# RANS Simulations of Aerodynamic Performance of NACA 0015 Flapped Airfoil

^{1}

^{2}

^{*}

## Abstract

**:**

^{6}for various incidence angles and a range of flap deflections is presented. The steady-state governing equations of continuity and momentum conservation are solved combined with the realizable k-ε turbulence model using the ANSYS-Fluent code (Version 13.7, ANSYS, Inc., Canonsburg, PA, USA). The primary objective of the study is to provide a comprehensive understanding of flow characteristics around the NACA 0015 airfoil as a function of the angle of attack and flap deflection at Re = 10

^{6}using the realizable k-ε turbulence model. The results are validated through comparison of the predictions with the free field experimental measurements. Consistent with the experimental observations, the numerical results show that increased flap deflections increase the maximum lift coefficient, move the zero-lift angle of attack (AoA) to a more negative value, decrease the stall AoA, while the slope of the lift curve remains unchanged and the curve just shifts upwards. In addition, the numerical simulations provide limits for lift increment $\Delta {C}_{l}$ and C

_{l, max}values to be 1.1 and 2.2, respectively, obtained at a flap deflection of 50°. This investigation demonstrates that the realizable k-ε turbulence model is capable of predicting flow features over an airfoil with and without flap deflections with reasonable accuracy.

## 1. Introduction

^{6}. In addition, despite numerous publications on the lift and drag of NACA airfoils, better understanding of airfoils with one hinged flap is still of interest [13].

^{6}.

^{6}by using the realizable k-ε turbulence model. The other objective is to validate the computational model by comparison of the results with the experimental data and earlier numerical simulation results. The flow problem here is of a boundary layer nature; therefore, the fluid motions near the airfoil surfaces are of interest. The Reynolds Averaged Navier–Stokes (RANS) models have been used extensively for wall-bounded flows [19]. On the other hand, many researchers consider the realizable k-ε model a suitable choice for analyzing the boundary layer flows under strong adverse pressure gradients or with separation [18].

## 2. Computational Modeling

#### 2.1. Formulation

#### 2.2. Evaluation of ${C}_{p},$ ${C}_{l}$ and ${C}_{f}$

_{p}, and the lift coefficient, C

_{l}, are evaluated as,

_{f}is the ratio of the surface shear stress, τ, to freestream dynamic pressure. That is,

#### 2.3. Computational Domain and Boundary Conditions

#### 2.4. Setting up of the Numerical Simulation Parameters

^{−8}was used for the continuity, x-velocity, y-velocity, k and ε. All solutions converged with the standard interpolation scheme for calculating cell-face pressure and second order up-wind density, momentum, turbulent kinetic energy, turbulent dissipation rate and energy interpolation schemes for turbulent flow.

## 3. Results and Discussion

#### 3.1. Mesh Independence Tests

^{5}and 10

^{6}are performed. The results of the two-equation realizable k-ε model of Shih et al. [20] were compared with those of the one-equation closure model of the Spalart–Allmaras (SA). The SA model was developed mainly for simulating aerodynamic flows. This model solves the modeled transport equation for the kinematic eddy (turbulent) viscosity [26]. The results obtained from SA and R-k-ε numerical models were compared with the experimental data of Rethmel [27]. Table 4 and Table 5 show the predicted values of the lift coefficients for six different meshes by using the Spalart–Allmaras (SA) and the R-k-ε turbulence models for Re = 10

^{5}and 10

^{6}, respectively. It is apparent that the realizable k-ε solutions obtained by Grids IV, V and VI are in good agreement with the experimental data. Despite the fact that the number of cells in Grid VI is approximately 3.7-times that of Grid IV, these grids provided nearly the same results for the lift coefficient. It is also seen that the SA model yields significantly higher ${C}_{l}$ values compared to the experiments. Regardless of the turbulence model used, the numerical results for these last three grids remain almost the same with increasing the number of cells from Grid IV–Grid VI.

