# A Parametric Study of Trailing Edge Flap Implementation on Three Different Airfoils Through an Artificial Neuronal Network

^{1}

^{2}

^{3}

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## Abstract

**:**

_{L}/C

_{D}, will increase or decrease, respectively. Besides, the use of a larger flap length will increase the higher values and decrease the lower values of the C

_{L}/C

_{D}ratio. In addition, an artificial neural network (ANN) based prediction model for aerodynamic forces was built through the results obtained from the research.

## 1. Introduction

_{L}) of airplane wings and to increase lift force during take-off and landing without changing the characteristics of cruising and high-speed flight. They are categorized by Abdelrahman and Johnson [20] as high-lift devices, which also include leading edge slats, slotted-flaps, and external airfoil flaps.

_{F}). In addition, as it has also been specified in the same section, this research increases the analysis ratio of some parameters with respect to the state of the art.

## 2. Aims and Methodology

_{F}) in the change of lift.

_{L}/C

_{D}, experiencing minimum and maximum figures respectively for these limits, as will be seen later in the results section.

_{L}/C

_{D}values, while stall regions will be studied in a following paper.

## 3. Numerical Setup

#### 3.1. Computational Configuration and Procedure

^{6}. The resulting flow speed is 15.11 m s

^{−1}. The Reynolds number is defined in Equation (1):

^{−5}m. Figure 6 shows the wall y+ distribution over the NACA0012 airfoil for two flap angle configurations β = 5° and −5°, angle of attack of α = 0° and flaplength of 8% of c.

^{®}Core i7-6700 CPU 3.40 GHz × 8 cores and 32 GB RAM on 64 bits Linux. Each domain corresponding to an O-grid mesh was automatically divided into eight subdomains to be solved in parallel, thereby reducing the simulation time.

_{D}on the airfoil has been calculated by the application of Equation (2) in the far field planes normal to the flow direction and applied to the streamwise velocity in different wake rakes (WR), according to Beans et al. [48] and Young [49].

_{D}has been calculated per meter of airfoil span.

_{L}was determined by the OpenFOAM inbuilt code, which determines the value by means of the Equation (3):

#### 3.2. Validation

_{L}–α; and, (b) drag coefficient to lift coefficient C

_{D}-C

_{L}in Figure 7, Figure 8 and Figure 9. Each pair of plots for each airfoil is represented by a different figure.

_{L}–α curves show that the lift CFD data at a Reynolds number of Re = 10

^{6}are coincident with the experimental ones [37]. Figure 7b, corresponding to the representation of the C

_{D}-C

_{L}curves, shows an over estimation of the drag CFD data with respect to the experimental ones. In order to highlight the trend of CFD data more clearly, the volume of CFD data used for the validation of the NACA 0012 airfoil is higher than the volume of the experimental points.

^{6}, but the experimental ones [19] were obtained at a Reynolds number of Re = 3 × 10

^{6}. This difference might explain an additional deviation in C

_{D}-C

_{L}curves. Therefore, Figure 8b shows that the CFD data for the drag are overestimated with respect to the experimental data. Figure 8a shows almost coincident C

_{L}–α curves for the CFD and the experimental data.

^{6}. Figure 9a shows coincident C

_{L}–α curves for the CFD and experimental data along the entire curve except for the last two points of the experimental curve. C

_{D}-C

_{L}curves of Figure 9b shows an over estimation of the CFD data with respect the CFD data. Therefore, a concurrency between experimental data and CFD does exist. In this last validation of airfoil S810, as in the first validation of NACA 0012, due to the high number of simulations performed and the limited volume of experimental data, the volume of CFD data is larger than the experimental data.

_{L}–α curves, and in spite of the minimum differences between CFD and experimental C

_{D}-C

_{L}curves, we can safely confirm the validation of the CFD model used in this study.

## 4. Results

#### 4.1. Lift-to-Drag Ratio C_{L}/C_{D} as a Function of the Angle of Attack, α, for Different Flap Angles β

_{L}/C

_{D}, as a function of the angle of attack, α, is used to show the results obtained from computational simulations. As explained in the previous section, simulations were performed for seventeen angles of attack, by combining eleven flap angles with five flaplengths. A flaplength of 8% of chord length c is chosen in this section. The curves corresponding to the rest of the flaplengths 9%, 10%, 12%, and 14% of c are included in Appendix A.

