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.

Modelado detallado de una central nuclear CANDU con CITVAP.

La línea de cálculo de INVAP consiste principalmente de los códigos CONDOR y CITVAP. Este último es la versión mejorada del código CITATION II que resuelve la ecuación de difusión neutrónica multigrupo por el método de diferencias finitas. CITVAP es ampliamente usado para estudiar reactores de investigación y reactores de potencia tales como PWR, BWR, VVER y últimamente se implemento nuevas funciones para estudiar una central PHWR tipo Atucha. Siguiendo con la línea de reactores PHWR, en este trabajo se estudian las capacidades y deficiencias del código de núcleo CITVAP para modelar una central nuclear tipo CANDU. Se plantean mejoras a realizar para un manejo mas eficiente desde el punto de vista del usuario, tanto de la gestión de combustibles, movimientos de barras de control y zonas líquidas como mejoras en el modelo termohidraulico. La metodología consiste en validar la línea de cálculo de INVAP, contrastando los resultados con el benchmark IAEA-tecdoc-887. El proceso de validación consiste en cálculos de celda en dos y tres dimensiones usando los códigos CONDOR y SERPENT respectivamente, obtención de secciones eficaces macroscópicas en función del quemado y cálculos de núcleo para distintas configuraciones de los dispositivos de control usando un núcleo fresco y una distribución de quemado en equilibrio. Se analizan las dificultades que se presentan al modelar el núcleo con las capacidades actuales del código y se plantean posibles soluciones a implementar. Para un estudio completo de un reactor CANDU, se estudian tres de la características distintivas de este tipo de reactor: la termohidraulica, la gestión de combustibles y los dispositivos de control de reactividad, distribución de potencia y apagado.

Modelado detallado de una central nuclear CANDU con CITVAP.

La línea de cálculo de INVAP consiste principalmente de los códigos CONDOR y CITVAP. Este último es la versión mejorada del código CITATION II que resuelve la ecuación de difusión neutrónica multigrupo por el método de diferencias finitas. CITVAP es ampliamente usado para estudiar reactores de investigación y reactores de potencia tales como PWR, BWR, VVER y últimamente se implemento nuevas funciones para estudiar una central PHWR tipo Atucha. Siguiendo con la línea de reactores PHWR, en este trabajo se estudian las capacidades y deficiencias del código de núcleo CITVAP para modelar una central nuclear tipo CANDU. Se plantean mejoras a realizar para un manejo mas eficiente desde el punto de vista del usuario, tanto de la gestión de combustibles, movimientos de barras de control y zonas líquidas como mejoras en el modelo termohidraulico. La metodología consiste en validar la línea de cálculo de INVAP, contrastando los resultados con el benchmark IAEA-tecdoc-887. El proceso de validación consiste en cálculos de celda en dos y tres dimensiones usando los códigos CONDOR y SERPENT respectivamente, obtención de secciones eficaces macroscópicas en función del quemado y cálculos de núcleo para distintas configuraciones de los dispositivos de control usando un núcleo fresco y una distribución de quemado en equilibrio. Se analizan las dificultades que se presentan al modelar el núcleo con las capacidades actuales del código y se plantean posibles soluciones a implementar. Para un estudio completo de un reactor CANDU, se estudian tres de la características distintivas de este tipo de reactor: la termohidraulica, la gestión de combustibles y los dispositivos de control de reactividad, distribución de potencia y apagado.

Applicazioni degli acciai inossidabili in sistemi per la produzione di energia.

Questo elaborato ha lo scopo di esporre quelli che sono i vantaggi derivanti dall' utilizzo degli acciai inossidabili, specificando il tipo di componente e le ragioni della scelta, nei sistemi per la produzione di energia: dalle turbine, agli impianti nucleari, fino agli impianti che sfruttano le energie alternative (solare, eolica, geotermica, biogas). Inizialmente viene fornito un quadro generale sui differenti tipi di acciai inox (martensitici, ferritici, austenitici e duplex, con le relative proprietà, sottolineandone vantaggi e svantaggi), descrivendone anche i sistemi di designazione, con particolare attenzione alla norma AISI (American Iron and Steel Institute). Una volta messe in risalto queste caratteristiche, vengono esaminati e descritti diversi sistemi di produzione di energia in cui gli acciai inox trovano applicazione: si parte dalle turbine (idraulica, a vapore e a gas), spiegando i benefici nell'utilizzo di particolari categorie di acciai inox nella realizzazione di alcuni dei componenti per questi impianti. Vengono quindi esaminati gli impianti nucleari, partendo da quelli che utilizzano come moderatore e fluido refrigerante acqua naturale, ("PWR", Pressurized Water Reactor) e ("BWR", Boiling Water Reactor), fino a quelli che utilizzano invece acqua pesante ("CANDU", Canadian Deuterium Uranium Reactor), nonchè i reattori veloci ("FBR", Fast Breeding Reactor). Infine, vengono esaminate le applicazioni degli acciai inox, nei sistemi per la produzione di energia che, sfruttano fonti alternative (elencate in precedenza).

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.

THE MICROSTRUCTURES OF ZR-EXCEL ALLOY: EFFECTS OF HEAVY ION IRRADIATION, PLASTIC DEFORMATION, THERMAL TREATMENT AND IN-SITU HEATING

Zr-Excel alloy (Zr-3.5Sn-0.8Nb-0.8Mo) is a dual phase (α + β) alloy in the as-received pressure tube condition. It has been proposed to be the pressure tube candidate material for the Generation-IV CANDU-Supercritical Water Reactor (CANDU-SCWR). In this dissertation, the effects of heavy ion irradiation, deformation and heat treatment on the microstructures of the alloy were investigated to enable us to have a better understanding of the potential in-reactor performance of this alloy. In-situ heavy ion (1 MeV) irradiation was performed to study the nucleation and evolution of dislocation loops in both α- and β-Zr. Small and dense type dislocation loops form under irradiation between 80 and 450 °C. The number density tends to saturate at ~ 0.1 dpa. Compared with the α-Zr, the defect yield is much lower in β-Zr. The stabilities of the metastable phases (β-Zr and ω-Zr) and the thermal-dynamically equilibrium phase, fcc Zr(Mo, Nb)2, under irradiation were also studied at different temperatures. Chemi-STEM elemental mapping was carried out to study the elemental redistribution caused by irradiation. The stability of these phases and the elemental redistribution are strongly dependent on irradiation temperature. In-situ time-of-flight neutron diffraction tensile and compressive tests were carried out at different temperatures to monitor lattice strain evolutions of individual grain families during these tests. The β-Zr is the strengthening phase in this alloy in the as-received plate material. Load is transferred to the β-Zr after yielding of the α-Zr grains. The temperature dependence of static strain aging and the yielding sequence of the individual grain families were discussed. Strong tensile/compressive asymmetry was observed in the {0002} grain family at room temperature. The microstructures of the sample deformed at 400 °C and the samples only subjected to heat treatment at the same temperature were characterized with TEM. Concentration of β phase stabilizers in the β grain and the morphology of β grain have significant effect on the stability of β- and ω-Zr under thermal treatment. Applied stress/strain enhances the decomposition of isothermal ω phase but suppresses α precipitation inside the β grains at high temperature. An α → ω/ZrO phase transformation was observed in the thin foils of Zr-Excel alloy and pure Zr during in-situ heating at 700 °C in TEM.