_{p}) profile for the airfoil predicted by Grids I, IV and VI using the R-k-ε turbulence model for α = 12°, δ = 0° and Re = 10

^{5}(a) and Re = 10

^{6}(b). Here, the predicted distributions of the pressure coefficient are compared with the experimental data of Rethmel [27]. It is seen that the model predictions for the pressure coefficient are generally comparable with the experimental data. In particular, the predictions obtained by Grids IV and VI are very close to each other and to the distribution of the experimental data for both Reynolds numbers.

^{5}and Re = 10

^{6}. The vertical axis (y) in Figure 5 denotes the vertical distance from the surface of the airfoil as a fraction of the chord length. It is seen that the model predictions for Grids IV and VI are almost identical. That is, further refinement of Grid IV does not have a noticeable effect on the velocity profile.

#### 3.2. NACA 0015 Airfoil with Zero Flap Deflection

_{p}) profile for the airfoil at some selected incidence angles. For small angles of attack, the C

_{p}distribution is characterized by a negative pressure peak near the leading edge on the suction side. Beyond this point, the C

_{p}value gradually increases along the chord of the airfoil. On the pressure side of the airfoil, the C

_{p}value reaches a maximum of C

_{p}= 1 at the stagnation line. This point is near the leading edge, but shifts slightly depending on the incidence angle. Further down the chord length of the airfoil, the pressure side C

_{p}value increases gradually until it equals the suction side value at the trailing edge.

_{p}negative value decreases on the airfoil upper side, and a pronounced shift of the stagnation position toward the trailing edge is found. This situation continues until α = 17°, at which the C

_{p}value starts to vary in an irregular manner.

^{6}. The lift and drag coefficients from the ANSYS-Fluent RANS simulations were calculated, and the results for the lift coefficient are shown in this figure. It is seen that the lift coefficient increases with the angle of attack up to about 13° and then decreases. The lift coefficient obtained from 2D potential flow analysis using the panel method, the RANS simulation results of Joslin et al. [29] and the large eddy simulation results of You and Moin [2] are also shown in this figure for comparison. In addition, the experimental data of Rethmel [27] for the NACA 0015 at chord Re = 10

^{6}and the data of Lasse and Niels [30] at a chord Re of 1.6 × 10

^{6}are also reproduced in Figure 10. It should be pointed out that the potential flow solution that treats the flow around the airfoil as inviscid and irrotational is an idealized case for extremely high Reynolds number flows [31].

_{p}on the airfoil as predicted by the present RANS simulation at the onset of stall (α = 12°). The experimental data of Rethmel [27] are reproduced in this figure for comparison. Excellent agreement in the chord-wise distributions of the predicted pressure coefficient with the experimental data is seen from this figure. This emphasizes the observation that the realizable k-ε turbulence model provides an accurate description of the pressure distribution around the airfoil at this incidence angle.

_{p}as predicted from the current RANS simulation at the fully-developed stall regime (α = 16°) and compares them with the experimental data of Rethmel [27]. There are noticeable differences between these pressure distributions.

^{6}and the drag coefficient measurements’ data of Sharma [33] for the NACA 0015 at Re = 0.7 × 10

^{6}are reproduced in this figure for comparison. In addition, the drag coefficient data of Sheldahl and Klimas [34] for the NACA 0015 at Re = 10

^{6}and those of Lasse and Niels [30] at Re = 1.6 × 10

^{6}are also shown in this figure. It is seen that the drag coefficient values predicted by the realizable k-ε model are in reasonable agreement with the experimental data and earlier numerical results for incident angle less than 13°. The drag coefficient is low at zero incidence angles and increases slowly with the angle of attack to the value of 0.038 at the stall condition. The slope of the drag coefficient with respect to incidence angle, $\frac{\partial {C}_{d}\text{}}{\partial \alpha},$ remains roughly constant at about 0.003. After the stall condition, the drag coefficient increases rapidly with the further increase of the angle of attack and reaches a value of 0.28 at α = 20°, which is more than seven-times the drag coefficient at the stall condition. The slope of the drag coefficient versus incidence angle, $\frac{\partial {C}_{d}\text{}}{\partial \mathsf{\alpha}}$, jumps to a value of 0.04 after the stall condition. It is also seen that the value of the drag coefficient decreases with the increase of the Reynolds number. It is also observed that for an incident angle beyond separation, the present model overestimates the experimental data for the drag coefficient. Further study of the accuracy of various turbulence models including the realizable k-ε turbulence model are left for a future work.

