Modelling the melting behaviour of hyperstoichiometric uranium dioxide fuel M. J. Welland, W. T....
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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
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Transcript of Modelling the melting behaviour of hyperstoichiometric uranium dioxide fuel M. J. Welland, W. T....
Modelling the melting behaviour of
hyperstoichiometric uranium dioxide fuel
M. J. Welland, W. T. Thompson, B. J. Lewis
Department of Chemistry and Chemical EngineeringRoyal Military College of CanadaKingston, Ontario
International VERCORS seminarGréoux les bains – FranceOctober 15-16, 2007
2/43
Outline Impetus Stoichiometric UO2
Stefan model Phase Field model, 1&2 dimensions
Non-stoichiometric UO2+x
Stefan model Application to fission heating Concluding remarks
3/43
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
Defective Fuel Behaviour
Potential for centreline melting
4/43
U-O Phase Diagram
UO2+x
5/43
Research Goals
FFO-102-2 (67 kW/m, O/U = 2.16)
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
6/43
Stefan Model Derivation: UO2 Heat balance in both phases and across interface Solid-liquid interface moves with time
Implemented on a moving mesh
7/43
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
8/43
QtuKTFusionHpTk
t
TCp
Phase Field Model Scalar field “φ” to represent phase transition
φ varies continuously between 0 and 1 (solid and liquid)
nuKTFusionGpT
Mt
221=
General heat equation
Phase field equation
Stored heat Conduction Latent heat effects
Rate of phase change Energy from phase change Interfacial energy effects Nucleation
Heat source
9/43
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
10/43
3120oK
Model Comparison/Laser Flash Experiment: Thermogram for Stoichiometric Fuel
Presented models use recently published material propertiesJ.K. Fink “Thermophysical properties of uranium dioxide”, J. Nucl Mat. 279 (2000) 1
1 2 3 4
11/43
Phase Field Results: 0msA
xia
l D
ep
th (
μm
)
100
80
60
40
20
02.00 0.4 0.8 1.2 1.6
Radius (mm)
1-D: Centreline
z
2-D: Axially symmetric
Contour: φ=.5 Temperature (K)
12/43
Phase Field Results: 20ms
Contour: φ=.5
Ax
ial
De
pth
(μ
m)
100
80
60
40
20
02.00 0.4 0.8 1.2 1.6
Radius (mm)
Temperature (K)
1-D: Centreline2-D: Axially symmetric
z
13/43
Phase Field Results: 34ms
Contour: φ=.5
Ax
ial
De
pth
(μ
m)
100
80
60
40
20
02.00 0.4 0.8 1.2 1.6
Radius (mm)
Temperature (K)
1-D: Centreline2-D: Axially symmetric
z
14/43
Phase Field Results: 48ms
Contour: φ=.5
Ax
ial
De
pth
(μ
m)
100
80
60
40
20
02.00 0.4 0.8 1.2 1.6
Radius (mm)
Temperature (K)
1-D: Centreline2-D: Axially symmetric
z
15/43
Phase Field Results: 52ms
Contour: φ=.5
Ax
ial
De
pth
(μ
m)
100
80
60
40
20
02.00 0.4 0.8 1.2 1.6
Radius (mm)
Temperature (K)
1-D: Centreline2-D: Axially symmetric
z
16/43
Phase Field Results: 57ms
Contour: φ=.5
Ax
ial
De
pth
(μ
m)
100
80
60
40
20
02.00 0.4 0.8 1.2 1.6
Radius (mm)
Temperature (K)
1-D: Centreline2-D: Axially symmetric
z
17/43
Phase Field Results: 62ms
Contour: φ=.5
Ax
ial
De
pth
(μ
m)
100
80
60
40
20
02.00 0.4 0.8 1.2 1.6
Radius (mm)
Temperature (K)
1-D: Centreline2-D: Axially symmetric
z
18/43
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
19/43
Stefan Model Derivation – UO2+x
UO2+x
UO2+x modeled as mobile oxygen interstitials in immobile UO2 lattice
20/43
Stefan Model Derivation – UO2+x
21/43
Non-Stoichiometric: UO2.01
[ms]
22/43
Non-Stoichiometric: UO2.03
[ms]
23/43
z
Stefan Model Prediction (UO2.03)
z
24/43
z
Stefan Model Prediction (UO2.03)
z
25/43
z
z
Stefan Model Prediction (UO2.03)
26/43
z
z
Stefan Model Prediction (UO2.03)
27/43
z
z
Stefan Model Prediction (UO2.03)
28/43
z
z
Stefan Model Prediction (UO2.03)
29/43
z
z
Stefan Model Prediction (UO2.03)
30/43
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
31/43
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
R
Liquid Solid
qL qS
Liquid Solid
Surface heating Volumetric heating
RHqq fnSnL =ˆˆ
32/43
Fission Heating: Proof of Concept Phase Field readily accommodates fission heating Test case: 84.7 kW/m
R
33/43
Phase Field readily accommodates fission heating Test case: 84.7 kW/m
φ
0
1
Fission Heating: Proof of Concept
34/43
Phase Field readily accommodates fission heating Test case: 84.7 kW/m
φ
0
1
Fission Heating: Proof of Concept
35/43
Phase Field readily accommodates fission heating Test case: 84.7 kW/m
φ
0
1
Fission Heating: Proof of Concept
36/43
Phase Field readily accommodates fission heating Test case: 84.7 kW/m
φ
0
1
Fission Heating: Proof of Concept
37/43
Phase Field readily accommodates fission heating Test case: 84.7 kW/m
φ
0
1
Fission Heating: Proof of Concept
38/43
Phase Field readily accommodates fission heating Test case: 84.7 kW/m
(300 days)
φ
0
1
Fission Heating: Proof of Concept
39/43
Phase Field Model is Versatile Suitable for scientific experimentation and
engineering design Single model for different physical conditions
Engineering design(safety analysis)
Phase field modelScientific experimentation
(material properties)
40/43
Concluding Remarks Stefan 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
41/43
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
42/43
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
Thank you for your attention.
M. J. Welland, W. T. Thompson, B. J. Lewis
Department of Chemistry and Chemical EngineeringRoyal Military College of CanadaKingston, Ontario
International VERCORS seminarGréoux les bains – FranceOctober 15-16, 2007
