Liquid-metal flows near a magnetic neutral point

A liquid-metal flow impinging upon a region of non-uniform d.c. magnetic field experiences a certain amount of braking owing to the effect of Lorentz forces acting on the metal. Practical electromagnetic flow control devices utilize this property to alter the flow rate at which a liquid metal emerges from a receptacle. As a preliminary step to understanding the three-dimensional behaviour a numerical model is constructed which examines the two-dimensional flow of liquid metal passing through a quadrupole magnetic field generated by four line currents. In the vicinity of the local neutral point it is found that the nonlinear flow becomes unidirectional and linear. This linear behaviour agrees well with analytic solutions for flow through an infinitely extended neutral point. The generalized forms of the magnetic fields which permit unidirectional flows to exist are investigated in both axisymmetric and two-dimensional geometries. Examples of these fields include both the extended neutral point and the uniform transverse magnetic field present in Hartmann flow. The optimum conditions for braking the flow with a specified field are characterized by the pressure and volume data. These variables are derived from the model for a range of values of field strengths and Reynolds numbers and allow a comparison to be made with the asymptotic results obtained from the linear theory for two-dimensional flows. The numerical scheme may be adapted for any type of magnetic field and also permits extensions to the more realistic axisymmetric case.