# Aerodynamic Characteristics of Different Airfoils under Varied Turbulence Intensities at Low Reynolds Numbers

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## Abstract

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## Featured Application

**The study of airfoil affected by the unsteady jet flow of turboelectric distributed propulsion aircraft was conducted, which lays a good foundation for future design of turboelectric distributed propulsion (TeDP) unmanned aerial vehicles (UAVs).**

## Abstract

## 1. Introduction

^{5}).

## 2. Numerical Approach

#### 2.1. Estimation Method of Turbulence Intensity

_{99%}, where the δ

_{99%}is the thickness of boundary layer. As for the flow affected by the inlet grid, the turbulence length scale is approximately equal to the grid aperture, namely l ≈ d. [6,21].

_{T}is the ratio of turbulence viscosity to laminar viscosity, which is directly proportional to the turbulent Reynolds number. In the high-Reynolds-number boundary layer, shear layer and fully developed pipe flow, the turbulence viscosity ratio is large, about 100–1000. However, in most free flow boundary layers, the turbulence viscosity ratio is quite small, usually 1–10.

#### 2.2. $\gamma -{\tilde{\mathrm{Re}}}_{\theta t}$ Transition Model

_{length}is the empirical correlation for controlling the length of transition region, $\Omega $ is vorticity, the constant terms are C

_{a1}= 2, C

_{e1}= 1, C

_{a2}= 0.06, C

_{e2}= 50, C

_{γ3}= 0.5.

## 3. Validation of Numerical Simulation Method

#### 3.1. Validation of Pressure Distribution

_{1}= 2.03 × 10

^{−5}c, y

^{+}= 0.25. The inflow velocity is V = 11.982 m/s.

#### 3.2. Validation of Aerodynamic Force

_{1}= 6.53 × 10

^{−4}c, y

^{+}= 0.25.

## 4. Effect of Turbulence Intensity on Airfoil at Different Reynolds Numbers

_{1}= 26,500 and Re

_{2}= 53,000 are chosen for further research, and the state of Re

_{3}= 212,000 is calculated as a complement. In addition, since NACA0012 is a popular symmetric airfoil, the SD7037 airfoil is selected for comparison. The SD7037 airfoil has a relative thickness of t/c = 9.20% and a relative camber of f/c = 3.02%. It operates at a low Reynolds number and it is favored for R/C model sailplanes because of its working lift range (the lift range over the low drag region) that begins near a C

_{L}of 0.2 and extends to near C

_{L}of 1.0 where the drag begins to increase more rapidly [37]. During the calculation, the turbulence intensity at the leading edge of airfoils is guaranteed to be Tu = 6% and Tu = 0.6%. The lift and drag characteristics are shown in Figure 9 and Figure 10.

_{1}= 26,500 and Re

_{2}= 53,000, the lift coefficient increases linearly with small angle of attack. At Re

_{2}= 53,000, the stalling angle of NACA0012 is 12°, while that of SD7037 is 15°. This shows that the SD7037 airfoil has better lift characteristics. At Tu = 0.6%, the lift coefficient is evidently nonlinear and the stalling angle is smaller for both of the airfoils. At Re

_{1}= 26,500, the stalling angle of both airfoils decreases to only 8°, and there is a sharp increase of drag around α = 10°. Figure 11 also indicates that the pressure drag of the airfoil suddenly increases at α = 10°, which may be the result of the development of the flow separation with the increase of the angle of attack. At Re

_{3}= 212,000, the lift coefficient of both airfoils increases further, and the stalling phenomenon delays, which is more evident at Tu = 0.6%. Notably, at α = 2° and α = 5°, the lift coefficient of the airfoil at Tu = 0.6% is bigger than that at Tu = 6%, which might have something to do with the generation of the LSB.

_{D,p}represents the coefficient of pressure drag, C

_{D,f}the coefficient of friction drag) indicates that the NACA0012 airfoil has a small pressure drag at small angle of attack. With the angle of attack increasing to 15°, the airfoil stalls and the pressure drag increases sharply at Tu = 0.6%. Besides, in comparison with a high level of turbulence intensity, the frictional drag is smaller at Tu = 0.6%. The variation of drag characteristics of the SD7037 airfoil is similar to NACA0012 (Figure 11b).

^{5}, cambered airfoils have better lift and drag characteristics than thick conventional airfoils with rounded-leading edges.

#### 4.1. The Influence of Turbulence Intensity Upon Airfoils at Re_{1} = 26,500

_{1}= 26,500, the aerodynamic characteristics of airfoils were analyzed at angles of attack of 5°, 8° and 10°. The pressure distribution and chordwise friction drag coefficient (C

_{f,X}) of airfoils in varied turbulence intensities is shown in Figure 12 and Figure 13.

