# New Two-BWT Blade Aerodynamic Design and CFD Simulation

^{*}

## Abstract

**:**

## 1. Introduction

- An aerodynamic design method for novel offshore Two-BWT blades is presented.
- The design variable control models (PCM, Three-PSM, and Two-PSM) are adopted.
- The wind speed distribution and blade pressure distribution in the Two-BWT flow field are investigated.

## 2. Determination of Two-Blade Wind Rotor Diameter

#### 2.1. Blade Aerodynamic Modeling

#### 2.2. Estimation of the Two-BWT Rotor Diameter

## 3. Determination of Aerodynamic Design Variables

#### 3.1. Airfoil Distribution Variables

_{1}is the sum of the hub radius and cylinder length of the blade root. Usually, the length of the cylindrical segment does not change much, so it can be determined in advance in the design—that is, it can be regarded as a constant value. l

_{2}, l

_{3}, l

_{4}, and l

_{5}are the distribution lengths of the three airfoils in the spanwise direction of the blade, respectively. During design, these length parameters can be freely changed within a certain range. In this way, the blade airfoil distribution can be written as

_{2}, l

_{3}, l

_{4}, and l

_{5}are all changed, the sum of the three is constant (the value is R − l

_{1}); this means that it just makes three of the four variables. For example, let l

_{2}, l

_{3}, and l

_{5}be variables, one has

#### 3.2. Chord Length Distribution Variables

_{i}, the value of the chord length c

_{i}is equal to $\left|{\delta}_{i}-{\delta}_{i}^{\prime}\right|$. According to the experience of blade chord length distribution, the chord length coordinate $({r}_{0},{c}_{0})$ at the root of the blade, the maximum chord length coordinate $({r}_{1},{c}_{1})$, and the chord length coordinate $({r}_{2},{c}_{2})$ at the blade tip are set in advance. In the reference [13], the distribution of chord length is in the form of the quadratic function, and here, the distribution of chord length is in the form of the sinusoidal function. Here, this chord distribution control is called the three-point sine method (Three-PSM). Its expression can be written as

#### 3.3. Twist Angle Distribution Variables

## 4. Optimizing Solving and Result Discussion

#### 4.1. Design Objective and Solutions

_{rated}, that is, min (n

_{rated})

#### 4.2. Result Discussion

_{1}= 10 m) for redesign, and the following results are obtained: when c

_{1}is equal to 3.2 m, ${a}_{0}=3.8$, ${a}_{3}=3.2$, ${b}_{0}=7$, ${\theta}_{0}={11.04}^{\circ}$, and the rotational speed of the wind rotor $\omega $ is equal to 1.75 rad/s; when c

_{1}is equal to 3.8 m, ${a}_{0}=4$, ${a}_{3}=3.8$, ${b}_{0}=8.6$, ${\theta}_{0}={12.36}^{\circ}$, and the rotational speed of the wind rotor $\omega $ is equal to 1.61 rad/s. Then, the location of the maximum chord length is set to 8 m and 12 m, respectively (the maximum chord length remains unchanged at c

_{1}= 3.5 m), and the following results are obtained: when r

_{1}is equal to 8 m, ${a}_{0}=3.966$, ${a}_{3}=3.5$, ${b}_{0}=7.787$, ${\theta}_{0}={11.01}^{\circ}$, and the rotational speed of the wind rotor $\omega $ is equal to 1.70 rad/s; when r

_{1}is equal to 12 m,${a}_{0}=3.966$, ${a}_{3}=3.5$, ${b}_{0}=7.872$, ${\theta}_{0}={11.13}^{\circ}$, and the rotational speed of the wind rotor $\omega $ is equal to 1.64 rad/s. The results are summarized in Table 3. The airfoil distribution does not change in the design results. The reason for this phenomenon is that the airfoil distribution is only related to the spanwise length, not the chord length. Therefore, when only changing the value and location of the maximum chord length, the airfoil distribution will not be affected. When changing the maximum chord length, the distributions of chord length and torsion angle change; the smaller the maximum chord length is, the smaller the maximum torsion angle is, but the rotational speed of the wind rotor increases. When changing the location of the maximum chord length, the chord length distribution function does not change (the coefficients ${a}_{0}$ and ${a}_{3}$ do not change). The main reason for this phenomenon is that the variation of the location of the maximum chord length is small compared to the spanwise length of the blade, which does not affect the expression of the distribution function. The designed blade shape is shown in Figure 7. Figure 7a–c show the blade shape when the maximum chord length is 3.2 m, 3.5 m, and 3.8 m, respectively. Figure 7d–f show the blade shape when the location of the maximum chord length is 8 m, 10 m, and 12 m, respectively.

