Finite Element Modelling Of Pellet-Cladding Interaction In Advanced Gas-Cooled Reactor

1. Finite Element Modelling Of Pellet-Cladding Interaction In Advanced Gas-Cooled Reactor Rizgar Mella Supervised by Mark Wenman Funded by EPSRC

2. The Advanced Gas-Cooled Reactor • Properties • 650°C coolant outlet temperature. • Coolant pressure 4MPa. • High gas temperature improves thermal efficiency, requiring stainless steel fuel cladding. • CO2 coolant • Large grained UO2 for improved fission product release. • Built for efficiency, typically electricity generation/heat generated ratio of 0.41 more efficient than many modern pressurised water reactor.

3. Statement Of Problem • Pellet-cladding interaction degrades fuel performance and increases fuel pin damage. Performance and damage strongly affect fuel dwell time and the efficient operation of a nuclear reactor. • A finite element model may assist in understanding the events at this interface and may offer insight on how to improve reactor modelling codes. • Modelling of pellet-cladding interaction is not straight forward: • There are whole pin contributions (Inner Fuel Temperature). • Multiple materials, with nonlinear properties. • Multiple time scales (Cracks vs. Oxide Growth). • Explicit damage has large deformations (Pellet-Pellet, Pellet-Cladding interaction). • Long-term material properties change (Fuel and Cladding Creep).

4. Fuel Modelling Is Complex Gas Model Cladding Model Fuel Restructuring Model

5. The Finite Element Method • Finite Element Method (FEM) seeks to transform partial differential equations (PDEs) into algebraic equations in terms of matrices. FEM has been solving many structural problems for 70 years. • Ku=F • (K is the stiffness matrix, u is a vector of unknowns, F is the nodal forces) • Can solve PDEs over complex geometries, by breaking the domain into elements which contain solution unknowns (nodes).

6. First Model Description I Nonlinear material properties are extracted from SLEUTH manual and atomistic calculations.

7. First Model Setup (Geometry) 0.7mm Adaptive Meshing Beginning with very few elements, residual or gradient driven mesh optimization will correct for that inaccuracy. URGAP (Thermal Gap Model) Accounts for fission gas convection, pressure enhanced heat transfer and incomplete energy transfer due to small gap thickness. Many sources indicate key phenomena are heavily influenced by pellet-cladding temperature difference. K. Lassmann, F. Hohlefeld, The revised URGAP model to describe the gap conductance between fuel and cladding, Nuclear Engineering and Design, Volume 103, Issue 2, 2 August 1987, Pages 215-221

8. First Model Outcome I (Heat and Oxygen Distributions) (m) (°C) (m) (m) Figure 4: Coupled diffusion and temperature; Radial temperature distribution (top left); X-Y axis thermal profile and Z-X axis thermal profile (bottom left); Thermal expansion with oxygen diffusion and without. X Z Kelvin

9. First Model Outcome II (Mechanics) Relative external surface temperature Von Mises Stress contribution from surface temperature Left relative temperature plot showing the initial effects of heat transfer due to first contact. Right the Von Mises stress just schematically showing the additional contribution to the stress from the temperature difference along the surface.

10. Material Point Finite Element Method • UINTAH Framework • (centre of accidental fires and explosions) • Nearly mesh free finite element method. • As the particles are free to move cracks and voids can form without mesh bias. • New particles can be created and destroyed arbitrarily. • Excellent history of calculating discrete damage. • Highly parallel. • Not as powerful as conventional finite element for structural mechanics calculations. • Initial damage distribution: two parameter Weibull distribution, mean 110MPa, shape factor 5.

11. MPFEM Model No initial fracture stress distribution applied

12. MPFEM Model With initial microstructural fracture stress distribution

13. Future • Moving forward to a more complete model: • Rigorous testing of model result against empirical data. • We have adaptivity in space, but is it safe to aggressively adapt in time. • Many models, each expressing different aspects of pellet-cladding modelling. These fragments of the full fuel pin situation need to be combined to give a complete picture. • Addition of long term material changes, and how they contribute to pellet-cladding interaction: • Porosity with its effects on surface roughness which alters URGAP parameters. • Microstructural changes alter thermal conductivity which in turn alters pellet expansion. • Fission gas production.

14. Acknowledgements Thank You All Questions Are Welcome • Thankfully Acknowledging • Uintah Computational Framework Group (University of Utah) • Imperial College High Performance Computing Centre • With thanks to EPSRC • With thanks to British Energy • All advice and supervision from the Atomistic Simulation Group, Imperial College • Important References • J.C. Ramirez, M. Stan, P. Cristea, Simulations of heat and oxygen diffusion in UO2 nuclear fuel rods, Journal of Nuclear Materials, Volume 359, Issue 3, 15 December 2006, Pages 174-184, ISSN 0022-3115, DOI: 10.1016/j.jnucmat.2006.08.018. • Chris Newman, Glen Hansen, Derek Gaston, Three dimensional coupled simulation of thermomechanics, heat, and oxygen diffusion in UO2 nuclear fuel rods, Journal of Nuclear Materials, Volume 392, Issue 1, 1 July 2009, Pages 6-15, ISSN 0022-3115, DOI: 10.1016/j.jnucmat.2009.03.035.