Numerical simulation of liquid-metal MHD flows in rectangular ducts

Abstract

To design self-cooled liquid metal blankets for fusion reactors, one must know about the behaviour of MHD flows at high Hartmann numbers. In this work, finite difference codes are used to investigate the influence of Hartmann number M, interaction parameter N, wall conductance ratio c, and changing magnetic field, respectively, on the flow.As liquid-metal MHD flows are characterized by thin boundary layers, resolution of these layers is the limiting issue. Hartmann numbers up to 103 are reached in the two-dimensional case of fully developed flow, while in three-dimensional flows the limit is 102. However, the calculations reveal the main features of MHD flows at large M. They are governed by electric currents induced in the fluid. Knowing the paths of these currents makes it possible to predict the flow structure.Results are shown for two-dimensional flows in a square duct at different Hartmann numbers and wall conductivities. While the Hartmann number governs the thickness of the boundary layers, the wall conductivities are responsible for the pressure losses and the structure of the flows. The most distinct feature is the side layers where the velocities can exceed those at the centre by orders of magnitude.The three-dimensional results are also for a square duct. The main interest here is to investigate the redistribution of the fluid in a region where the magnetic field changes. Large axial currents are induced leading to the ‘M-shaped’ velocity profiles characteristic of MHD flow. So-called Flow Channel Inserts (FCI), of great interest in blanket design, are investigated. They serve to decouple the load carrying wall from the currents in the fluid. The calculations show that the FCI is indeed a suitable measure to reduce the pressure losses in the blanket.