Data-driven turbulence modelling for magnetohydrodynamic flows in annular pipes

TL;DR

This paper introduces a data-driven turbulence modeling approach for magnetohydrodynamic flows in annular pipes, improving accuracy over standard models by incorporating LES data and MHD-specific features.

Contribution

It develops a novel correction method using neural networks and tensor basis functions to enhance RANS models for MHD turbulence, accounting for magnetic effects.

Findings

Reduces errors in mean flow predictions.

Generalizes to different Hartmann numbers.

Incorporates MHD effects while maintaining invariance.

Abstract

We present a data-driven approach to Reynolds-averaged Navier-Stokes turbulence closure modelling in magnetohydrodynamic (MHD) flows. In these flows the magnetic field interacting with the conductive fluid induces unconventional turbulence states such as quasi two-dimensional (2D) turbulence, and turbulence suppression, which are poorly represented by standard Boussinesq models. Our data-driven approach uses time-averaged Large Eddy Simulation (LES) data of annular pipe flows, at different Hartmann numbers, to derive corrections for the $k$-$\omega$ SST model. Correction fields are obtained by injecting time averaged LES fields into the MHD RANS equations, and examining the remaining residuals. The correction to the Reynolds-stress anisotropy is approximated with a modified Tensor Basis Neural Network (TBNN). We extend the generalised eddy hypothesis with a traceless antisymmetric tensor representation of the Lorentz force to obtain MHD flow features, thus keeping Galilean and frame invariance while including MHD effects in the turbulence model. The resulting data-driven models are shown to reduce errors in the mean flow, and to generalise to annular flow cases with different Hartmann numbers from those of the training cases.