The theoretical approach for viscous and end effects on an MHD pump for sodium circulation

Abstract

The analyses of the viscous and end effects on a magnetohydrodynamic (MHD) pump for the sodium coolant circulation in Fast Reactors was carried out based on the MHD laminar flow analysis and the electromagnetic field theory. A one-dimensional MHD analysis for the liquid metal flowing through an annular channel has been performed on the basis of a simplified model of equivalent current sheets instead of three-phase currents in the discrete primary windings. The calculations show that the developed pressure difference resulted from electromagnetic and viscous forces in the liquid metal is expressed in terms of the slip, and that the viscous loss effects are negligible compared with electromagnetic driving forces except in the low-slip region where the pumps operate with very high flow velocities comparable with the synchronous velocity of the electromagnetic fields, which is not applicable to the practical MHD pumps. A two-dimensional electromagnetic field analysis based on an equivalent current sheet model has found the vector potentials in closed form by means of the Fourier transform method. The resultant magnetic fields and driving forces exerted on the liquid metal reveal that the end effects due to finiteness of the pump length are formidable. Calculations of each magnetic force contribution indicate that the end effects are originated from the magnetic force caused by the induced current generated by the liquid metal movement across the magnetic field rather than the one produced by externally applied magnetic fields by three-phase winding currents. It is concluded that since the influences of the end effects in addition to viscous losses are extensive particularly in high-velocity operations of the MHD pumps, it is necessary to find ways to suppress them, such as proper selection of the pump parameters and compensation of the end effects.