_{f,X}becomes negative at 18%c, which indicates that the flow is separated (Figure 13a and Figure 15a). The streamline around NACA0012 wraps a slender eddy due to the laminar separation (Figure 15a). The SD7037 airfoil also experiences flow separation, but the separation point is slightly delayed, at about 25%c (Figure 17a).

#### 4.2. The Influence of Reynolds Number on the Airfoil

_{2}= 53,000 are shown in Figure 18.

_{3}= 212,000, the position of the LSB transfers to 6%–13%c, and the size of the LSB becomes evidently smaller. In addition, the valley value of C

_{f,X}represents the onset of laminar flow transition, and peak value after the valley of C

_{f,X}represents the finish of the transition to turbulent flow. Figure 19 shows that the transition point moves forward from 42%c through 17%c to 12%c, and the reattachment point also moves forward from 80%c through 25%c to 13%c. It can be concluded that, the increasing Reynolds number results in earlier transition and reattachment, contributing to an overall decrease in separation bubble length, as stated in [38].

_{2}= 53,000 are shown in Figure 20.

## 5. Discussion

_{1}= 26,500, an eddy similar to a long laminar separation bubble emerges on the upper surface of the airfoil, but fails to reattach to the wall. At Re

_{2}= 53,000, a small short laminar separation bubble is generated near the leading edge. At Re

_{3}= 212,000, an LSB occurs on the upper surface of the airfoil near the trailing edge. These phenomena show that the generation of separation bubbles is closely related to the Reynolds number if the Reynolds number is too small, the laminar flow is not able to reattach to the wall after the transition, and it is difficult to form an LSB. As the Reynolds number increases, a complete LSB structure arises and the morphology of the LSB alters from a long separation bubble or a short separation bubble near the leading edge to a separation bubble near the trailing edge of the NACA0012 airfoil. It is worth noting that a separation bubble occurs at the trailing edge of the SD7037 airfoil at Re

_{1}= 26,500, Tu = 6%, indicating that SD7037 has better low-Reynolds-number aerodynamic performance.

_{R}− Re

_{S}= 50,000 (where Re

_{R}is the Reynolds number of reattachment, Re

_{S}is the Reynolds number of separation), which indicates that the separation flow of the airfoil will no longer reattach when the Reynolds number is less than 5 × 10

^{4},. Meanwhile, if the Reynolds number is slightly higher than 5 × 10

^{4}, a separation bubble will occur. Additionally, if the low-Reynolds-number performance of the airfoil is excellent, the reattachment will also occur when the Reynolds number is less than 5 × 10

^{4}.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

C_{D} | Coefficient of drag |

C_{L} | Coefficient of lift |

C_{P} | Coefficient of pressure |

C_{D,p} | Coefficient of pressure drag |

C_{D,f} | Coefficient of friction drag |

C_{f,X} | Coefficient of friction in X direction |

Tu | Turbulence intensity |

l | Turbulence length scale |

R_{T} | Ratio of turbulence viscosity to laminar viscosity |

Tu_{inlet} | Turbulence intensity at the inlet of wind tunnel |

ε | Turbulence dissipation rate |

k | Turbulent kinetic energy |

γ | Intermittence factor |

Re_{v} | Vorticity Reynolds number |

Sr | Strouhal number |

d_{1} | First layer grid element to wall distance |

TeDP | Turboelectric distributed propulsion |

URANS | Unsteady Reynolds-averaged Navier-Stokes |

${\tilde{\mathrm{Re}}}_{\theta t}$ | Transition momentum thickness Reynolds number |

LSB | Laminar separation bubble |

FSTI | Freestream turbulence intensity |

SST | Shear stress transport |

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**Figure 2.**Comparison of numerical calculation and experiment results of pressure distribution. CFD: computational fluid dynamics; EXP: experiment.

**Figure 4.**Decay law of turbulence intensity along the flow direction. (

**a**) Turbulence intensity change in experiment; (

**b**) Turbulence intensity change in numerical simulation.

**Figure 5.**Comparison of numerical calculation and experiment results. (

**a**) C

_{L}vs α; (

**b**) C

_{D}vs α.

