# Pulsed Blowing Interacting with a Leading-Edge Vortex

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Delta Wing Model

#### 2.2. Experimental Setup

#### 2.3. Numerical Setup

## 3. Results and Discussion

#### 3.1. Vortex Breakdown

#### 3.2. Stall

#### 3.3. Post-Stall

#### 3.4. Pulsed Blowing

#### 3.4.1. Delay of Vortex Breakdown

#### 3.4.2. Shear Layer Reattachment

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CFD | Computational fluid dynamics |

CFL | Courant–Friedrichs–Levy |

DES | Detached eddy simulation |

LES | Large eddy simulation |

RANS | Reynolds averaged Navier–Stokes |

VFE-2 | Vortex Flow Experiment 2 |

PIV | Particle image velocimetry |

SST | Shear stress transport |

TKE | Turbulent kinetic energy |

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**Figure 1.**(

**a**) Delta wing model (length dimensions in mm) and (

**b**) measured slot exit velocity signal.

**Figure 2.**The DES switch function takes a value above one in the LES region (red). Blue represents the RANS region.

**Figure 3.**Computational grid: (

**a**) detail view of the leading-edge surface mesh and (

**b**) O-grid blocking.

**Figure 4.**Smoke visualization of the core flow $\alpha =23\xb0$ showing different breakdown positions corresponding to consecutive instances: (

**a**) ${t}_{1}$ and (

**b**) ${t}_{1}+\Delta t$.

**Figure 5.**Plane along the vortex core, $\alpha =23\xb0$, $Re=1.0\times {10}^{6}$: (

**a**) measured and (

**c**) computed averaged axial velocity with $k/{U}_{\infty}^{2}$ isolines; (

**b**) measured and (

**d**) computed instantaneous in-plane vorticity with isolines representing $u=0$. DES views (

**c**,

**d**) shifted by 0.1 in the relative chordwise and spanwise direction.

**Figure 6.**Computed Q-criterion $Q={10}^{5}$ s${}^{-2}$ colored by the relative axial velocity; $\alpha =23\xb0$, $Re=1.0\times {10}^{6}$; (

**a**) side view and (

**b**) top view.

**Figure 7.**Plane along the vortex core, $\alpha =35\xb0$, $Re=0.5\times {10}^{6}$: (

**a**) measured and (

**c**) computed averaged axial velocity with $k/{U}_{\infty}^{2}$ isolines; (

**b**) measured and (

**d**) computed instantaneous in-plane vorticity with isolines representing $u=0$. DES views (

**c**,

**d**) shifted by 0.1 in the relative chordwise and spanwise direction).

**Figure 8.**Computed Q-criterion $Q={10}^{5}$ s${}^{-2}$ colored by the relative axial velocity; $\alpha =35\xb0$, $Re=0.5\times {10}^{6}$; (

**a**) side view and (

**b**) top view.

**Figure 9.**Plane along the vortex core, $\alpha =45\xb0$, $Re=0.5\times {10}^{6}$: (

**a**) measured and (

**c**) computed averaged axial velocity with $k/{U}_{\infty}^{2}$ isolines; (

**b**) measured and (

**d**) computed instantaneous in-plane vorticity with isolines representing $u=0$. DES views (

**c**,

**d**) shifted by 0.3 in the relative chordwise and spanwise direction.

**Figure 10.**Computed Q-criterion $Q={10}^{5}$ s${}^{-2}$ colored by the relative axial velocity; $\alpha =45\xb0$, $Re=0.5\times {10}^{6}$; (

**a**) side view and (

**b**) top view.

**Figure 11.**Mean aerodynamic coefficients of longitudinal motion for three angles of attack, comparing the baseline with actuated cases and WTT with CFD. (

**a**) Lift coefficient; (

**b**) drag coefficient; (

**c**) pitching moment coefficient.

**Figure 12.**Axial and azimuthal relative velocity profiles at two chord stations (upstream: line, downstream: dashed line) across the vortex comparing baseline (red, black) with perturbed flow (green blue): (

**a**) $\alpha =23\xb0$ ($x/{c}_{r}=0.50$, 0.70) and (

**b**) $\alpha =35\xb0$ ($x/{c}_{r}=0.15$, 0.50).

**Figure 13.**Phase averaged vorticity distribution at $\alpha =35\xb0$ (

**a**) during blowing and (

**b**) $T/2$ after blowing.

**Figure 14.**Q-criterion $Q={10}^{5}$ s${}^{-2}$ at $\alpha =35\xb0$ (

**a**) during blowing and (

**b**) $T/2$ after blowing.

**Figure 15.**Phase averaged vertical velocity profiles across the forced vortex core at $\alpha =35\xb0$, $x/{c}_{r}=0.65$, and $y/s=0.36$. (

