# Influence of the Blunt Trailing-Edge Thickness on the Aerodynamic Characteristics of the Very Thick Airfoil

^{*}

## Abstract

**:**

## 1. Introduction

_{L}(lift coefficient) of the wind turbine airfoils [8,9,10,11,12,13]. In the design of large wind turbine blades, the thick BTE airfoil is increasingly serving as a bridge between structural strength and aerodynamic characteristics [14,15].

_{Lmax}increased significantly while increasing the trailing-edge thickness after truncating the Go-490 airfoil with a relative thickness of 20%. In addition, Tanner [8], Ramjee [9], Sato [10], Law [11], and Fuglsang [12] all experimentally investigated the aerodynamic characteristics of airfoils with relative thicknesses from 6% to 43% at different Reynolds numbers and trailing-edge thicknesses. However, in the above studies, the BTE is generated by truncating the trailing edge. In this way, the airfoil’s relative thickness is changed. Timmer et al. [22] summarized the experimental data of wind turbine airfoils developed by Delft University of Technology with a relative thickness from 21% to 30% and studied the effects of the trailing-edge wedge, the Gurney flap, and the vortex generators on the aerodynamic performance of the DU series of airfoils. These airfoils were designed to be the BTE with a very limited relative thickness. In 2006, Baker et al. [13] studied the aerodynamic characteristics of the FB-3500 airfoil under different blunt trailing-edge thicknesses through experiment and numerical simulation. The BTE airfoil is generated by symmetrical thickening, in which the relative thickness of the airfoil remains 35%. The results showed that increasing the trailing-edge thickness could improve the aerodynamic characteristics of the thick airfoil.

## 2. Method

#### 2.1. Experimental Setup

^{6}, 2.5 × 10

^{6}, and 3.0 × 10

^{6}) and under free and fixed transition conditions. The pressure tests are performed at 1° intervals from −15° to 25°. The test plan is presented in Table 1.

#### 2.2. Numerical Method and Validation

^{6}. The turbulence model used in the simulation is the k-ω SST model. The results are shown in Table 3. It can be seen that the simulated C

_{L}is all higher than the experimental data [22], and with grid numbers increasing, the numerical results gradually approach the experimental data. The calculated C

_{D}is a little higher than the experimental data, which are similar to the simulation results of Gao et al. [35] using the S-A model. From Table 3, the results calculated with Grid C are closer to the experimental data. The lift coefficient is slightly closer to the experimental results than that of Grid B, but at the same time, the number of cells is 44% larger than that of Grid B. To maintain the accuracy of the simulation and save calculation resources, the grid density in this paper will be same as that of Grid B for the remaining numerical simulations.

_{L}and C

_{D}curves and the C

_{P}distribution.

_{L}, the simulation results of the S-A model and k-ω SST are in good agreement with the experimental data before the stall AoA of about 12.8° but overestimate after the stall. When approaching the stall AoA, the simulation results of the Reynolds stress model (RSM) underestimate the lift of the airfoil and overestimate its drag. However, after the stall, the simulated results of the Reynolds stress model agree well with the experimental data. For C

_{D}, the present results are all higher than the experiment data before the stall but a little underestimated after the stall. For the C

_{P}distribution, the simulation results of the S-A model and k-ω SST are in good agreement with the experimental data. Overall, the simulation results of the S-A model and k-ω SST agree quite well with the experimental data before stall, while the simulation results of the k-ε realizable model and RSM agree quite well with the experimental data after stall.

## 3. Results and Discussion

#### 3.1. Analysis of Aerodynamic Characteristics of the NWT600 Airfoil

^{6}, Re = 2.5 × 10

^{6}, and Re = 3.0 × 10

^{6}, the C

_{L}, C

_{D}, C

_{M}, and L/D of the NWT600 airfoil under the free and fixed transition conditions are measured experimentally, as shown in Figure 8.

_{L}of the airfoil decreases when the AoA increases. A similar phenomena also appears in the numerical results of the FB-3500-0050 airfoil by Baker et al. [13] and the C

_{L}curve of the TR-44 airfoil simulated by Standish et al. [36] using the MSES. The AoA range of the negative lift gradient is much bigger in this study.

_{L}under the fixed transition condition is usually lower than that under the free transition condition, while the C

_{D}is usually higher [13,36]. However, the case of the NWT600 airfoil is quite different. The C

_{L}of the NWT600 airfoil under the fixed transition condition is higher than that under the free transition condition at most AoAs. The C

_{D}under the fixed transition condition is lower than that under the free transition condition at a part of the AoAs. For example, for the experimental data with Re = 2.0 × 10

^{6}, when AoA is less than −8°, the drag coefficient under the fixed transition condition is lower than that under the free transition condition.

