Analysis of the oscillatory liquid metal flow in an alternate MHD generator

Abstract

The zero-mean oscillatory flow of a liquid metal in an alternate magnetohydrodynamic electric generator is explored analytically. The flow, confined in a two-dimensional insulating wall duct under a transverse magnetic field, is driven by an externally imposed oscillatory pressure gradient. The flow behaviour is analyzed in two different regions. First, asymptotic solutions for low and high oscillating frequencies in the uniform magnetic field region far from the magnet edges are used to explore the phase lag produced by the Lorentz force between the velocity and the axial pressure gradient. In addition, the entrance flow region where the oscillatory fluid motion interacts with the non-uniform magnetic field is studied. A perturbation analysis of the boundary layer flow in this region reveals that non-linear effects lead to the appearance of steady streaming vortices superimposed on the harmonic flow. The influence of these vortices on the performance of the generator is analyzed.