# Numerical Simulation of the Transient Flow around the Combined Morphing Leading-Edge and Trailing-Edge Airfoil

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions, the UN’s International Civil Aviation Organization (ICAO) organized negotiations and has given recommendations that include increasing aircraft innovation and “streamlining” flying operations. The aviation sector’s main objectives encompass enhancing air travel quality and affordability, reducing CO

_{2}, NOX, and noise emissions, and addressing safety concerns [1]. These challenges have spurred a greater need for innovative research to develop more efficient and environmentally friendly aircraft. The Research Laboratory in Active Controls, Avionics, and AeroServoElasticity (LARCASE) has continued to explore numerous strategies to reduce aircraft fuel consumption and emissions [2,3,4,5,6,7,8].

## 2. Morphing Model

#### 2.1. Computational Domain and Grid Definitions

^{6}with a freestream velocity of U∞ = 34.5 m/s and a turbulence intensity of Tu = 0.1%.

#### 2.2. Validation of Results

^{6}), reduced frequency (k = 0.10), and angles of attack ranging from 5 to 25 degrees, with a mean incidence angle of 15 degrees. Two simulations were conducted: one was validated against experimental data, and the other was validated by comparison to numerical data from [55] for the same settings.

## 3. Discussion of Results

## 4. Conclusions

- (a)
- Before the start of the airfoil morphing, an increase in lift coefficient is followed by a highly unsteady stall. A similar trend is shown for drag coefficients for all studied cases. The vortex structure, along with the velocity fluctuation, depicts this highly unsteady behavior.
- (b)
- As the morphing starts synchronously, the lift and drag coefficients of the CoMpLETE airfoil vary with the deflection magnitude and frequency. The maximum deflection is achieved at the time of 2 s in Case 1.1 and at 1.62 s in Case 1.3, respectively. Low deflection frequencies, such as 0.5 Hz give higher average lift coefficients and more stable flow, i.e., the average lift coefficient was 1.58 in Case 1.3, lower than that in Cases 1.1 and 1.2, where it was found to be 2.12.
- (c)
- The results also indicate that deflecting the trailing edge significantly impacted the airfoil performance in terms of lift coefficient increase. In comparison, the downward leading-edge motion significantly enhanced the post-stall lift situation by suppressing leading-edge separation and preventing the formation of the DSV.
- (d)
- The comparison of airfoil motion at the leading-edge morphing location at 0.2c and 0.15c showed that flow remains primarily attached to the airfoil in the case of the morphing location of 0.2c, and significant velocity fluctuations are seen in the case of morphing location of 0.15c. These results are due to a changed leading-edge shape, where the velocity streamlines move more intensely due to a sharper gradient in Case 0.15c, further lowering the local pressure.
- (e)
- The analysis of asynchronous CoMpLETE airfoil cases further validates the findings mentioned above. In the case where the trailing edge deflects earlier, higher lift coefficients can be obtained, with a more significant impact on airfoil performance. However, large velocity fluctuations were observed, and the DSV’s occurrence and detachment were not influenced. In comparison, the downward leading-edge motion significantly enhanced the post-stall lift situation by suppressing the leading-edge separation and preventing the formation of the DSV.
- (f)
- This asynchronous morphing motion needs further investigation because several parameters affect its performance, such as morphing start times, durations, and phase offsets.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\alpha $ | Angle of attack |

${\alpha}_{m}$ | Mean incidence angle |

${\alpha}_{a}$ | Amplitude incidence angle |

${A}_{D}$ | Droop nose deflection |

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

${C}_{L,max}$ | Maximum lift coefficient |

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

${C}_{D,max}$ | Maximum drag coefficient |

$c$ | Chord |

${C}_{P}$ | Pressure coefficient |

$k$ | Reduced frequency |

$M$ | Maximum value of the percentage chord line |

${M}_{ST}$ | Morphing starting time |

$P$ | Chordwise position of the maximum camber |

$t$ | Time |

s | Seconds |

${U}_{\infty}$ | Freestream velocity |

${U}_{inst}$ | Local velocity component |

${W}_{le}$ | Value of the maximum deflection of the leading edge |

${y}_{f}$ | Final y-coordinate of the new morphing airfoil camber line |

LEV | Leading-edge vortex |

TEV | Trailing-edge vortex |

DSV | Dynamic stall vortex |

CoMpLETE | Combined morphing leading edge and trailing edge |

UDF | User defined function |

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**Figure 1.**CoMpLETE (combined morphing leading edge and trailing edge) airfoils inspired by the cetacean species.

**Figure 3.**Numerical modeling of a camber line [53].

**Figure 4.**Computational domain with (

**a**) overall mesh, (

**b**) mesh around the reference airfoil, (

**c**) mesh around the downward morphing airfoil, (

**d**) mesh around the upward morphing airfoil, and (e) mesh around the asynchronous morphing airfoil.

**Figure 6.**Comparisons of the numerical results for the lift coefficient versus the angle of attack for three different grid sizes.

**Figure 8.**CoMpLETE airfoil for three different cases at 0.5 Hz, 1 Hz, and 2 Hz (

**a**) shows an average growth of lift coefficients vs. time with the inserted figure of transient lift without baseline average, (

**b**) shows an average growth of drag coefficients vs. time with the inserted figure of transient drag without baseline average, and (

**c**) shows the lift coefficients for one cycle after the morphing starts at t = 1.5 s.

**Figure 9.**Power spectral density of lift coefficient for CoMpLETE airfoil for three different cases at 0.5 Hz, 1 Hz, and 2 Hz.

