Effects of Boundary Layers upon Current Distribution and Internal Resistance in Segmented Magnetohydrodynamic Channels

Abstract

The effects of nonuniform properties of an equilibrium plasma in a segmented magnetohydrodynamic generator are investigated. The current distribution is distorted more for laminar flow than for turbulent flow. The shape of the current streamlines depends strongly on wall temperature, free stream Mach number, and boundary layer thickness. For fine segmentation ratio (s/h≈0.1), the current densities are uniform at distances 10% of the channel height away from the walls. Since the two-dimensional effects are confined to this narrow region, the changes of the current distribution outside this region are due to changes in flow properties. The current distribution on the electrode is most sensitive to the electrode temperature. For hot walls, current shorting between adjacent electrodes is important and is significantly affected by the boundary layer type and free stream Mach number. Boundary layer thickness is of minor importance. Shorting decreases as the wall temperature decreases and eventually disappears when the walls are sufficiently cold. The internal resistance of the channel is within 70% of its uniform property value for hot wall (2700°K) conditions for both laminar and turbulent flows. In the cold wall case (1500°K), the internal resistance increases about 3 times over its constant property value for turbulent flow but as high as 350 times for laminar flow. For cold-wall laminar flow, the internal resistance increases almost linearly with boundary layer thickness. The comparison with experiments is favorable.