2017 Water Reactor Fuel Performance Meeting September 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jeju Jeju Island, Korea

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1 Validation of PLEIADES/ALCYONE 2.0 fuel performance code Vincent Marelle 1, Patrick Goldbronn, Clément Introïni, Stéphane Bernaud, Antoine Bouloré, Michel Casella, Clara Fillaux, Jérôme Julien, Katherine Mer-Nkonga, and Laurence Noirot CEA, DEN, Cadarache, Saint Paul Lez Durance, France, 1 vincent.marelle@cea.fr ABSTRACT: ALCYONE is a multi-dimensional (1D, 2D or 3D) fuel performance code dedicated to pressurized water reactors (PWR). This code is co-developed in the PLEIADES platform by the CEA, EDF and AREVA and simulates fuel pellets and cladding evolutions during base irradiation, power ramps and accidental situations. Sophisticated chemical and physical models are used. The thermal and mechanical behavior is solved with the finite element method (FEM) based code CAST3M. ALCYONE 2.0 has been released in December 2016 and includes several new features: improvements in incidental and accidental situations modeling, new models available for 2D and 3D schemes and an evolution of the neutron model to simulate gadolinium fuel. ALCYONE 2.0 uses the new PLEIADES 2.0 platform which has induced substantial evolutions in the code. The integration of ALCYONE in the new PLEIADES platform has been checked by a comparison between ALCYONE 1.4, the former version of ALCYONE, and ALCYONE 2.0 using identical models in both versions. Then behavior differences between these two versions of the code have been evaluated by using the recommended models of each version. Finally, the quality of ALCYONE results has been assessed by a comparison between ALCYONE 2.0 and measurements. The validation base of ALCYONE 2.0 contains more than 350 objects representing various irradiation situations: base irradiation, power ramp or accidental situations. These objects are simulated with different modeling schemes (1D, 2D and 3D) and using different kinds of gas models (industrial or advanced models). Due to code optimization and the use of slices parallelization, a new feature of PLEIADES 2.0 platform for multi-slices schemes, computation times have been significantly reduced. Some enhancements are still in progress to improve the computation - measurement comparison, especially for 2D - 3D schemes and accidental situations (LOCA, RIA). KEYWORDS: PLEIADES - ALCYONE - fuel performance code - validation. I. INTRODUCTION ALCYONE 1 is a multi-dimensional fuel performance code co-developed in the PLEIADES 2 platform by the CEA, EDF and AREVA. It is dedicated to the modeling of the in-reactor behavior of PWR fuel rods during normal (base irradiation) and off-normal (power ramps and accidental situations) operating conditions and incorporates several calculation schemes. A one-dimensional reference scheme, based on a one-dimensional axi-symmetric description of the fuel element associated to a discrete axial decomposition of the fuel rod in stacked independent fuel slices, is used to study the behavior of the complete fuel rod. A two-dimensional scheme which describes PCI at the mid-pellet plane of a pellet fragment is available to assess precisely stress concentration in the cladding near a pellet crack tip 3. A three-dimensional model of the complete pellet fragment and overlying cladding is also of interest when detailed studies of Pellet-Cladding Interaction (PCI) at pellet pellet interfaces are required 4. The different schemes use the Finite Element (FE) code Cast3M to solve the thermo-mechanical problem and share the same physical material models at each node or integration points of the FE mesh. 1

2 Moreover, two advanced schemes (MARGARET and RACHEL) can be used in 1D. MARGARET is an advanced gas model which describes more precisely gas diffusion and gas release in the fuel and RACHEL is a model dedicated to helium release in MOX fuels. Finally, accidental schemes are used to simulate accidental situations with the activation of specific models and constitutive laws. One of the key features of ALCYONE is the integration of a thermochemical model which is very useful to predict cladding failure during PCI power ramps. II. ALCYONE 2.0 PRESENTATION II.A. PLEIADES PLEIADES is a simulation platform dedicated to the behavior of nuclear fuels. Main parts of PLEIADES environment are described in figure 1. The PLEIADES architecture provides generic tools for multiphysics algorithms, data exchange based on SALOME software, and links with fuel databases. It includes tools for pre-processing and post-processing with user-friendly interfaces. PLEIADES platform also provides a physical components library for fuel simulation embedded in C++ classes in a unified software environment. The computational algorithm is built with the architecture and the physical component library, with a user interface dedicated to each fuel concept. Some of the fuel performance codes of PLEIADES platform are dedicated to specific fuel concept studies (ALCYONE for PWR, GERMINAL for SFR, MAIA for MTR ). The VER application is devoted to simulation at the volume element scale for generic fuel microstructure analyses. And finally, LICOS is used for preliminary fuel design studies on non-standard geometries. II.B. ALCYONE 2.0 new models Fig. 1. PLEIADES software environment. ALCYONE 2.0 includes several new features: improvements in incidental and accidental situations modeling, new models available for 2D and 3D schemes, an evolution of the neutron model to simulate gadolinium fuel and FE 2 modeling. 2