_{L}/C

_{D}curves, the C

_{L}/C

_{D}ratio of each airfoil for the same angle of attack, α, increases and it decreases as a function of the β angle in the same proportion with respect to the curve, β = 0°.

_{L}/C

_{D}for the three airfoils studied. As shown in Figure 10, Figure 11 and Figure 12, depending on the flap angle, the maximum values of the C

_{L}/C

_{D}are obtained for the following intervals of the angle of attack: α = [8–10°] in the case of airfoil NACA 0012 and α = [6–8°] in the case of NACA 64(3)-618 and S810 airfoils.

_{L}/C

_{D}ratio values for different β angles are almost overlapping. These near overlaps are shown in Figure 10 and Figure 12, corresponding to airfoils NACA 0012 and S810, respectively, where the drag increases in the same proportion for α positive angles and for negative ones in the case of NACA 0012, and almost in the same proportion in the case of S810. However, as shown in Figure 11, drag increases substantially as the positive value of α increases for the NACA 64(3)-618 airfoil and less so when the negative value of α increases.

_{L}/C

_{D}curve for the intermediate flap position β = 0° defines a symmetrically odd function as the positive and negative angle of α increases, due to the symmetry of the airfoil with respect to the horizontal Cartesian axis C

_{L}/C

_{D}= 0. However, in the case of the other two profiles, NACA 64(3)-618 and S810, there is no symmetrical evolution in the values of the curves due to the fact that they are non-symmetrical airfoils.

_{L}/C

_{D}curves cross the α axis and acquire negative values at a specific value of α, in all the C

_{L}/C

_{D}curves shown in Figure 10, Figure 11 and Figure 12. A negative value of C

_{L}/C

_{D}means that the value of C

_{L}is negative. This change in the distribution of airfoil pressures happens due to a reorientation of the lift force, in such a way that as the value of the negative α angle increases, the pressure gradient in the opposite direction also increases and, consequently, the suction originates in the lower surface. The C

_{L}/C

_{D}curves acquire negative values of α ≤ 1° for the NACA 0012 airfoil, of α < −2° for the NACA 64(3)-618 airfoil, and of α ≤ 0° for the S810 airfoil. These intersection values are for a flaplength of 8% and could vary depending on the flaplength chosen for the representation of the C

_{L}/C

_{D}curves of each airfoil, as shown in Appendix A.

#### 4.2. C_{L}/C_{D} Ratio as a Function of FlapLengths, L_{F}, for Intermediate Angles of Attack, α

_{L}/C

_{D}ratio is shown in this section, with a view to defining which of them optimizes the operation of a TEF better. Three extreme flap positions were chosen for each airfoil, in order to compare the different flap lengths: flap with a position of: β = 0° (no deflection ≡ intermediate lift force); β = −5° (deflected towards the lower surface ≡ maximum lift force); and, β = 5° (deflected towards the upper surface ≡ minimum lift force).

_{L}/C

_{D}ratio of four intermediate angles of attack, α = −3°, α = 0°, α = 3° and α = 6°, will be compared for different flaplengths of 8%, 9%, 10%, 12%, and 14% of c.

_{L}/C

_{D}of four angles of attack as a function of the different flap lengths for the angles β = 0°, β = −5°, and β = 5°, respectively.

_{L}/C

_{D}ratio are observed as a function of flaplength. This is because for β = 0°, the variation of flaplength does not vary the geometry of the airfoil as the flap is an integrated part of it. However, Figure 13b, corresponding to the position of flap β = −5°, clearly shows an upward trend of the C

_{L}/C

_{D}ratio for all of the four intermediate angles of attack as the flap length increases. This trend indicates that when the flap is deflected towards the lower surface in its extreme position, β = −5°, a position in which the highest lift force is obtained, the maximum C

_{L}/C

_{D}ratio is obtained with a 14% flap length. Figure 13c, corresponding to the position of flap β = 5°, shows a downward trend of the C

_{L}/C

_{D}ratio as the flap length increases. This downward trend indicates that when the flap is deflected towards the upper surface at its extreme position, β = 5°, a position in which the least lift force is obtained, the minimum C

_{L}/C

_{D}ratio is obtained with a flaplength of 14% of c. Therefore, a greater flaplength maximizes the lift in the positions in which the highest lift force is obtained, and minimizes the lift in the positions in which the lowest lift force is obtained.

_{L}/C

_{D}ratio in the positions in which the highest lift force is obtained and minimize it in the positions in which the lowest lift force is obtained. Moreover, as shown in plots A4 (a) and A5 (a) of Figure A4 and Figure A5, for the horizontal position of the flap, β = 0°, there is no variation of the C

_{L}/C

_{D}values as a function of flaplength either.

