Sensitivity Formulation Including Velocity Effects for Electromagnetic Induction Systems

Sensitivity formulation and calculation is an important task in several electromagnetic induction systems, notably those used for measurement, nondestructive testing (NDT), and inductive imaging systems such as magnetic induction tomography (MIT). Previously, the sensitivity formulation used in these cases did not consider the velocity of the objects being imaged as these are considered to be static compared to the rate of change of the applied ac field. More recently, practical applications such as eddy current NDT for high-speed rail or wheel inspection and liquid metal flow imaging have used the interaction between the velocity of the material and an applied magnetic field for inspection purposes. Clearly in these applications the effects of velocity are fundamental to the operation of the technique. However, a direct sensitivity formulation for the velocity term has not yet been reported. In this paper, we present a derivation of the sensitivity coefficients for general induction measurement systems taking into account of the effect of moving objects. The sensitivity formulation is derived from electromagnetic field theory. It is believed that this is a more complete formulation than those previously reported. The sensitivity formulation has been validated on a test example based on contactless inductive flow tomography (CIFT). This example consists of a refractory tube carrying liquid metal. The tube is surrounded by an array of coils which apply a dc field. The secondary magnetic field caused by the velocity of the liquid metal is measured with an array of magnetometers. The sensitivity of the magnetometer signal to the axial component of the velocity, derived from the new formulation, is compared to values obtained from an independent numerical model based on the finite difference method. A good agreement was obtained for the cases considered, some of which are reported here.