# Free-Form Deformation Parameterization on the Aerodynamic Optimization of Morphing Trailing Edge

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. FFD Parameterization Technique

#### 2.2. DAFoam Optimization Framework

#### 2.3. Optimization Numerical Setup

#### 2.4. Optimization Process for a Morphing Trailing Edge Flap

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Embedded UAS-S45 airfoil in FFD blocks for five cases with (

**A**) 8, (

**B**) 12, (

**C**) 16, (

**D**) 20, (

**E**) 24 control points from a side view, and (

**F**) an isometric view of the FFD block with 24 control points.

**Figure 4.**Overall optimization process of the UAS-S45 morphing wing trailing edge within the DAFoam optimization framework.

**Figure 6.**Illustration of the morphing trailing edge for the UAS-S45 airfoil for (

**a**) case 1, (

**b**) case 2, (

**c**) case 3, (

**d**) case 4, and (

**e**) case 5, after optimization.

**Table 1.**List of research conducted on at LARCASE using different optimization algorithms and parametrization methods.

Year | Author | Morphing Approach | Optimization Process | Parameterization Method | Objective Functions |
---|---|---|---|---|---|

2015 | Gabor et al. [7] | Upper surface | Artificial Bee Colony (ABC) + BFGS | NURBS | Transition delay |

2016 | Gabor et al. [8] | Upper surface | Artificial Bee (ABC) + BFGS | NURBS | Lift-to-drag ratio maximization |

2016 | Gabor et al. [9] | Upper surface | Artificial Bee Colony (ABC) | NURBS | Drag minimization |

2017 | Koreanschi et al. [10] | Upper surface and aileron | Genetic Algorithm (GA) | Cubic spline | Drag minimization And transition delay |

2021 | Bashir et al. [11] | Leading and trailing edge | Particle Swarm Optimization (PSO) | Bezier-PARSEC | Drag minimization and endurance maximization |

2022 | Bashir et al. [12] | Leading edge | Black Widow Optimization (BWO) | Class shape transformation (CST) | Drag minimization and endurance maximization |

2022 | Bashir et al. [13] | Trailing edge | Black Widow Optimization (BWO) | Makima | Lift-to-drag ratio maximization |

2023 | Negahban et al. [14] | Combined chord and trailing edge morphing | Gradient-based optimization with discrete adjoint method | FFD | Drag minimization |

Function/Variable | Description | Case | ||||
---|---|---|---|---|---|---|

Objective function | 1 | 2 | 3 | 4 | 5 | |

max. ${C}_{l}$/${C}_{d}$ | Lift-to-drag ratio | |||||

With respect to: | ||||||

y | TE FFD control points | 8 | 12 | 16 | 20 | 24 |

α | Angle of attack | 1 | 1 | 1 | 1 | 1 |

Total design variables | 9 | 13 | 17 | 21 | 25 | |

Subject to: | ||||||

${C}_{l}=0.38514$ | Constraint function | |||||

$0\le \Delta y\le 15mm$ | Design variable bounds | |||||

$\Delta {y}_{z=0}^{upper}=\Delta {y}_{z=1}^{upper}$ | Linear constraint |

Case Nr. | Control Points | Run Time (Sec.) | Itr. Nr. | Optimality Error | Initial Cl/Cd | Opt. Cl/Cd | Gain % |
---|---|---|---|---|---|---|---|

1 | 8 | 218.732 | 6 | 9.63 × 10^{−7} | 34.548 | 38.522 | 10.3 |

2 | 12 | 258.512 | 6 | 4.55 × 10^{−6} | 34.532 | 39.547 | 12.7 |

3 | 16 | 504.096 | 7 | 2.67 × 10^{−6} | 34.524 | 40.058 | 13.8 |

4 | 20 | 10,925.43 | 50 | 1.60 × 10^{−2} | 34.523 | 39.002 | 11.5 |

5 | 24 | 12,203.12 | 50 | 6.20 × 10^{−3} | 34.521 | 38.663 | 10.7 |

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**MDPI and ACS Style**

Negahban, M.H.; Bashir, M.; Botez, R.M.
Free-Form Deformation Parameterization on the Aerodynamic Optimization of Morphing Trailing Edge. *Appl. Mech.* **2023**, *4*, 304-316.
https://doi.org/10.3390/applmech4010017

**AMA Style**

Negahban MH, Bashir M, Botez RM.
Free-Form Deformation Parameterization on the Aerodynamic Optimization of Morphing Trailing Edge. *Applied Mechanics*. 2023; 4(1):304-316.
https://doi.org/10.3390/applmech4010017

**Chicago/Turabian Style**

Negahban, Mir Hossein, Musavir Bashir, and Ruxandra Mihaela Botez.
2023. "Free-Form Deformation Parameterization on the Aerodynamic Optimization of Morphing Trailing Edge" *Applied Mechanics* 4, no. 1: 304-316.
https://doi.org/10.3390/applmech4010017