^{6}and Ma = 0.149, which is consistent with the experimental condition at Re = 2.0 × 10

^{6}. The setting of the numerical simulation is exactly the same as that in the numerical validation. Many numerical simulations of the NWT600 airfoil are performed based on various turbulence models, including the Spalart–Allmaras model, k-ω SST model, k-ε realizable model, and Reynolds stress (linear pressure-strain) model, and the results simulated with these turbulence models are compared. All the simulations are considered to be fully turbulent. At the same time, the reason why the aerodynamic characteristics of the NWT600 airfoil are so different from those of the conventional thin airfoils is explored.

_{L}, C

_{D}, C

_{M}, and L/D are shown in Figure 9. The variation trends of the aerodynamic force coefficients with the four turbulence models agree qualitatively well with those of the experimental data, although the numerical values deviate from the experimental data. Among these turbulence models, the Reynolds stress (linear pressure-strain) model gives the best agreement with the experimental data, and differences between the results of the other three models are small.

_{L}after stall also deviate more or less from the experimental data. Therefore, it is not surprising that the present numerical results with severe flow separation deviate from the experimental data.

_{P}distribution of the simulation results and the experimental data at different AoAs. From the C

_{P}distribution curve, it can be observed that although there is a difference in values between the force coefficient simulated by the RANS model and the experimental data, the variation trend of the pressure distribution curves along the airfoil surface at different AoAs is consistent with the experimental data. The reason for the value difference of the force coefficient is that the RANS method overestimates the pressure of the airfoil surface in most cases, especially in the separation region (i.e., the horizontal part of the C

_{P}distribution curve). Although the 2D steady-state RANS models overestimate the pressure of the airfoil surface in most cases, it is qualitatively acceptable to predict the surface pressure distribution of the very thick airfoil. Although there is a deviation between the aerodynamic force value predicted by the RANS method and the experimental data, it is reasonable for reference.

_{P}curve of the upper surface intersects that of the lower surface. The pressure force direction around the leading edge is opposite to that around the trailing edge. Therefore, the lower and upper surfaces of the NWT600 airfoil cannot be simply called the pressure side and suction side, respectively.

_{P}distribution curves of the upper and lower airfoil gradually approach each other. The moment gradually decreases to about 0. The variation trend of the pressure distribution from AoA = 0° to AoA = 15° is similar to that from AoA = −15° to AoA = 0°. The moment changes to a positive pitching moment and gradually increases. When the AoA is over 15°, the positive lift force around the leading edge continues to increase, but the negative lift force around the trailing edge gradually decreases. With the increasing of AoA, the direction of incoming flow is gradually parallel to the trailing edge profile of the lower surface. Therefore, the suction force on the lower trailing edge gradually decreases. The positive pitching moment of the airfoil decreases gradually.

#### 3.2. Influence of the BTE Thickness on the Aerodynamic Characteristics of the NWT600 Airfoil

_{0}, y

_{0}), and set the new coordinate point on the profile curve after modification as (x, y), which can be expressed as follows:

_{t}represents the location of the maximum thickness; c is the chord length; n is the power exponent. n = 1 corresponds to a linear distribution. The larger the n is, the smaller the thickness increment will be at the beginning of the thickening process. In this study, n is equal to five. Six airfoils with different trailing-edge thicknesses have been obtained. The BTE relative thicknesses of these airfoils are shown in Table 4, and the airfoils are shown in Figure 12.

_{L}, C

_{D}, C

_{M}, and L/D of the six airfoils. From the C

_{L}curve, it can be clearly observed that with the trailing-edge thickness increasing, the variation trend of the C

_{L}curve gradually becomes similar to the trend of the conventional thin airfoil, and the AoA range where the slope of the C

_{L}curve is negative gets shorter. At positive AoAs, C

_{L}increases with the BTE thickness. When the BTE thickness is thickened to 30% chord length, the phenomenon of C

_{L}decreasing with increasing AoA disappears completely. For the C

_{D}, with the increasing of the BTE thickness, the C

_{D}increases at large AoAs and decreases at small AoAs. The moment coefficient also changes greatly. The moment coefficient curve at positive AoAs is continuously shifted downward.

_{Lmax}of the NWT600 airfoil is 0.519, and the corresponding AoA is −12 degrees. The C

_{Lmax}of the NWT600_30 airfoil is 0.802 at 25 degrees. The maximum L/D also increases significantly. The L/D

_{max}of the NWT600 airfoil is 4.308 at −10 degrees. The L/D

_{max}of the NWT600_30 airfoil is 9 at 4 degrees.

