Formulation and Assessment of a Cross-Plane Electrical Model for Magnetohydrodynamic Channels

Abstract

A model for calculating cross-plane current and electric field distributions in MHD generator channels is formulated and numerically solved. The chief advantage of this model is that its solution can be implemented on the IBM 3033 digital computer in less than 1 CPU second and thus the model can be conveniently coupled to a full three-dimensional gasdynamics analysis. The model is equally valid for Faraday, diagonal-insulating-sidewall, and diagonal-conducting-sidewall channels. Accuracy of the model is calibrated by comparing its predictions with the results of three-dimensional finite-segmentation analyses. The model is found to perform best for channels with low wall temperatures and low electrode pitch-to-height ratios and when the boundary layers are thick. A discussion is given of the roles of the nonuniformity in normal current density, as predicted by the model, leading to velocity overshoots in the boundary layers, and of the transverse nonuniformity in Hall current density, generating secondary flows.