_{L}/C

_{D}ratio decreases slightly, instead of increasing.

#### 4.3. C_{L}/C_{D} Ratio as a Function of the Flap Angle β and the Different Flap Lengths L_{F}

_{L}/C

_{D}ratio variation as a function of the flap angle β and the different flaplengths in the form of a three-dimensional surface. As the flap is deployed towards the pressure area of the airfoil and negative β increases, the lift increases, and the C

_{L}/C

_{D}ratio also increases. If the flap is deployed towards the suction zone and positive β increases, the lift decreases, and the C

_{L}/C

_{D}ratio also decreases. In addition, a greater flaplength maximizes the C

_{L}/C

_{D}ratio in the positions in which the highest lift force is obtained, and minimizes the C

_{L}/C

_{D}ratio in the positions in which the lowest lift force is obtained.

_{L}/C

_{D}ratio increases less, shows no increase at all, and can even decrease.

_{F}, on the C

_{L}/C

_{D}ratio for certain angles of attack, α, the next step will be to build a prediction model of aerodynamic forces taking into account all the parameters studied throughout this research. This model is based on an artificial neural network (ANN).

#### 4.4. Modeling of the CFD Results with an Artificial Neural Network

_{L}/C

_{D}ratio of the three different airfoils as a function of the flap angle β and the different flap lengths L

_{F}. Moreover, the ANN contains the model of the C

_{L}/C

_{D}ratio for different values of the angle of attack, α of the incoming airflow. This model was built using Matlab [52] mathematical software.

_{F}and β), one hidden layer with 25 neurons and one output layer with 1 neuron, corresponding to the output of the ANN (the C

_{L}/C

_{D}ratio). The training process of the ANN has been carried out with a data set of 220 tuples and the distribution of the data has been set to 90% for the training, 5% for the validation, and 5% for the test.

_{x}due of α = 0°), the wake turbulence kinetic energy TKE and the pressure coefficient Cp have been studied for a select number of cases of the three airfoils NACA 0012, NACA 64(3)-618 and S810.

#### 4.5. Streamwise Velocity

#### 4.6. Turbulence Kinetic Energy

#### 4.7. Pressure Coefficient

## 5. Conclusions

_{L}/C

_{D}ratio in the positions in which the highest lift force is obtained, and minimizes the C

_{L}/C

_{D}ratio in the positions in which the lowest lift force is obtained.

_{L}/C

_{D}ratio variation as a function of the flap angle β and the different flaplengths has been addressed.

_{L}/C

_{D}were obtained, with a flaplength of 14% and with a flap angle β = −5°. The maximum C

_{L}/C

_{D}ratio values are, 53.67 [-], 53.89 [-], and 46.94 [-] for the airfoils NACA 0012, NACA64(3)-618, and S810 respectively.

_{L}/C

_{D}ratio variation of the airfoils as a function of flap angle, β, and flap length, L

_{F}, based on an ANN has been shown in Section 4.4. As the numerical and graphical results show, this approach might represent a good option to facilitate future computational automatic-control tools for TEFs installed on airfoils.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

