Concerning the exact solution for an internal transmit-receive eddy current probe at arbitrary locations and orientations within two non-concentric conductive tubes

The motivation for this work was to assess the performance of the rotary transmit-receive Eddy Current Testing (ET) probe used to monitor the eccentric air gap between the Pressure Tubes (PT) and Calandria Tubes (CT) of CANDU® fuel channels. In recent years, a substantial effort has been made to develop models to support qualification of this inspection technique, however the combined effect of probe tilt, liftoff, PT resistivity, and the eccentric gap of the PT relative to the CT remained elusive. To support this effort, a new solution for the electromagnetic interaction of eddy current fields with multi-layered eccentric cylindrical media that allows for arbitrarily situated and oriented coils was developed in this work. All electromagnetic coupling coefficients arising from the probe and layered conductors were determined and substituted into Kirchhoff's circuit equations to calculate the induced voltage in the receive coil. Disagreements less than 5.5% in the probe's amplitude and 5.1° in phase between finite element and this model over the expected inspection parameter range provides confidence in its general use.