Data Driven Turbulence Modeling for Magnetohydrodynamic Flows

Abstract

The motion of liquid metals is described by the equations of magnetohydrodynamics (MHD), that com bine the Maxwell equations and the Navier-Stokes equations. In these type of flows, the magnetic field interacting with the conductive metal induces large pressure losses and unconventional turbulence states such as quasi 2D turbulence, turbulence suppression and flow anisotropy. Currently this turbu lence behaviour can be captured in higher fidelity Computational Fluid Dynamics (CFD) simulations such as Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), but the high computa tional cost of these simulations make them impractical for industrial applications compared to Reynolds AveragedNavier-Stokes(RANS).However, theeddyviscositymodelswhicharetypicallyusedinRANS are not able to capture anisotropic turbulence states occurring in MHD flows, which results in sig nificant discrepancies in the mean velocity field. Hence, this work presents a data-driven approach to model MHD turbulence. To achieve this time-averaged LES data of annular pipe flow cases at differ ent Hartmann numbers are used to derive corrections for the k − ω SST model. Two correction fields are obtained through a frozen RANS simulation in which the mean LES fields are inserted into the RANS equations. The Reynolds stress anisotropy term is approximated with a modified Tensor Basis Neural Network (TBNN). Moreover, for modelling the turbulence production correction a Scalar Basis Neural Network (SBNN) is proposed and compared to a Sparse Algebraic Regression using the SpaRTA approach. The resulting data driven models are able to reduce the error of the Reynolds stress anisotropy values and the mean flow velocity fields, and can generalise to annular flow cases with different Hartmann numbers from those of the training cases.