Flow stability of liquid metal flow under transverse magnetic field

Abstract

A stability analysis of a viscous incompressible liquid metal flow in an annular linear induction electromagnetic pump for sodium coolant circulation of LMR (Liquid Metal Reacters) is carried out when transverse magnetic fields permeate an electrically conducting sodium fluid across the narrow annular gap. Due to a negligible skin effect, the radial magnetic field is assumed to be constant over the narrow channel gap, and the steady state solution of an axial velocity is obtained as a function of radius r . Small perturbations for MHD fields in the form of f(r)ej(wt-k*r), where w is the angular frequency and k is the wave vector of perturbation, are considered and perturbed MHD equations are linearized. The solutions of t he perturbed equations are sought in the form of linear combination of independent orthogonal functions in the non-dimensional radial interval (0,1) and each orthogonal function is chosen to satisfy boundary conditions of adhesion at the solid walls of the channel. Under assumption that solutions of the equations are not oscillated rapidly according to radial coordinater, finite numbers of orthogonal polynomials are considered. As a result, simultaneous equations with coefficients of steady-state solutions are arranged and dispersion relations between angular frequency and wave number of perturbed state are sought. The imaginary part of the angular frequency (wi) is taken into consideration from the condition of the existence of nontrivial solution of the system , which yields the relation between critical Reynolds number (Recr) and Hartmann number (Ha) - In the present study, critical Reynolds number and Wave numbers are plotted on the Hartmann number for long wave perturbation, thus, it is shown that a magnetic field has a significant stabilizing effect on liquid metal flow.