Analysis of optimum power extraction in a MHD generator with spatially varying electrical conductivity

Analytical expressions for optimum power extracted in an MHD generator, with constant channel width, uniform magnetic field and constant electrical conductivity have been proposed by Neuringer. In this paper, a numerical approach to study optimum power extraction in a MHD generator for an arbitrary geometry, magnetic field and electrically conductivity has been developed. This is accomplished by coupling a flow solver to an optimization code. Using this approach, Neuringer's analysis has been extended to study MHD channels with spatially varying electrical conductivity. An Euler flow solver coupled to an optimization code is used to predict fluid-dynamical variables, optimum power extracted and the voltage drop in the external load corresponding to optimum power extraction. Neuringer's results showed that in an MHD uniform channel with constant conductivity, most of the power delivered to the external load takes place near the extremities. Using our coupled flow/optimizer approach, we show that a more uniform axial power density distribution can be obtained with a spatially varying electrical conductivity distribution, thus making it a useful tool in design/analysis of practical MHD generators.