Large eddy simulation of magnetohydrodynamic turbulent duct flows

Abstract

Turbulent duct flows in a uniform magnetic field are examined at low magnetic Reynolds number. Large-eddy simulation is conducted to reveal a sidewall effect on the skin friction. The duct has a square cross section and entirely insulated walls. The duct flow has two kinds of boundary layers: Hartmann layer and sidewall layer. The Hartmann layer is located on the wall perpendicular to the magnetic field, while the sidewall layer exists on the wall parallel to the magnetic field. As the magnetic field increases in the range of turbulent flows, the Hartmann layer becomes thin because of the “Hartmann flattening”—a flattening effect of the flow by the Lorentz force. The sidewall layer, however, becomes thick because of the turbulence suppression until the laminarization takes place. When the Reynolds number, Re, based on the hydraulic diameter, molecular viscosity, and bulk velocity is 5 300, the Hartmann and sidewall layers are laminarized at the same Hartmann number that is proportional to the magnetic field. When the Hartmann layer is laminarized at Re=29 000, the sidewall layer remains turbulence. This is due to a sidewall effect and is the condition that a local maximum takes place in the skin friction profile. When the sidewall layer is laminarized, the flow totally becomes laminar and the skin friction becomes minimum.