Numerical Modelling of Eddy Current Probes for CANDU® Fuel Channel Inspection

Multi-frequency Eddy Current (EC) inspection with a transmit-receive probe (two horizontally offset coils) is used to monitor the Pressure Tube (PT) to Calandria Tube (CT) gap of CANDU® fuel channels. Accurate gap measurements are crucial to ensure fitness of service; however, variations in probe liftoff, PT electrical resistivity, and PT wall thickness can generate systematic measurement errors. Validated mathematical models of the EC probe are very useful for data interpretation, and may improve the gap measurement under inspection conditions where these parameters vary. As a first step, exact solutions for the electromagnetic response of a transmit-receive coil pair situated above two parallel plates separated by an air gap were developed. This model was validated against experimental data with flat-plate samples. Finite element method models revealed that this geometrical approximation could not accurately match experimental data with real tubes, so analytical solutions for the probe in a double-walled pipe (the CANDU® fuel channel geometry) were generated using the Second-Order Vector Potential (SOVP) formalism. All electromagnetic coupling coefficients arising from the probe, and the layered conductors were determined and substituted into Kirchhoff’s circuit equations for the calculation of the pickup coil signal. The flat-plate model was used as a basis for an Inverse Algorithm (IA) to simultaneously extract the relevant experimental parameters from EC data. The IA was validated over a large range of second layer plate resistivities (1.7 to 174 µΩ∙cm), plate wall thickness (~1 to 4.9 mm), probe liftoff (~2 mm to 8 mm), and plate-to plate gap (~0 mm to 13 mm). The IA achieved a relative error of less than 6% for the extracted FP resistivity and an accuracy of ±0.1 mm for the LO measurement. The IA was able to achieve a plate gap measurement with an accuracy of less than ±0.7 mm error over a ~2.4 mm to 7.5 mm probe liftoff and ±0.3 mm at nominal liftoff (2.42±0.05 mm), providing confidence in the general validity of the algorithm. This demonstrates the potential of using an analytical model to extract variable parameters that may affect the gap measurement accuracy.

Comprehensive Characterization of Measurement Data Gathered by the Pressure Tube to Calandria Tube Gap Probe

Multi-frequency eddy current measurements are employed in estimating pressure tube (PT) to calandria tube (CT) gap in CANDU fuel channels, a critical inspection activity required to ensure fitness for service of fuel channels. In this thesis, a comprehensive characterization of eddy current gap data is laid out, in order to extract further information on fuel channel condition, and to identify generalized applications for multi-frequency eddy current data. A surface profiling technique, generalizable to multiple probe and conductive material configurations has been developed. This technique has allowed for identification of various pressure tube artefacts, has been independently validated (using ultrasonic measurements), and has been deployed and commissioned at Ontario Power Generation. Dodd and Deeds solutions to the electromagnetic boundary value problem associated with the PT to CT gap probe configuration were experimentally validated for amplitude response to changes in gap. Using the validated Dodd and Deeds solutions, principal components analysis (PCA) has been employed to identify independence and redundancies in multi-frequency eddy current data. This has allowed for an enhanced visualization of factors affecting gap measurement. Results of the PCA of simulation data are consistent with the skin depth equation, and are validated against PCA of physical experiments. Finally, compressed data acquisition has been realized, allowing faster data acquisition for multi-frequency eddy current systems with hardware limitations, and is generalizable to other applications where real time acquisition of large data sets is prohibitive.