A two-dimensiona l electrical model of multi-electro de linear generators is presented. The electrode-wall boundary layers are included in the treatment, and an allowance can be made for the effects of electrode arcs and slag layers. The external electrical properties of the MHD channel flow are defined by a set of four resistance matrices. Analytical expressions for the matrix elements are given. The formulation allows a rapid, straight- forward determination of a generator's electrical characteristics and is suitable for analyzing the electrical nonuniformities often observed in slagging channels. HEN effects due to finite electrode segmentation in linear MHD generators were first studied, both analytical1'2 and numerical3'4 methods were applied to the problem. These early works analyzed two-dimensional geometry and assumed that the plasma conductivity, Hall parameter, and flow velocity across the magnetic field were constant. Later numerical calculations57 employed various simplifying techniques to deal with nonuniform properties. Recent work810 treats three-dimensional effects as well as near-wall and near-electrode phenomena. In a generating duct, the electrodes will be connected to external consolidation and control circuitry.11 To investigate the time-dependent interaction of such circuitry with the MHD channel, perhaps under fault conditions, numerical techniques using a spatial grid may be unsatisfactor y due to the large amount of computer time required. There is a need for a simple model which will allow the external electrical characteristics of a channel to be evaluated rapidly for an arbitrary distribution of current among the electrodes. In- vestigation of nonuniform current distributions is also necessary to provide an understanding of the Hall voltage nonuniformities which are frequently observed in slagging generators.11'12 In the present work, an analytical model of an MHD channel with nonuniform currents is derived. The model, which is two-dimension al, accounts for electrode segmentation and includes the effect of boundary layers on the electrode walls. Practical formulas which permit rapid determination of the electrical characteristics are given. In 1976, Solbes and Lowenstein13 made an analytical study of nonuniformiti es using the Fourier transform technique to calculate the potential difference across a channel produced by a 6-function current source on one channel wall with an identical sink on the opposite wall. In 1979, Koester and Nelson14 analyzed nonuniform generator operation by superposing potential distributions; they found good agreement with experimental data. Initially, the potential distributions were determined numerically; later Koester and Schlueter15 calculated potentials by integrating the 6-function solution of Solbes and Lowenstein over the electrode width. Kuo et al. 16 have also deduced the potential distribution produced by 5-function current sources, obtaining results which differ from those of Solbes and Lowenstein. The zero boundary-layer formulas given here were first presented in 1981 by Trung et al. 17 The effect of including variable fluid properties along the channel has been described by Simpson and Scott,18t and in 1982 the author191 reported preliminary results of a linear generator stability analysis employing the present model in conjunction with the z transform; these results are consistent with experimental observations of nonuniformiti es. In the limit of 5-function current sources and zero boundary-layer thickness, the formulation here agrees with that of Solbes and Lowenstein13 but not with Kuo et al. 16 The zero boundary-layer formulas also agree with the values Koester and Schlueter15 obtained by integration.20
Read full abstract