# Numerical Study of the Effect of the Reynolds Number and the Turbulence Intensity on the Performance of the NACA 0018 Airfoil at the Low Reynolds Number Regime

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Model and Its Validation

#### 2.1. Numerical Domain and CFD Solver Settings

^{−6}was used for all computed variables.

#### 2.2. Computing Domain Size Effect

#### 2.3. Turbulence Intensity Effect and Mesh Sensitivity Studies

#### 2.4. Validation of the Numerical Model

## 3. Results

#### 3.1. Reynolds Number Effect on Lift and Drag Coefficients

#### 3.1.1. Lift Force Coefficient

#### 3.1.2. Drag Force Coefficient

#### 3.2. Turbulence Intensity Effect on Lift and Drag Coefficients

#### 3.2.1. Lift Force Coefficient

- 1.
- An increase in TI causes a decrease in the $d{C}_{L}/d\alpha $ derivative in the first area, an increase in the $d{C}_{L}/d\alpha $ derivative in the second area, and an increase in ${\alpha}_{t}$.
- 2.
- An increase in Re causes a decrease in the $d{C}_{L}/d\alpha $ derivative in the first region and an almost linear increase in the ${\alpha}_{t}$ angle.
- 3.

#### 3.2.2. Drag Force

#### 3.3. Static Pressure

## 4. Conclusions

- One of the key achievements of this paper is the analysis of the aerodynamic characteristics of the NACA 0018 airfoil in relation to the turbulence intensity. The decay rate of turbulence intensity strongly depends on the turbulence intensity at the inlet. The higher the turbulence intensity at the inlet, the higher the decay rate. For the lowest turbulence intensity analyzed in this work, equal to 0.1%, the decay rate is almost constant. In the vicinity of the nose of the profile, the turbulence intensity is very low regardless of the inlet’s turbulence intensity. The results shown in Figure 4b,c have practical applications when using the mesh described in the paper [6]. The data shown in these graphs can be used to interpolate the turbulence intensity at the inlet in order to obtain a specific value of the turbulence intensity on the airfoil.
- All calculations carried out in this paper, regardless of the Reynolds number and the turbulent intensity, showed a zero-lift coefficient at a zero angle of attack.
- The presence of a wide laminar-separation bubble in the boundary layer results in the occurrence of two aerodynamic derivatives of the lift coefficient in the range of angles of attack before stall. The increase in Reynolds number primarily causes a linear increase in the first region. On the other hand, the aerodynamic derivative in the second region is almost independent of the Reynolds number.
- At a Reynolds number of 50,000, a faster increase in drag is observed starting from an angle of attack of 6 deg. For higher Reynolds numbers, the increase in drag coefficient as a function of the angle of attack is much smoother. The drag coefficients differ very little for low angles of attack and Reynolds numbers higher than 100,000.
- Generally, the effect of the turbulence intensity on the lift coefficient is much lower than the Reynolds number effect. The increase in turbulence intensity causes the lift coefficient to decrease in the first region and increase in the second region. Differences in lift coefficients for high angles of attack decrease with increasing the Reynolds number and the turbulence intensity.
- The increase in turbulence intensity causes a decrease in the aerodynamic derivative $d{C}_{L}/d\alpha $ in the first region and its increase in the second region. Increasing turbulence intensity also increases the transition angle of attack. This trend is visible for all the Reynolds numbers studied in this work.
- For angles of attack higher than the transition angle of attack, there is no longer a laminar-separation bubble on the pressure surface of the airfoil.
- Drag coefficients are less sensitive to the turbulence intensity than the lift coefficients, except for the lowest investigated Reynolds number of 50,000. In general, an increase in the angle of attack causes an increase in the drag coefficient.
- The Reynolds number has a much greater effect on the pressure distributions than the turbulence intensity. The effect of Reynolds number and turbulence intensity is much greater on the suction side of the profile.
- The performed numerical analyzes showed clear differences in the characteristics of the drag coefficient for a Reynolds number of 50,000. For the other considered Reynolds numbers in the range of 100,000 to 200,000, the changes in the drag coefficients are rather linear as a function of both the turbulence intensity and the Reynolds number.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$c$ | chord length |

