A comparison between RANS turbulence models and DNS of turbulent MHD channel flows

Understanding and modeling the turbulent flow of electrically conducting fluids in channels is central to a variety of liquid metal applications, including the design of blankets for fusion reactors and the control of melt-pools in additive manufacturing. In addition to being a fundamental configuration for studying wall-bounded turbulence, channel flow is a widely used benchmark for the development of Reynolds-Averaged Navier-Stokes (RANS) models. Including magnetohydrodynamic (MHD) effects in such models is critical for many engineering and astrophysical applications. Direct numerical simulations (DNS) support the development of RANS models as well as providing detailed insights into the effect of boundary layers on MHD turbulence. In this study, we present DNS of fully turbulent channel flow of an electrically conducting fluid under a transverse magnetic field performed with the open-source spectral element code Nek5000. Our simulations target a friction Reynolds number up to Re_τ =2000 at low magnetic Reynolds numbers (Re_M < 1), consistent with liquid metal applications for which the magnetic Prandtl number is of the order of 10^-5. We analyze the mean flow and turbulence statistics in the resulting Hartmann flows. We examine differences with MHD turbulence in periodic boxes and neutral fluid channel flow. We also provide detailed comparisons between our DNS results with MHD and non-MHD RANS turbulence models.