first 6th mode shape of E-glass/epoxy material. (

**a**) 1st mode. (

**b**) 2nd mode. (

**c**) 3rd mode. (

**d**) 4th mode. (

**e**) 5th mode. (

**f**) 6th mode.

Design Parameter | Value | Unit |
---|---|---|

Rated power | 5 | [kW] |

Design Wind speed | 10.5 | m/s] |

Number of blades | 3 | [-] |

Design tip speed ratio | 6 | [-] |

Design angle of attack | 6 | [°] |

Rotor radius | 2.5 | [m] |

Design rotational speed | 240 | [rpm] |

Density of air | 1.22 | [kg/m^{3}] |

Airfoil type | NACA4412 | [-] |

Material | E-Glass/Epoxy [24] | Carbon/Epoxy [24] | Braided Composite [24,25] |
---|---|---|---|

${E}_{1}$(GPa) | 48.7 | 136.7 | 62.8 |

${E}_{2}$(GPa) | 16.8 | 8.2 | 62.8 |

${G}_{12}$(GPa) | 5.83 | 4.45 | 9.68 |

${G}_{23}$(GPa) | 6 | 2.91 | 7.97 |

${\upsilon}_{12}$ | 0.28 | 0.29 | 0.33 |

${\upsilon}_{23}$ | 0.20 | 0.42 | 0.40 |

${X}_{T}$(MPa) | 1170 | 1604 | 460 |

${X}_{C}$(MPa) | 977 | 1305 | 420.4 |

${Y}_{T}$(MPa) | 30.5 | 40.5 | 526.2 |

${Y}_{C}$(MPa) | 114 | 239.7 | 420.4 |

$\rho $(kg/m^{3}) | 2000 | 1518 | 1800 |

Section Name | Location (m) | Shell Layup | Thickness (m) | Shear Web Lay-Up | Thickness (m) |
---|---|---|---|---|---|

1 | 0.200–0.400 | [(±45)3/08/(±45)]s | 0.0064 | [(±45)3/09/(±45)]s | 0.0070 |

2 | 0.400–0.600 | [(±45)3/07/(±45)]s | 0.0058 | [(±45)3/08/(±45)]s | 0.0064 |

3 | 0.600–0.811 | [(±45)3/06/(±45)]s | 0.0052 | [(±45)3/07/(±45)]s | 0.0058 |

4 | 0.811–1.022 | [(±45)2/06/(±45)]s | 0.0048 | [(±45)3/06/(±45)]s | 0.0052 |

5 | 1.022–1.233 | [(±45)2/05/(±45)]s | 0.0042 | [(±45)2/06/(±45)]s | 0.0048 |

6 | 1.233–1.444 | [(±45)2/04/(±45)]s | 0.0036 | [(±45)2/05/(±45)]s | 0.0042 |

7 | 1.444–1.655 | [(±45)2/03/(±45)]s | 0.0030 | [(±45)2/04/(±45)]s | 0.0036 |

8 | 1.655–1.866 | [(±45)2/02/(±45)]s | 0.0024 | [(±45)2/03/(±45)]s | 0.0030 |

9 | 1.866–2.077 | [(±45)/02/(±45)]s | 0.0020 | [(±45)2/02/(±45)]s | 0.0024 |

10 | 2.077–2.288 | [(±45)/01/(±45)]s | 0.0014 | [(±45)/02/(±45)]s | 0.0020 |

11 | 2.288–2.500 | [(±45)/01/(±45)] | 0.0007 | [(±45)/01/(±45)]s | 0.0014 |

$\mathit{Z}\left(\mathit{m}\right)$ | ${\Delta}\mathit{Z}\left(\mathit{m}\right)$ | ${\mathit{F}}_{\mathit{T}}\left(\mathit{N}/\mathit{m}\right)$ | ${\mathit{F}}_{\mathit{N}}\left(\mathit{N}/\mathit{m}\right)$ |
---|---|---|---|

