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. As a critical component of turbulence modeling, the constitutive relationship between the Reynolds stress tensor and the mean flow quantities, modeled using machine learning methods, faces a pressing challenge: the lack of generalizability. To address this issue, we propose a novel tensor basis normalization technique to improve machine learning turbulence models, grounded in the general effective-viscosity hypothesis. In this study, we utilize direct numerical simulation (DNS) 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 NACA0012 airfoil, and 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.