# Influence of Mach Number of Main Flow on Film Cooling Characteristics under Supersonic Condition

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Physical Model

## 3. Computational Domain and Boundary Conditions

## 4. Division of Grids and Verification of Grid Independence

## 5. Computational Method

^{−5}; the residual curve tends to be flat; and the wall temperature tends to be stable.

## 6. Results and Analysis

#### 6.1. Wall Cooling Efficiency and Wall Temperature Distribution

#### 6.2. Longitudinal Cross-Section Flow Field at Incident Position

#### 6.3. Vortices Distribution in the Cross Section Downstream

#### 6.4. Phenomenon of Stratified Flow of the Main Flow in Hypersonic Speed

#### 6.4.1. Changes of the Stratified Flow Phenomenon along the Streamwise Flow

#### 6.4.2. Changes of the Stratified Flow Phenomenon with Ma_g

## 7. Conclusions

- (1)
- Under supersonic main stream conditions, the increasing of Ma_g always causes the film jet to main flow ratio to decrease. The relatively small amount of film jet weakens its mixing with the main flow, leading to a better attachment of the film.
- (2)
- Multi-interfacial layered structures were formed as the film jet flew across shock waves. At the interfaces of the film jet and shock waves, additional pressure was exerted on the film towards the wall. The pressure increased as the Mach number of main flow increased; this contributed to the increased adhesion of the gas film, which caused the cooling enhancement under supersonic condition.
- (3)
- In the vicinity of the film hole exit, a local low pressure region was formed under the influence of the supersonic main flow. An aerodynamic convergent–divergent state was formed in the film hole, devastating the state of supersonic congestion of the film hole and further enhancing the film cooling effect.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Schematic diagram on the pressure distribution of the AA section (with the cooling hole inlet pressure of 0.25 MPa).

**Figure 10.**Schematic diagram on the distribution of Mach number in the center longitudinal section (with the P*_c of 0.25 MPa).

**Figure 16.**Pressure contour map of the central longitudinal section through the hole (with Ma_g = 1.8).

Total Temperature of Main Flow, T _{t}_g | Mach Number of Main Flow, Ma_g | Total Temperature of Film Jet, T _{t}_c | Total Pressure of Film Jet, P _{t}_c | Static Pressure at Main Flow Outlet, P _{b} |
---|---|---|---|---|

1900 K | 1.2–2.5 | 500 K | 0.25 MPa | 101,325 Pa |

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**MDPI and ACS Style**

Zhang, B.; Chen, Y.-X.; Wang, Z.-g.; Li, J.-Q.; Ji, H.-h.
Influence of Mach Number of Main Flow on Film Cooling Characteristics under Supersonic Condition. *Symmetry* **2021**, *13*, 127.
https://doi.org/10.3390/sym13010127

**AMA Style**

Zhang B, Chen Y-X, Wang Z-g, Li J-Q, Ji H-h.
Influence of Mach Number of Main Flow on Film Cooling Characteristics under Supersonic Condition. *Symmetry*. 2021; 13(1):127.
https://doi.org/10.3390/sym13010127

**Chicago/Turabian Style**

Zhang, Bo, Yuan-Xiang Chen, Zhi-guo Wang, Ji-Quan Li, and Hong-hu Ji.
2021. "Influence of Mach Number of Main Flow on Film Cooling Characteristics under Supersonic Condition" *Symmetry* 13, no. 1: 127.
https://doi.org/10.3390/sym13010127