TEF | Trailing Edge Flap |

DTEF | Deformable Trailing Edge Flap |

CFD | Computational Fluid Dynamics |

C_{L} | Lift coefficient [-] |

C_{D} | Drag coefficient [-] |

α | Angle of attack [deg] |

β | Flap angle [deg] |

c | Airfoil chord length [m] |

L_{F} | Flaplength [% of c] |

R | Radius [nº of c] |

U | Constant velocity [m s^{−1}] |

P | No gradient pressure [N m^{−2}] |

ν_{t} | Turbulent viscosity [m^{2} s^{−1}] |

k | Kinetic energy [m^{2} s^{−2}] |

ω | Dissipation rate [s^{−1}] |

I | Turbulence intensity [%] |

l | Mixing length [m] |

Re | Reynolds number [-] |

${\mathbf{U}}_{\infty}$ | Free stream velocity [m s^{−1}] |

ρ | Density [kg m^{−3}] |

y+ | Dimensionless wall distance [-] |

μ | Absolute viscosity [kg m^{−1} s^{−1}] |

y | First cell height [m] |

u | Streamwise velocity [m s^{−1}] |

u_{x} | x component of u [m s^{−1}] |

b | Span [m] |

A | Area determined by c and b [m^{2}] |

F_{L} | Lift force [N] |

TKE | Turbulence kinetic energy [m^{2} s^{−2}] |

Cp | Pressure Coefficient [-] |

BC | Boundary Conditions |

RANS | Reynolds Averaged Navier-Stokes |

SST | Shear Stress Transport |

R | Correlation coefficient [-] |

MSE | Mean Square Error [-] |

ANN | Artificial Neural Network |

MLP-BP | Multi Layer Percep.with Back Propagation |

BME | Blade Element Momentum |

NACA | Nat’l Adv. Comm. of Aeronautics |

NREL | Nat’l Renewable Energy Laboratory |

HAWT | Horizontal Axis Wind Turbines |

## Appendix A

**Figure A1.**Lift-to-drag ratio C

_{L}/C

_{D}curves as a function of angle of attack, α, for different angles, β. NACA 0012 airfoil with different flaplengths of: (

**a**) 9%, (

**b**) 10%, (

**c**) 12% and (

**d**) 14% of chord length c.

**Figure A2.**Lift-to-drag ratio C

_{L}/C

_{D}curves as a function of angle of attack α for different angles, β. NACA 64(3)-618 Airfoil with different flaplengths of: (

**a**) 9%, (

**b**) 10%, (

**c**) 12% and (

**d**) 14% of chord length c.

**Figure A3.**Lift-to-drag ratio C

_{L}/C

_{D}curves as a function of angle of attack, α, for different angles, β. S810 Airfoil with different flaplengths of: (

**a**) 9%, (

**b**) 10%, (

**c**) 12% and (

**d**) 14% of chord length c.

## Appendix B

**Figure A4.**Variation of the C

_{L}/C

_{D}ratio as a function of different flaplengths, L

_{F}, for intermediate angles of attack, α. Rated for three different flap positions: (

**a**) β = 0°, (

**b**) β = −5°and (

**c**) β = 5°. NACA 64(3)-618 Airfoil.

**Figure A5.**Variation of the C

_{L}/C

_{D}ratio as a function of different flaplengths L

_{F}, for intermediate angles of attack, α. Rated for three different flap positions: (

**a**) β = 0°, (

**b**) β = −5°and (

**c**) β = 5°. S810 Airfoil.

## Appendix C

**Figure A6.**C

_{L}/C

_{D}ratio variation as a function of the flap angle, β, and the different flaplengths, L

_{F}, for intermediate angles of attack: (

**a**) α = −3°, (

**b**) α = 0°, (

**c**) α = 3° and (

**d**) α = 6°. NACA 64(3)-618 Airfoil.

**Figure A7.**C

_{L}/C

_{D}ratio variation as a function of the flap angle, β, and the different flaplengths, L

_{F}, for intermediate angles of attack (

**a**) α = −3°, (

**b**) α = 0°, (

**c**) α = 3° and (

**d**) α = 6°. S810 Airfoil.

## Appendix D

**Figure A8.**The surface represents the ANN. The results of the CFD are indicated by black dots for the intermediate angles of attack (

**a**) α = −3°, (

**b**) α = 0°, (

**c**) α = 3° and (

**d**) α = 6°. NACA 64(3)-618 Airfoil.

**Figure A9.**The surface represents the ANN. The results of the CFD are indicated by black dots for the intermediate angles of attack (

**a**) α = −3°, (

**b**) α = 0°, (

**c**) α = 3° and (

**d**) α = 6°. S810 Airfoil.

## Appendix E

**Figure A10.**Results of the normalized streamwise velocity checked in the wake locations of x/c = 1.05, 1.25 and 1.5 for an angle of attack of α = 0° and flap positions of β = −5°, β = 0° and β = 5°. (

**a**) Curves corresponding to the flaplengths of 8% of c and 14% of c distributed in the wake region. Enlargements of the disturbed areas in superimposed curves: (

**b**) flaplength of 8% of c, (

**c**) flaplength of 14% of c. Airfoil NACA 64(3)-618.

**Figure A11.**Results of the normalized wake TKE checked in the wake locations of x/c = 1.05, 1.25 and 1.5 for an angle of attack of α = 0° and flap positions of β = −5°, β = 0° and β = 5°. (

**a**) Curves corresponding to the flaplengths of 8% of c and 14% of c distributed in the wake region. Enlargements of the disturbed areas in superimposed curves: (

