LINEAR-STABILITY ANALYSIS FOR HIGH-VELOCITY BOUNDARY-LAYERS IN LIQUID-METAL MAGNETOHYDRODYNAMIC FLOWS

This paper presents a linear stability analysis for the fully developed liquid-metal flow in a constant-area rectangular duct with thin metal walls and with a strong, uniform, transverse magnetic field. For the steady flow, there are large velocities inside the boundary layers adjacent to the sides which are parallel to the applied magnetic field. There are two independent eigenvalue problems for the linear stability of the high-velocity side layers. The first problem involves disturbance vorticity which is perpendicular to the magnetic field, and these disturbances decay for all wavelengths and Reynolds numbers. The second problem involves disturbance vorticity which is parallel to the magnetic field, and the critical Reynolds number for these disturbances is 313. The critical disturbance involves a short axial scale and a high velocity in the direction perpendicular to the side. Both of these characteristics have positive implications for the heat transfer through this boundary layer. This heat transfer is important in liquid-lithium cooling systems or "self-cooled blankets" for magnetic confinement fusion reactors. In such blankets, a high-velocity boundary layer occurs adjacent to the "first wall", which faces the fusing plasma.