## 5. Flow Field Modeling and Simulation

#### 5.1. Modeling and Flow Field Setup

^{−5}m high so that the y+ value around the entire wind rotor surface is close to 1, as shown in Figure 10.

^{−6}. Finally, the number of iterations is set to 1500.

#### 5.2. Mesh Sensitivity Analysis

#### 5.3. Model Feasibility Verification

#### 5.4. Simulation Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Salvador, C.B.; Arzaghi, E.; Yazdi, M.; Jahromi, H.A.F.; Abbassi, R. A multi-criteria decision-making framework for site selection of offshore wind farms in Australia. Ocean Coast. Manag.
**2022**, 224, 106196. [Google Scholar] [CrossRef] - Dai, J.; Yang, X.; Wen, L. Development of wind power industry in China: A comprehensive assessment. Renew. Sustain. Energy Rev.
**2018**, 97, 156–164. [Google Scholar] [CrossRef] - Dai, J.; Hu, W.; Yang, X.; Yang, S. Modeling and investigation of load and motion characteristics of offshore floating wind turbines. Ocean Eng.
**2018**, 159, 187–200. [Google Scholar] [CrossRef] - Çiftci, C.; Erdoğan, A.; Genç, M.S. Investigation of the mechanical behavior of a new generation wind turbine blade technology. Energies
**2023**, 16, 1961. [Google Scholar] [CrossRef] - Chudzik, S. Wind Microturbine with Adjustable Blade Pitch Angle. Energies
**2023**, 16, 945. [Google Scholar] [CrossRef] - Martynowicz, P. Experimental study on the optimal-based vibration control of a wind turbine tower using a small-scale electric drive with MR damper support. Energies
**2022**, 15, 9530. [Google Scholar] [CrossRef] - Hou, Z.; Lv, X.; Zhuang, S. Optimized extreme learning machine-based main bearing temperature monitoring considering ambient conditions’ effects. Energies
**2021**, 14, 7529. [Google Scholar] [CrossRef] - Qin, Z.; Qiang, S.; Zhang, M.; Rong, X.; Liao, C.; Wang, J.; Xu, J. Design and structural responses of a 38-meter sectional wind turbine blade under extreme static loads. Compos. Struct.
**2022**, 290, 115487. [Google Scholar] [CrossRef] - Serafeim, G.P.; Manolas, D.I.; Riziotis, V.A.; Chaviaropoulos, P.K.; Saravanos, D.A. Optimized blade mass reduction of a 10MW-scale wind turbine via combined application of passive control techniques based on flap-edge and bend-twist coupling effects. J. Wind Eng. Ind. Aerodyn.
**2022**, 225, 105002. [Google Scholar] [CrossRef] - Bagherpoor, T.; Xuemin, L. Structural optimization design of 2MW composite wind turbine blade. Energy Procedia
**2017**, 105, 1226–1233. [Google Scholar] [CrossRef] - Vesel, R.W.; McNamara, J.J. Performance enhancement and load reduction of a 5 MW wind turbine blade. Renew. Energy
**2014**, 66, 391–401. [Google Scholar] [CrossRef] - Damiano, M.; Russo, A.; Sellitto, A.; Vecchio, E.; Stellato, T.; Riccio, A. Design of a composite wind turbine blade manufactured with the ONE SHOT BLADE® technology. Mater. Today: Proc.
**2021**, 34, 103–105. [Google Scholar] [CrossRef] - Juchuan, D.; Shanghong, Z.; Xiyun, Y.; Deshun, L.; Zejun, W. Design and optimizaiton of aerodynamic shape and operating characteristics of large scale wind turbine blade. J. Mech. Eng.
**2015**, 51, 138–145. [Google Scholar] - Pinto, R.L.U.d.F.; Gonçalves, B.P.F. A revised theoretical analysis of aerodynamic optimization of horizontal-axis wind turbines based on BEM theory. Renew. Energy
**2017**, 105, 625–636. [Google Scholar] [CrossRef] - Bavanish, B.; Thyagarajan, K. Optimization of power coefficient on a horizontal axis wind turbine using bem theory. Renew. Sustain. Energy Rev.
**2013**, 26, 169–182. [Google Scholar] [CrossRef] - Laalej, S.; Bouatem, A.; AlMers, A.; El Maani, R. Wind turbine performances prediction using BEM approach with Jonkman-Buhl brake state model coupled to CFD method. Mater. Today Proc.
**2022**, 65, 3829–3838. [Google Scholar] [CrossRef] - Esfahanian, V.; Salavati Pour, A.; Harsini, I.; Haghani, A.; Pasandeh, R.; Shahbazi, A.; Ahmadi, G. Numerical analysis of flow field around NREL Phase II wind turbine by a hybrid CFD/BEM method. J. Wind Eng. Ind. Aerodyn.
