Axisymmetric liquid-metal pipe flow through a non-uniform magnetic field containing a neutral point

Axisymmetric liquid-metal pipe flow passes through a quadrupole magnetic field that is generated by a pair of 'oppositely sensed' d.c. current coils. As a result of this arrangement, the flow experiences a degree of braking, mostly in the vicinity of the magnetic neutral point, owing to the effect of Lorentz forces acting upon the liquid-metal. Usefully, the system represents a practical and novel electromagnetic (e.m.) valve capable of regulating the flow of molten metal emanating from a tun-dish, for example. Linear theory predicts the development of a counter-intuitive unidirectional 'slug-like' profile throughout the liquid-metal pipe flow at large values of the Hartmann number, M, in the presence of an idealized axisymmetric neutral point that extends to infinity. We confirm that this behaviour is also apparent, but over a narrow region spanning the neutral point, in the case of a more realistic liquid-metal pipe flow acted upon by a pair of oppositely sensed d.c. current coils. The axial pressure gradient along the wall of this flow manifests a sharp peak at large M centred on the neutral point that is generated by the steep gradients in the slug profile there. In fact, the pressure drop developed across this region is approximately equal to the net braking effect of the e.m. valve. © 2007 Cambridge University Press.