Hydrogen distribution in Zircaloy under a temperature gradient: Modeling, Simulation and Experiments

Open Access
Courty, Olivier Fabrice
Graduate Program:
Nuclear Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Arthur Thompson Motta, Thesis Advisor
  • Nuclear
  • Materials
  • Cladding
  • Zirconium
  • Hydrogen
  • Diffusion
  • Precipitation
  • X-Ray
  • Diffraction
  • simulation
  • finite element
As a result of corrosion during normal operation in nuclear reactors, hydrogen can enter the zirconium fuel cladding and precipitate as brittle hydride particles, which can severely degrade the cladding ductility. According to previous observations, the distribution of the hydrides in the cladding is not homogeneous and responds to temperature and stress gradients. Due to the heterogeneity of the temperature distribution, hydrides tend to accumulate in the colder areas. This accumulation creates local spots of weak cladding that can favor crack initiation. Therefore, the estimation of the average concentration of the hydrides in the cladding is not sufficient to accurately estimate the risk of cladding failure. An estimation of the local hydride distribution is necessary to help predict future and this is the subject of the current work. The hydride distribution is governed by three competing phenomena. Hydrogen in solid solution diffuses under a concentration gradient due to Fick’s law and under a temperature gradient due to the Soret effect. Finally, precipitation of hydrides occurs once the hydrogen solubility limit is reached. This precipitation has its own kinetics. All of these phenomena are strongly temperature dependent. The complex interplay of these separate phenomena can explain why the hydrogen and hydride distribution depends on temperature. In the current study, different models describing these phenomena have been developed in order to study the behavior of hydrogen in the cladding. Due to the complexity of the modeling, it is usually not possible to find an analytical solution for the hydrogen and hydride distribution for nuclear fuel rod geometries, and so numerical solutions were obtained from the implementation of the model in computer. A 1-D difference code has been created to compute hydrogen distribution in simple geometries. A more detailed model was then implemented in the 3D fuel performance code BISON in order to calculate the hydrogen distribution for more sophisticated geometries, such as a nuclear fuel rod. The results shown by these simulations explain the formation of specific radial distribution of hydrides. The simulations predict that before precipitation occurs, hydrogen tends to accumulate in the colder spots due to the Soret effect. Once the solubility limit is reached, hydrogen precipitates and forms a rim close to the outer edge of the cladding. This is due to the competition between precipitation and diffusion. The simulation also show an axial transfer of hydrogen from the top of the rod, where the oxidation rate is high, to the bottom of the rod, where the hydrogen will precipitate. In the future, the implemented model will be able to provide additional information on the azimuthal hydrogen distribution. The model used to describe hydrogen behavior is semi-empirical. In particular, two empirical constants have to be determined that do not have consistent values in the literature. Therefore, two experiments were designed and performed in order to measure these constants. The first constant is the heat of transport Q*, which determined the Soret effect. This was measured by applying a gradient to a Zircaloy plate that was previously charged with hydrogen. The measured value for Q* was 58.5 kJ/mol and is higher than previous measurement. The results confirm the large variability of the measurement of the heat of transport. The second constant is the rate of precipitation α2 from Marino, which describes the rate at which the supersaturated hydrogen in solid solution precipitates into zirconium hydrides. This rate is measured through an in situ X-Ray diffraction experiment in transmission, at the Advanced Photon Source of the Argonne National Laboratory. The results are between 0.013 s-1/2 and 0.034 s-1/2 and are in the same range of values as found in previous experiments. However, no clear trend of temperature dependence has been identified. The current work involves preliminary approach to calculate an estimation of the thickness of the hydride rim. The simulations directly based on the model predict a very high concentration in the rim that is not seen experimentally. However, once a limit to the concentration of hydrides was set, the simulations provide rim thickness close to 100 microns, which is consistent with experimental observation. The work also proposes suggestions to improve the model governing hydrogen and hydrides distribution in the future.