The aim of this work has been to apply the techniques of non-destructive testing and evaluation to the graphite fuel channel bricks which form the core of an Advanced Gas-Cooled reactor. Two modes of graphite degradation have been studied: subsurface cracks originating from the keyway corners of the bricks and the reduction in material density caused by radiolytic oxidation.This work has focused on electromagnetic inspection techniques. Brick cracking has been studied using a multi-frequency eddy current technique with the aim of determining quantitative information. In order to accurately control the crack dimensions this work has used radially machined slots as an analogue. Two sensor geometries were studied and it was determined that slots of at least 10 mm through-wall extent could be located.A novel, empirical method of determining the slot size is presented using a brick machined with a series of reference slots. Machined slots originating from a keyway could be sized to within 2 mm using this method. A parametric 3D finite element study was also carried out on this problem. These simulations could distinguish the location of the slots and had some sensitivity to their size, however, the model was found to be overly sensitive to the specific mesh used.Two new contributions to the inverse problem are presented. The first is a minor extension to the usual adjoint problem in which one system now contains a gradiometer. The second is a proposed solution to the ambiguous nature of the inner product required by the sensitivity formulation. This solution has been validated with finite element modelling.Density reduction has been studied via its relationship with electrical conductivity using a technique based on impedance spectroscopy. An inverse eddy current problem has been solved using the regularised Gauss-Newton method to determine the conductivity of the brick over its cross section. The associated forward problem has been solved using the finite element method on a simplified geometry. Tikhonov regularisation has been employed to overcome the ill-posed nature of the inverse problem.This method has been applied to a range of sample and sensor geometries and found to produce excellent results from laboratory data provided the finite element model is well calibrated. Bore or surface conductivity values can be reproduced to better than 1% with the accuracy reducing with distance from the sensor. The sensitivity of the algorithm to the regularisation parameter has been studied using the L-curve method and the effect of two regularisation operators has also been examined. A new method of choosing the regularisation parameter a priori is proposed and tested. Data taken during reactor outages produces physically realistic profiles although the results appear off-set from electrical resistivity values measured using the four-point method. The focus of future work should be to remove this effect which will likely require improvements to the forward model.
|Date of Award||1 Aug 2015|
- The University of Manchester
|Supervisor||Anthony Peyton (Supervisor)|
- eddy current
- finite element