^{6}, are also reproduced in this table for comparison. It is seen that the results of the present realizable k-ε model for the peak turbulence intensity are in qualitative agreement with those reported by Zhang et al. [17]. Table 6 also shows the expected increasing trend of turbulence intensity with the angle of incidence.

#### 3.3. NACA 0015 Airfoil with Flap Deflection

_{f}) are presented in Figure 15. The comparison of the static pressure contours for zero flap deflection and for the deflected flap at the same angle of attack shows that the flap deflection increases the negative pressure over the entire upper surface of the main airfoil and increases the positive pressure on the lower surface near the trailing edge. The pressure on the lower surface increases rapidly with flap deflection, while the pressure on the upper surface increases gradually. The pressures on both the upper and the lower surfaces of the flap increase with flap deflection.

^{6}and for different Mach numbers. Luchian [36] investigated the aerodynamic performance of the NACA 0015 airfoil with a 27.5% trailing edge plain flap for different flap deflection angles at Re = 10

^{6}by using three different codes (Javafoil 2.20, Martin Hepperle, Braunschweig, Germany, Profili2.20, Stefano Duranti, Feltre, Italy, and XFLR5 6.06, techwinder, Paris, France). Williamson [37] conducted experiments on the W1015 airfoil, which is identical to the NACA 0015 airfoil for wide range of low Reynolds numbers and trailing edge flap deflections. It is evident that the lift coefficient increases sharply with the increase of the flap deflection up to about 10°–15°, and then, the rate of increase becomes slower up to δ

_{f}= 40°. The present model predictions are in general agreement with the results of Hassan [16] for high Reynolds numbers for flap deflections up to δ

_{f}= 20°, the results of Luchian [36] at low Reynold numbers for flap deflections up to δ

_{f}= 30° and the experimental data of Williamson [37] for low Reynolds numbers for a wide range of flap deflections up to δ

_{f}= 40°.

_{f}= 20°, and then, the rate of increase becomes much shaper. For example, the drag coefficient at δ

_{f}= 30° is more than two-times its value at δ

_{f}= 15°. The trend is somewhat different for the AoA of α = 10°, where the drag coefficient increases gradually with the flap deflection up to δ

_{f}= 15°, and then, the drag coefficient increases sharply. The drag coefficient for δ

_{f}= 30° in this case is more than five-times its value at (δ

_{f}= 10°). When compared with the earlier results, the drag coefficients obtained by the realizable k-ε model in this study are reasonably accurate for the AoA = 5° and in the entire range of flap deflections up to δ

_{f}= 30°. It is clear that for the AoA = 10° and δ

_{f}> 15°, the predicted drag values are somewhat higher than those predicted by both the Profili and XFLR5 codes, but below the values obtained by the Javafoil code.

^{5}at zero flap deflection and 10° flap deflection.

_{f}= 10° together with their corresponding reference values at δ

_{f}= 0°. Figure 18b presents an enlarged section of the lift coefficient for small angles of attack. In addition, the increments in the values of the lift coefficient are shown in Figure 18b. It is seen that the lift increment value $\Delta \text{}{C}_{l}$ due to the flap angle is roughly the same for a large range of incidence angles below the stall angle. That is, ${\left(\Delta \text{}{C}_{l}\right)}_{1}$ $\cong $ ${\left(\Delta \text{}{C}_{l}\right)}_{2}$ for the airfoils with zero and 10° flap angle.

