Assessment of neural network augmented Reynolds averaged Navier Stokes turbulence model in extrapolation modes

This study proposes and validates a novel machine-learned (ML) augmented linear Reynolds averaged Navier Stokes (RANS) model, and the applicability of model assessed in both interpolation and extrapolation modes for periodic hill (Hill) test case, which involves complex flow regimes, such as attached boundary layer, shear-layer, and separation and reattachment. For this purpose, the ML model is trained using direct numerical simulation (DNS)/LES datasets for nine different cases with different flow separation and attachment regimes, and by including various percentages of the Hill DNS dataset during the training, ranging from no data (extrapolation mode) to all data (interpolation mode). The predictive capability of the ML model is then assessed using a priori and a posteriori tests. Tests reveal that the ML model's predictability improves significantly as the Hill dataset is partially added during training, e.g., with the addition of only 5% of the hill data increases correlation with DNS to 80%. Such models also provide better turbulent kinetic energy (TKE) and shear stress predictions than RANS in a posteriori tests. Overall, the ML model for TKE production is identified to be a reliable approach to enhance the predictive capability of RANS models. The study also performs (1) parametric investigation to evaluate the effect of training and neural network hyperparameters, and data scaling and clustering on the ML model accuracy to provide best practice guidelines for ML training; (2) feature importance analysis using SHapley Additive exPlanations (SHAP) function to evaluate the potential of such analysis in understanding turbulent flow physics; and (3) a priori tests to provide guidelines to determine the applicability of the ML model for a case for which reference DNS/LES datasets are not available.