# The Influence of External Flow Field on the Flow Separation of Overexpanded Single-Expansion Ramp Nozzle

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation Methods and Validation

_{t}) is 419.9 mm

^{2}, and the aspect ratio of the throat is 2.5. The area of the nozzle exit (A

_{exit}) is 1290.58 mm

^{2}, the expansion length is 92 mm, and the contraction length is 30 mm. This model was used to conduct a cold airflow wind tunnel experiment, and the details of the experimental scheme are provided in a previous study [29].

^{−4}. The viscous model is the renormalization group (RNG) k–ε model, which is a well-validated turbulence model for predicting the separation flow field of the nozzle [27,28,29,30]. The simulation model has the same conditions as the experiment, and the settings are listed in Table 1. Due to the complex flow structure formed by separation and reattachment in SERN, y

^{+}cannot be controlled in a small range. The y

^{+}value varied between 10 and 80 in the simulation, thus meeting the requirements of the turbulence model.

## 3. Results and Discussion

#### 3.1. Nozzle Design

_{in}* = P

_{exit}*, T

_{in}* = T

_{exit}*.

#### 3.2. Simplified Acceleration Process

#### 3.3. Effect of Acceleration

_{0}, as shown in Figure 14. According to the analysis of the results, RSS (ramp)–FSS transition occurred under the four cases, indicating that the external Mach number variation rate did not affect the principle of the separation flow field and had a negligible effect on the duration of the transition process. With an increase in the Mach number, the critical Mach number corresponding to the transition points also gradually increased, and the variation in peak thrust during the transition process similarly increased.

#### 3.4. Real Take-off Acceleration Process

## 4. Conclusions

- (1)
- The external flow Mach number had a significant effect on the overexpansion flow field of the RBCC nozzle. With an increase in the external Mach number, sequential transitions of RSS (ramp) to FSS and FSS to no-flow separation pattern occurred.
- (2)
- The transition principle of the flow separation patterns in the real ascending path was similar to the case with external flow varying linearly, but the Mach number corresponding to the transition points was considerably different. The variation rate of the external Mach number affected the nozzle performance during the transition process.
- (3)
- The higher the variation rate of the external flow Mach number, the more obvious the airflow accumulation effect of the external flow field, which caused an increase in the static pressure at the outlet and a decrease in the real nozzle pressure ratio, delaying the transition of flow separation patterns.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

SERN | Single-expansion ramp nozzle |

RBCC | Rocket-based combined cycle |

CFD | Computational fluid dynamics |

RSS | Restricted shock separation |

RSS (ramp) | Restricted shock separation with separation bubble forming on the ramp |

RSS (flap) | Restricted shock separation with separation bubble forming on the flap |

FSS | Free shock separation |

SWBLI | Shock wave/boundary layer interaction |

NPR | Nozzle pressure ratio |

UDF | User-defined functions |

A_{t} | Area of the nozzle throat |

A_{in} | Area of the nozzle inlet |

A_{exit} | Area of the nozzle exit |

P_{a} | Ambient pressure |

P* | Total pressure |

h_{t} | Height of the nozzle throat |

Ma_{∞} | Mach number of freestream |

Ma_{in} | Mach number of nozzle inlet |

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**Figure 1.**Flow separation patterns during SERN shutdown: (

**a**) shock wave structure in RSS (ramp) pattern; (

**b**) shock wave structure in RSS (flap) pattern.

**Figure 7.**The link between the design area ratio of SERN and the inlet Mach number under various flying situations.

**Figure 9.**Mach contours of the flow field under different NPR, Ma = 0: (

**a**) NPR = 4.9; (

**b**) NPR = 10.5; (

**c**) NPR = 20.1.

**Figure 10.**Mach contour of the flow field under different flight conditions: (

**a**) NPR = 4.9, Ma = 2.0; (

**b**) NPR = 10.5, Ma = 2.5; (

**c**) NPR = 20.1, Ma = 3.0.

**Figure 11.**The transition from RSS (ramp) to FSS during the acceleration process: (

**a**) t

_{0}, Ma = 1.86; (

**b**) t

_{0}+ 0.004 s, Ma = 1.864; (

**c**) t

_{0}+ 0.009 s, Ma = 1.869; (

**d**) t

_{0}+ 0.02 s, Ma = 1.88.

