Assisted Turbulence Modeling via Data Assimilation and Machine Learning for Turbomachinery Flows

Abstract This work presents the development and assessment of a hybrid framework coupling numerical simulation, experimental samples, data assimilation (DA) and machine learning (ML) to investigate the flow within an axial compressor stage. The methodology first implements a Multi-Fidelity Ensemble Kalman Filter (MFEnKF) which integrates experimental PIV data with a two-fidelity numerical simulation setup, combining steady-state RANS on a fixed grid with unsteady hybrid RANS/LES simulations on a moving grid. This data assimilation step successfully reduces discrepancies between experiments and CFD realizations. Besides, it provides additional high fidelity samples when compared with the available PIV data. This enriched database is used to train machine learning (ML) tools, with the objective to obtain black-box forcing terms to be included in the discretized form of the Navier-Stokes equations. These models are expected to preserve the accuracy of the DA results while not longer requiring the input of experimental data. The neural network architecture used here maps local physical features such as the velocity, the velocity gradients and the turbulent viscosity, to obtain the volume forcing terms. The analysis of the performance of such ML models shows that global accuracy is preserved but localized increased errors in specific regions of the compressor, such as close to the blade tips, can exceed those observed from the baseline RANS simulations. To resolve this issue, a Mixture of Experts (MoE) method is employed, which classifies and combines the trained ML tools for different flow regions. The discrepancy with experimental data of this method is systematically lower than the one observed for the baseline RANS solution and very similar to the one obtained with the MFEnKF.