The prediction of inter-electrode breakdown in magnetohydrodynamic generators

Abstract

Introduction: In this paper, a method of calculation of inter-electrode electrical breakdown phenomena in magnetohydrodynamic generators is presented. Interelectrode breakdown is observed to occur in experimental MHD generators with channel pressures near atmospheric whenever the Hall voltage between adjacent electrode segments exceeds a critical value which varies between 30 and 100 volts. When breakdown occurs, the local Hall voltage across the segments decreases suddenly and a large axial current is believed to flow over the insulator segment. If the generator volume to surface area is large enough, the breakdown current can drive into the electrode wall under the action of the Lorentz force and cause physical destruction of the channel wall.

Since the breakdown development is an inherently unsteady electrical shorting occurring in general within a turbulent, compressible fluid mechanical boundary layer, the description of the flow will be framed in terms of the turbulent fluid equations with Lorentz forces present. The time scale for development of the breakdown arc for MHD generators operating under power generation conditions can be estimated to be of the order of 10-3 sec. The turbulent fluctuations at the Reynolds numbers of interest have time scales of the order of 10-6 sec. Thus, the fluid will be described in terms of mean velocity, pressure, temperature, etc., over the turbulent time scale, but these mean variables will be considered to be functions of time over the electrical breakdown time scale. The breakdown arc can in general be expected to be a three dimensional phenomenon. Experimental evidence bearing on this point in MHD generator channels is at this time still contradictory.

Examination of the electrode walls of combustion driven generators reveals definite spots along the magnetic field direction of the electrode at which arc damage occurs. In closed cycle generators, however, careful image converter diagnostic of the discharge structure in the magnetic field direction indicates that electrothermal arc streamers which are significantly nonuniform in the axial direction across the electrode are quite uniform in the magnetic field direction along the electrode and essentially layered or two dimensional structures. In the present study we shall treat the two dimensional breakdown arc within the context of a two dimensional boundary layer theory. Three dimensional models can follow the initial results of a two dimensional model if the two dimensional model proves inadequate in describing experimental observations. In Part II a formulation of the unsteady fluid equations for the electrode wall boundary layer is presented.

In Part III expressions for the turbulent transport terms are presented and discussed. In Part IV the electrical problem is formulated and the procedure for calculation of the instantaneous electric field and current distribution corresponding to the instantaneous distribution of velocity and electrical conductivity in the boundary layer region is presented. In Part V a computational procedure for the solution of the unsteady boundary layer equations with Lorentz forces is described.