Estimation of Solid Fraction Based on Equivalent Magnetic Circuit in TMR-Based Electromagnetic Tomography

For the gas–liquid–solid fluidized beds with magnetic catalyst, the solid fraction can be estimated through the reconstructed permeability distribution using the electromagnetic tomography (EMT) based on the tunneling magneto resistance (TMR) sensor. Considering that the existence of mixed phase and obscure phase interface leads to the inaccurate estimation of phase fraction, a new approach to estimating the solid fraction is proposed. Firstly, the equivalent magnetic circuit analysis method is introduced to abstract the magnetic field distribution, and the relationship between the boundary measurement data and the equivalent permeability of the cross section is derived. Then, the effective medium model is employed to estimate the solid fraction of the cross section based on the equivalent permeability. The solid fraction estimation method based on the above proposed method is more accurate than that based on the gray level of reconstructed images, especially when the permeability distribution is complex. When the true solid fraction is in the range of 0%–100%, the average of the absolute error of simulation and experiment is 2.5% and 4.8%, respectively.