_{f}= 0°, the slope of the lift curve for the W1015 airfoil is slightly lower than the slope of the lift curve for the NACA 0015. It should also be pointed out that the W1015 airfoil was tested at Re = 4 × 10

^{5}, and the NACA 0015 results are for Re = 10

^{6}. It is also known that for the same angle of attack, a higher Reynolds number gives higher lift coefficient and consequently a greater slope of the lift curve. The lift curves for both airfoils are nearly linear at low angles of attack (below 10°).

**∆**C

_{l}values. A linear region is observed at smaller flap deflections of 0 ≤ δ

_{f}≤ 15°. In this region, the slope of the

**Δ**C

_{l}curve is constant, indicating fully-attached flow conditions. The second region is the transitional region, as it acts as a connection between linear and nonlinear regions. It is normally marked as the leveling or decreasing of

**Δ**C

_{l}values that is caused by the separation of flow from the upper surface of the flap. Separation from the upper surface normally occurs around a flap deflection of 10–20 deg. The actual flap deflection for flow separation depends on the Reynolds number, airfoil thickness, flap-chord ratio, angle of attack and the size of the gap around the nose of the flap. The third region is nonlinear in nature due to the reduced nonlinear increase of

**Δ**C

_{l}values with flap deflection. In this region, the flow is largely separated over the upper surface of the flap.

_{f}≤ 20°, it is seen that the lift increment

**Δ**C

_{l}varies linearly in the simulations. The simulations of Hassan [16] were for a high Reynolds number flow and have a linear trend, but a higher slope. For high flap deflections (δ

_{f}> 20°) and a high Reynolds number, Hassan [16] did not provide any data. From Figure 19, it is concluded that the present model predictions are reasonably accurate at least for low Reynolds number flows.

_{f}≤ 15°. For flap deflections larger than 15°, however, the increasing slope of the maximum lift coefficient is reduced and reaches a plateau for the flap deflection in the range of 40° < δ

_{f}< 60°. Thus, it can be concluded that deflection of the flap δ

_{f}> 40° does not provide additional benefit in regard to the maximum lift coefficient. Figure 19a also shows that the trends of the maximum lift coefficient obtained by the present realizable k-ε model are comparable to those of the experimental data of Williamson [37] for the W1015 airfoil, as well as the results of Hassan [16] for the NACA 0015 airfoil. The magnitudes are, however, somewhat different, and the present simulation results lie in between the results of Williamson [37] and Hassan [16].

_{l, max}is achieved decreases with increasing the flap deflection. Deflecting the flap by 20° decreases the stall angle of attack by 1.75° in the present study, while leading to a decrease of 1.5° in the experimental study of Williamson [37] and 0.75° in the results of Hassan [16]. The further increase in the flap deflection decreases the stall angle of attack. The present model predicts that lowering the flap by 40° decreases the stall angle of attack by 2°, while Williamson’s [37] data suggest a decrease of the stall angle of attack by 4°.

_{f}2°, 5°, 10°, 15°, 20°, 25°, 30° and 40° and for zero incidence angle. It is observed that at the zero incidence angle, the flap deflection has a pronounced influence on the turbulence intensity around the flapped airfoil. Even a small deflection in flap angle disturbs the flow and creates regions of high turbulence intensity in the upper surface of the flapped airfoil. These regions expand with increasing of the flap deflection and shift from the main airfoil towards the flap section. For δ

_{f}≤ 15°, the realizable k-ε model predicts that the peak turbulence intensity occurs in the boundary layer near both the upper and lower surfaces of the main airfoil close to the leading edge and with a lower level of turbulence intensity in the wake region. For δ

_{f}≥ 15°, however, the maximum turbulence intensity occurs in the wake region close to the flap in addition to the boundary layer regions. This is due to the fact that the region with recirculating flow becomes larger as the wake width increases with the flap deflection. At high flap deflections, the flow separates from the flap, and high pressure acting on the pressure side of the flapped airfoil and consequently marked increase in the drag occur compared to situations where the flow remains attach to the surface.

