8th World Congress on Industrial Process Tomography

# Reconstruction of velocity fields in electromagnetic flow tomography using different magnetic field excitations

Marko Vauhkonen and Ossi Lehtikangas

Department of Applied Physics, University of Eastern Finland, P.O.Box 1627, FI-70211, Kuopio, Finland, Marko.Vauhkonen@uef.fi

## ABSTRACT

Electromagnetic flow meters are a gold standard in measuring mean flow velocity of conductive liquids and slurries in process industry. A drawback of the approach is that the velocity field cannot be determined. Moreover, the lack on axial symmetry can lead to systematic errors in flow rate measurements. Asymmetric flows are often encountered near valves, pipe elbows and T-junction, and in multiphase flows such as oil-in-water flows in oil industry. Electromagnetic flow tomography (EMFT) has been proposed for estimating velocity fields in pipes. The imaging modality uses multiple magnetic B-field excitations produced by pairs of coils and multiple electrodes attached to the surface of the pipe to measure the induced boundary voltages. In earlier studies, the authors have proposed a method for reconstructing two-dimensional velocity field on a pipe cross section. The method uses a finite element based computational forward model for computing boundary voltages and a Bayesian framework for inverse problem to reconstruct the velocity field. In this work, effects of different B-field excitations on the velocity field reconstructions in EMFT are tested with numerical simulations. Especially the reconstruction of axisymmetric velocity fields with the same mean velocity is challenging, since they all produce the same boundary voltages when uniform magnetic B-fields are used. Therefore, for accurate reconstruction of axisymmetric velocity fields highly non-uniform B-fields are also needed. The results show, that axisymmetric velocity fields can be well reconstructed by using e.g. anti-Helmholtz excitations together with uniform B-field. The results also show that asymmetric velocity fields can be well reconstructed by using uniform B-fields only.

### Keywords Electromagnetic flow tomography, Finite element method, Inverse problems, Magnetic field excitation, Velocity field reconstruction

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