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A Parametric Study on the LES Numerical Setup to Investigate Fan/OGV Broadband Noise^{ †}

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^{‡}

## Abstract

**:**

## 1. Introduction

## 2. Analytical Models

## 3. Trailing Edge Noise (TEN)

- [trip method]: Geom or Source (defined in Section 3.2);
- [trip position]: position of the trip as a percentage of the chord from the leading edge;
- [trip height]: height of the trip relative the boundary layer displacement thickness ${\delta}^{*}$;
- [cell type]: near-wall cell type, P for prisms and T for tetrahedra;
- [y${}^{+}$]: value of ${y}^{+}$ at the wall. A value around 1 is used for wall resolved (WR) simulations, while larger values of ${y}^{+}$ indicate wall modeled (WM) simulations. In the latter cases, a simple wall model is used, with a dimensionless wall velocity ${u}^{+}=\frac{1}{\kappa}ln\left(A{y}^{+}\right)$ for ${y}^{+}>11.45$ with $\kappa =0.41$ and $A=9.2$;
- [wake size]: cell size in the wake relative to the Taylor scale;
- [spanwise BC]: PERIO for periodic (by default), SYM for symmetry;
- [spanwise extension]: Sp0.1c and Sp1c for 10% and 100% of the chord, respectively.

#### 3.1. Influence of the Mesh Type and Refinement at the Wall

#### 3.2. Influence of the Tripping Methodology

#### 3.3. Influence of the Trip Height

#### 3.4. Influence of the Spanwise Extent and Boundary Condition

#### 3.5. Influence of the Mesh in the Wake Region

#### 3.6. Acoustic Far-Field Predictions

## 4. Turbulence Interaction Noise (TIN)

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LES | Large eddy simulation |

DNS | Direct numerical simulation |

TEN | Trailing edge noise |

TIN | Turbulence interaction noise |

OGV | Outlet guide vanes |

UHBR | Ultra high bypass ratio |

PSD | Power spectral density |

WPS | Wall pressure spectra |

PWL | Power level |

RMS | Root mean square |

NSCBC | Navier-Stokes characteristic boundary conditions |

TTGC | Two Steps Taylor Galerkin |

WM | Wall-modeled |

WR | Wall-resolved |

## References

- Gonzalez-Martino, I.; Casalino, D. Noise from a Rotor Ingesting a Turbulent Boundary Layer Using Very-Large Eddy Simulations. In Proceedings of the 25th AIAA/CEAS Aeroacoustics Conference, Delft, The Netherlands, 20–23 May 2019; p. 2585. [Google Scholar]
- Winkler, J.; Wu, H.; Moreau, S.; Carolus, T.; Sandberg, R.D. Trailing-edge broadband noise prediction of an airfoil with boundary-layer tripping. J. Sound Vib.
**2020**, 482, 115450. [Google Scholar] [CrossRef] - Lewis, D.; Moreau, S.; Jacob, M.C. Broadband Noise Predictions on the ACAT1 Fan Stage Using Large Eddy Simulations and Analytical Models. In Proceedings of the AIAA AVIATION 2020 FORUM, Virtual, 15–19 June 2020; p. 2519. [Google Scholar]
- Casalino, D.; Hazir, A.; Mann, A. Turbofan broadband noise prediction using the Lattice Boltzmann Method. AIAA J.
**2018**, 56, 609–628. [Google Scholar] [CrossRef] - Amiet, R.K. Noise due to turbulent flow past a trailing edge. J. Sound Vib.
**1976**, 47, 387–393. [Google Scholar] [CrossRef] - Roger, M.; Moreau, S. Back-scattering correction and further extensions of Amiet’s trailing-edge noise model. Part 1: Theory. J. Sound Vib.
**2005**, 286, 477–506. [Google Scholar] [CrossRef] - Amiet, R.K. Acoustic radiation from an airfoil in a turbulent stream. J. Sound Vib.
**1975**, 41, 407–420. [Google Scholar] [CrossRef] - Poinsot, T.J.; Lele, S. Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys.
**1992**, 101, 104–129. [Google Scholar] [CrossRef] - Schonfeld, T.; Rudgyard, M. Steady and unsteady flow simulations using the hybrid flow solver AVBP. AIAA J.
**1999**, 37, 1378–1385. [Google Scholar] [CrossRef] - Nicoud, F.; Toda, H.B.; Cabrit, O.; Bose, S.; Lee, J. Using singular values to build a subgrid-scale model for large eddy simulations. Phys. Fluids
**2011**, 23, 085106. [Google Scholar] [CrossRef][Green Version] - Colin, O.; Rudgyard, M. Development of high-order Taylor–Galerkin schemes for LES. J. Comput. Phys.
**2000**, 162, 338–371. [Google Scholar] [CrossRef] - Van Driest, E.R. Turbulent boundary layer in compressible fluids. J. Aeronaut. Sci.
**1951**, 18, 145–160. [Google Scholar] [CrossRef] - Goody, M. Empirical spectral model of surface pressure fluctuations. AIAA J.
**2004**, 42, 1788–1794. [Google Scholar] [CrossRef] - Boudet, J.; Monier, J.F.; Gao, F. Implementation of a roughness element to trip transition in large-eddy simulation. J. Therm. Sci.
**2015**, 24, 30–36. [Google Scholar] [CrossRef] - Jiménez, J.; Hoyas, S.; Simens, M.P.; Mizuno, Y. Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech.
**2010**, 657, 335. [Google Scholar] [CrossRef][Green Version] - Corcos, G. The structure of the turbulent pressure field in boundary-layer flows. J. Fluid Mech.
**1964**, 18, 353–378. [Google Scholar] [CrossRef] - Guedel, A.; Robitu, M.; Descharmes, N.; Amor, D.; Guillard, J.R. Prediction of the blade trailing-edge noise of an axial flow fan. In Proceedings of the Turbo Expo: Power for Land, Sea, and Air, Vancouver, BC, Canada, 6–10 June 2011; Volume 54648, pp. 355–365. [Google Scholar]
- Efimtsov, B.M. Characteristics of the field of turbulent wall pressure fluctuations at large Reynolds numbers. Sov. Phys. Acoust.
**1982**, 28, 289–292. [Google Scholar] - Salze, É.; Bailly, C.; Marsden, O.; Jondeau, E.; Juvé, D. An experimental characterisation of wall pressure wavevector-frequency spectra in the presence of pressure gradients. In Proceedings of the 20th AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, USA, 16–20 June 2014; p. 2909. [Google Scholar]
- Ramaprian, B.; Patel, V.; Sastry, M. The symmetric turbulent wake of a flat plate. AIAA J.
**1982**, 20, 1228–1235. [Google Scholar] [CrossRef] - Smirnov, A.; Shi, S.; Celik, I. Random flow generation technique for large eddy simulations and particle-dynamics modeling. J. Fluids Eng.
**2001**, 123, 359–371. [Google Scholar] [CrossRef] - Passot, T.; Pouquet, A. Numerical simulation of compressible homogeneous flows in the turbulent regime. J. Fluid Mech.
**1987**, 181, 441–466. [Google Scholar] [CrossRef]