**2013**, 120, 29–36. [Google Scholar] [CrossRef] - Avvad, M.; Vishwanath, K.C.; Kaladgi, A.R.; Muneer, R.; Kareemullah, M.; Navaneeth, I.M. Performance analysis of aerofoil blades at different pitch angles and wind speeds. Mater. Today Proc.
**2021**, 47, 6249–6256. [Google Scholar] [CrossRef] - Huang, S.; Qiu, H.; Wang, Y. Aerodynamic performance of horizontal axis wind turbine with application of dolphin head-shape and lever movement of skeleton bionic airfoils. Energy Convers. Manag.
**2022**, 267, 115803. [Google Scholar] [CrossRef] - Yen, S.-C.; Liu, W.-S.; San, K.-C.; Wang, W.-F. Design of wind-turbine blades for improving aerodynamic performance using hybrid blades. Ocean Eng.
**2021**, 227, 108889. [Google Scholar] [CrossRef] - Alkhabbaz, A.; Yang, H.-S.; Weerakoon, A.H.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] - Jia, L.; Hao, J.; Hall, J.; Nejadkhaki, H.K.; Wang, G.; Yan, Y.; Sun, M. A reinforcement learning based blade twist angle distribution searching method for optimizing wind turbine energy power. Energy
**2021**, 215, 119148. [Google Scholar] [CrossRef] - Tahani, M.; Kavari, G.; Masdari, M.; Mirhosseini, M. Aerodynamic design of horizontal axis wind turbine with innovative local linearization of chord and twist distributions. Energy
**2017**, 131, 78–91. [Google Scholar] [CrossRef] - Tahani, M.; Kavari, G.; Mirhosseini, M.; Ghiyasi, S. Different functionalized chord and twist distributions in aerodynamic design of HAWTs. Environ. Prog. Sustain. Energy
**2019**, 38, 13108. [Google Scholar] [CrossRef] - Rahgozar, S.; Pourrajabian, A.; Kazmi, S.A.A.; Kazmi, S.M.R. Performance analysis of a small horizontal axis wind turbine under the use of linear/nonlinear distributions for the chord and twist angle. Energy Sustain. Dev.
**2020**, 58, 42–49. [Google Scholar] [CrossRef] - Pourrajabian, A.; Dehghan, M.; Rahgozar, S. Genetic algorithms for the design and optimization of horizontal axis wind turbine (HAWT) blades: A continuous approach or a binary one? Sustain. Energy Technol. Assess.
**2021**, 44, 101022. [Google Scholar] [CrossRef] - Sessarego, M.; Feng, J.; Ramos-García, N.; Horcas, S.G. Design optimization of a curved wind turbine blade using neural networks and an aero-elastic vortex method under turbulent inflow. Renew. Energy
**2020**, 146, 1524–1535. [Google Scholar] [CrossRef] - Lanzafame, R.; Messina, M. Fluid dynamics wind turbine design: Critical analysis, optimization and application of BEM theory. Renew. Energy
**2007**, 32, 2291–2305. [Google Scholar] [CrossRef] - Dai, J.C.; Hu, Y.P.; Liu, D.S.; Long, X. Aerodynamic loads calculation and analysis for large scale wind turbine based on combining BEM modified theory with dynamic stall model. Renew. Energy
**2011**, 36, 1095–1104. [Google Scholar] [CrossRef] - Jonkman, J.; Butterfield, S.; Musial, W.; Scott, G. Definition of a 5-MW Reference Wind Turbine for Offshore System Development; National Renewable Energy Lab.(NREL): Golden, CO, USA, 2009.
- Moriarty, P.; Hansen, A. Aerodyn Theory Manual; NREL/TP-500-36881; National Renewable Energy Laboratory: Golden, CO, USA, 2005.
- Wang, L.; Quant, R.; Kolios, A. Fluid structure interaction modelling of horizontal-axis wind turbine blades based on CFD and FEA. J. Wind Eng. Ind. Aerodyn.
**2016**, 158, 11–25. [Google Scholar] [CrossRef] [Green Version] - Ji, B.; Zhong, K.; Xiong, Q.; Qiu, P.; Zhang, X.; Wang, L. CFD simulations of aerodynamic characteristics for the three-blade NREL Phase VI wind turbine model. Energy
**2022**, 249, 123670. [Google Scholar] [CrossRef] - Eltayesh, A.; Castellani, F.; Burlando, M.; Hanna, M.B.; Huzayyin, A.; El-Batsh, H.M.; Becchetti, M. Experimental and numerical investigation of the effect of blade number on the aerodynamic performance of a small-scale horizontal axis wind turbine. Alex. Eng. J.
**2021**, 60, 3931–3944. [Google Scholar] [CrossRef]

