A General Formulation of the Postulate for Minimum Volume of the MHD Generator Duct with Fixed Outer Boundary Values

The most important data for describing the influence of the MHD expansion group (consisting of nozzle, duct and diffuser) on the characteristic parameters of the overall cycle, in particular on the overall efficiency, are the thermodynamic-state quantities at the entrance of the nozzle and at the exit of the diffuser, ''the outer boundary values''. With these data unchanged, variation of the shape of the expansion line does not affect the overall performance of the process. Therefore the question arises which expansion shape is best from the point of view of an MHD generator, if the outer boundary values are fixed,or, in general, as a function of the outer boundary values. As the generator duct is the most complicated and, especially with the magnet, the most expensive element of the expansion group, minimizing of the duct volume is a reasonable criterion to be applied in the determination of the expansion shape. The paper shows how this criterion leads to a simple differential relationship between the electrical conductivity of the working gas, the gas velocity and the cross-section of the channel. If this relationship is used to complete the system of differential equations governing the energy conversion process, the resulting expansion shape is optimal with respect to minimum duct volume. Usually a somewhat arbitrary condition is taken to determine the expansion shape, e. g. the gas velocity or Mach number is postulated to be constant. There are some optimization procedures known in the literature which, however, refer to either the inlet or the outlet state of the duct, i.e. only one point of the expansion line falls on the optimum line. These computations are included as special cases in the more general treatment of the present paper. Finally an example is calculated for the MHD expansion under consideration of the optimization criterion. (author)