# An Investigation of Scale-Resolving Turbulence Models for Supersonic Retropropulsion Flows

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## Abstract

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## 1. Introduction

**Figure 1.**Characteristic flow field for supersonic retropropulsion (taken from [8]).

## 2. Materials and Methods

#### 2.1. Governing Equations

#### 2.2. Numerical Implementation

## 3. Results

#### 3.1. Supersonic Mixing Layer

#### 3.2. Supersonic Retropropulsion Flows

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Stream velocity similarity profiles with comparison to experimental data [21].

**Figure 3.**Mixing layer y-velocity contours at the y-centerline. The RANS results (${f}_{k}=1.0$) do not exhibit unsteadiness and thus have a y-velocity of zero. The velocity is nondimensionalized by the upper plate velocity.

**Figure 9.**(

**Top**): Log of density gradient centerline contours for BPANS CC model. (

**Bottom**): Experimental schlieren [4].

**Figure 10.**SRP geometrical flow feature schematic for the single-nozzle configuration [4].

**Figure 11.**Q-criterion isosurfaces (15,000 per second) for the three angles of attack for BPANS CC $({f}_{k}=0.2)$ colored by pressure.

**Figure 13.**Overall Sound Pressure Level (OASPL) in decibels on the nose of the vehicle for the three angles of attack for BPANS CC $({f}_{k}=0.2)$.

**Figure 14.**Pressure spectra plot for BPANS CC $({f}_{k}=0.2)$ and SA-Catris DES compared to experimental data [23].

**Table 1.**SRP geometrical flow features compared to experimental data [4].

Case/Flow Feature | ${\mathit{L}}_{\mathit{s}}\left[\mathit{m}\right]$ | ${\mathit{R}}_{\mathit{s}}\left[\mathit{m}\right]$ | ${\mathit{L}}_{\mathit{J}}\left[\mathit{m}\right]$ | ${\mathit{R}}_{\mathit{J}}\left[\mathit{m}\right]$ |
---|---|---|---|---|

Experiment | 0.183 | 0.246 | 0.129 | 0.077 |

$\mathrm{BPANS}\text{}\mathrm{CC}\text{}({f}_{k}=0.2$) | 0.182 | 0.245 | 0.126 | 0.076 |

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**MDPI and ACS Style**

Nastac, G.; Frendi, A.
An Investigation of Scale-Resolving Turbulence Models for Supersonic Retropropulsion Flows. *Fluids* **2022**, *7*, 362.
https://doi.org/10.3390/fluids7120362

**AMA Style**

Nastac G, Frendi A.
An Investigation of Scale-Resolving Turbulence Models for Supersonic Retropropulsion Flows. *Fluids*. 2022; 7(12):362.
https://doi.org/10.3390/fluids7120362

**Chicago/Turabian Style**

Nastac, Gabriel, and Abdelkader Frendi.
2022. "An Investigation of Scale-Resolving Turbulence Models for Supersonic Retropropulsion Flows" *Fluids* 7, no. 12: 362.
https://doi.org/10.3390/fluids7120362