# Small Wind Turbine Blade Design and Optimization

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## Abstract

**:**

_{P}) higher than 40% at a low wind speed of 5 m/s. Two symmetric in shape airfoils were used to get the final optimized airfoil. The main objective is to optimize the blade parameters that influence the design of the blade since the small turbines are prone to show low performance due to the low Reynolds number as a result of the small size of the rotor and the low wind speed. Therefore, the optimization process will select different airfoils and extract their performance at the design conditions to find the best sections which form the optimal design of the blade. The sections of the blade in the final version mainly consist of two different sections belong to S1210 and S1223 airfoils. The optimization process goes further by investigating the performance of the final design, and it employs the blade element momentum theory to enhance the design. Finally, the rotor-design was obtained, which consists of three blades with a diameter of 4 m, a hub of 20 cm radius, a tip-speed ratio of 6.5 and can obtain about 650 W with a Power coefficient of 0.445 at a wind-speed of 5.5 m/s, reaching a power of 1.18 kW and a power coefficient of 0.40 at a wind-speed of 7 m/s.

## 1. Introduction

## 2. Subject Theory

_{rel}is the relative wind speed between the blade section and the wind, the C

_{L}is the lift coefficient, the C

_{D}is the drag coefficient, and β is the relative angle between the lift and drag coefficients.

_{P}and the torques coefficient C

_{Q}satisfies

_{Q}, R, α, λ, and V.

## 3. Design Methodology

_{P}) higher than 40% at an average wind speed of 20 km/h, using multiple stages of optimization and different tools which might help during the optimization process, as well as showing the effect of the different factors on the overall performance of the wind turbine blade. The structural design of the blade will also be taken into consideration to make sure that the blade can withstand the stresses applied to it without breaking or deforming.

^{3}with a dynamic viscosity of 1.81 × 10

^{−5}kg.s/m at 15 °C, the blade length must be less than or equal to 2 m. Therefore, the Reynolds number will be less than or equal to 100,000. The selected number of blades in the designed turbine was three blades, and the tip speed ratio spans from 4 to 8. Finally, the internal to external radius ration was selected between 0.10 to 0.12. Due to the low wind speed and small rotor area, and it was necessary to find a set of airfoils suitable for low Reynolds number applications.

_{P}), which is calculated using the Trapezoidal and Simpson methods. Since the C

_{P}differs in each section of the blade, it is necessary to use integration to obtain the overall C

_{P}for the entire blade. In addition, the program returns the optimal values of the chord and the optimal AoA for each section of the airfoil. At the end of the iterative process, the program will return the optimal values of the design parameters that are summarized in Table 1.

## 4. Results and Discussion

_{L}/C

_{D}versus the AoA using Qblade software. It is noticed that the interpolated airfoil S1210–S1223 showed higher C

_{L}/C

_{D}at different Reynolds numbers with the range of AoA shown in Figure 5. At a Reynolds number of 100,000, the interpolated airfoil showed a higher C

_{L}⁄C

_{D}ratio than S1210 and S1223 for AoA lower than 4.2 degrees. In addition, the interpolated airfoil showed a higher C

_{L}⁄C

_{D}ratio for the whole range of AoA when the Reynolds number is set at 75,000. The impact of the Reynolds number on the C

_{L}⁄C

_{D}ratio of the S1210–S1223 airfoil is depicted in Figure 5b. It is seen that the C

_{L}⁄C

_{D}ratio is higher in the case of selecting the highest possible Reynolds number at low wind speed. Accordingly, the Reynolds number was settled 100,000 during the simulation, and it was determined that an interpolated blade between the profiles ‘S1210′, ‘S1223′ will tick all the criteria boxes in terms of high C

_{L}⁄C

_{D}ratio on low Reynolds numbers, and gives relatively high performance given the limitations.

^{3}and an air viscosity of 1.81 × 10

^{−5}kg.s/m, 40 blade elements, 100 iterations, maximum 0.001 for convergence, and a relaxation factor of 0.3. In addition, the analysis conditions were set at wind range at a speed from 1 m/s to 7 m/s, rotor range in rotational speed from 138 rpm to 500 rpm, and a pitch angle from 0° to 10°. The length of a blade is a significant factor affecting the power extracted from the wind, looking back at Equation (7), the relation between the length of the blade (R) and power (P

_{r}) is squared.

