Fluid Flow of a Liquid Metal in a Cylinder Driven by a Rotating Magnetic Field

Abstract

An electric conducting fluid flow in a cylinder driven by a rotating magnetic field is numerically studied. A time-averaged Lorentz force term is derived on the condition that the skin effect can be neglected and then it is incorporated into the Navier-Stokes equation as a body force term. The axisymmetric velocity profile of basic flow for an infinitely long cylinder case depends only on the Hartmann number. A set of steady disturbance equations was successfully solved using the HSMAC method. For various cases of the basic flow i.e. the Hartmann numbers, the corresponding critical rotational Reynolds numbers for the onset of secondary flow were obtained instead of using the conventional magnetic Taylor number. The numerical results reveal that the critical Reynolds number takes its minimum at a certain Hartmann number. On the other hand, for a case of finite length cylinder, the no-slip condition at the flat walls generates the Bödewadt-like boundary layers and consequently the flow structure is changed significantly.

Stability of an Axisymmetric Liquid Metal Flow Driven by a Multi-Pole Rotating Magnetic Field

“…In this subsection, we discuss the influence of the electric potential that appeared in Ohm's law, which governs the electric current density. Table 2 shows the comparison of the critical Reynolds number for various Hartmann numbers with and without taking the electric potential into account at m = 1 [36]. When the Hartmann number is very small, since the term of the time-derivative of the vector potential is far superior to that of the induced electromotive force, the divergence-free condition for the electrical current density is automatically satisfied due to the employment of the Coulomb gauge.…”