## 4. Conclusions

^{6}at different flap deflections was conducted. The airfoil with the deflected trailing edge flap was treated as a single element with no gap between the airfoil and the flap leading edge. A parabolic computational domain with 104,000 structured cells along with 10% turbulence intensity at the far-pressure field at its boundaries was used in the analysis. The grid sensitivity was performed to satisfy the mesh independence condition. For different configurations with and without flap deflections, flows over the airfoil were simulated, and the resulting lift and drag coefficients were validated by comparison with earlier experimental data and numerical simulation results. Based on the presented results, the following conclusions are drawn:

- The simulation results showed that the realizable k-ε model is a suitable turbulence model for simulating the flow characteristics around an airfoil at different angle of attacks and flap deflections.
- Results showed that the increasing incidence angle was associated with the increasing lift coefficient up to the maximum of 1.15 at α = 13°, after which the lift coefficient sharply decreases. Before stall, the slope of the lift versus incidence angle curve, $\frac{\partial {C}_{l}}{\partial \mathsf{\alpha}}$, remained roughly constant at about 0.101. After the stall angle of attack, the lift coefficient decreased sharply with further increase of the incident angle, leading to a lift coefficient of 0.79 at α = 17°.
- The value of the drag coefficient was low at zero incidence angles and increased slowly with the angle of attack to the value of 0.038 at the stall condition. The slope of the drag versus incidence angle curve, $\frac{\partial {C}_{d}\text{}}{\partial \mathsf{\alpha}}$, remained roughly constant at about 0.003. After the stall condition, the drag increased rapidly with the further increase of the angle of attack to reach a value of 0.28 at α = 20°, which was more than seven-times the drag coefficient at the stall condition. The slope of the drag versus incidence angle curve, $\frac{\partial {C}_{d}\text{}}{\partial \mathsf{\alpha}}$, jumped to a value of 0.04 after the stall condition.
- For the case with zero flap deflection, the turbulence intensity around the airfoil increased with incident angle and would reach a maximum of 49% at α = 20°.
- The presented results showed that flap deflection significantly affected the aerodynamic performance of the airfoil. For the same angle of attack, increasing δ
_{f}enhanced both the lift and drag coefficients. - The lift increment ($\Delta {C}_{l}$) increased with the flap deflection angle. This trend continued until a maximum value was reached, and then, the lift increment remained constant. The maximum lift coefficient was 2.02 for the range of parameters studied.
- Increased flap deflection moved the zero-lift incidence angle of the airfoil from 0° to negative values. For δ
_{f}= 5° and δ_{f}= 10°, the zero-lift incidence angle were, respectively, α = −1.9° and α = −2.7°. - Increased flap deflection decreased the stalling angle of attack (α
_{stall}) for which the maximum lift coefficient was reached. The stalled angles of attack were α = 13°, 12.25° and 11.25°, respectively, for flap deflections of δ_{f}= 0°, 10° and 20°. - For all investigated flap deflections, the slope of the lift versus incidence angle, $\frac{\partial {C}_{l}\text{}}{\partial \mathsf{\alpha}}$, remained roughly constant at about $0.1$, and the lift curve just shifts upwards due to increased flap deflection.
- For the zero incident angle, the turbulence level increased with the increase of flap deflection and reached to 27% at δ
_{f}= 40°.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Mesh clustering toward airfoil surface and deflected flap regions. (

**a**) Airfoil with 0° flap deflection; (

**b**) airfoil with 10° flap deflection; (

**c**) airfoil with 40° flap deflection.

**Figure 4.**Comparison of pressure coefficient curves along the sides of airfoil from different grids at α = 12° and δ = 0° with the experimental data of Rethmel [27] at (

**a**) Re = 10

^{5}and (

**b**) Re = 10

^{6}.

**Figure 5.**Velocity profiles on the upper surface of airfoil at a 20% cord location from the leading edge at α = 12° and δ = 0° and for (

**a**) Re = 10

^{5}and (

**b**) Re = 10

^{6}.