**Figure 2.**Wind turbine, blade, and elemental forces. (

**a**) Wind turbines; (

**b**) Wind turbine blade; (

**c**) Local elemental forces.

**Figure 6.**Performance curve of Two−TWB. (

**a**) Power coefficient under different tip speed ratios; (

**b**) Thrust coefficient under different tip speed ratios; (

**c**) Power coefficient under different pitch angles; (

**d**) Thrust coefficient under different pitch angles.

**Figure 7.**Blades with different maximum chord length values and locations. (

**a**) Blade shape with a maximum chord length of 3.2 m; (

**b**) Blade shape with maximum chord length of 3.5 m; (

**c**) Blade shape with a maximum chord length of 3.8 m; (

**d**) Blade shape with maximum chord length position of 8 m; (

**e**) Blade shape with maximum chord length position of 10 m; (

**f**) Blade shape with maximum chord length position of 12 m.

**Figure 8.**Effect of the value and location of the maximum chord length. (Note: MCL is the abbreviation for maximum chord length and MCLL is the abbreviation for maximum chord length location.). (

**a**) chord length of MCL; (

**b**) Twist angle of MCL; (

**c**) Power coefficient of MCL; (

**d**) chord length of MCLL; (

**e**) Twist angle of MCLL; (

**f**) Power coefficient of MCLL.

**Figure 9.**Flow field settings of the Two-BWT. (

**a**) Flow field space settings; (

**b**) Flow field meshing; (

**c**) Blade surface meshing; (

**d**) Local area mesh for wind rotor.

**Figure 11.**Rotor torque calculation results under different mesh numbers. (

**a**) Single-blade simulation; (

**b**) Wind rotor simulation.

**Figure 13.**Wind speed cloud map at different locations. (

**a**) 6 m away from the front of the wind rotor; (

**b**) 4 m away from the front of the wind rotor; (

**c**) 2 m away from the front of the wind rotor; (

**d**) Wind.rotor plane; (

**e**) 2 m behind the wind rotor; (

**f**) 4 m behind the wind rotor; (

**g**) 6 m behind the wind rotor; (

**h**) 8 m behind the wind rotor; (

**i**) 10 m behind the wind rotor.

**Figure 14.**Flow field and streamline of the Two−BWT. (

**a**) 3D wind speed cloud map of the whole flow field; (

**b**) Wind speed cloud map of the axial section of the whole flow field; (

**c**) Streamline distribution maps of the whole flow field; (

**d**) Streamline distribution maps of the axial section of the whole flow field.

**Figure 15.**Pressure cloud maps at different sections of the Two−BWT blade. (

**a**) At 8% R section; (

**b**) At 9%R section; (

**c**) At 10%R section; (

**d**) At 13%R section; (

**e**) At 15%R section; (

**f**) At 17%R section; (

**g**) At 25%R section; (

**h**) At 35%R section; (

**i**) At 45%R section; (

**j**) At 60%R section; (

**k**) At 75%R section; (

**l**) At 90%R section.

**Table 1.**Blade aerodynamic parameter distribution [30].

Node | RNodes/m | Twist Angle/° | Chord/m | Airfoil |
---|---|---|---|---|

1 | 2.8667 | 13.308 | 3.542 | Cylinder |

2 | 5.6000 | 13.308 | 3.854 | Cylinder |

3 | 8.3333 | 13.308 | 4.167 | Cylinder |

4 | 11.7500 | 13.308 | 4.557 | DU40_A17 |

5 | 15.8500 | 11.480 | 4.652 | DU35_A17 |

6 | 19.9500 | 10.162 | 4.458 | DU35_A17 |

