# Digitalization and Quantitative Flow Visualization of Surrounding Flow over a Specially-Shaped Column-Frame by Luminescent Mini-Tufts Method

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Set-Ups

#### Experiment and Model

## 3. Data Processing Method

_{N_pic}is the matrix of the number N_pic grey image.

^{c}

_{i}

_{−1}is the center of the previous recognized point; i is the sequence number of the recognized points.

^{i}

_{j}is the jth element in the ith y-axis array which is to find the ith recognized point; x

^{i}

_{j}is the jth element in the ith x-axis array which is to find the ith recognized point.

## 4. Analysis Processing

_{ref}) (normalized area). The reference area is obtained by calculating the averaged tuft area in the present image.

## 5. Results and Discussion

_{t}) dividing the angle of attack (θ

_{a}) varies at different positions of luminescent mini-tuft (p). The illustration of this fact for different θ

_{a}is given in Figure 8. Since the angle of attack 0° cannot be divide, the y-axis in Figure 8b directly represents the mean mini-tuft inclination angle. In Figure 8, different colors mean different zones, and different mini-tuft length (r) is distinguished by different markers.

_{t}/θ

_{a}are around 1. In Figure 8b, at the end of the tufts, θ

_{t}is around 0. This phenomenon shows that the tufts follow the inflow well. In Figure 8a,b or Figure 8c, there is a pink line with triangle or square markers separating the other lines, which is from the last group in zone 4 with the tuft length of 40–45 mm. From around 20 mm until the end of the tuft, the behavior is different with the other tufts.

_{ref}with different tuft length are listed in Table 1. The maximum values of mean A/A

_{ref}when θ

_{a}= 4° are from mini-tufts with length of [55, +∞) mm. The maximum values of mean A/A

_{ref}when θ

_{a}= 0° and θ

_{a}= −4° are from mini-tufts with length of [45, 55) mm, and the minimum values of mean A/A

_{ref}when θ

_{a}= 4°, 0°, and −4° are from mini-tufts with a length of (0, 35) mm. Regardless of tuft length, the mean A/A

_{ref}values with different θ

_{a}are all equal to 0.98. It indicates that the angle of attack does not affect the instantaneous oscillation intensity.

_{ref}of the different zones are calculated, as shown in Figure 6 and in Table 2, Table 3 and Table 4.

_{ref}values in zone 2 and zone 3 are larger than that in zone 1 and 4, which indicates that the transient fluid oscillates more intensively on middle part than on both ends of the model. The square deviation at different zones shows that the oscillation intensity on both ends is more dispersed than the middle part of the model.

## 6. Conclusions

- (1)
- The time-averaged digital mini-tufts are calculated for analyzing the time-averaged flow behavior. For more intuitive observation of features, the mean digital mini-tufts of each group of the time-averaged digital mini-tufts are calculated. The current method proposed is realized well for the digitalization of mini-tufts.
- (2)
- With regard to the target model in the experiment, though the angle of attack varies, the latter segment (after around 20 mm) of almost all tufts follow the inflow direction on the model surface well.
- (3)
- The mean tuft transient oscillation under the same flow surrounding the same model is not impacted by the angle of attack.
- (4)
- According to the mean values of A/A
_{ref}, the tufts on the middle part of the model are larger than those on the two terminals, which indicates that the transient fluid is oscillating more intensively on the middle part of the irregularity cylinder than on the two terminals of the model.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Experimental set-up: model with luminescent mini-tufts and photography device, Reprinted with permission from Ref. [30]. 2019, Elsevier.

**Figure 8.**Mean luminescent mini-tuft angle varies on different positions of tuft. (

**a**) θ

_{a}= 4°; (

**b**) θ

_{a}= 0°; (

**c**) θ

_{a}= −4°.

**Figure 9.**Transient oscillation of luminescent mini-tuft variations with their transversal position on the model (r’s unit is mm). (

**a**) θ

_{a}= 4°; (

**b**) θ

_{a}= 0°; (

**c**) θ

_{a}= −4°.

Tuft Length | θ_{a} = 4° | θ_{a} = 0° | θ_{a} = −4° |
---|---|---|---|

r < 35 | 0.65 | 0.67 | 0.69 |

35 ≤ r < 45 | 1.12 | 0.97 | 0.98 |

45 ≤ r < 55 | 1.10 | 1.13 | 1.12 |

r ≥ 55 | 1.17 | 1.06 | 1.00 |

Zone Number | Mean | Square Deviation |
---|---|---|

1 | 0.89 | 0.23 |

2 | 1.02 | 0.17 |

3 | 1.02 | 0.20 |

4 | 0.96 | 0.22 |

Zone Number | Mean | Square Deviation |
---|---|---|

1 | 0.97 | 0.25 |

2 | 1.03 | 0.16 |

3 | 0.99 | 0.19 |

4 | 0.91 | 0.22 |

Zone Number | Mean | Square Deviation |
---|---|---|

1 | 0.96 | 0.22 |

2 | 1.04 | 0.17 |

3 | 0.99 | 0.20 |

4 | 0.92 | 0.28 |

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**MDPI and ACS Style**

Ma, S.; Chen, L.
Digitalization and Quantitative Flow Visualization of Surrounding Flow over a Specially-Shaped Column-Frame by Luminescent Mini-Tufts Method. *Aerospace* **2022**, *9*, 507.
https://doi.org/10.3390/aerospace9090507

**AMA Style**

Ma S, Chen L.
Digitalization and Quantitative Flow Visualization of Surrounding Flow over a Specially-Shaped Column-Frame by Luminescent Mini-Tufts Method. *Aerospace*. 2022; 9(9):507.
https://doi.org/10.3390/aerospace9090507

**Chicago/Turabian Style**

Ma, Shuang, and Lin Chen.
2022. "Digitalization and Quantitative Flow Visualization of Surrounding Flow over a Specially-Shaped Column-Frame by Luminescent Mini-Tufts Method" *Aerospace* 9, no. 9: 507.
https://doi.org/10.3390/aerospace9090507