**Figure 6.**Static pressure and velocity magnitude contours around the NACA 0015 airfoil at different incidence angles.

**Figure 8.**Pressure coefficient curves along the upper and lower surfaces of the airfoil with 0° flap deflection for different incidence at Re = 10

^{6}.

**Figure 9.**Skin friction coefficient curves along the airfoil with 0° flap deflection for different incidence angles at Re = 10

^{6}.

**Figure 10.**Comparison of lift coefficient C

_{l}values of the airfoil at 0° flap deflection as a function of (α) at chord Re = 10

^{6}with experimental and numerical results.

**Figure 11.**Comparison of predicted pressure coefficients around the airfoil at angle of attack (AoA) = 12° and AoA = 16° with the experimental data of Rethmel [27].

**Figure 12.**Comparison of drag coefficient of airfoil at 0° flap deflection versus angle of attack at chord Reynolds number Re = 10

^{6}with the experimental data and earlier numerical results.

**Figure 13.**Comparison of the lift-to-drag ${C}_{l}$/${C}_{d}$ ratio of the airfoil at 0° flap deflection versus the angle of attack at chord Re = 10

^{6}with experimental data and earlier numerical results.

**Figure 14.**Turbulence intensity contours (%) for flow around the airfoil at various incidence angles. Enlarged views of certain regions are shown on the contours on the left and right for clarity.

**Figure 15.**Static pressure and velocity magnitude contours around the NACA 0015 flapped airfoil at an angle of attack of 0° for different flap deflections.

**Figure 18.**Lift increment at flap deflection of 10° and validation with the experimental data of Williamson [37].

**Figure 21.**Contours of turbulence intensity (%) around the flapped airfoil at AoA = 0° and various flap deflections.

Grid | No. of Cells | ${\mathit{N}}_{\mathit{x}}$ | ${\mathit{N}}_{\mathit{y}}$ | Max ${\mathit{y}}^{+}$ | Min ${\mathit{y}}^{+}$ | Aver ${\mathit{y}}^{+}$ |
---|---|---|---|---|---|---|

I | 24,910 | 690 | 35 | 32.5 | 4.8 | 13.85 |

II | 53,040 | 884 | 50 | 16.5 | 3.4 | 06.55 |

III | 76,128 | 976 | 65 | 12 | 1 | 05.50 |

IV | 103,192 | 1184 | 75 | 9.2 | 0.8 | 04.20 |

V | 141,168 | 1384 | 85 | 8.8 | 0.7 | 04.05 |

VI | 367,235 | 1850 | 90 | 1.01 | 0.01 | 0.500 |

Grid | Leading Edge up to 30% of Chord | Trailing Edge up to 70% of Chord | Wake Region | Height |
---|---|---|---|---|

I | 90 | 325 | 275 | 35 |

II | 110 | 374 | 400 | 50 |

III | 112 | 384 | 480 | 65 |

IV | 116 | 468 | 600 | 75 |

V | 120 | 544 | 720 | 85 |

VI | 128 | 597 | 1125 | 90 |

**Table 3.**Estimated size of the first cell height near the wall as a fraction of airfoil chord length.

Grid | Max ${\mathit{y}}^{+}$ | Min ${\mathit{y}}^{+}$ | Aver ${\mathit{y}}^{+}$ | Max $\mathsf{\Delta}\mathit{y}$ | Min $\mathsf{\Delta}\mathit{y}$ | Aver $\mathsf{\Delta}\mathit{y}$ |
---|---|---|---|---|---|---|

I | 32.5 | 4.8 | 13.85 | 7.65 × 10^{−4} c | 1.00 × 10^{−4} c | 3.17 × 10^{−4} c |

II | 16.5 | 3.4 | 6.55 | 3.78 × 10^{−4} c | 7.80 × 10^{−5} c | 1.50 × 10^{−4} c |