**Figure 13.**Variation in the nozzle thrust with Mach number for different increase rates of Mach number.

**Figure 14.**Variation in nozzle thrust with time for different increase rates of Mach number, after an adjustment.

**Figure 15.**Constant Mach number contour at Mach 1.8 with different increase rates of Mach number: (

**a**) 0.2/s; (

**b**) 0.5/s; (

**c**) 1/s; (

**d**) 2/s.

**Figure 16.**Constant pressure contour at Mach 1.8 with different increase rates of Mach number: (

**a**) 0.2/s; (

**b**) 0.5/s; (

**c**) 1/s; (

**d**) 2/s.

**Figure 17.**Relationship between the Mach number and the flight altitude with flight time in a direct ascending path.

**Figure 18.**Variation in the nozzle performance with Mach number in the direct ascending path: (

**a**) thrust; (

**b**) lift; (

**c**) moments.

**Figure 19.**Mach contour of the flow field in RSS (ramp) at different Mach numbers: (

**a**) Ma = 0.5; (

**b**) Ma = 1.0, (

**c**) Ma = 1.5; (

**d**) Ma = 2.0.

**Figure 20.**The transition from RSS (ramp) to FSS in the direct rising path: (

**a**) t

_{0}, Ma = 2.0606; (

**b**) t

_{0}+ 0.003 s, Ma = 2.0693; (

**c**) t

_{0}+ 0.008 s, Ma = 2.0840; (

**d**) t

_{0}+ 0.015 s, Ma = 2.1048.

**Figure 21.**Variation in the flow field during the transition from FSS to no-flow separation pattern: (

**a**) Ma = 2.2; (

**b**) Ma = 2.4; (

**c**) Ma = 2.6; (

**d**) Ma = 2.8.

Property | Setting |
---|---|

Materials | Ideal gas, compressible |

Dimensionality | 2D |

Discretization method | Second-order upwind |

Solution method | Density-based solver |

Solution formulation | Implicit |

Time dependence | Steady |

Turbulent model | k-epsilon RNG |

Near-wall treatment | Standard wall function |

Pressure—inlet | Total pressure = 124,008.5 Pa, temperature = 296.5 K |

Pressure—far-field | Ma = 0, static pressure = 35,422.69 Pa, temperature = 296.5 K |

Pressure—outlet | Total pressure = 35,422.69 Pa, temperature = 296.5 K |

Wall | Adiabatic |

Ma_{∞} | Altitude (km) | Ambient Static Pressure, P_{a} (Pa) | Combustor Total Pressure, P_{c}* (Pa) | NPR |
---|---|---|---|---|

0 | 0 | 101,325 | ||

2 | 8.3 | 34,061.1 | 166,899.4 | 4.9 |

2.5 | 11.3 | 21,781.0 | 228,700.5 | 10.5 |

3 | 13.6 | 15,084.1 | 303,190.4 | 20.1 |

4 | 17.3 | 8473.5 | 558,403.6 | 65.9 |

5 | 20.1 | 5414.4 | 904,746.2 | 167.1 |

6 | 24.4 | 2811.0 | 705,561.0 | 251 |

9 | 28.2 | 1580.5 | 1,134,799.0 | 718 |

10 | 31.1 | 1017.6 | 1,996,229 | 1961.7 |

12 | 33.5 | 710.4 | 3,368,361.6 | 4741.5 |

Design Parameters | Value |
---|---|

Total pressure of the inlet P_{D}* (Pa) | 888,732.02 |

Total temperature of the inlet T_{D}* (K) | 2000 |

Static pressure of the inlet P_{D} (Pa) | 115,250.77 |

Ambient pressure P_{a} (Pa) | 1580.53 |

Height of inlet h_{t} (mm) | 100 |

The ratio of specific heat γ | 1.33 |

Flight Mach Numbers | Thrust Coefficient |
---|---|

3 | 0.8011 |

4 | 0.9636 |

5 | 0.9784 |

6 | 0.9770 |

8 | 0.9747 |

9 | 0.9725 |

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## Share and Cite

**MDPI and ACS Style**

Yu, Y.; Mao, Y.; Yu, T.; Yang, Y.; Xu, S.; Liang, S.
The Influence of External Flow Field on the Flow Separation of Overexpanded Single-Expansion Ramp Nozzle. *Aerospace* **2023**, *10*, 958.
https://doi.org/10.3390/aerospace10110958

**AMA Style**

Yu Y, Mao Y, Yu T, Yang Y, Xu S, Liang S.
The Influence of External Flow Field on the Flow Separation of Overexpanded Single-Expansion Ramp Nozzle. *Aerospace*. 2023; 10(11):958.
https://doi.org/10.3390/aerospace10110958

**Chicago/Turabian Style**

Yu, Yang, Yuepeng Mao, Tao Yu, Yalin Yang, Shulin Xu, and Sijia Liang.
2023. "The Influence of External Flow Field on the Flow Separation of Overexpanded Single-Expansion Ramp Nozzle" *Aerospace* 10, no. 11: 958.
https://doi.org/10.3390/aerospace10110958