**b**) flaplength of 8% of c, (

**c**) flaplength of 14% of c. Airfoil NACA 64(3)-618.

**Figure A12.**Results of the normalized streamwise velocity checked in the wake locations of x/c = 1.05, 1.25 and 1.5 for an angle of attack of α = 0° and flap positions of β = −5°, β = 0° and β = 5°. (

**a**) Curves corresponding to the flaplengths of 8% of c and 14% of c distributed in the wake region. Enlargements of the disturbed areas in superimposed curves: (

**b**) flaplength of 8% of c, (

**c**) flaplength of 14% of c. Airfoil S810.

**Figure A13.**Results of the normalized wake TKE checked in the wake locations of x/c = 1.05, 1.25 and 1.5 for an angle of attack of α = 0° and flap positions of β = −5°, β = 0° and β = 5°. (

**a**) Curves corresponding to the flaplengths of 8% of c and 14% of c distributed in the wake region. Enlargements of the disturbed areas in superimposed curves: (

**b**) flaplength of 8% of c, (

**c**) flaplength of 14% of c. Airfoil S810.

## Appendix F

**Figure A14.**Results of the pressure coefficient Cp for an angle of attack of α = 0°, flaplengths of 8% of c and 14% of c, and flap positions of β = −5°, β = 0° and β = 5°. Airfoil NACA 64(3)-618.

**Figure A15.**Results of the pressure coefficient Cp for an angle of attack of α = 0°, flaplengths of 8% of c and 14% of c, and flap positions of β = −5°, β = 0° and β = 5°. Airfoil S810.

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**Figure 1.**Detailed sketch of the airfoils with TEF installed and analyzed in this study where c, β, α, and L

_{F}are the airfoil chord length, the flap angle, the angle of attack, and the flaplength, respectively.

**Figure 3.**Procedure sketch showing the different combinations between flaplength, flap angle, and angle of attack for the airfoil NACA 0012.

**Figure 4.**Domain used for the numerical simulations in this study with an enlargement view of the airfoil in the center of the domain.

**Figure 5.**Mesh snapshots around the trailing edge flap for two different flap positions: (

**a**) β = 5°and (

**b**) β = −5°. Mean camber line has been added in dashed lines. Airfoil NACA 0012.

**Figure 6.**Wall y+ distribution over the airfoil for an angle of attack of α = 0°, flaplength of 8% of chord length c and two different flap positions: (

**a**) β = 5°and (

**b**) β = −5°. Airfoil NACA 0012.

**Figure 7.**Comparison between experimental data and CFD data for NACA 0012: (

**a**) lift coefficient C

_{L}against angle of attack α; (

**b**) drag coefficient C

_{D}against lift coefficient C

_{L}.

**Figure 8.**Comparison between experimental data and CFD data for NACA 64(3)-618: (

**a**) lift coefficient C

_{L}against angle of attack α; (

**b**) drag coefficient C

_{D}against lift coefficient C

_{L}.

**Figure 9.**Comparison between experimental data and CFD data for S810: (

**a**) lift coefficient C

_{L}against angle of attack α; (

**b**) drag coefficient C

_{D}against lift coefficient C

_{L}.

**Figure 10.**Lift-to-drag ratio C

_{L}/C

_{D}curves as a function of the angle of attack, α, for different angles β. The NACA 0012 airfoil with a flap length of 8% of chord length c.

**Figure 11.**Lift-to-drag ratio C

_{L}/C

_{D}curves as a function of the angle of attack, α, for different angles β. The NACA 64(3)-618 airfoil with a flap length of 8% of chord length c.

**Figure 12.**Lift-to-drag ratio C

_{L}/C

_{D}curves as a function of the angle of attack, α, for different angles β. The S810 airfoil with a flap length of 8% of chord length c.

**Figure 13.**Variation of the C

_{L}/C

_{D}ratio as a function of different flaplengths, L

_{F}, for intermediate angles of attack, α. Rated for three different flap positions: (

**a**) β = 0°, (

**b**) β = −5°, and (

**c**) β = 5°. NACA 0012 Airfoil.

**Figure 14.**C

_{L}/C

_{D}ratio variation as a function of the flap angle β and the different flaplengths L

_{F}for intermediate angles of attack (

**a**) α = −3°, (

**b**) α = 0°, (

**c**) α = 3° and (

**d**) α = 6°. NACA 0012 Airfoil.

**Figure 15.**The surface represents the ANN. The results of the CFD are indicated by black dots for the intermediate angles of attack (