7 | 24.0500 | 9.011 | 4.249 | DU30_A17 |

8 | 28.1500 | 7.795 | 4.007 | DU25_A17 |

9 | 32.2500 | 6.544 | 3.748 | DU25_A17 |

10 | 36.3500 | 5.361 | 3.502 | DU21_A17 |

11 | 40.4500 | 4.188 | 3.256 | DU21_A17 |

12 | 44.5500 | 3.125 | 3.010 | NACA64_A17 |

… | … | … | … | … |

17 | 61.6333 | 0.106 | 1.419 | NACA64_A17 |

Spanwise Length/m | Twist Angle/° | Chord Length/m | Airfoil |
---|---|---|---|

3.500 | 11.06 | 2.200 | DU30 |

5.500 | 10.45 | 2.674 | DU25 |

7.500 | 9.82 | 3.086 | DU25 |

9.500 | 9.18 | 3.427 | DU21 |

11.500 | 8.53 | 3.493 | DU21 |

13.500 | 7.87 | 3.460 | DU21 |

15.500 | 7.22 | 3.402 | DU21 |

17.500 | 6.56 | 3.319 | DU21 |

19.500 | 5.92 | 3.212 | DU21 |

21.500 | 5.29 | 3.080 | DU21 |

23.500 | 4.68 | 2.926 | NACA64 |

25.500 | 4.09 | 2.750 | NACA64 |

27.500 | 3.53 | 2.554 | NACA64 |

29.500 | 2.99 | 2.338 | NACA64 |

31.500 | 2.49 | 2.106 | NACA64 |

33.500 | 2.03 | 1.858 | NACA64 |

35.500 | 1.61 | 1.596 | NACA64 |

37.500 | 1.23 | 1.322 | NACA64 |

39.500 | 0.90 | 1.039 | NACA64 |

41.500 | 0.62 | 0.748 | NACA64 |

42.500 | 0.50 | 0.600 | NACA64 |

${\mathit{r}}_{1}$ (m) | ${\mathit{c}}_{1}$ (m) | ${\mathit{a}}_{0}$ | ${\mathit{a}}_{3}$ | ${\mathit{b}}_{0}$ | ${\mathit{\theta}}_{0}$ (°) | $\mathit{\omega}$ (rad/s) | ${\mathit{l}}_{2}$ (m) | ${\mathit{l}}_{3}$ (m) | ${\mathit{l}}_{5}$ (m) |
---|---|---|---|---|---|---|---|---|---|

10 | 3.2 | 3.800 | 3.2 | 7.000 | 11.04 | 1.75 | 2 | 4 | 19.95 |

3.5 | 3.966 | 3.5 | 7.820 | 11.06 | 1.67 | ||||

3.8 | 4.000 | 3.8 | 8.600 | 12.36 | 1.61 | ||||

8 | 3.5 | 3.966 | 3.5 | 7.787 | 11.01 | 1.70 | |||

10 | 3.966 | 3.5 | 7.820 | 11.04 | 1.67 | ||||

12 | 3.966 | 3.5 | 7.872 | 11.13 | 1.64 |

Mesh Size | Blade Simulation | Wind Rotor Simulation | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

0.035 m | 0.04 m | 0.05 m | 0.06 m | 0.07 m | 0.055 m | 0.06 m | 0.07 m | 0.08 m | 0.09 m | |

Rotor torque (Nm) | 1,150,238 | 1,132,342 | 1,087,524 | 1,044,600 | 1,000,030 | 1,071,540 | 1,063,252 | 992,447 | 926,710 | 846,790 |

Number of meshes | 9,246,797 | 7,349,406 | 4,944,918 | 3,611,421 | 2,677,254 | 9,069,465 | 7,974,692 | 6,090,860 | 4,991,385 | 4,243,162 |

Wind Speed (m/s) | Rotational Speed of the Wind Rotor (rad/s) | Power (kW) | Deviation (%) | |
---|---|---|---|---|

Theoretically Calculated Value Based on BEM | Values Based on CFD Simulations | |||

10.2 | 1.67 | 1565 | 1515 | 3.2 |

10.6 | 1.67 | 1710 | 1633 | 4.5 |

11.0 | 1.67 | 1855 | 1762 | 5.0 |

11.4 | 1.67 | 2000 | 1891 | 5.5 |

11.8 | 1.67 | 2120 | 2012 | 5.1 |

12.2 | 1.67 | 2235 | 2129 | 4.7 |

12.6 | 1.67 | 2336 | 2256 | 3.4 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, G.; Dai, J.; Zhang, F.; Zuo, C.
New Two-BWT Blade Aerodynamic Design and CFD Simulation. *Machines* **2023**, *11*, 399.
https://doi.org/10.3390/machines11030399

**AMA Style**

Li G, Dai J, Zhang F, Zuo C.
New Two-BWT Blade Aerodynamic Design and CFD Simulation. *Machines*. 2023; 11(3):399.
https://doi.org/10.3390/machines11030399

**Chicago/Turabian Style**

Li, Guo, Juchuan Dai, Fan Zhang, and Chengming Zuo.
2023. "New Two-BWT Blade Aerodynamic Design and CFD Simulation" *Machines* 11, no. 3: 399.
https://doi.org/10.3390/machines11030399