# Experimental Observations of Transient Flows in Separation Control Using a Plasma Actuator

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Results

#### 3.1. Baseline Flow Characteristics

#### 3.1.1. Separated Flow

#### 3.1.2. Attached Flow

#### 3.2. Reattachment Transient Process

#### 3.3. Separation Transient Process

#### 3.3.1. Flow Field Analysis

#### 3.3.2. Surface Pressure Analysis

## 4. Quantitative Evaluation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

z | First POD coefficient |

$\sigma $ | Standard deviation |

${\overline{z}}_{\mathrm{att}}$ | Time average of z during pseudo-stationary controlled conditions |

${\overline{z}}_{\mathrm{sep}}$ | Time average of z during fully separated conditions |

AC | Alternating current |

c | Wing chord |

f | Frequency of sinusoidal wave |

${f}^{+}$ | Burst frequency |

${F}^{+}$ | Nondimensional burst frequency |

PA | Plasma actuator |

t | Time |

${t}_{\mathrm{off}}$ | Instant at which the plasma actuator is turned off |

${t}_{\mathrm{on}}$ | Instant at which the plasma actuator is turned on |

${t}_{\mathrm{on}/\mathrm{off}}$ | Instant at which the plasma actuator is either turned on or off |

T | Period of sinusoidal wave |

${T}^{+}$ | Period of burst |

${T}_{\mathrm{off}}$ | Inactive period during burst |

${T}_{\mathrm{on}}$ | Active period during burst |

U | Horizontal component of wind velocity |

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

V | Voltage |

## Appendix A. Experimental Results

${\mathit{F}}^{+}=1$ | ${\mathit{F}}^{+}=2$ | ${\mathit{F}}^{+}=3$ | ${\mathit{F}}^{+}=6$ | |||
---|---|---|---|---|---|---|

Case 1 | Case 2 | |||||

$0<t{U}_{\infty}/c<10$ | mean(z) | 179.2 | 219.6 | 257.6 | 281.8 | 289.0 |

mean($\sigma $(z)) | 107.3 | 113.3 | 97.1 | |||

$20<t{U}_{\infty}/c<30$ | mean(z) | −116.4 | −334.2 | −306.3 | −320.6 | −328.7 |

mean($\sigma $(z)) | 35.2 | 73.6 | 40.0 |

## Appendix B. Analysis of F^{+} = 1

**Figure A1.**z of first POD mode during complete separation (

**left**) and steady plasma actuator activation for ${F}^{+}=1$ (

**right**).

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**Figure 3.**Measurements of periods of bursting signal (

**left**) and temporal structure of test runs (

**right**).

**Figure 4.**Analysis of a singular case with synchronization issues. (

**a**) Spatial distribution of first POD mode of U for 30 runs. (

**b**) Temporal evolution of first POD mode of U of a single run without ensemble average. (

**c**) Standard deviation of U values after complete processing.

**Figure 6.**Analysis of first POD mode during normally separated flow conditions. (

**a**) First POD coefficient z of 30-run ensemble average for ${F}^{+}=2$, 3, 6. (

**b**) Standard deviation of first POD coefficient z of 30-run ensemble for ${F}^{+}=2$, 3, 6.

**Figure 7.**Flow visualization and reconstruction from first POD coefficient of ensemble average during normally separated flow conditions for ${F}^{+}=3$. (

**a**) Ensemble-averaged flow field at $t{U}_{\infty}/c=5$ (ensemble for ${F}^{+}=3$). (

**b**) Reconstructed flow field from the first POD mode at $t{U}_{\infty}/c=5$ (ensemble for ${F}^{+}=3$).

**Figure 8.**Analysis of first POD mode during PA actuation and pseudo-stationary flow conditions. (

**a**) First POD coefficient z of 30-run ensemble average for actuation with ${F}^{+}=2$, 3, 6. (

**b**) Standard deviation of first POD coefficient z of 30-run ensemble for actuation with ${F}^{+}=2$, 3, 6.

**Figure 9.**Flow visualization and reconstruction from first POD coefficient of ensemble average during PA actuation and pseudo-stationary flow conditions for ${F}^{+}=3$. (

**a**) Averaged flow field at $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=15$ (ensemble for ${F}^{+}=3$). (

**b**) Reconstructed flow field from first POD mode at $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=15$ (ensemble for ${F}^{+}=3$).

**Figure 10.**z value of first POD mode during reattachment transient process. (

**a**) First POD coefficient z of 30-run ensemble average for ${F}^{+}=2$, 3, 6. (

**b**) First POD coefficient z of 30-run ensemble average for ${F}^{+}=2$ and its standard deviation range. (

**c**) First POD coefficient z of 30-run ensemble average for the actuation with ${F}^{+}=3$ and its standard deviation range. (

**d**) First POD coefficient z of 30-run ensemble average for the actuation with ${F}^{+}=6$ and its standard deviation range.