**Figure 6.**Airfoil pressure distribution affected by different turbulence intensities at three angles of attack. (

**a**) α = 5°; (

**b**) α = 10°; (

**c**) α = 15°.

**Figure 7.**Flow characteristic such as turbulent kinetic energy and streamline shape at Tu = 6%, (

**a**) α = 5°; (

**b**) α = 10°; (

**c**) α = 15°.

**Figure 8.**Flow characteristic such as turbulent kinetic energy and streamline shape at Tu = 0.6%, (

**a**) α = 5°; (

**b**) α = 10°; (

**c**) α = 15°.

**Figure 9.**Aerodynamic characteristics of NACA0012 at different Reynolds numbers and turbulence intensities. (

**a**) C

_{L}vs α; (

**b**) C

_{D}vs α.

**Figure 10.**Aerodynamic characteristics of SD7037 at different Reynolds numbers and turbulence intensities. (

**a**) C

_{L}vs α; (

**b**) C

_{D}vs α.

**Figure 11.**The component of the drag coefficient of airfoils varies with the angle of attack at different Reynolds numbers and turbulence intensities. (

**a**) NACA0012; (

**b**) SD7037.

**Figure 12.**Airfoil pressure distribution affected by different turbulence intensities at three angles of attack. (

**a**) α = 5°; (

**b**) α = 8°; (

**c**) α = 10°.

**Figure 13.**Airfoil chordwise skin friction drag coefficient affected by different turbulence intensities at three angles of attack. (

**a**) α = 5°; (

**b**) α = 8°; (

**c**) α = 10°.

**Figure 14.**The NACA0012 airfoil characteristics such as turbulent kinetic energy and streamline shape at Tu = 0.6%; (

**a**) α = 5°; (

**b**) α = 8°; (

**c**) α = 10°.

**Figure 15.**The NACA0012 airfoil characteristics such as turbulent kinetic energy and streamline shape at Tu = 0.6%, (

**a**) α = 5°; (

**b**) α = 8°; (

**c**) α = 10°.

**Figure 16.**The SD7037 airfoil characteristic such as turbulent kinetic energy and streamline shape at Tu = 6%, (

**a**) α = 5°; (

**b**) α = 8°; (

**c**) α = 10°.

**Figure 17.**The SD7037 airfoil characteristic such as turbulent kinetic energy and streamline shape at Tu = 0.6%, (

**a**) α = 5°; (

**b**) α = 8°; (

**c**) α = 10°.

**Figure 18.**Airfoil aerodynamic performance at α = 10°, Re

_{2}= 53,000. (

**a**) Pressure distribution; (

**b**) Coefficient of chordwise friction drag.

**Figure 19.**The chordwise friction drag coefficient of airfoil at α = 8° under the Reynolds number of (

**a**) Re

_{1}= 26,500; (

**b**) Re

_{2}= 53,000; (

**c**) Re

_{3}= 212,000.

**Figure 20.**Airfoil aerodynamic performance at α = 5°, Re

_{2}= 53,000. (

**a**) Pressure distribution; (

**b**) Coefficient of chordwise friction drag; (

**c**) Effective shape of NACA0012 at Tu = 0.6%.

**Table 1.**Results of the mesh independency study. AOA: angle of attack; R: ratio of errors between Fine and Exp.

AOA | Coarse | Medium | Fine | Exp | R |
---|---|---|---|---|---|

2 | 0.1324 | 0.1256 | 0.1123 | 0.098 | 0.146 |

5 | 0.3276 | 0.3207 | 0.2950 | 0.282 | 0.046 |

8 | 0.6323 | 0.6218 | 0.6224 | 0.612 | 0.017 |

10 | 0.7314 | 0.7421 | 0.7507 | 0.785 | 0.044 |

12 | 0.7231 | 0.7748 | 0.7893 | 0.856 | 0.078 |

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**MDPI and ACS Style**

Zhang, Y.; Zhou, Z.; Wang, K.; Li, X.
Aerodynamic Characteristics of Different Airfoils under Varied Turbulence Intensities at Low Reynolds Numbers. *Appl. Sci.* **2020**, *10*, 1706.
https://doi.org/10.3390/app10051706

**AMA Style**

Zhang Y, Zhou Z, Wang K, Li X.
Aerodynamic Characteristics of Different Airfoils under Varied Turbulence Intensities at Low Reynolds Numbers. *Applied Sciences*. 2020; 10(5):1706.
https://doi.org/10.3390/app10051706

**Chicago/Turabian Style**

Zhang, Yang, Zhou Zhou, Kelei Wang, and Xu Li.
2020. "Aerodynamic Characteristics of Different Airfoils under Varied Turbulence Intensities at Low Reynolds Numbers" *Applied Sciences* 10, no. 5: 1706.
https://doi.org/10.3390/app10051706