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.

Laminar and transitional liquid metal duct flow near a magnetic point dipole

“…The aim of this article is to investigate the structure formation and the locally resolved Lorentz force fields in a liquid metal duct flow in the presence of a magnetic point dipole field. The flow and magnetic field configurations are similar to recent laboratory experiments on LFV using liquid InGaSn alloy at room temperature 24 . We conduct three-dimensional DNS based on the quasi-static approximation of the induction equation.…”

Local Lorentz force and ultrasound Doppler velocimetry in a vertical convection liquid metal flow

“…The volume fluxV of the cooling water is measured using an axial turbine flow sensor. The LLFV measurement system [17] consists of a cubic permanent magnet of side length 5 mm, which is placed on a parallel spring. The deflection of the spring through the force acting on the magnet is measured by a laser interferometer.…”

“…The forces are directed opposite to the flow and act as a brake on the fluid motion. At the same time, due to Newton's Third Law, a force in the range of micro-to millinewton acts on the permanent magnet which can be measured by precision methods [17]. It has the same * Corresponding author: till.zuerner@tu-ilmenau.de magnitude as the sum of all Lorentz forces in the liquid, but is directed in the opposite direction -the magnet is in effect dragged along with the flow.…”

Contact-free measurement of the flow field of a liquid metal inside a closed container

“…So far, the L2F2 has been used for duct flow experiments only [10]. In this paper, we will present the application of the L2F2 to a liquid metal flow in a closed cylindrical container at room temperature.…”