**a**) Phase definition; (

**b**) axial velocity; (

**c**) spanwise velocity.

**Figure 16.**Phase averaged vortex axis location at $\alpha =35\xb0$, ${F}^{+}=2.6$: (

**a**) xy-plane and (

**b**) $x/{c}_{r}=0.65$.

**Figure 17.**Phase averaged vorticity distribution at $\alpha =45\xb0$ (

**a**) PIV axial vorticity, blowing on, when the jets are switched off, and (

**b**) PIV axial vorticity, blowing off, $T/4$ after blowing.

**Figure 18.**Q-criterion $Q={10}^{5}$ s${}^{-2}$ at $\alpha =45\xb0$ (

**a**) when the jets are switched off and (

**b**) $T/4$ after blowing.

**Figure 19.**Phase averaged vertical velocity profiles across the forced vortex core at $\alpha =45\xb0$, $x/{c}_{r}=0.65$ and $y/s=0.34$. (

**a**) Axial velocity; (

**b**) spanwise velocity.

**Figure 20.**Phase averaged vortex axis location at $\alpha =45\xb0$, ${F}^{+}=1.0$: (

**a**) xy-plane and (

**b**) $x/{c}_{r}=0.65$.

Test Case | $\mathit{\alpha}$ | ${\mathit{U}}_{\mathbf{\infty}}$ | $\mathbf{Re}$ | f | ${\mathit{F}}^{+}$ | ${\mathit{c}}_{\mathit{\mu}}$ | $\mathbf{\Delta}\mathit{t}$ | $\mathit{\tau}$ | CFL |
---|---|---|---|---|---|---|---|---|---|

Vortex breakdown | $23\xb0$ | 24 m/s | $1.0\times {10}^{6}$ | 65 Hz | 2.6 | 0.14% | $1.9\times {10}^{-5}$ s | $5\times {10}^{-4}$ | 0.2 |

Stalled flow | $35\xb0$ | 12 m/s | $0.5\times {10}^{6}$ | 32 Hz | 2.6 | 0.55% | $3.9\times {10}^{-5}$ s | $5\times {10}^{-4}$ | 0.2 |

Post-stall | $45\xb0$ | 12 m/s | $0.5\times {10}^{6}$ | 12 Hz | 1.0 | 0.85% | $1.0\times {10}^{-4}$ s | $1\times {10}^{-3}$ | 0.5 |

Flow Region | O-Grid Layer | Layer Thickness | Minimum Cell Spacing | Growth Factor |
---|---|---|---|---|

Viscous region | 1st | 3 mm | 0.01 mm | 1.13 |

Focus region | 2nd | 27 mm | 0.48 mm | 1.04 |

Focus region | 3rd | 190 mm | 1.30 mm | 1.04 |

Departure region | 4th | 300 mm | 6.10 mm | 1.20 |

**Table 3.**Relative chordwise positions $x/{c}_{r}$ of the breakdown ($\alpha =23\xb0$) and stagnation location ($35\xb0$).

$\mathit{\alpha}=23\xb0$ | $\mathit{\alpha}=35\xb0$ | |||
---|---|---|---|---|

Baseline | ${\mathit{F}}^{+}=2.6$ | Baseline | ${\mathit{F}}^{+}=2.6$ | |

PIV: | 0.55 | 0.58 | 0.24 | 0.43 |

DES: | 0.66 | 0.76 | 0.32 | 0.45 |

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**MDPI and ACS Style**

Buzica, A.; Breitsamter, C.
Pulsed Blowing Interacting with a Leading-Edge Vortex. *Aerospace* **2020**, *7*, 4.
https://doi.org/10.3390/aerospace7010004

**AMA Style**

Buzica A, Breitsamter C.
Pulsed Blowing Interacting with a Leading-Edge Vortex. *Aerospace*. 2020; 7(1):4.
https://doi.org/10.3390/aerospace7010004

**Chicago/Turabian Style**

Buzica, Andrei, and Christian Breitsamter.
2020. "Pulsed Blowing Interacting with a Leading-Edge Vortex" *Aerospace* 7, no. 1: 4.
https://doi.org/10.3390/aerospace7010004