# Mitigation of Shock-Induced Separation Using Square-Shaped Micro-Serrations—A Preliminary Study

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Description of the Computational Domain and Boundary Conditions

#### 2.2. Numerical Method

#### 2.3. Code Validation

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^{−1}. The deflection angle of the oblique incident shock is 12°. Figure 3 presents the comparison between the experimental and numerical surface pressure distributions, where the zero of the x-axis, named “CoordinateX”, is the impinging point of the inviscid shock wave and the $y$-axis is the surface pressure ratio based on the incoming static pressure. The curve obtained by simulation is essentially in agreement with the experimental results, including the starting point of the pressure jump, which suggests the initial position of the separation. It should be noted that the pneumatic shock generator, as mentioned above, is used to generate the incident shock. Therefore, the expansion wave emitting from the end of the wedge shock generator is not considered in this validation; it is also possible that, due to this reason, the pressure obtained from the simulation differs from the experimental results near the reattachment point.

^{−4}m. All of the other cases meet this cell size limitation after refining, and the final number of grid points is approximately 2 × 10

^{6}. In addition, a slat with a length of 0.1 mm has 7 grid points, and there are more grid points when the slat size is larger.

## 3. Results and Discussion

#### 3.1. Vorticity-Based Criterion for Separation Assessment

#### 3.2. Effects of a Single Stair on Shock-Induced Separation

#### 3.3. Effects of Serration Size on Shock-Induced Separation

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Comparison between experimental [42] and numerical surface pressure distributions.

**Figure 4.**Surface pressure distributions with different refinement levels (${M}_{0}$ = 2.5, ${h}_{U}$ = 0, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 5.**Computed contour plots of vorticity magnitude and streamline distributions near the separation point (${M}_{0}$ = 2.5, ${h}_{U}$ = 0, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 6.**Comparison of surface ${C}_{f}$ and vorticity magnitude distribution (${M}_{0}$ = 2.5, ${h}_{U}$ = 0, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 7.**Separation length and location of the separation point (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 8.**Contours of the Mach number distributions with stair heights of (

**a**) 0.4 and (

**b**) 1.0 and (

**c**) surface pressure distributions near the separation point (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 9.**Comparison of the pressure distributions for the stair and micro-serration configurations at typical sizes (

**a**) 0.1, (

**b**) 0.4,(

**c**) 1.0 and (

**d**) 4.0 (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 10.**Pressure distributions of micro-serration configurations with different (

**a**) depths and (

**b**) widths at ${h}_{U}$ = 0.4 (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 11.**(

**a**) Pressure distributions and (

**b**) separation length of micro-serration configurations with different depths at ${h}_{U}$ = 0.1 (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 12.**(

**a**) Pressure distributions and (

**b**) separation length of micro-serration configurations with different widths at ${h}_{U}$ = 0.1 (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 13.**Role of vortices in separation control. (

**a**) The vortices in the micro-serrations. (

**b**) Comparison of velocity profiles upstream of the separation point. (

**c**) Pressure distributions before the first pressure plateau (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 14.**Vortices upstream of the separation point with different widths of the micro-serration: (

**a**) $w$ = 0.05, (

**b**) $w$ = 0.1 (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

**Figure 15.**Location of vortices in the micro-serration with different depths: (

**a**) $h$ = 0.2 and (

**b**) $h$ = 1.0; the micro-serration is not fully displayed (${M}_{0}$ = 2.5, $\alpha $ = 15°, ${I}_{P}$ = 65).

Parameters | Explanations |
---|---|

${M}_{0}$ | Incoming Mach number |

${h}_{U}$ | Dimensionless height of the first windward stair at $x$ = 0 |

$w$ | Dimensionless width of the micro-serration |

$h$ | Dimensionless depth of the micro-serration |

$\alpha $ | The deflection angle of incident shock (deg.) |

${I}_{P}$ | The impinging point of the inviscid incident shock at the bottom wall ($x={I}_{P}$, $y=$ 0) |

Separation Point | Reattachment Point | Separation Length | |
---|---|---|---|

${C}_{f}$ | 5.32 | 82.53 | 77.21 |

Vorticity magnitude | 5.69 | 82.02 | 76.33 |

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**MDPI and ACS Style**

Yu, F.; Gao, Z.; Zhang, Q.; Yue, L.; Chen, H.
Mitigation of Shock-Induced Separation Using Square-Shaped Micro-Serrations—A Preliminary Study. *Aerospace* **2024**, *11*, 148.
https://doi.org/10.3390/aerospace11020148

**AMA Style**

Yu F, Gao Z, Zhang Q, Yue L, Chen H.
Mitigation of Shock-Induced Separation Using Square-Shaped Micro-Serrations—A Preliminary Study. *Aerospace*. 2024; 11(2):148.
https://doi.org/10.3390/aerospace11020148

**Chicago/Turabian Style**

Yu, Fangyou, Zhanbiao Gao, Qifan Zhang, Lianjie Yue, and Hao Chen.
2024. "Mitigation of Shock-Induced Separation Using Square-Shaped Micro-Serrations—A Preliminary Study" *Aerospace* 11, no. 2: 148.
https://doi.org/10.3390/aerospace11020148