An Empirical Wall-Pressure Spectrum Model for Aeroacoustic Predictions Based on Symbolic Regression

TL;DR

This work tackles the lack of robust, fast wall-pressure spectrum models for aeroacoustic predictions by introducing a three-band empirical WPS derived from symbolic regression. The model uses boundary-layer inputs obtainable from quick tools like XFOIL and yields five equations (three band spectra plus two boundary frequencies) that are blended across frequency to predict the full spectrum. Trained on two airfoils across APG/FPG and a range of Reynolds numbers, the SR-based model demonstrates good extrapolation to unseen geometries and wind-turbine trailing-edge noise, outperforming several semi-empirical counterparts and aligning with field measurements to within about 1 dB in the relevant frequency range. The approach enables robust, design-friendly Amiet-based predictions with substantially broadened applicability for rotating blades and aeroacoustic optimization.

Abstract

Fast-turn around methods to predict airfoil trailing-edge noise are crucial for incorporating noise limitations into design optimization loops of several applications. Among these aeroacoustic predictive models, Amiet's theory offers the best balance between accuracy and simplicity. The accuracy of the model relies heavily on precise wall-pressure spectrum predictions, which are often based on single-equation formulations with adjustable parameters. These parameters are calibrated for particular airfoils and flow conditions and consequently tend to fail when applied outside their calibration range. This paper introduces a new wall-pressure spectrum empirical model designed to enhance the robustness and accuracy of current state-of-the-art predictions while widening the range of applicability of the model to different airfoils and flow conditions. The model is developed using AI-based symbolic regression via a genetic-algorithm-based approach, and applied to a dataset of wall-pressure fluctuations measured on NACA 0008 and NACA 63018 airfoils at multiple angles of attack and inflow velocities, covering turbulent boundary layers with both adverse and favorable pressure gradients. Validation against experimental data (outside the training dataset) demonstrates the robustness of the model compared to well-accepted semi-empirical models. Finally, the model is integrated with Amiet's theory to predict the aeroacoustic noise of a full-scale wind turbine, showing good agreement with experimental measurements.

Figures (9)

• Figure 1: Frequency bands of a generic WPS.
• Figure 2: Airfoils' coordinates.
• Figure 3: Schematic view of the experimental set-up.
• Figure 4: Sensitivity of the boundary layer parameters on the predicted wall-pressure spectra.
• Figure 5: Predicted and measured WPS of several cases from the training dataset.