## Abstract

The internal, low Mach number, turbulent flow-induced acoustic field of a cylindrical 90◦ pipe bend with a curvature radius 𝑅𝑚∕𝐷 = 1.02 is investigated using hybrid Computational Aero-Acoustics (CAA). Incompressible Large-Eddy Simulation (LES) is used to computationally describe the turbulent flow field at bulk Reynolds numbers 𝑅𝑒𝐵 = 5000, 12 000, 26 000 and 66 000. The incompressible LES predicts all salient flow features, like the separation from the inner wall of the bend followed by a turbulent recirculation zone, in good agreement with

literature. The internal flow-induced noise is predicted by Acoustic Propagation Simulations (APS) applying Lighthill’s Equation (LE), Ribner’s Dilatation Equation (RDE) and the Perturbed Convective Wave Equation (PCWE), provided with acoustic source terms obtained from the incompressible LES. The turbulent recirculation zone is the most active region for generating acoustic sources. Among the two constituent components of the PCWE source term, the local pressure time derivative term turned out as clearly dominant in this region, so that PCWE and RDE predicted similar acoustic fields. The sub-grid scale (SGS) model applied in LES notably

contributes only at high frequencies to the total LE source term, starting from 𝑓 = 2000 Hz for the lower Reynolds numbers and beyond for the higher. The mapping of source terms from the boundary layer resolving LES grid onto the typically coarser preferably uniform APS grid leads to lower high-frequency signal amplitudes for coarser APS mesh size in regions with small turbulent structures. The impact of this amplitude reduction on the predicted acoustics sound power levels was still very small, exhibiting relative differences less than 0.7% for the different APS meshes. Despite the LES-specific limitations expected from the decrease of directly resolved content for higher Reynolds numbers, the use of increasingly underresolved source terms did not significantly lower the accuracy of finally predicted acoustics. The comparison of the acoustic results against data from dedicated measurements generally showed very good agreement for all Reynolds numbers.

literature. The internal flow-induced noise is predicted by Acoustic Propagation Simulations (APS) applying Lighthill’s Equation (LE), Ribner’s Dilatation Equation (RDE) and the Perturbed Convective Wave Equation (PCWE), provided with acoustic source terms obtained from the incompressible LES. The turbulent recirculation zone is the most active region for generating acoustic sources. Among the two constituent components of the PCWE source term, the local pressure time derivative term turned out as clearly dominant in this region, so that PCWE and RDE predicted similar acoustic fields. The sub-grid scale (SGS) model applied in LES notably

contributes only at high frequencies to the total LE source term, starting from 𝑓 = 2000 Hz for the lower Reynolds numbers and beyond for the higher. The mapping of source terms from the boundary layer resolving LES grid onto the typically coarser preferably uniform APS grid leads to lower high-frequency signal amplitudes for coarser APS mesh size in regions with small turbulent structures. The impact of this amplitude reduction on the predicted acoustics sound power levels was still very small, exhibiting relative differences less than 0.7% for the different APS meshes. Despite the LES-specific limitations expected from the decrease of directly resolved content for higher Reynolds numbers, the use of increasingly underresolved source terms did not significantly lower the accuracy of finally predicted acoustics. The comparison of the acoustic results against data from dedicated measurements generally showed very good agreement for all Reynolds numbers.

Originalsprache | englisch |
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Aufsatznummer | 106323 |

Seitenumfang | 14 |

Fachzeitschrift | Computers & Fluids |

Jahrgang | 279 |

DOIs | |

Publikationsstatus | Veröffentlicht - 30 Juli 2024 |

## ASJC Scopus subject areas

- Allgemeiner Maschinenbau
- Allgemeine Computerwissenschaft

## Fields of Expertise

- Advanced Materials Science