1. Modelling the melting behaviour of hyperstoichiometric uranium dioxide fuel
M. J. Welland, W. T. Thompson, B. J. Lewis
Department of Chemistry and Chemical Engineering
Royal Military College of Canada
Kingston, Ontario
International VERCORS seminar
Gréoux les bains – France
October 15-16, 2007

2. Outline Impetus Stoichiometric UO2 Non-stoichiometric UO2+x
Stefan model
Phase Field model, 1&2 dimensions
Non-stoichiometric UO2+x
Application to fission heating
Concluding remarks

3. Defective Fuel Behaviour
Defects in the sheath can occur in < 0.1% of bundles
Coolant allowed to make contact with UO2  UO2+x
Fuel element performance degradation
Reduced gap heat transfer coefficient
Fuel oxidation
Reduced thermal conductivity
Lower incipient melting point
Potential for centreline melting

4. U-O Phase Diagram
UO2+x

5. Research Goals
Develop a model to describe centreline melting in operational, defective nuclear fuel elements
Canadian Nuclear Safety Commission: Generic Action Item (GAI 94G02)
Centreline melting in defective fuel?
Increase operating margins
Improve current safety analysis
FFO (67 kW/m, O/U = 2.16)

6. Stefan Model Derivation: UO2
Heat balance in both phases and across interface
Solid-liquid interface moves with time
Implemented on a moving mesh

7. Phase Field Model
Stefan model cannot accommodate fission heating easily
Phase Field model is a more robust technique
Derived from first principles (Theory of Irreversible Processes)
More complicated to derive but easier and more versatile to implement
Uses same thermodynamic function as used to develop U-O phase diagram
Links thermodynamics with kinetics

8. Phase Field Model Scalar field “φ” to represent phase transition
φ varies continuously between 0 and 1 (solid and liquid)
General heat equation
Stored heat
Conduction
Latent heat effects
Heat source
Phase field equation
Rate of phase change
Energy from phase change
Interfacial energy effects
Nucleation

9. Laser Flash Experiments
Heat deposited on surface
Good for determining material properties
Can be simulated with Stefan or Phase Field model
D. Manara, C. Ronchi, M. Sheindlin, M. Lewis, M. Brykin, “Melting of stoichiometric and hyperstoichiometric uranium dioxide” J. Nucl. Mat. 342 (2005) 148

10. Presented models use recently published material properties
Model Comparison/Laser Flash Experiment: Thermogram for Stoichiometric Fuel
3120oK 1 2 3 4
Presented models use recently published material properties
J.K. Fink “Thermophysical properties of uranium dioxide”, J. Nucl Mat. 279 (2000) 1

11. Phase Field Results: 0msz
Radius (mm)
2.0
0.4
0.8
1.2
1.6
100 80 60 40 20
Axial Depth (μm)
Contour: φ=.5
Temperature (K)
2-D: Axially symmetric
1-D: Centreline

12. Phase Field Results: 20msz
Radius (mm)
2.0
0.4
0.8
1.2
1.6
100 80 60 40 20
Axial Depth (μm)
Contour: φ=.5
Temperature (K)
2-D: Axially symmetric
1-D: Centreline

13. Phase Field Results: 34msz
Radius (mm)
2.0
0.4
0.8
1.2
1.6
100 80 60 40 20
Axial Depth (μm)
Contour: φ=.5
Temperature (K)
2-D: Axially symmetric
1-D: Centreline

14. Phase Field Results: 48msz
Radius (mm)
2.0
0.4
0.8
1.2
1.6
100 80 60 40 20
Axial Depth (μm)
Contour: φ=.5
Temperature (K)
2-D: Axially symmetric
1-D: Centreline

15. Phase Field Results: 52msz
Radius (mm)
2.0
0.4
0.8
1.2
1.6
100 80 60 40 20
Axial Depth (μm)
Contour: φ=.5
Temperature (K)
2-D: Axially symmetric
1-D: Centreline