**Figure 2.**Mean and RMS velocities as a function of ${y}^{+}$ for different LES cases using different near-wall mesh type and refinements (

**left**), and tripping methods (

**right**).

**Figure 3.**Wall pressure spectra (WPS) in the vicinity of the plate trailing edge (at 98% of the chord from the leading edge), for (

**left**) GeomX10H4-P01W30 simulation, (

**center**) GeomX10H4-P25W30 simulation, and (

**right**) GeomX10H4-T25W30 simulation.

**Figure 4.**Iso-surfaces of Q-criterion ($Q{C}^{2}/{U}^{2}=1000$), colored by the velocity magnitude, for (

**a**) GeomX10H1-P25W30 simulation and (

**b**) GeomX10H4-P25W30 simulation.

**Figure 5.**Comparison of the mean velocity profiles (

**left**) and WPS in the vicinity of the trailing edge (

**right**) between LES simulations using different trip heights.

**Figure 6.**Spanwise correlation length, ${l}_{z}$, for different spanwise boundary conditions (

**left**), and different spanwise extents (

**right**), in comparison with empirical models.

**Figure 7.**Comparison of the wake characteristics with empirical models in the near wake region (

**left**) and the intermediate wake region ((

**right**), for the computation GeomX10H4-P25W30, at different streamwise positions $x/\theta $).

**Figure 8.**Asymptotic evolution of the wake’s parameters, for the three mesh refinements in the wake region, and comparison with the corresponding analytical solution.

**Figure 9.**Direct prediction of the far-field PSD of pressure fluctuations from LES, in comparison to Amiet’s theory (various correlation laws), for an observer at ${90}^{\circ}$ and a distance of $8c$ from the plate.

**Figure 10.**Comparison of the power spectral level PWL for the different meshes at a distance of $8c$ (

**left**) and the pressure PSD ${90}^{\circ}$ from the plate’s leading edge at a distance of $8c$ for MESH4 (

**right**) with the analytical solution of Amiet’s theory.

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**MDPI and ACS Style**

Al-Am, J.; Clair, V.; Giauque, A.; Boudet, J.; Gea-Aguilera, F.
A Parametric Study on the LES Numerical Setup to Investigate Fan/OGV Broadband Noise. *Int. J. Turbomach. Propuls. Power* **2021**, *6*, 12.
https://doi.org/10.3390/ijtpp6020012

**AMA Style**

Al-Am J, Clair V, Giauque A, Boudet J, Gea-Aguilera F.
A Parametric Study on the LES Numerical Setup to Investigate Fan/OGV Broadband Noise. *International Journal of Turbomachinery, Propulsion and Power*. 2021; 6(2):12.
https://doi.org/10.3390/ijtpp6020012

**Chicago/Turabian Style**

Al-Am, Jean, Vincent Clair, Alexis Giauque, Jérôme Boudet, and Fernando Gea-Aguilera.
2021. "A Parametric Study on the LES Numerical Setup to Investigate Fan/OGV Broadband Noise" *International Journal of Turbomachinery, Propulsion and Power* 6, no. 2: 12.
https://doi.org/10.3390/ijtpp6020012