A Machine Learning FRPM Model for Broadband Noise Prediction

The Fast Random Particle Mesh (FRPM) method predicts broadband noise by generating synthetic turbulent velocity fields based on the turbulence kinetic energy and dissipation rate modeled by the Reynolds-Averaged Navier-Stokes (RANS) equations, thus circumventing the often exorbitant computational cost of scale-resolving simulations otherwise required to capture broadband noise sources. This paper presents the numerical framework of a data-enhanced FRPM model, the parameters of which are re-adjusted optimally and automatically to different geometries and flow conditions using field-inversion machine learning (FIML). To that end, an adjoint-based field-inversion (inverse optimization) process is developed to solve for the optimal model parameters by minimizing the discrepancy between the FRPM and high-fidelity reference solutions. A machine learning model is then trained to predict FRPM model parameters across different flow scenarios using the optimal model parameters, thereby enabling adaptive tuning of the stochastic turbulence generation for improved predictive accuracy. The field-inversion framework is employed to optimally adjust the FRPM model parameters for test cases including a backward-facing step and three different airfoils, showing excellent recovery of turbulence statistics compared to scale-resolving simulation. It was found that the non-smoothness features in the solution which arises from the field inversion process has a strong impact on the predictive accuracy of the machine learning model.