Optimal Coil Currents in Electromagnetic Flow Tomography

Abstract

Electromagnetic flow meters are a gold standard in measuring the mean flow velocity of conductive liquids and slurries in process industry. A drawback of this approach is that the velocity field cannot be determined. Velocity field information is important for characterizing multiphase flows in the process industry. Recently, electromagnetic flow tomography has been proposed for estimating velocity fields in process pipes. The modality uses multiple magnetic field excitations produced by coils and a set of electrodes attached to the inner surface of the pipe to measure the induced voltages. In earlier studies, a method for reconstructing 2-D velocity field on a pipe cross section has been developed. The method utilizes a finite-element-based computational forward model for computing boundary voltages and a Bayesian framework for inverse problem to reconstruct the velocity field. Magnetic field excitations affect the boundary voltage measurements and, hence, the reconstructed velocity field. Optimization of excitations is especially important when imaging axisymmetric flows, since all axisymmetric velocity fields having the same mean velocity produce the same boundary voltage data when uniform magnetic field excitations are used. In this paper, two methods for optimizing coil currents and resulting magnetic fields are proposed. The methods are based on maximizing the norm of the boundary voltage measurements or minimizing the uncertainty in the reconstructed velocity field estimates. The results show that by optimizing coil currents it is possible to obtain accurate velocity field estimates using just one or two optimal excitations.