evaluation of the oxygen-induced zircaloy embrittlement in icare/cathare
DESCRIPTION
ALIAS CZ. Evaluation of the Oxygen-Induced Zircaloy Embrittlement in ICARE/CATHARE. Ladislav Belovsky ALIAS CZ s.r.o., Czech republic [email protected] Presented at the 11 th International QUENCH Workshop , October 25-27, 2005 , Forschungszentrum Karlsruhe, Germany. - PowerPoint PPT PresentationTRANSCRIPT
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Evaluation of the Oxygen-Induced Zircaloy
Embrittlement in ICARE/CATHARE
Ladislav Belovsky
ALIAS CZ s.r.o., Czech [email protected]
Presented at the 11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Motivation for Development of a New Model (ZROB)
• ICARE/CATHARE: … applicable also for LOCA and beyond DBA analyses
• Acceptance criteria for ECCS for LWRs ( 10CFR50.46 ): Evaluation of post-quench cladding embrittlement (17% ECR by B-J since 1973).
• The 17% ECR criterion currently under revision by USNRC:– High burnup (hydrogen, pre-oxide).
– New Zr-based alloys
• Exp. research indicates that embrittlement is a combined function of :– Oxygen content & distribution metal (beta phase)– Hydrogen content (& distribution ?) in metal
• Modeling of Zircaloy embrittlement in ICARE/CATHARE in two steps:– 1. step: Oxygen-induced embrittlement (O-diffusion in beta phase)– 2. step: Impact of hydrogen onto embrittlement (O-solubility & diffusion, hydrides, …)
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Modeling Features & Assumptions
• ZROB receives beta layer boundaries from oxidation module (ZROX or UZRO)
• ZROB calculates 1D oxygen diffusion in beta layer >970 °C (oxygen-free ZR in ZROX):
– Oxidizing surface: - Beta layer (ZR) always covered with O-stabilized alpha layer (ZRO). - Boundary concentration at ZR/ZRO: Zircaloy-Oxygen phase
diagram
– Non-oxidizing surface: Zero oxygen flux.
– Uniform meshing, Cylindrical coordinates, Implicit finite-difference method, Gauss elimination.
– Initial condition: Constant concentration profile (as-received material).
• ZROB deduces from the oxygen concentration profile in the beta layer :
1. Thickness of beta layer with less than specified O-concentration ( …, 0.6, 0.7, … wt% O ).
2. Fractional saturation of beta layer.
3. embrittled Zircaloy components after quenching (Chung-Kassner 1 and/or Pawel 2 criterion).
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Diffusion Equation for Oxygen in ZR Layer
• Oxygen mass balance in ith segment:
• Oxygen fluxes at segment boundaries: Ji = Di ·ΔC/ΔR
CN
CN-1
Ci+1 CiCi-1
C2
C1
RN RN-1 Ri+1 Ri Ri-1 R2 R1
rN rN-1 ri+1 ri ri-1 r2 r1rN+1
i-th segment (regular)
inner segment
outer segment
r
C
thickness of ZR layer
Ji+1 JiJN+1 J1
ii
i
ii JJt
Crr
122
1
Example of two-sided oxidation
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Oxygen diffusion coefficient in ZR layer
> 970 °C (-Zr) : D = 2.63·10-6 exp(-28200/(1.987·T)) J. Nucl. Mat. 68 (1977)
< 820 °C (-Zr) : D = 1.32·10-4 exp(-48200/(1.987·T)) J. Nucl. Mat. 67 (1977)
1.E-18
1.E-16
1.E-14
1.E-12
1.E-10
1.E-08
4 6 8 10 12 14
10000 / T [ 1/K]
D [
m2/s
]
beta-Zralpha-Zr(a+b)-Zr
970 820 °C
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Oxygen solubility SO in ZR layer at ZR/ZRO interface
• >1007 °C : SO = exp(5.02 – 8220 / T[K]) [wt%] As-received Zircaloy (Chung-Kassner 3)
• 970-1007 °C : SO = 5.246·10-3·(T[K]-1233)
• < 970 °C : SO = 0
T [
C ]
Oxygen concentration [ at% ]
-Zr
ZrO2
-Zr
inner clad surface
outer surface
Phase diagramZry-O
SO
ZRO
ZR
700
900
1100
1300
1500
1700
1900
2100
0.0 0.4 0.8 1.2 1.6 2.0 2.4
Oxygen concentration [ wt% ]
Tem
per
atu
re [
C]
Zr-O
Zry: Chung-KassnerI/C UZRO: Berdyshev
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Input & Output Data
• Input: – MACR xxxx User name of the oxidizing Zircaloy macro-component (eg. CLAD1).– CINI Initial O-concentration in as-received Zircaloy: 0.1 wt% ( 0 -
1.5 )– COXX User defined critical O-concentration: 0.55 wt% ( 0 - 2 )– DTMX Max. length of internal sub-time step within global Δt: 0.5 s ( 0.001 - 10 )– NMAX Max. number of concentration points in ZR: 15
( 4 - 100 )
• Output:
– Fractional saturation of beta layer FBS = CAV / SO
– CAV : Average concentration of oxygen in ZR layer
– SO : Boundary concentration of oxygen in ZR (oxygen solubility)
– Thickness THICXX within ZR with max. COXX [wt%] oxygen(another six variables THIC04 to THIC09 are automatically calculated for 0.4 to 0.9 wt%)
– If embrittlement criterion fulfilled < 400 K (Chung-Kassner 1 or Pawel 2), component state DISLOCAT.
