# Rapid noise prediction models for serrated leading and trailing edges

## TL;DR

This paper introduces simplified, efficient noise prediction models for serrated edges on flat plates, enabling rapid and accurate estimation of noise spectra crucial for optimizing designs in aeroacoustic applications.

## Contribution

The paper develops practical, easy-to-implement models that approximate complex Wiener-Hopf based noise predictions, significantly improving computational efficiency and usability.

## Key findings

- Models closely match original Wiener-Hopf predictions.
- Predictions agree well with experimental data for sawtooth serrations.
- Noise spectra can be computed within milliseconds on standard computers.

## Abstract

Leading- and trailing-edge serrations have been widely used to reduce the leading- and trailing-edge noise in applications such as contra-rotating fans and large wind turbines. Recent studies show that these two noise problems can be modelled analytically using the Wiener-Hopf method. However, the resulting models involve infinite-interval integrals that cannot be evaluated analytically, and consequently implementing them poses practical difficulty. This paper develops easily-implementable noise prediction models for flat plates with serrated leading and trailing edges, respectively. By exploiting the fact that high-order modes are cut-off and adjacent modes do not interfere in the far field except at sufficiently high frequencies, an infinite-interval integral involving two infinite sums is approximated by a single straightforward sum. Numerical comparison shows that the resulting models serve as excellent approximations to the original models. Good agreement is also achieved when the leading-edge model predictions are compared with experimental results for sawtooth serrations of various root-to-tip amplitudes. Importantly, the models developed in this paper can be evaluated robustly in a very efficient manner. For example, a typical far-field noise spectrum can be calculated within milliseconds for both the trailing- and leading-edge noise models on a standard desktop computer. Due to their efficiency and ease of numerical implementation, these models are expected to be of particular importance in applications where a numerical optimization is likely to be needed.