# Numerical Simulation of Pressure Fluctuation near an Expansion Corner in a Supersonic Flow of M = 3.01

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## Abstract

**:**

## 1. Introduction

## 2. The Expansion Corner Problem and Numerical Method for Simulation

## 3. Characteristics and Definition of U-Zone, M-Zone and D-Zone

- (1)
- U-zone is the region upstream of the characteristic line ${C}_{U}$.
- (2)
- M-zone is the region between the characteristic lines ${C}_{U}$ and ${C}_{D}$.
- (3)
- D-zone is the region downstream of the characteristic line ${C}_{D}$.

- (a)
- wall surface, with ${y}^{+}=0$ and labelled point “1”.
- (b)
- buffer layer, with ${y}^{+}\approx 30$ and labelled point “2”.
- (c)
- log-law layer, with ${y}^{+}\approx 300$ and labelled point “3”.
- (d)
- outer layer, with ${y}^{+}>1000$ and labelled point “4”.

## 4. The ${\mathbf{Cp}}_{\mathbf{rms}}$ and PSD in the U-Zone, M-Zone and D-Zone

#### 4.1. The Distribution of $C{p}_{rms}$ in Various Zones

#### 4.2. The $PSD$ in Various Zones

## 5. Summary of Fluctuating Properties and Feedback Mechanism

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A model of the expansion probelm. The Mach angles ${\mu}_{1}=arcsin{\displaystyle \frac{1}{M{a}_{1}}}=19.4{}^{\circ}$ and ${\mu}_{2}=arcsin{\displaystyle \frac{1}{M{a}_{2}}}=15.3{}^{\circ}$ are marked in the figure.

**Figure 3.**Normalized pressure p along the flow direction on the wall (${p}_{1}$ is the pressure in the freestream).

**Figure 8.**The distribution of $C{p}_{rms}$ in different layers within boundary layer near expansion corner.

**Figure 14.**The distribution of the correlation coefficient between different layers near expansion corner.

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**MDPI and ACS Style**

Zhang, L.; Wu, Z.-N. Numerical Simulation of Pressure Fluctuation near an Expansion Corner in a Supersonic Flow of M = 3.01. *Fluids* **2021**, *6*, 268.
https://doi.org/10.3390/fluids6080268

**AMA Style**

Zhang L, Wu Z-N. Numerical Simulation of Pressure Fluctuation near an Expansion Corner in a Supersonic Flow of M = 3.01. *Fluids*. 2021; 6(8):268.
https://doi.org/10.3390/fluids6080268

**Chicago/Turabian Style**

Zhang, Lei, and Zi-Niu Wu. 2021. "Numerical Simulation of Pressure Fluctuation near an Expansion Corner in a Supersonic Flow of M = 3.01" *Fluids* 6, no. 8: 268.
https://doi.org/10.3390/fluids6080268