**Figure 10.**Local velocity component at the leading-edge probe position for the CoMpLETE airfoil at (

**a**) 0.5 Hz, (

**b**) 1 Hz, and (

**c**) 2 Hz at an angle of attack of 22°.

**Figure 11.**Pressure coefficients accompanied by velocity streamline and vorticity contours at different times for (

**a**) Case ‘1.1’ and (

**b**) Case ‘1.2’.

**Figure 12.**Pressure coefficients, velocity streamline, and vorticity contours at different times for (

**a**) Case ‘1.1’ and (

**b**) Case ‘1.2’.

**Figure 13.**CoMpLETE airfoil for Cases 1.4 with (

**a**) lift and (

**b**) drag coefficient transient responses, at an angle of attack of 22°.

**Figure 14.**CoMpLETE airfoil for Cases 1.5 with (

**a**) lift and (

**b**) drag coefficient transient responses at an angle of attack of 22°.

**Figure 15.**Comparison of (

**a**) transient lift coefficient for Case (1.4) and (1.5) at 0.5 Hz. (

**b**) Comparison of instantaneous velocity responses for Case (1.4) and (1.5) at 0.5 Hz.

**Figure 16.**CoMpLETE airfoil for three different cases with (

**a**) lift and (

**b**) drag coefficient transient responses at an angle of attack of 22°.

**Figure 17.**Pressure coefficients, velocity streamline, and vorticity contours at different times for (

**a**) Case ‘1.4’ and (

**b**) Case ‘1.5’.

**Figure 18.**Pressure coefficients, velocity streamline, and vorticity contours at different times for (

**a**) Case ‘1.4’ and (

**b**) Case ‘1.5’.

**Figure 19.**CoMpLETE airfoil for Case 2.1 with (

**a**) lift and (

**b**) drag coefficient transient responses at an angle of attack of 22°.

**Figure 20.**Comparison of transient (

**a**) lift and (

**b**) drag coefficient for Case 1.2 and Case 2.2 at 1 Hz.

**Figure 21.**Pressure coefficients, velocity streamline, and vorticity contours at different times for (

**a**) Case ‘1.2’ and (

**b**) Case ‘2.2’.

**Figure 22.**Comparison of transient (

**a**) lift and (

**b**) drag coefficients for Case 1.4 and Case 2.4 at 0.5 Hz.

**Figure 23.**Comparison of transient (

**a**) lift and (

**b**) drag coefficients for Case 1.5 and Case 2.5 at 0.5 Hz.

**Figure 24.**Pressure coefficients, velocity streamline, and vorticity contours at different times for (

**a**) Case ‘1.4’ and (

**b**) Case ‘2.4’.

**Table 1.**Airfoil with morphing of the leading edge starts at 0.2c, and the trailing-edge morphing starts at 0.75c.

Morphing Case | Leading-Edge Morphing Starting Time (s) | Trailing-Edge Morphing Starting Time (s) | Morphing Deflection Frequency (Hz) |
---|---|---|---|

Case 1.1 | t = 1.5 | t = 1.5 | 0.5 |

Case 1.2 | t = 1.5 | t = 1.5 | 1 |

Case 1.3 | t = 1.5 | t = 1.5 | 2 |

Case 1.4 | t = 1.4 | t = 1.85 | 0.5 |

Case 1.5 | t = 1.85 | t = 1.4 | 0.5 |

**Table 2.**Airfoil with morphing of the leading edge starts at 0.15c, and the trailing-edge morphing starts at 0.75c.

Morphing Case | Leading-Edge Morphing Starting Time (s) | Trailing-Edge Morphing Starting Time (s) | Morphing Deflection Frequency (Hz) |
---|---|---|---|

Case 2.1 | t = 1.5 | t = 1.5 | 0.5 |

Case 2.2 | t = 1.5 | t = 1.5 | 1 |

Case 2.3 | t = 1.5 | t = 1.5 | 2 |

Case 2.4 | t = 1.4 | t = 1.85 | 0.5 |

Case 2.5 | t = 1.85 | t = 1.4 | 0.5 |

Grid Size | Number of Cells | Min Length | Max Length | Bias Factor |
---|---|---|---|---|

1 | 62,626 | 0.001 | 0.06 | 1.12 |

2 | 103,212 | 0.001 | 0.035 | 1.08 |

3 | 206,038 | 0.001 | 0.02 | 1.05 |

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**MDPI and ACS Style**

Bashir, M.; Negahban, M.H.; Botez, R.M.; Wong, T.
Numerical Simulation of the Transient Flow around the Combined Morphing Leading-Edge and Trailing-Edge Airfoil. *Biomimetics* **2024**, *9*, 109.
https://doi.org/10.3390/biomimetics9020109

**AMA Style**

Bashir M, Negahban MH, Botez RM, Wong T.
Numerical Simulation of the Transient Flow around the Combined Morphing Leading-Edge and Trailing-Edge Airfoil. *Biomimetics*. 2024; 9(2):109.
https://doi.org/10.3390/biomimetics9020109

**Chicago/Turabian Style**

Bashir, Musavir, Mir Hossein Negahban, Ruxandra Mihaela Botez, and Tony Wong.
2024. "Numerical Simulation of the Transient Flow around the Combined Morphing Leading-Edge and Trailing-Edge Airfoil" *Biomimetics* 9, no. 2: 109.
https://doi.org/10.3390/biomimetics9020109