0.200 | 0.200 | −1.535 | 2.930 |

0.400 | 0.200 | −4.415 | 8.825 |

0.600 | 0.200 | 27.610 | 57.455 |

0.811 | 0.211 | 38.052 | 81.014 |

1.022 | 0.211 | 36.047 | 93.246 |

1.233 | 0.211 | 35.260 | 106.279 |

1.444 | 0.211 | 34.701 | 120.023 |

1.655 | 0.211 | 34.492 | 134.815 |

1.866 | 0.211 | 33.881 | 147.971 |

2.077 | 0.211 | 32.781 | 161.331 |

2.288 | 0.211 | 29.654 | 172.156 |

2.500 | 0.212 | 9.8160 | 81.7452 |

Mesh Segments | No. Nodes | No. Elements | Max. Total Deflection [mm] | Difference |
---|---|---|---|---|

1 | 19,824 | 3694 | 18.392 | - |

2 | 26,722 | 7431 | 18.371 | −0.021 |

3 | 34,624 | 11,385 | 18.365 | −0.006 |

4 | 45,857 | 15,124 | 18.361 | −0.004 |

5 | 74,154 | 24,475 | 18.356 | −0.005 |

6 | 108,789 | 35,970 | 18.354 | −0.002 |

7 | 225,602 | 75,053 | 18.358 | 0.004 |

E-Glass/Epoxy | Braided Composite | Carbon/Epoxy | |||||||
---|---|---|---|---|---|---|---|---|---|

QBlade | ANSYS | Difference % | QBlade | ANSYS | Difference % | QBlade | ANSYS | Difference % | |

Von mises stress [MPa] | 38.51 | 39.68 | 2.94 | 39.20 | 39.75 | 1.38 | 39.96 | 40.37 | 1.015 |

Tip deflection[mm] | 43.20 | 46.46 | 7.016 | 29.32 | 33.54 | 6.61 | 16.86 | 18.29 | 7.81 |

Mode | E-glass/Epoxy | Braided Composite | Carbon/Epoxy | ||||||
---|---|---|---|---|---|---|---|---|---|

QBlade | ANSYS | Difference % | QBlade | ANSYS | Difference % | QBlade | ANSYS | Difference % | |

1 | 15.13 | 16.17 | 6.43 | 19.80 | 20.06 | 1.30 | 28.29 | 29.58 | 4.36 |

2 | 36.19 | 38.46 | 5.90 | 48.32 | 47.70 | 1.30 | 74.11 | 70.20 | 5.57 |

3 | 45.39 | 48.94 | 7.25 | 63.41 | 60.71 | 4.45 | 92.20 | 89.50 | 3.02 |

4 | 99.56 | 98.34 | 1.24 | 130.59 | 122 | 7.04 | 185.14 | 179.83 | 2.95 |

5 | 165.82 | 161.01 | 2.99 | 196.43 | 199.76 | 1.67 | 289.23 | 294.56 | 1.81 |

6 | 172.93 | 169.09 | 2.27 | 221.15 | 209.78 | 5.42 | 315.67 | 309.51 | 1.99 |

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## Share and Cite

**MDPI and ACS Style**

Deghoum, K.; Gherbi, M.T.; Sultan, H.S.; Jameel Al-Tamimi, A.N.; Abed, A.M.; Abdullah, O.I.; Mechakra, H.; Boukhari, A.
Optimization of Small Horizontal Axis Wind Turbines Based on Aerodynamic, Steady-State, and Dynamic Analyses. *Appl. Syst. Innov.* **2023**, *6*, 33.
https://doi.org/10.3390/asi6020033

**AMA Style**

Deghoum K, Gherbi MT, Sultan HS, Jameel Al-Tamimi AN, Abed AM, Abdullah OI, Mechakra H, Boukhari A.
Optimization of Small Horizontal Axis Wind Turbines Based on Aerodynamic, Steady-State, and Dynamic Analyses. *Applied System Innovation*. 2023; 6(2):33.
https://doi.org/10.3390/asi6020033

**Chicago/Turabian Style**

Deghoum, Khalil, Mohammed Taher Gherbi, Hakim S. Sultan, Adnan N. Jameel Al-Tamimi, Azher M. Abed, Oday Ibraheem Abdullah, Hamza Mechakra, and Ali Boukhari.
2023. "Optimization of Small Horizontal Axis Wind Turbines Based on Aerodynamic, Steady-State, and Dynamic Analyses" *Applied System Innovation* 6, no. 2: 33.
https://doi.org/10.3390/asi6020033