Electric arc behavior in a boundary layer

Abstract

The objective of this work is to understand how the size of an arc on the electrode of an magnetohydrodynamic (MHD) generator or accelerator depends on operating parameters such as boundary-layer shape and current density. Arc size has an important bearing on device lifetime and performance. A boundary layer in an MHD device is a region of exceedingly steep gradients including, in particular, the gradient of electrical conductivity. A theory relating arc size to the characteristics of these gradients is developed and compared with behavior observed in various MHD devices, most recently that in the Component Development and Integration Facility in Butte, Montana. Nomenclature A = sublayer thickness B = magnetic flux density, (T) Cf = friction coefficient C p = specific heat at constant P D -arc-column diameter E -electric field strength F c = contraction factor h = arc enthalpy-ambient enthalpy / = arc current j = current density A/cm 2 k = Boltzmann's constant k s -effective roughness height t = mixing length m = molecular weight n e = electron number density P = pressure Pr -Prandtl number R = universal gas constant Re x -Reynolds number R k = roughness Reynolds number r 0 = arc-column radius T = temperature u = velocity V = voltage, (V) y = distance from electrode wall y 0 -a distance related to roughness a = recombination coefficient /3 = Hall parameter d = velocity thickness c = ionization energy, turbulent diffusivity K = thermal conductivity /* = viscosity p = gas density, p a , in arc colomn a = electrical conductivity T = shear stress, recombination time Subscripts a = arc column = core flow or arc-column region = edge of arc column = region of uniform current flow = spreading region = top of arc column = wall = x component = y component

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“…Since the cause of the temperature increase is Joule heating in this case, current concentration at a certain spot results in a rather large heating locally. This concentration can be explained by electrothermal instability, [21][22][23][24][25] well recognized in plasma physics, schematically illustrated in Fig. 3.…”