Nonlinear eddy viscosity <italic>k-ω</italic> turbulence model for incompressible low <italic>Re</italic><sub>M</sub> magnetohydrodynamic flows

Abstract

By modelling the magnetic source term in transporting equation of turbulent kinetic energy in a term by term manner, a nonlinear-eddy-viscosity k- model suitable for arbitratry magnetic field orientation was proposed at low magnetohydrodynamic Reynolds number assumption. In the present model, Kenjeres-Hanjalic model and Song's nonlinear viscosity model were employed to close the velocity-electric field correlations and the turbulent normal stresses respectively. The relaminarization process was modeled by the low Reynolds number k-  model meanwhile. The model was then validated with DNS and experiment results. The relative error was below 5% for the velocity profile and 10% for the friction coefficient, proving the applicability of the present model for engineering applications.