# Efficient Scale-Resolving Simulations of Open Cavity Flows for Straight and Sideslip Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Cavity Model and Mesh

#### 2.1. Description of the Cavity

#### 2.2. Mesh

## 3. Simulation Methodologies

#### 3.1. Hybrid RANS-LES Approach

#### 3.2. Scale-Adaptive Approach

#### 3.3. Wall Treatment

#### 3.4. Artificial Forcing

#### 3.5. Computational Time Requirements

## 4. Results and Discussion

#### 4.1. Prediction of Acoustic Spectrum

#### 4.2. Performance of the Different SAS Variants

#### 4.2.1. Prediction of SPL

#### 4.2.2. Prediction of RMS Pressure

#### 4.2.3. Prediction of the Turbulent Flow Field

#### 4.2.4. Prediction of von Karman Length Scale ${L}_{vK}$ and Boundary Layer Thicknesses

#### 4.3. Impact of Asymmetric Flow Conditions

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Weapon bay model with the position of probes [22].

**Figure 4.**${y}^{+}$ distance over the cavity walls in the DES-WF simulation at an instant of time [22].

**Figure 5.**Forcing zone in SAS-F simulation [22].

**Figure 8.**Comparison of the RMS pressure predicted by the DES-WF, SAS-WR, SAS-WF and SAS-F simulations [22].

**Figure 9.**Resolved turbulent kinetic energy in the DES-WF, SAS-WR, SAS-WF and SAS-F simulations [22].

**Figure 10.**Instantaneous vorticity magnitude in the DES-WF, SAS-WR, SAS-WF and SAS-F simulations [22].

**Figure 11.**Distribution of the Reynolds stress $\overline{{u}^{\prime}{w}^{\prime}}$ in the DES-WF, SAS-WR, SAS-WF and SAS-F simulations [22].

**Figure 12.**Prediction of the von Karman Length scale, ${L}_{vK}$ in the SAS-WR, SAS-WF and SAS-F simulations [22].

Mesh A | Mesh B | Mesh C | |
---|---|---|---|

Number of mesh nodes | $20.2\times {10}^{6}$ | $5.1\times {10}^{6}$ | $1.4\times {10}^{6}$ |

${y}^{+}$ of the first element | $1.0$ | $1.0$ | $1.0$ |

Number of prism cells | 35 | 35 | 35 |

Resolution in Regions I and II | $3.12\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ | $6.24\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ | $12.48\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ |

DES-WF | SAS-WR | SAS-WF | SAS-F | |
---|---|---|---|---|

Number of mesh nodes | $12.5\times {10}^{6}$ | $5.1\times {10}^{6}$ | $2.5\times {10}^{6}$ | $2.5\times {10}^{6}$ |

${y}^{+}$ of the first element | >100.0 | <1.0 | >100.0 | >100.0 |

Number of prism cells | 10 | 35 | 10 | 10 |

Resolution in Region I | $3.23\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ | $6.24\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ | $6.24\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ | $6.24\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ |

Resolution in Region II | $1.28\times {10}^{-3}\phantom{\rule{3.33333pt}{0ex}}L$ | - | - | - |

DES-WF | SAS-WR | SAS-WF | SAS-F | |
---|---|---|---|---|

Number of outer iterations per time step | 200 | 200 | 200 | 200 |

Physical time step size | 1.5 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}$ | 7 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}$ | 7 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}$ | 7 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}$ |

Drop in density residual within one time step | ∼O (${10}^{2}$) | ∼O (${10}^{2}$) | ∼O (${10}^{2}$) | ∼O (${10}^{2}$) |

Comp. cost reduction relative to DES-WR | $50\%$ | $90\%$ | $95\%$ | $95\%$ |

**Table 4.**Prediction of Rossiter frequencies by modified Rossiter model (Equation (22)), experiment and the simulations.

Mode | Theory | Exp. | DES-WF | SAS-WR | SAS-WF | SAS-F |
---|---|---|---|---|---|---|

1 | 263 | 272 | 278 | 279 | 280 | 285 |

2 | 670 | 755 | 722 | 719 | 719 | 743 |

3 | 1076 | 1160 | 1167 | 1159 | 1159 | 1143 |

4 | 1484 | 1600 | 1611 | 1599 | 1519 | 1600 |

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**MDPI and ACS Style**

Rajkumar, K.; Tangermann, E.; Klein, M.
Efficient Scale-Resolving Simulations of Open Cavity Flows for Straight and Sideslip Conditions. *Fluids* **2023**, *8*, 227.
https://doi.org/10.3390/fluids8080227

**AMA Style**

Rajkumar K, Tangermann E, Klein M.
Efficient Scale-Resolving Simulations of Open Cavity Flows for Straight and Sideslip Conditions. *Fluids*. 2023; 8(8):227.
https://doi.org/10.3390/fluids8080227

**Chicago/Turabian Style**

Rajkumar, Karthick, Eike Tangermann, and Markus Klein.
2023. "Efficient Scale-Resolving Simulations of Open Cavity Flows for Straight and Sideslip Conditions" *Fluids* 8, no. 8: 227.
https://doi.org/10.3390/fluids8080227