The impact of non-frozen turbulence on the modelling of the noise from serrated trailing edges

TL;DR

This study reveals that accounting for non-frozen turbulence in boundary layer models significantly improves the accuracy of noise predictions from serrated trailing edges, addressing discrepancies with experimental data.

Contribution

It introduces a new turbulence model that relaxes the frozen turbulence assumption, incorporating decay of coherence to better predict trailing edge noise.

Findings

The coherence function decays along the streamwise direction.

The new model predicts lower noise reductions, aligning with experiments.

Overprediction in previous models is due to phase decoherence effects.

Abstract

Serrations are commonly employed to mitigate the turbulent boundary layer trailing-edge noise. However, significant discrepancies persist between model predictions and experimental observations. In this paper, we show that this results from the frozen turbulence assumption. A fully-developed turbulent boundary layer over a flat plate is first simulated using the large eddy simulation (LES) method, with the turbulence at the inlet generated using the digital filter method (DFM). The space-time correlations and spectral characteristics of wall pressure fluctuations are examined. The simulation results demonstrate that the coherence function decays in the streamwise direction, deviating from the constant value of unity assumed in the frozen turbulence assumption. By considering an exponential decay function, we relax the frozen turbulence assumption and develop a prediction model that accounts for the intrinsic non-frozen nature of turbulent boundary layers. To facilitate a direct comparison with frozen models, a correction coefficient is introduced to account for the influence of non-frozen turbulence. The comparison between the new and original models demonstrates that the new model predicts lower noise reductions, aligning more closely with the experimental observations. The physical mechanism underlying the overprediction of the noise model assuming frozen turbulence is discussed. The overprediction is due to the decoherence of the phase variation along the serrated trailing edge. Consequently, the ratio of the serration amplitude to the streamwise frequency-dependent correlation length is identified as a crucial parameter in determining the correct prediction of far-field noise.