16. Phase Field Results: 57msz
Radius (mm)
2.0
0.4
0.8
1.2
1.6
100 80 60 40 20
Axial Depth (μm)
Contour: φ=.5
Temperature (K)
2-D: Axially symmetric
1-D: Centreline

17. Phase Field Results: 62msz
Radius (mm)
2.0
0.4
0.8
1.2
1.6
100 80 60 40 20
Axial Depth (μm)
Contour: φ=.5
Temperature (K)
2-D: Axially symmetric
1-D: Centreline

18. Application to Non-Stoichiometric UO2+x
Non-congruent melting/freezing
Solidus, liquidus and melting temperature coupled
Developed in Stefan model
Yet to be implemented in Phase Field model
Thermochemical modelling to provide state functions for both phases completed

19. Stefan Model Derivation – UO2+x
UO2+x modeled as mobile oxygen interstitials in immobile UO2 lattice

20. Stefan Model Derivation – UO2+x

21. Non-Stoichiometric: UO2.01
[ms]

22. Non-Stoichiometric: UO2.03
[ms]

23. Stefan Model Prediction (UO2.03)z z

24. Stefan Model Prediction (UO2.03)z z

25. Stefan Model Prediction (UO2.03)z z

26. Stefan Model Prediction (UO2.03)z z

27. Stefan Model Prediction (UO2.03)z z

28. Stefan Model Prediction (UO2.03)z z

29. Stefan Model Prediction (UO2.03)z z

30. Melting from Fission Heating
Heat from nuclear fission generated within the body of the material
Compare: heat deposited on surface in laser flash
Presented Stefan model is unable to simulate fission heating

31. Limits of the Stefan Model
Stefan model explicitly tracks the rate of the melting (movement of solid-liquid interface)
Melting rate determined by heat flux across interface
Surface heating
Volumetric heating R qL qS
Liquid
Solid
Liquid
Solid

32. Fission Heating: Proof of Concept
Phase Field readily accommodates fission heating
Test case: 84.7 kW/m R

33. Fission Heating: Proof of Concept
Phase Field readily accommodates fission heating
Test case: 84.7 kW/m 1 φ

34. Fission Heating: Proof of Concept
Phase Field readily accommodates fission heating
Test case: 84.7 kW/m 1 φ

35. Fission Heating: Proof of Concept
Phase Field readily accommodates fission heating
Test case: 84.7 kW/m 1 φ

36. Fission Heating: Proof of Concept
Phase Field readily accommodates fission heating
Test case: 84.7 kW/m 1 φ

37. Fission Heating: Proof of Concept
Phase Field readily accommodates fission heating
Test case: 84.7 kW/m 1 φ

38. Fission Heating: Proof of Concept
Phase Field readily accommodates fission heating
Test case: 84.7 kW/m
(300 days) 1 φ

39. Phase Field Model is Versatile
Suitable for scientific experimentation and engineering design
Single model for different physical conditions
Scientific experimentation
(material properties)
Engineering design
(safety analysis)
Phase field model

40. Concluding Remarks Stefan model Phase Field model
Developed for congruent and non-congruent melting
Reproduces laser flash results
Phase Field model
Developed for congruent melting
Reproduces Stefan model and laser flash results
Easily handles multiple dimensions
Demonstrated potential for:
Non-congruent melting
Volumetric heating

41. Concluding Remarks
Examination of simplifications currently used in fuel performance and accident codes
specific heat representations
Models are valid for any phase transitions
Able to include ‘λ-transition’
Can assist in experimental design
Directly addresses CNSC GAI 94G02

42. Acknowledgements Advice and discussions with D. Manara (ITU)
Research support
Natural Sciences and Engineering Research Council of Canada/CANDU Owners Group collaborative research grant
Defense Research and Development Board award

43. Thank you for your attention.
M. J. Welland, W. T. Thompson, B. J. Lewis
Department of Chemistry and Chemical Engineering
Royal Military College of Canada
Kingston, Ontario
International VERCORS seminar
Gréoux les bains – France
October 15-16, 2007