Data-driven approach for modeling Reynolds stress tensor with invariance preservation

TL;DR

This paper develops machine learning models, FCNN and TBNN, to predict Reynolds stress tensors in turbulent flows while preserving Galilean invariance, improving accuracy over traditional RANS models.

Contribution

It introduces invariant-preserving neural network models for turbulence modeling, incorporating invariants of kinetic energy gradients for enhanced prediction accuracy.

Findings

Both models outperform traditional RANS in predicting anisotropy tensor.

Inclusion of turbulence kinetic energy gradient invariants improves model accuracy.

TBNN provides better velocity profiles due to integration of physical knowledge.

Abstract

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) [Ling et al. (2016)] are established. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier-Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user's defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.