AC/DC Modelling of Eddy Currents in Graphite Bricks at UK AGRs
EDF Energy use an Eddy Current Inspection Tool (ECIT) to test the properties of graphite bricks in the cores of UK Advanced Gas-cooled Reactors (AGRs). The tool comprises a coil containing an alternating current which generates a magnetic field, inducing eddy currents within the nearby graphite. The secondary magnetic field generated by these currents interacts with the primary field to alter the impedance of two receiving coils. By measuring the amplitude and phase of the voltage response relative to the driving current, information can be derived about the electrical resistivity of the graphite brick. This can be converted to a measure of graphite density and therefore provides a non-invasive means of determining spatial variability of the brick density.
Quintessa have modelled this system using COMSOL Multiphysics® simulation software to determine the extent to which heterogeneities in density are visible in the eddy current data and to compare results from modelled density profiles with real inspection scans. A partial segment of the brick is modelled, with the emitter and two receiver coils represented as line currents. The COMSOL Multiphysics® AC/DC module Magnetic Fields Interface is used to solve for the electromagnetic fields in the graphite and calculate the resultant voltage difference in the receiver coils.
Externally-modelled electrical conductivity profiles can be imported into the COMSOL® graphite material properties using an Interpolation Function. Features in the graphite bricks such as methane holes can also be defined, using variables which specify the spatial material properties of each feature. The Size Expression node can be used to refine the mesh around these features. By defining features using spatial variation in material properties rather than creating geometric objects with different materials, movement of the coil with respect to the brick can be modelled without requiring any change in geometry or mesh. An ECIT scan past the brick is modelled using a Parameter Sweep to rotate the graphite material properties with respect to the coils.
A Parameter Sweep is also used to calculate results at four different AC frequencies. At lower frequencies, eddy currents can penetrate further into the graphite bricks. At higher frequencies, smaller features are resolvable close to the surface of the brick. Using a range of input frequencies maximises the spatial information that can be determined from the brick. The outputs of interest are the difference in voltage amplitude and phase between the two receiver coils. These can be exported from COMSOL Multiphysics®
and converted into graphite density profiles. Comparing these modelled profiles against brick scan measurements has provided insight into interpretation of the measurements.
