Effects of the Seeding Position on the Electrical Characteristics of a Linear Faraday-Type MHD Generator

This paper deals with a theoretical investigation of the influences of the seeding position on the electrical characteristics of a linear Faraday-type MHD generator. The generator has a pair of parallel plate electrodes of finite length. For mathematical simplicity, several assumptions are made. First, the problem is entirely two-dimensional. Second, the velocity profile is fully developed. Third, the magnetic field is applied uniformly all over the region of interest and perpendicular to the plane considered. Fourth, the seeding material is injected uniformly at a plane perpendicular to the flow direction, and thus the working fluid is electrically conductive only downstream of the seeding plane. The electrical conductivity of the seeded fluid and the electron and ion mean free times are assumed constant. Fifth, the induced magnetic field is negligibly small compared with the applied field. Using this mathematical model, the effects of the position of the seeding plane on the electrical characteristics of the generator are analysed by means of conformal mapping. Since the integration in the transformation formula cannot be carried out analytically for the general values of the Hall parameters of the working fluid, the analysis is made by using the derivative expression of the transformation function. The analysis includes variations in the generator aspect ratio and the seeding aspect ratio, as well as the Hall parameters of the working fluid. As the seeding aspect ratio increases, the internal resistance of the generator decreases and the current density on the electrodes rapidly increases near the entrance. But when the seeding aspect ratio becomes as great as 0.5, the electrical characteristics of the generator become quite similar to the limiting case where the seeding plane is infinitely upstream. The interferences of current distortion due to the end effects of both sides of the electrode are also analysed. When the generator aspect ratio becomes greater than 2, the current distortions on both sides of the electrode do not any longer interfere this being independent of seeding aspect ratio and Hall parameter. (author)