**Figure 11.**Flow visualization during reattachment transient process. (

**a**) Flow visualization of 30-run ensemble average of the actuation with ${F}^{+}=6$ at $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=0.8$. (

**b**) Flow visualization of 30-run ensemble average of the actuation with ${F}^{+}=6$ at $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=1.8$. (

**c**) Flow visualization of 30-run ensemble average of the actuation with ${F}^{+}=6$ at $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=3.8$. (

**d**) Flow visualization of 30-run ensemble average of the actuation with ${F}^{+}=6$ at $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=6$.

**Figure 12.**z value of first POD mode during separation transient process. (

**a**) First POD coefficient z of 30-run ensemble average for the actuation with ${F}^{+}=2$, 3, 6. (

**b**) First POD coefficient z of 30-run ensemble average for the actuation with ${F}^{+}=2$ and its standard deviation range. (

**c**) First POD coefficient z of 30-run ensemble average for the actuation with ${F}^{+}=3$ and its standard deviation range. (

**d**) First POD coefficient z of 30-run ensemble average for the actuation with ${F}^{+}=6$ and its standard deviation range.

**Figure 13.**Flow visualization during separation transient process. (

**a**) Flow visualization of 30-run ensemble average of the actuation with ${F}^{+}=6$ at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=3.6$. (

**b**) Flow visualization of single run of the actuation with ${F}^{+}=6$ ensemble at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=3.6$. (

**c**) Flow visualization of 30-run ensemble average of the actuation with ${F}^{+}=6$ at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=6.0$. (

**d**) Flow visualization of single run of the actuation with ${F}^{+}=6$ ensemble at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=6.0$. (

**e**) Flow visualization of 30-run ensemble average of the actuation with ${F}^{+}=6$ at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=12.6$. (

**f**) Flow visualization of single run of the actuation with ${F}^{+}=6$ ensemble at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=12.6$.

**Figure 14.**Pressure measurements at 0.1 c of 30-run ensemble average for ${F}^{+}2$, 3, 6 during separation transient process. (

**a**) Pressure at 0.1 c of 30-run ensemble average for ${F}^{+}=2$, 3, 6. (

**b**) Pressure and its standard deviation at 0.1 c of 30-run ensemble average for ${F}^{+}=2$. (

**c**) Pressure and its standard deviation at 0.1 c of 30-run ensemble average for ${F}^{+}=3$. (

**d**) Pressure and its standard deviation at 0.1 c of 30-run ensemble average for ${F}^{+}=6$.

**Figure 15.**Analysis of first POD mode during PA actuation with pseudo-stationary flow conditions. (

**a**) Graphical representation of completion ratios $C{R}_{2.5}$, $C{R}_{5}$, and $C{R}_{15}$ at times $(t-{t}_{\mathrm{on}/\mathrm{off}}){U}_{\infty}/c=$ 2.5, 5, and 15, respectively. (

**b**) Graphical representation of times ${t}_{0.3}$, ${t}_{0.6}$, and ${t}_{0.9}$, which reach completion ratios of 0.3, 0.6, and 0.9, respectively.

**Figure 16.**Analysis of transient process completion ratio. (

**a**) Completion ratio at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=2.5$ (red) and $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=2.5$ (blue). (

**b**) Completion ratio at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=5$ (red) and $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=5$ (blue). (

**c**) Completion ratio at $(t-{t}_{\mathrm{off}}){U}_{\infty}/c=15$ (red) and $(t-{t}_{\mathrm{on}}){U}_{\infty}/c=15$ (blue). (

**d**) Times after PA state switch (off → on) to achieve completion ratios of 0.3, 0.6, and 0.9. (

**e**) Times after PA state switch (on → off) to achieve completion ratios of 0.3, 0.6, and 0.9.

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## Share and Cite

**MDPI and ACS Style**

Viguera, R.; Anzai, Y.; Sasaki, Y.; Nonomura, T.
Experimental Observations of Transient Flows in Separation Control Using a Plasma Actuator. *Actuators* **2023**, *12*, 218.
https://doi.org/10.3390/act12060218

**AMA Style**

Viguera R, Anzai Y, Sasaki Y, Nonomura T.
Experimental Observations of Transient Flows in Separation Control Using a Plasma Actuator. *Actuators*. 2023; 12(6):218.
https://doi.org/10.3390/act12060218

**Chicago/Turabian Style**

Viguera, Rodrigo, Yoshiki Anzai, Yasuo Sasaki, and Taku Nonomura.
2023. "Experimental Observations of Transient Flows in Separation Control Using a Plasma Actuator" *Actuators* 12, no. 6: 218.
https://doi.org/10.3390/act12060218