Advancing Reynolds-Averaged Navier–Stokes Turbulence Models with Machine Learning and Data-Driven Methods

Reynolds-averaged Navier-Stokes (RANS) methods are fundamental to turbulent flow simulations in industrial and technical applications, offering computational efficiency by solving the equations for statistically averaged flow fields while incorporating the effects of unresolved turbulence through modeling the Reynolds stress tensor. This thesis investigates the application of machine learning and data-driven methods to advance RANS turbulence modeling, intending to derive accurate, robust and generalizable models and model augmentations. Two complementary studies address eddy viscosity models and Reynolds stress models individually. The first study applies the Field Inversion and Machine Learning (FIML) framework to augment the k-omega SST model, enhancing its ability to predict flow separation and reattachment in wall-bounded flows over smooth, curved surfaces. A correction term is introduced into the omega-equation to mitigate the underprediction of turbulence intensity in separated shear layers. Field inversion is used to determine the spatial distribution of the correction term for various flow configurations, and a neural network is trained on this data to represent the correction term based on local invariant flow features. RANS computations incorporating the neural network-augmented k-omega SST model achieved accurate predictions of separating flows while avoiding unnecessary corrections in undisturbed flow regions. An algebraic, closed-form correction term has been derived subsequently, showing accurate predictive performance, even for cases significantly different from those used in the development. The second study introduces a novel approach for modeling the pressure redistribution term for second-moment closure modeling in Reynolds stress models. This approach integrates a neural network into a conventional algebraic formulation, enabling the neural network outputs to represent the formulation's coefficients as a functional relationship based on local invariant flow features. The neural network demonstrated good predictive accuracy based on the data, with coefficients in free-stream conditions closely aligning with those from physically grounded models. However, applying the neural network in a near-wall baseline RSM did not achieve convergent solutions in RANS computations. An algebraic formulation resembling the neural network model has been developed, incorporating insights gained from RANS computation to ensure accuracy and robustness in channel and boundary layer flow cases when implemented within the baseline RSM.