_{P}of the blade was increased to almost 0.45, which is relatively high considering the size and the speed of the wind. Figure 7 depicts the impact of the design parameters on the power coefficient which are represented by the rotor diameter, tip speed ratio, and the internal to external radius ratio. In Figure 7a, it is noticed that the C

_{P}value is slightly increased with increasing the rotor diameter (D) at the same tip speed ratio (λ). On the other hand, the increase of tip speed ratio will yield in increasing C

_{P}for the same rotor diameter, which is true if the length of the rotor blade is greater than 3 m as depicted in Figure 7b. In addition, it was observed that the C

_{P}value decreases with an increase in the internal to external radius ratio (r

_{R}) at the same tip speed ratio as shown in Figure 7c. The maximum C

_{P}is obtained corresponding to D = 4 m, λ = 6, and r

_{R}= 0.1 m. In Figure 8a, it was noticed that the power generated can increase to almost double just by increasing the velocity by 2 m/s, the rated power at 5.5 m/s will be around 650 Watts. In Figure 8b, the results showed that C

_{P}is increasing proportionally with increased rotor diameter. In Figure 8c, since the design was based on an optimal average wind speed of 5.5 m/s, the maximum C

_{P}of 0.445 was obtained around that value. When the speed diverges from the design wind speed, it is normal for the C

_{P}to drop.

## 5. Validation of the Proposed Approach

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ρ | Density of air (1.22 kg/m^{3}) |

N | Number of blades |

D | Blade Diameter (m) |

P | Mechanical Power (W) |

V | Upstream wind-speed (m/s) |

C_{P} | Power coefficient |

C_{Q} | Torque coefficient |

c | Cross section Area at radius r (m^{2}) |

λ, λ_{0} | tip-speed ratio, optimum |

F_{L} | Lift force (N) |

F_{D} | Drag force (N) |

C_{L} | Lift coefficient |

C_{D} | Drag coefficient |

F_{T} | Tangential force (N) |

τ_{r} | Torque per unit-length (N) |

V_{rel} | Relative wind speed (m/s) |

R | Radius of the rotor (m) |

Φ | Angle of relative wind (deg) |

β | Pitch angle (deg) |

⍵ | Rotational Speed (rad/s) |

A | Area (m^{2}) |

R_{r} | External radius to internal radius ratio (r / R) |

V | Average wind speed (m/s) |

a | Axial Induction factor |

a’ | Radial Induction factor |

C_{line} | Chord line |

AoA | Angle of Attack |

r | Internal radius (Distance between the axis of rotation and the blade section) (m) |

Re | Reynolds number |

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**Figure 1.**Blade sectional aerodynamic angles and forces coefficients, where || indicates parallel relation and ∟indicates perpendicular relation.

**Figure 4.**The sections of the airfoils S1210, S1223, and the interpolated airfoil section S1210–S1223.

**Figure 5.**

**C**vs. AoA for (

_{L}/C_{D}**a**) S1210, S1223, S1210–S1223 airfoils with Re = 100,000, (

**b**) S1210–S1223 airfoils with Re = 100,000, Re = 75,000, Re = 50,000, (

**c**) S1210, S1223, S1210–S1223 airfoils with Re = 60,000, (

**d**) S1210, S1223, S1210–S1223 airfoils with Re = 75,000.

**Figure 6.**Resultant blade from XFOIL and MATLAB with Airfoil sections along the length of the blade.

**Figure 7.**The impact of design parameters on C

_{P}(

**a**) D vs. C

_{P}at r

_{R}= 0.10 m at various tip speed ratios; (

**b**) C

_{P}vs. λ at r

_{R}= 0.10 m at various blade diameters; (

**c**) C

_{P}vs. r

_{R}at D = 3 m at various tip speed ratios.

Number of Variables and Output Parameters | Symbol | Description |
---|---|---|

1 | $N$ | Number of Blades |

2 | $\mathsf{\lambda}$ | Tip speed ratio (unitless) |

3 | $D$ | Rotor diameter (m) |

4 | $\mathsf{\omega}$ | Angular velocity (rad/s) |

5 | $a$ | Induction factor (unitless) |

6 | $V$ | Wind speed (m/s) |

7 | $Cp$ | Power coefficient (%) |

8 | $Power$ | Watts |

9 | $r$/R | Internal-to-external radius ratio |

λ | No. of Blades | D (m) | ⍵ (rad/s) | a | V (m/s) | r/R | C_{P(trap)} | C_{P(sim)} |
---|---|---|---|---|---|---|---|---|

6 | 3 | 4 | 16.5 | 0.275 | 5.5 | 0.1 | 0.391876 | 0.405566 |

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**MDPI and ACS Style**

Muhsen, H.; Al-Kouz, W.; Khan, W.
Small Wind Turbine Blade Design and Optimization. *Symmetry* **2020**, *12*, 18.
https://doi.org/10.3390/sym12010018

**AMA Style**

Muhsen H, Al-Kouz W, Khan W.
Small Wind Turbine Blade Design and Optimization. *Symmetry*. 2020; 12(1):18.
https://doi.org/10.3390/sym12010018

**Chicago/Turabian Style**

Muhsen, Hani, Wael Al-Kouz, and Waqar Khan.
2020. "Small Wind Turbine Blade Design and Optimization" *Symmetry* 12, no. 1: 18.
https://doi.org/10.3390/sym12010018