${C}_{D}$ | drag coefficient |

${C}_{L}$ | lift coefficient |

${C}_{P}$ | static pressure coefficient |

$d{C}_{L}/d\alpha $ | rate of change of lift coefficient with angle of attack |

$l$ | turbulence length scale |

$L$ | length from the airfoil’s trailing edge to the domain’s outlet boundary |

$Re$ | chord-based Reynolds number |

$TI$ | turbulence intensity on the airfoil |

$T{I}_{0}$ | inlet turbulence intensity |

${V}_{0}$ | free stream wind velocity [m/s] |

$\alpha $ | angle of attack |

${\alpha}_{t}$ | transition angle of attack (the angle between the first and the second region) |

${\delta}_{99}$ | boundary-layer thickness |

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**Figure 3.**The computing domain and the distance from the trailing edge to the outlet, L (

**a**). The influence of the domain length on the drag coefficient (

**b**) and the lift coefficient (

**c**).

**Figure 4.**Segment definition for calculating the dependence $TI\left(x\right)$, where $T{I}_{0}$—segment start point and TI—segment endpoint (

**a**), turbulence intensity as a function of distance from the airfoil nose (

**b**,

**c**), coefficients of aerodynamic forces as a function of time for different values of turbulence intensity (

**d**–

**g**).

**Figure 5.**Aerodynamic characteristics of the NACA 0018 profile: lift force coefficient as a function of the angle of attack (

**a**) and drag coefficient (

**b**). Comparison of CFD results with the experiment [24].

**Figure 8.**$d{C}_{L}/d\alpha $ derivatives for two regions. The comparison between present results and data available in the literature [79].

**Figure 9.**Lift coefficient vs. angle of attack for $Re=150\times {10}^{3}$ and $TI=0.25\%$. An approach for determining the transition angle, ${\alpha}_{t}$ (

**a**). The transition angle vs. Reynolds number for $TI=0.25\%$ (

**b**).

**Figure 13.**The aerodynamic derivatives $d{C}_{L}/d\alpha $ as a function of Reynolds number for the first region (

**a**) and for the second region (

**b**). Transition angle of attack as a function of Reynolds number (

**c**).

**Figure 15.**Effect of turbulence intensity on drag coefficient: (

**a**) for Reynolds number of 50,000 and (

**b**) for Reynolds number of 150,000.

**Figure 16.**Static pressure coefficient on the suction side at different Reynolds numbers; angle of attack effect.

**Figure 17.**Static pressure coefficient on pressure side at different Reynolds numbers; angle of attack effect.

**Figure 18.**Static pressure coefficient on the pressure side (solid lines) and the suction side (dashed lines). Reynolds number effect (upper plots); turbulence intensity effect (lower plots).

Number of Mesh Elements | TI on the Airfoil [%] ^{1} | ||
---|---|---|---|

Mesh | AoA = 4° | AoA = 10° | |

Extra coarse | 600,000 | −0.00041 | −0.00041 |

Coarse | 700,000 | −0.00016 | −0.00016 |

Medium | 800,000 | 0.24916 | 0.25065 |

Fine | 900,000 | 0.00011 | 0.00011 |

Extra fine | 1,000,000 | 0.00020 | 0.00020 |

^{1}Only absolute values for the “Medium” case are presented. For others, differences from the “Medium” case.

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**MDPI and ACS Style**

Michna, J.; Rogowski, K. Numerical Study of the Effect of the Reynolds Number and the Turbulence Intensity on the Performance of the NACA 0018 Airfoil at the Low Reynolds Number Regime. *Processes* **2022**, *10*, 1004.
https://doi.org/10.3390/pr10051004

**AMA Style**

Michna J, Rogowski K. Numerical Study of the Effect of the Reynolds Number and the Turbulence Intensity on the Performance of the NACA 0018 Airfoil at the Low Reynolds Number Regime. *Processes*. 2022; 10(5):1004.
https://doi.org/10.3390/pr10051004

**Chicago/Turabian Style**

Michna, Jan, and Krzysztof Rogowski. 2022. "Numerical Study of the Effect of the Reynolds Number and the Turbulence Intensity on the Performance of the NACA 0018 Airfoil at the Low Reynolds Number Regime" *Processes* 10, no. 5: 1004.
https://doi.org/10.3390/pr10051004