Integral parameters of an MHD generator with a channel of circular cross section and nonuniform conductivity of the fluid stream

S. A. Medin - I. M. Rutkevich

Abstract
The integral electrical parameters of an MHD generator are analyzed for the case where the working medium is an isotropically conducting one but the conductivity is not uniform over the channel section. Certain general properties of the integral parameters are established for cylindrical MHD channels of arbitrary cross section. In the case of a uniform velocity profile and an arbitrary conductivity distribution over the cross section, the optimum values of the mean power density and of the electrical efficiency are expressed in terms of the equivalent conductivity σ_e and the maximum load factor k_m. The latter two parameters ate determined from the solution to special boundary-value problems associated with an elliptic equation with variable coefficients. A direct calculation of parameters σ_e and k_m is shown for the problem of determining the current distribution in a circular pipe with two end electrodes. The interelectrode region is regarded as ideally cut into segments with a constant tangential electric field applied to each. The nonuniform conductivity is simulated by a series of axially symmetric profiles. Methods of synthesizing the external electric circuit are also discussed here.