Bubble detection in liquid metal by perturbation of eddy currents: Model and experiments

A model has been developed to predict the response of an eddy current flow meter (ECFM) to the passage of a non-conductive inclusion moving in a cylindrical tube filled with a liquid metal. The model can be solved analytically for small inclusion diameters and moderate AC frequencies of the excitation signal. This condition is expressed as vbSω≪1, where vb is the dimensionless inclusion volume and Sω is a function of the ratio between the characteristic length of the system and the penetration depth of the magnetic field. The magnetic induction equation for this problem has also been solved numerically. A very good agreement between the analytical model and numerical solutions has been found for vbSω≪1. Two experimental setups have been designed. First, the ECFM model has been validated by comparing the response due to the passage of traveling beads of known diameters in a low melting point alloy. In a second experiment, the diameters of ascending argon bubbles have been estimated with the ECFM model. The numerical model predicts the gas volume with very good accuracy in the range of bubble diameters studied, between 1.5 and 6 mm, while the analytical model only deviates significantly from the experimental data when vbSω≳0.1. Moreover, we establish that the ECFM can also measure the radial deviation of the bubble trajectory, and the results are consistent with the theoretical limit for isolated bubbles between the regimes of oscillating/zigzag motion of ellipsoidal bubbles and non-oscillating motion of spherical bubbles. Another observation is that the dependence of the ECFM response on the shape of the bubble is negligible; indeed, the ECFM response is well approximated by a linear relation with the bubble volume as is assumed in the analytical model. Finally, an estimation of the terminal rising velocity of bubbles was also carried out.