Electromagnetic interaction between a permanent magnet and laminar flow of a moving sphere in a conducting liquid

Abstract

Lorentz force velocimetry (LFV) is a non-contact electromagnetic flow measurement technique for electrically conducting liquids. It is based on measuring the flow-induced force acting on an externally arranged permanent magnet. Motivated by extending LFV to liquid metal two-phase flow measurement, in a previous test we considered the free rising of non-conductive bubbles/particles in a thin tube of liquid metal (GaInSn) initially at rest. We observed that the Lorentz force signals strongly depend on the size of the bubble/particle and on the position, where it is released. Moreover, the force signals cannot be reproduced in detail, which necessitates a statistical analysis. This is caused by chaotic trajectories due to the rising velocities of about 200 mm/s. Therefore, in this paper, we use an improved setup for controlled particle motions in liquid metal. In this experiment, the particle is attached to a straight fishing line, which suppresses any lateral motion, and is pulled by a linear driver at a controllable velocity (0-200 mm/s). For comparison, we solve the induction problem numerically using Oseen's analytical solution of the flow around a translating sphere that is valid for small but finite Reynolds numbers. This simplification is made since the precise hydrodynamic flow is difficult to measure or to compute. The aim of the present work is to check if our simple numerical model can provide Lorentz forces comparable to the experiments. Although Oseen's solution becomes inaccurate near the sphere for finite Reynolds numbers, it provides a fore-aft asymmetry of the flow and is globally well-behaved. It provides an upper limit to the measurement results. We recover the peak-delay of the Lorentz force signals as well.