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Results: Numerical Against Analytical Solution
• Non-moving boundary diffusion problem in a slab, thickness l = 0.7 mm
– Outer surface: oxidizing, boundary concentration from Chung-Kassner 3 correlation– Inner surface: zero oxygen flux– Initial O-conc.: 0.1 wt% (1000 wt ppm)– Constant temperature 1000 °C, 1400 °C
• Analytical solution (Carslaw & Jaeger 4): – Oxygen concentration C(x, t) after t seconds at distance x from the surface:
• Numerical solution by ZROB :– Clad diameter 9 m ( slab)– Default input data
• Comparison: Good agreement (see next figures)
02
2200 2
)12(cos4
)12(exp12
)1(41,
k
k
B l
xk
l
tDk
kCCCtxC
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Results: Numerical Against Analytical Solution Cont’d
Temperature
1000 °C
-4
-2
0
2
4
6
8
10
12
14
16
18
0 100 200 300 400 500 600 700
Distance from the outer cladding surface [micron]
Ox
yg
en
co
nc
en
tra
tio
n
[kg
/m3 ]
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Re
l. d
iffe
ren
ce
(A
- Z
RO
B)
/ A
[%
]
AnalyticalZROBRel. difference [%]60 s
400 s 1140 s
60 s
400 s
1140 s
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Results: Numerical Against Analytical Solution Cont’d
Temperature
1400 °C
-20
-10
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600 700
Distance from the outer cladding surface [micron]
Ox
yg
en
co
nc
en
tra
tio
n
[kg
/m3 ]
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Re
l. d
iffe
ren
ce
(A
- Z
RO
B)
/ A
[%
]
AnalyticalZROBRel. difference [%]
40 s
480 s
480 s
40 s
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Results: Sensitivity to Meshing and Time step
• Temperature 1400 °C
-1
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70 80 90 100
Number of concentration points NMAX [-]
Ma
x.
rela
tiv
e d
iffe
ren
ce
[%
] 40 s
480 s
-1
0
1
2
3
4
5
6
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Internal sub-time step DTMX [ s ]
Ma
x.
rela
tiv
e d
iffe
ren
ce
[%
]
40 s
480 s
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Results: Isothermal Oxidation (As-received Zircaloy)
• Temperature 1200 °C
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Results: Isothermal Oxidation (As-received Zry) Cont’d
• Temperature 1300 °C
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Results: Transient Oxidation (As-received Zry)
• Linear heat-up and cool-down between 800 and 1300 °C at 1 °C/s
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
• Absorbed hydrogen CH increases the oxygen solubility SO in beta phase.
• CEA 5, 6 experimental data available for 1200 °C.
• Saturation of this effect at 600 wppm H.
• Billone (ANL, 2005) 7: Fit to CEA data (additive term to Chung-Kassner 3 correlation):
SO = exp(5.02 – 8220 / T) + 0.6· (1 - exp[-0.006· CH]) [wt%] T[K], CH [ wppm].
• The increased solubility limitaccelerates the filling of betaphase with oxygen.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 200 400 600 800 1000
H [wppm]
O-s
olu
bili
ty in
bet
a [w
t%]
CEA Experiment
ANL Fit to data
Oxygen Solubility in Hydrided Zircaloy
0.6
1200 °C
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
• Beta layer poor in oxygen (~ < 0.6 wt%) disappears faster in hydrided Zircaloy.
FBS = CAV / CB, FBSA = (CAV – CINI) / (CB - CINI), where CINI … initial oxygen conc. in as received Zry.
Results: Isothermal Oxidation (Hydrided Zircaloy)
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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany
Conclusions
• Zry embrittlement module ZROB available since mid 2005 (ICARE2-V3mod1.4).
– Applied embrittlement criteria: Chung-Kassner (1980) & Pawel (1974) … to be revised.
• Effect of hydrogen is under testing:– Increased oxygen solubility due to H: ready for implementation into ZROB– Increased oxygen diffusion coefficient : – Impact of hydrides onto embrittlement :
• References
[ 1] H. M. Chung, T. F. Kassner: NUREG/CR-1344 (1980).
[ 2] R. E. Pawel: Oxygen diffusion in beta Zircaloy during steam oxidation. J. Nucl. Mat. 50 (1974).
[ 3] H. M. Chung, T. F. Kassner: Pseudobinary Zircaloy-Oxygen Phase Diagram. J. Nucl. Mat. 84 (1979)
[ 4] H. S. Carslaw, J. C. Jaeger: Conduction of Heat in Solids. Oxford, Clarendon Press, 2nd edition (1959), p.100.
[ 5] L. Portier et al.: 14th Int. Symp. Zirconium Nucl. Ind., June 13-17, 2004, Stockholm, to be published by ASTM.[ 6] J-C. Brachet et al.: NRC Nucl. Safety Research Conf., Oct. 25-28, 2004, Washington.[ 7] M. C. Billone: LOCA Embrittlement Criterion. Argonne National Laboratory (April 2005).
… to be experimentally investigated