Enhancing generalizability of machine learning general effective-viscosity turbulence model via tensor basis normalization

With the rapid advancement of machine learning techniques, the development and study of machine learning turbulence models have become increasingly prevalent. The constitutive relationship between the Reynolds stress tensor and the mean flow quantities is a critical part of turbulence modeling. When modeled with machine learning methods, however, it faces a significant challenge: the lack of generalizability. To address this issue, we propose a novel tensor basis normalization technique to improve the generalizability of machine learning turbulence models, grounded in the general effective-viscosity hypothesis. In this study, we utilize direct numerical simulation results of periodic hill flows as training data to develop a symbolic regression-based turbulence model based on the general effective-viscosity hypothesis. Furthermore, we construct a systematic validation dataset to evaluate the generalizability of our symbolic regression-based turbulence model. This validation set includes periodic hills with different aspect ratios from the training dataset, zero pressure gradient flat plate flows, three-dimensional incompressible flows over a National Advisory Committee for Aeronautics 0012 airfoil, T106 turbine cascade compressible flows, and National Aeronautics and Space Administration Rotor 37 transonic axial compressor rotor flows. These validation cases exhibit significant flow characteristics and geometrical variations, progressively increasing their differences from the training dataset. Such a diverse validation set is a robust benchmark to assess the generalizability of the proposed turbulence model. Finally, we demonstrate that our symbolic regression-based turbulence model performs effectively across validation cases, encompassing various separation features, geometries, and Reynolds numbers.