Viscous liquid metal flow near a corner induced by a distributed direct current

Ch. Stomp - J.-P. Brancher

L.E.M.T.A., 2, Avenue de la Foret de Haye, P.B. 160, 54504 Vandoeuvre Cedex, France

Abstract
We consider a steady, viscous, liquid metal flow near a formed by two rigid walls corner of an angle a varying from 0° to 180°. The interaction between a distributed direct current (DC) and its magnetic field gives rise to a vortical flow near the edge. Partial self-similar solutions superimposed on Moffatt eddies are presented in the linear case. It is shown that for a greater than a certain critical angle, the flow pattern corresponding to the partial solution includes a separating zero-value streamline. The whole flow near the intersection depends on the ratio of a real-valued exponent and a real part of the complex-valued exponent of the stream function. For example, if the real part of the first complex-valued exponent is less than the smallest real exponent, Moffatt vortices are preponderant near the origin. For greater radii, eddies vanish and electromagnetic forces govern the flow. For two values of a, the partial solution diverges everywhere in the fluid domain. We can remove the singularity by adapting an arbitrary constant of the homogeneous solution. If the curl of electromagnetic forces is considered to be confined in a domain of finite radius, the exact analytic solution can be found using Mellin-Fourier integral transform. Then, the separating zero-value streamline doesn t appear in any case. The values of corner angle, for which the solution diverges, correspond to a double real pole in the residue calculus. Table 1, Figs 9, Ref. 8.