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

TL;DR

This paper introduces a tensor basis normalization technique to enhance the generalizability of machine learning turbulence models, validated across diverse flow scenarios and geometries, addressing a key challenge in turbulence modeling.

Contribution

The study proposes a novel tensor basis normalization method based on the effective-viscosity hypothesis, improving the generalizability of symbolic regression-based turbulence models.

Findings

Model performs well across diverse flow cases

Tensor basis normalization improves model robustness

Validated on flows with different geometries and Reynolds numbers

Abstract

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.