Modeling the effects of cathode wall nonuniformities in magnetohydrodynamic generators

Abstract

THE effect of cathode wall nonuniformities on the electrical performance of Faraday loaded generators is modeled analytically. An approximate three-dimensional model is formulated to determine the distributions of the electrical variables within the magnetohydrodynamic (MHD) channel in the presence of cathode nonuniformities. Nonuniformities in this model are treated as a coarser resegmentation of the cathode wall. In addition, a twodimensional electrical model is used to study the effects of cathode slag shorting on local electrical characteristics. These two models are described and calculated results using both models are compared with experimental data. Contents Cathode nonuniformities appear in MHD generators operating with slag-laden flows. These nonuniformities originate at the cathode wall when groups of electrodes are shorted by electrically polarized slag coatings.1 The resulting change in the effective segmentation of the cathode wall causes a few insulator gaps to sustain the total Hall voltage of the generator. In this paper, an approximate threedimensional electrical model of cathode nonuniformities is formulated. This electrical model has been incorporated into an MHD design and prediction computer code2 in order to assess the effects of these nonuniformities on the overall Faraday generator performance. The effects of cathode nonuniformities can be modeled by arbitrarily increasing the slag-layer electrical conductivity to account for slag polarization. However, the approach of this paper is to model the slag polarization-cathode nonuniformity effects as a change in the effective segmentation of the cathode wall. The approximate three-dimensional model is a finiteregion integral model formulated to study the effects of finite segmentation. In order to analyze finite segmentation effects via this finite element model, transverse profiles of the electric fields and currents are required.3 A two-dimensiona l electrodynamic model was used to perform a parametric study of these electrical profiles. Four parameters were investigated: the number of shorted cathodes, Hall parameter, size of the generator, and wall electrical conductivity. The objective of this two-dimensional calculation is to identify the transverse variation of the Hall electric field (Ex) distribution over the electrodes and the Faraday current density (Jy) distribution over th einterelectro de insulators. In addition, electrical boundary-layer lengths of these distributions are sought for use as a profile cutoff in the finite-region model. These electrical boundary-layer lengths (Ij and fj) are defined as the distances over which the Hall field or Faraday current density build up to the core values. In what follows each of the two models will be described briefly, and comparisons of the