III | 12 | 1 | 5.50 | 2.75 × 10^{−4} c | 2.30 × 10^{−5} c | 1.26 × 10^{−4} c |

IV | 9.2 | 0.8 | 4.20 | 2.11 × 10^{−4} c | 1.83 × 10^{−5} c | 9.93 × 10^{−5} c |

V | 8.8 | 0.7 | 4.05 | 2.02 × 10^{−4} c | 1.60 × 10^{−5} c | 9.27 × 10^{−5} c |

VI | 1.01 | 0.01 | 0.500 | 2.38 × 10^{−5} c | 2.35 × 10^{−7} c | 1.18 × 10^{−5} c |

**Table 4.**Lift coefficient values for the NACA 0015 airfoil at α = 12°, δ = 0° and Re = 10

^{5}using RANS models. SA, Spalart–Allmaras.

Grid | ${\mathit{C}}_{\mathit{l}}$ Exp. | ${\mathit{C}}_{\mathit{l}}$ (R-k-ε Model) | ${\mathit{C}}_{\mathit{l}}$ (SA Model) |
---|---|---|---|

I | 0.90 ± 0.005 | 0.7654 | 0.9845 |

II | 0.90 ± 0.005 | 0.8292 | 1.0276 |

III | 0.90 ± 0.005 | 0.8412 | 1.0988 |

IV | 0.90 ± 0.005 | 0.9091 | 1.1169 |

V | 0.90 ± 0.005 | 0.9016 | 1.1199 |

VI | 0.90 ± 0.005 | 0.9073 | 1.1178 |

**Table 5.**Lift coefficient values for the NACA 0015 airfoil at α = 12°, δ = 0° and Re = 10

^{6}using RANS models.

Grid | ${\mathit{C}}_{\mathit{l}}$ Exp. | ${\mathit{C}}_{\mathit{l}}$ (R-k-ε Model) | ${\mathit{C}}_{\mathit{l}}$ (SA Model) |
---|---|---|---|

I | 1.12 ± 0.005 | 8.546 × 10^{−1} | 1.0034 |

II | 1.12 ± 0.005 | 9.655× 10^{−1} | 1.1642 |

III | 1.12 ± 0.005 | 9.891× 10^{−1} | 1.2521 |

IV | 1.12 ± 0.005 | 1.1463 | 1.316 |

V | 1.12 ± 0.005 | 1.1491 | 1.3230 |

VI | 1.12 ± 0.005 | 1.1484 | 1.3201 |

**Table 6.**Comparison of the maximum turbulence intensity (TI) at different incidence angles with the results of Zhang et al. [17].

AoA | Maximum TI (%) Current Study | Maximum TI (%) Zhang et al. [17] |
---|---|---|

0° | 8.892 | 13.95 |

5° | 12.645 | 18.04 |

10° | 19.986 | 28.75 |

15° | 38.015 | 42.11 |

20° | 49.768 | 51.20 |

AoA | ∆C_{l} | ∆C_{l} |
---|---|---|

W1015 (Re = 4 × 10^{5}) | NACA 0015 (Re = 10^{6}) | |

0 | 0.435 | 0.477 |

4.0 | 0.433 | 0.476 |

8.0 | 0.430 | 0.463 |

12.0 | 0.420 | 0.441 |

© 2017 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 ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Obeid, S.; Jha, R.; Ahmadi, G.
RANS Simulations of Aerodynamic Performance of NACA 0015 Flapped Airfoil. *Fluids* **2017**, *2*, 2.
https://doi.org/10.3390/fluids2010002

**AMA Style**

Obeid S, Jha R, Ahmadi G.
RANS Simulations of Aerodynamic Performance of NACA 0015 Flapped Airfoil. *Fluids*. 2017; 2(1):2.
https://doi.org/10.3390/fluids2010002

**Chicago/Turabian Style**

Obeid, Sohaib, Ratneshwar Jha, and Goodarz Ahmadi.
2017. "RANS Simulations of Aerodynamic Performance of NACA 0015 Flapped Airfoil" *Fluids* 2, no. 1: 2.
https://doi.org/10.3390/fluids2010002