_{P}distribution of the airfoils with different BTE thicknesses. It can be observed that the increase in the trailing-edge thickness obviously changes the C

_{P}distribution of the airfoil at all AoAs, but the chord line position of the peak pressure point and the variation trend of the C

_{P}distribution curve are not changed. It can be found that, as the BTE thickness increases, the pressure of the leeward side (the side where the separation occurs) has a little change. The pressure increase on the windward side of the airfoil during the thickening process is the major cause of the significant improvement in the aerodynamic characteristics. It further verifies the analysis in the previous part.

## 4. Summary

_{P}distribution curves of the lower and upper surfaces intersect, so that the aerodynamic forces around the leading edge and trailing edge are in opposite directions. The aerodynamic performance of the NWT600 airfoil is very poor.

_{Lmax}and the L/D

_{max}of the airfoil are significantly increased. The C

_{D}is slightly reduced at small AoAs. The aerodynamic characteristics of the airfoil are significantly improved.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

AoA | angle of attack [°] |

C_{L} | lift coefficient [-] |

C_{Lmax} | maximum lift coefficient [-] |

C_{D} | drag coefficient [-] |

C_{M} | moment coefficient [-] |

L/D | lift-to-drag ratio [-] |

C_{P} | pressure coefficient [-] |

Ma | Mach number [-] |

Re | Reynolds number [-] |

c | chord length [m] |

BTE | blunt trailing edge |

RANS | Reynolds-averaged Navier–Stokes |

S-A | Spalart–Allmaras model |

RSM | Reynolds stress model |

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Model | Run No. | Transition | Re | AoA Region | ΔAoA |
---|---|---|---|---|---|

NWT600 | 1 | Fixed | 2.0 ×10^{6} | −15° to 25° | 1° |

2 | Fixed | 2.5 × 10^{6} | −15° to 25° | 1° | |

3 | Fixed | 3.0 × 10^{6} | −15° to 25° | 1° | |

4 | Free | 2.0 × 10^{6} | −15° to 25° | 1° | |

5 | Free | 2.5 × 10^{6} | −15° to 25° | 1° | |

6 | Free | 3.0 × 10^{6} | −15° to 25° | 1° |

Parameters | Grid A | Grid B | Grid C |
---|---|---|---|

Far-field radius/c | 50 | 50 | 50 |

Wrap-around points | 240 | 400 | 480 |

Normal layers | 120 | 200 | 240 |

First layer height/m | 1.0 × 10^{−5} | 1.0 × 10^{−5} | 1.0 × 10^{−5} |

Total cells number | 2.88 × 10^{4} | 8.00 × 10^{4} | 11.52 × 10^{4} |

Y plus | <1.00 | <1.00 | <1.00 |

Grid A | Grid B | Grid C | CFD [35] | Experiment [22] | |
---|---|---|---|---|---|

Total number of cells | 2.88 × 10^{4} | 8.00 × 10^{4} | 11.52 × 10^{4} | - | - |

C_{L} | 1.3941 | 1.3903 | 1.3819 | 1.3750 | 1.380 |

C_{D} | 0.0238 | 0.0234 | 0.0232 | 0.0206 | 0.014 |

Airfoil | NWT600_06 | NWT600_10 | NWT600_15 | NWT600_20 | NWT600_30 |
---|---|---|---|---|---|

Relative thickness of the trailing edge | 6% | 10% | 15% | 20% | 30% |

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## Share and Cite

**MDPI and ACS Style**

Pei, Z.; Xu, H.-Y.; Deng, L.; Li, L.-X.
Influence of the Blunt Trailing-Edge Thickness on the Aerodynamic Characteristics of the Very Thick Airfoil. *Wind* **2023**, *3*, 439-458.
https://doi.org/10.3390/wind3040025

**AMA Style**

Pei Z, Xu H-Y, Deng L, Li L-X.
Influence of the Blunt Trailing-Edge Thickness on the Aerodynamic Characteristics of the Very Thick Airfoil. *Wind*. 2023; 3(4):439-458.
https://doi.org/10.3390/wind3040025

**Chicago/Turabian Style**

Pei, Zhen, He-Yong Xu, Lei Deng, and Ling-Xiao Li.
2023. "Influence of the Blunt Trailing-Edge Thickness on the Aerodynamic Characteristics of the Very Thick Airfoil" *Wind* 3, no. 4: 439-458.
https://doi.org/10.3390/wind3040025