# The Impact of Steady Blowing from the Leading Edge of an Open Cavity Flow

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Results and Discussion

#### 3.1. Jet Behaviour under Quiescent Conditions

#### 3.2. Time-Averaged Flow Field

#### 3.2.1. Jet Impact on the Cavity Flow Topology

#### 3.2.2. Jet Impact on the Cavity Separated Shear Layer

#### 3.2.3. Jet Impact on the Return Flow

#### 3.3. Jet Impact on the Oscillations of the Cavity Separated Shear Layer

#### 3.4. Further Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

b | Local jet half width [m] |

${C}_{\mu}$ | Jet’s momentum coefficient [%] |

D | Cavity depth [m] |

f | Repetition rate of the particle image velocimetry [Hz] |

h | Characteristic slot width [m] |

J | Jet’s momentum flux per unit width [kg/m·s${}^{2}$] |

L | Cavity length [m] |

$LE$ | Cavity leading edge |

M | Mach number |

$R{e}_{Bulk}$ | Reynolds number based on the bulk velocity of the jet |

$R{e}_{D}$ | Reynolds number based on the cavity depth |

$R{e}_{dia}$ | Reynolds number based on the model diameter |

$R{e}_{\theta}$ | Reynolds number based on the boundary layer momentum thickness |

$St$ | Non-dimensional frequency $St=fL/{U}_{f}$ |

t | Time [s] |

$TE$ | Cavity trailing edge |

<${u}^{\prime}$> | Time-averaged streamwise velocity fluctuation [m/s] |

U | The streamwise velocity [m/s] |

${U}_{0}$ | Jet exit velocity [m/s] |

${U}_{f}$ | The free stream velocity [m/s] |

<${v}^{\prime}$> | Time-averaged normal-to-wall velocity fluctuation [m/s] |

V | Normal-to-wall velocity [m/s] |

W | Cavity width [m] |

x | The streamwise distance from the reference point [m] |

y | The vertical distance from the reference point [m] |

z | The spanwise distance from the reference point [m] |

${\delta}_{\omega}$ | The vorticity thickness [m] |

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**Figure 4.**Shift of the jet centre along the x-axis for actuator without the cavity model [quiescent condition] with different J values.

**Figure 5.**Time-averaged velocity streamlines and $U/{U}_{0}$ contours for actuator with the cavity model [quiescent condition] with different J values.

**Figure 6.**The time-averaged V velocity distribution along $y/D=-0.9$ for actuator with the cavity model [quiescent condition] with different J values.

**Figure 7.**Contours of the time-averaged $U/{U}_{f}$ for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

**Figure 8.**The vorticity thickness of the cavity separated shear layer along x-axis for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

**Figure 9.**The time-averaged PIV raw images and the time-averaged $U/{U}_{f}$ profiles for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J. C.S.S.L. denotes the cavity separated shear layer.

**Figure 10.**Profiles of the time-averaged $V/{U}_{f}$ along the centre of the main recirculation vortex for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

**Figure 11.**Distribution of $U/{U}_{f}$ along the cavity floor ($y/D=-0.9$) for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

**Figure 12.**Surface oil flow visualisations for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J: (

**a**) no jet, (

**b**) $J=0.11$ kg/m·s${}^{2}$, (

**c**) $J=0.44$ kg/m·s${}^{2}$, and (

**d**) $J=0.96$ kg/m·s${}^{2}$.

**Figure 13.**Unsteady wall pressure power spectral density at $x/L=0.5$ for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

**Figure 14.**Contours of the time-averaged dimensionless time-averaged Reynolds shear stress <${u}^{\prime}{v}^{\prime}$>/${U}_{f}^{2}$ for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

**Figure 15.**Contours of the time-averaged ${\omega}_{z}L/{U}_{f}$ at the cavity leading edge region for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

**Figure 16.**Snapshots of the instantiation vorticity and the fluctuating velocity streamlines with different filter sizes. The dashed arrow indicates the free stream direction. $R{e}_{D}\approx $ 50,000; sharp edge at LE; no-jet.

**Figure 18.**Dimensionless time-averaged streamwise velocity profiles in the last quarter of the cavity $3<L/D<4$ for the uncontrolled and controlled by the injection and suction with $Bc=1\%$ cases; $R{e}_{D}=$ 5000; $L/D=4$. Note: $Y=y/D$, ${U}_{av}$ is the dimensionless time-averaged streamwise velocity (Suponitsky et al. [25]).

${\mathit{Re}}_{\mathit{Bulk}}$ | J(kg/m·s${}^{2}$) | ${\mathit{C}}_{\mathit{\mu}}$ (%) |
---|---|---|

290 | 0.11 | 0.57 |

465 | 0.44 | 2.31 |

965 | 0.96 | 5.04 |

**Table 2.**Growth rate of the cavity separated shear layer for $R{e}_{D}\approx $ 50,000; sharp edge at LE; different J.

J(kg/m·s${}^{2}$) | No Jet | $0.11$ | $0.44$ | $0.96$ |
---|---|---|---|---|

$d{\delta}_{\omega}/dx$ | 0.180 | 0.183 | 0.229 | 0.256 |

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**MDPI and ACS Style**

Haddabi, N.A.; Kontis, K.; Zare-Behtash, H.
The Impact of Steady Blowing from the Leading Edge of an Open Cavity Flow. *Aerospace* **2021**, *8*, 255.
https://doi.org/10.3390/aerospace8090255

**AMA Style**

Haddabi NA, Kontis K, Zare-Behtash H.
The Impact of Steady Blowing from the Leading Edge of an Open Cavity Flow. *Aerospace*. 2021; 8(9):255.
https://doi.org/10.3390/aerospace8090255

**Chicago/Turabian Style**

Haddabi, Naser Al, Konstantinos Kontis, and Hossein Zare-Behtash.
2021. "The Impact of Steady Blowing from the Leading Edge of an Open Cavity Flow" *Aerospace* 8, no. 9: 255.
https://doi.org/10.3390/aerospace8090255