Interaction of a small permanent magnet with a liquid metal duct flow

Abstract

If a permanent magnet is located near a liquid metal flow, the magnet experiences a Lorentz force, which depends on the velocity of the flow. This effect is embodied in a noncontact flow measurement technique called Lorentz force velocimetry (LFV). Although LFV is already under way for global flow measurement in metallurgy, the possibility of using LFV for local velocity measurement has not yet been explored. The present work is devoted to a comprehensive investigation of the Lorentz force acting upon a permanent magnet near a liquid metal flow in a square duct when the size of the magnet is sufficiently small to be influenced by only parts of the fluid flow. We employ a combination of laboratory experiments in the turbulent regime, direct numerical simulations of laminar and turbulent flows using a custom-made code, and Reynolds-averaged Navier-Stokes (RANS) simulations using a commercial code. We address three particular flow regimes, namely the kinematic regime where the back-reaction of the Lorentz force on the flow is negligible, the low-Reynolds number dynamic regime and the high-Reynolds number dynamic regime both being characterized by a significant modification of the flow by the Lorentz force. In all three regimes, the Lorentz force is characterized by a nondimensional electromagnetic drag coefficient CD, which depends on the dimensionless distance between the magnet and the duct h, the dimensionless size of the magnet d, the Reynolds number Re, and the Hartmann number Ha. We demonstrate that in the kinematic regime, CD displays a universal dependence on the distance parameter, expressed by the scaling laws CD ∼ h−2 for h ≪ 1 and CD ∼ h−7 for h ≫ 1. In the dynamic regime at low Re, the magnet acts as a magnetic obstacle and expels streamlines from its immediate vicinity. In the dynamic regime at high Re, we present experimental data on CD(Re) for 500 ≤ Re ≤ 104 and on CD(h) for 0.4 ≤ h ≤ 1 and demonstrate that they are in good agreement with numerical results obtained from RANS simulations for the same range of parameters.