Transition of an electromagnetically driven liquid metal flow from laminar to turbulent in a toroidal square duct

Abstract

The electromagnetically driven liquid metal flow in a toroidal duct of a square cross-section is studied numerically searching for the critical Reynolds (Re) and Hartmann (Ha) numbers where transition occurs. Results are reported for Ha up to 500, building a transition map of critical Reynolds and Hartmann numbers and showing two distinct regimes of transition signified by the destabilization of the secondary flow: The first, for Ha < 18, where the Lorentz force is balanced by fluid momentum diffusion and the second, for Ha >= 18, where it is balanced by fluid inertia. In both cases, the destabilization of the secondary flow occurs primarily near the concave sidewall. For Ha >= 18 the transition follows approximately the relationship Re = 16.803 Ha(1.43) for values of Re and Ha in the range 80 < Re/Ha < 224. Copyright (C) EPLA, 2013