**a**) α = −3°, (

**b**) α = 0°, (

**c**) α = 3° and (

**d**) α = 6°. NACA 0012 Airfoil.

**Figure 16.**Results of the normalized streamwise velocity checked in the wake locations of x/c = 1.05, 1.25 and 1.5 for an angle of attack of α = 0° and flap positions of β = −5°, β = 0° and β = 5°. (

**a**) Curves corresponding to the flaplengths of 8% of c and 14% of c distributed in the wake region. Enlargements of the disturbed areas in superimposed curves: (

**b**) flaplength of 8% of c, (

**c**) flaplength of 14% of c. Airfoil NACA 0012.

**Figure 17.**Results of the normalized wake TKE checked in the wake locations of x/c = 1.05, 1.25 and 1.5 for an angle of attack of α = 0° and flap positions of β = −5°, β = 0° and β = 5°. (

**a**) Curves corresponding to the flaplengths of 8% of c and 14% of c distributed in the wake region. Enlargements of the disturbed areas in superimposed curves: (

**b**) flaplength of 8% of c, (

**c**) flaplength of 14% of c. Airfoil NACA 0012.

**Figure 18.**Results of the pressure coefficient Cp for an angle of attack of α = 0°, flaplengths of 8% of c and 14% of c, and flap positions of β = −5°, β = 0° and β = 5°. Airfoil NACA 0012.

β [°] | Non-Orthogonality (Average) | Maximum Skewness | |
---|---|---|---|

NACA 0012 | −5 | 27.70 | 0.54 |

0 | 27.68 | 0.49 | |

+5 | 27.70 | 0.54 | |

NACA 64(3)-618 | −5 | 22.28 | 0.87 |

0 | 22.16 | 0.79 | |

+5 | 22.11 | 0.85 | |

S810 | −5 | 26.39 | 0.67 |

0 | 26.33 | 0.61 | |

+5 | 26.32 | 0.67 |

Reynolds Number [-] | ρ [kg m^{−3}] | μ [kg m^{−1} s^{−1}] | c [m] | ${\mathbf{U}}_{\mathbf{\infty}}$ [m s^{−1}] |
---|---|---|---|---|

10^{6} | 1.225 | 1.8375 × 10^{−5} | 1 | 15.11 |

β [°] | Wall y+ [-] | |||
---|---|---|---|---|

Min | Average | Max | ||

NACA 0012 | −5 | 0.02 | 0.55 | 1.29 |

0 | 0.02 | 0.55 | 1.18 | |

5 | 0.02 | 0.55 | 1.09 | |

NACA 64(3)-618 | −5 | 0.01 | 0.56 | 0.95 |

0 | 0.01 | 0.57 | 1.02 | |

5 | 0.02 | 0.59 | 1.09 | |

S810 | −5 | 0.02 | 0.68 | 1.15 |

0 | 0.02 | 0.67 | 1.11 | |

5 | 0.02 | 0.68 | 1.06 |

Airfoil | R [-] | MSE [-] |
---|---|---|

NACA0012 | 0.9995 | 0.0248 |

NACA 64(3)-618 | 0.9998 | 0.0173 |

S810 | 0.99986 | 0.0165 |

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## Share and Cite

**MDPI and ACS Style**

Rodriguez-Eguia, I.; Errasti, I.; Fernandez-Gamiz, U.; Blanco, J.M.; Zulueta, E.; Saenz-Aguirre, A.
A Parametric Study of Trailing Edge Flap Implementation on Three Different Airfoils Through an Artificial Neuronal Network. *Symmetry* **2020**, *12*, 828.
https://doi.org/10.3390/sym12050828

**AMA Style**

Rodriguez-Eguia I, Errasti I, Fernandez-Gamiz U, Blanco JM, Zulueta E, Saenz-Aguirre A.
A Parametric Study of Trailing Edge Flap Implementation on Three Different Airfoils Through an Artificial Neuronal Network. *Symmetry*. 2020; 12(5):828.
https://doi.org/10.3390/sym12050828

**Chicago/Turabian Style**

Rodriguez-Eguia, Igor, Iñigo Errasti, Unai Fernandez-Gamiz, Jesús María Blanco, Ekaitz Zulueta, and Aitor Saenz-Aguirre.
2020. "A Parametric Study of Trailing Edge Flap Implementation on Three Different Airfoils Through an Artificial Neuronal Network" *Symmetry* 12, no. 5: 828.
https://doi.org/10.3390/sym12050828