Theoretical and numerical approaches to the forward problem and sensitivity calculation of a novel contactless inductive flow tomography (CIFT)

A completely contactless flow measurement technique based on the principle of EM induction measurements-contactless inductive flow tomography (CIFT)-has been previously reported by a team based at Forschungszentrum Dresden-Rossendorf (FZD). This technique is suited to the measurement of velocity fields in high conductivity liquids, and the possible applications range from monitoring metal casting and silicon crystal growth in industry to gaining insights into the working of the geodynamo. The forward problem, i.e. calculating the induced magnetic field from a known velocity profile, can be described as a linear relationship when the magnetic Reynolds number is small. Previously, an integral equation method was used to formulate the forward problem; however, although the sensitivity matrices were calculated, they were not explicitly expressed and computation involved the solution of an ill-conditioned system of equations using a so-called deflation method. In this paper, we present the derivation of the sensitivity matrix directly from electromagnetic field theory and the results are expressed very concisely as the cross product of two field vectors. A numerical method based on a finite difference method has also been developed to verify the formulation. It is believed that this approach provides a simple yet fast route to the forward solution of CIFT. Furthermore, a method for sensor design selection based on eigenvalue analysis is presented.