Contribution to Modeling of Hydrogen Effect on Oxygen Diffusion in Zy-4 Alloy During High Temperature Steam Oxidation
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Contribution to Modeling of Hydrogen Effect on Oxygen Diffusion in Zy-4 Alloy During High Temperature Steam Oxidation Benoıˆt Maze`res • Clara Desgranges • Caroline Toffolon-Masclet • Daniel Monceau
Received: 18 July 2012 / Published online: 18 January 2013 Ó Springer Science+Business Media New York 2013
Abstract Previous studies have shown that the numerical model EKINOX-Zr was able to simulate with accuracy oxide growth and oxygen diffusion into the matrix during high-temperature oxidation of Zy-4. In this study, the aim of the development was to evaluate if the observed effect of hydrogen cladding content on the increase of oxygen solubility in the high-temperature bZr was only a thermodynamic effect. Previous experimental studies have shown that hydrogen induces an evolution of equilibrium oxygen concentration at the aZr/bZr interface. The present work showed that EKINOX-Zr linked with the thermodynamic database Zircobase reproduced the evolution induced by hydrogen during the high-temperature steam oxidation. However, the results showed also that additional studies are necessary to better understand hydrogen behavior during high-temperature oxidation of Zr. Keywords Zy-4 Zr High-temperature Oxidation Modeling Numerical simulation
B. Maze`res C. Desgranges (&) CEA, DEN, DPC, SCCME, Laboratoire d’Etude de la Corrosion Non Aqueuse, 91191 Gif-Sur-Yvette, France e-mail: [email protected] B. Maze`res e-mail: [email protected] C. Toffolon-Masclet CEA, DEN, DMN, SRMA, Laboratoire d’Analyse Microstructurale des Mate´riaux, 91191 Gif-Sur-Yvette, France e-mail: [email protected] D. Monceau Institut Carnot CIRIMAT, ENSIACET, 4 Alle´e Emile Monso, BP 44632, 31030 Toulouse Cedex 4, France e-mail: [email protected]
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Oxid Met (2013) 79:121–133
Nomenclature EPMA Electron probe micro analyse dxi is the metal/oxide interface velocity dt dxj is the aZr/bZr interface velocity dt
PBR ¼ 1; 56 is the Pilling–Bedworth ratio between Zr metal matrix and the associated oxide is the oxygen coefficient diffusion in the oxide Dox Da is the oxygen coefficient diffusion in aZr(O) Db is the oxygen coefficient diffusion in bZr J is the oxygen flux c is the oxygen concentration t is the time JVn k is the anionic vacancy flux from slab n to n ? 1 n is the anionic vacancy diffusion vacancies in the slab n DVk is the anionic vacancy concentration in the slab n XVnþ1 k Xn is the molar volume of the slab n en is the thickness of the slab n n dX V is the rate of change of the anionic vacancies concentration Xn ¼ K VK
dt
c ox Cvap Coxa Coxa Cba Cb a
is linked with the oxide type MOc is the oxygen boundary concentration in the oxide at the steam/oxide interface is the oxygen boundary concentration in the oxide at the metal/oxide interface is the oxygen boundary concentration in aZr(O) at the metal/oxide interface is the oxygen boundary concentration in aZr(O) at the aZr(O)/bZr interface is the oxygen boundary concentration in bZr at the aZr(O)/bZr interface
Introduction The loss-of-coolant-accident
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