Comprehensive Modelling for Eddy Current Based Pressure Tube to Calandria Tube Gap Measurements
The separation between the pressure tube (PT) and calandria tube (CT), known as gap, in the CANada Uranium Deuterium (CANDU®) nuclear reactor fuel channels is monitored using a drive-receive eddy current probe. Gap measurement accuracy is crucial to ensure contact does not occur between the PT and CT, as contact can lead to cracking of the PT. Variation of in-reactor parameters can compromise gap measurement accuracy. Validated models of the eddy current response to changes in gap can be used to help identify parameters whose variations most affect gap measurement accuracy. However, current models are limited, since they assume the PT and CT are infinite parallel conductive plates, thereby, neglecting the potential effects of PT and CT curvature. Finite Element Method (FEM) models of flat-plate geometry, true PT-CT gap probe geometry, and concentric tube geometry were developed to explore how different geometric approximations can model gap response. The concentric tube geometry, where the CT remains axially concentric with the PT, accurately accounted for curvature of the PT and varied gap by changing the radius of the CT, had the possibility of an analytical solution. Comparison between the three FEM models and experimental measurements showed that both curved models gave similar accuracy and were more accurate than the flat-plate geometry model. A Second Order Vector Potential (SOVP) formalism was used to develop a semi-analytical model of the concentric tube geometry. This semi-analytical model was shown to be three to five times more accurate than the analytical flat-plate model, when compared with experimental measurements for varying PT wall thickness and resistivity. Using the semi-analytical concentric model, a sensitivity analysis was performed to evaluate which parameter variations had the largest effect on gap measurements. It was shown that variations in liftoff had the largest effect on predicted gap and were approximately two to three times more influential than the next most sensitive parameter variation, PT wall thickness. The analysis demonstrated the necessity for accurate PT wall thickness measurements, currently obtained by ultrasonic techniques. Variation of PT resistivity was the next most significant, a parameter whose variation is currently uncompensated for in PT to CT gap measurements.