3 To better simulate transient situations, a one-dimension axial gas circulation model in macro-porosities called Perm1D has been added allowing to have non uniform internal gas pressure in the free volumes of the rod. Moreover, for a better simulation of LOCA experiments performed in HALDEN reactor, the radiative thermal exchange between the rod and the heater located around it is now simulated in ALCYONE. ALCYONE neutron model (called PRODHEL) has been extended to gadolinium fuel. The goal of this model is to calculate the absorbative gadolinium consumption depending on the radial location in the fuel pellet, heavy isotopes and some fission products evolution, helium production and power radial profile for gadolinium fuels. For this purpose, a specific modeling with two-group energy has been implemented. It uses two-group cross-sections for each isotope considered. Dish filling under irradiation is an important phenomenon to accurately predict PCMI behavior. It is simulated natively in the 3D calculation scheme which describes the dish in the mesh. Dish filling model is also a new feature to simulate this phenomenon in the 1D and 2D(r, ) calculation schemes. A multiscale behavior model based on a multilevel finite element (FE 2 ) approach takes into account fuel heterogeneities 5. FE 2 calculation is another new functionality of ALCYONE 2.0 that gives the possibility of calculating precisely the stresses distribution in a heterogeneous microstructure. It is useful for MOX fuels for instance. III. VALIDATION RESULTS III.A. Validation process Due to major changes between ALCYONE 2.0 and the former version ALCYONE 1.4 including new code architecture, ALCYONE 2.0 validation has been performed in three steps on the different ALCYONE modeling schemes (standard 1D, 2D and 3D, accidental schemes and advanced schemes). The first step is a comparison between ALCYONE 1.4 and 2.0 results using the same models (called V1.4_trunk and V2) in order to check the correct integration of ALCYONE 2.0 models in the new PLEIADES architecture. The next step is a comparison between standard ALCYONE 1.4 and ALCYONE 2.0 results (called V1.4 and V2). Due to the integration of new models in ALCYONE 2.0, results are not expected to be exactly equivalent. The goal of this step is to evaluate these differences. And the final step is a validation comparison between ALCYONE 2.0 results and experimental measurements in order to evaluate the accuracy of the code. III.B. Validation base Standard 1D ALCYONE validation base includes 124 cases: 79 base irradiations of UO 2 or MOX rods with Zy4 or M5 cladding and with a burnup up to 80 GWd/t, 37 pellet cladding interaction (PCI) power ramps of UO 2 or MOX rods with Zy4 or M5 cladding, 8 analytical experiments of UO 2 rods. MARGARET validation base includes 109 rods with Zy4 or M5 cladding: 40 UO 2 base irradiations, 22 UO 2 PCI power ramps, 47 MOX base irradiations. RACHEL validation base includes 12 rods with Zy4 or M5 cladding: 10 MOX base irradiations, 2 MOX power transients. 3

4 LOCA validation base includes 2 UO 2 experiments with Zy4 and Zirlo cladding. 3D validation base includes 44 PCI power ramps (with its preceding base irradiation) with Zy4 and M5 cladding: 38 UO2 rods, 6 MOX rods. 2D validation base is identical to 3D validation base except for 3 UO 2 rods which were excluded. It therefore includes 41 PCI power ramps. RIA validation base includes 10 rods each of them being calculated in 1D and in 3D: 9 UO 2 and MOX rods with Na coolant and Zy4 or M5 cladding, 1 UO 2 rod with Zirlo cladding and water coolant. In sum-up, ALCYONE 2.0 validation base includes more than 350 rods representing various irradiation situations: base irradiation, power ramp or accidental situations. These objects are simulated with different modeling schemes (1D, 2D and 3D) and using different kinds of gas models (industrial or advanced models). III.C. Validation results In this article, validation results are limited to ALCYONE standard 1D scheme but these results are representative for other schemes. Fig. 2 to 6 show ALCYONE calculation comparisons for step 1 and 2 for respectively cladding external diameter, fuel elongation, clad elongation, external corrosion thickness and fraction gas release. As expected, ALCYONE V1.4_trunk and V2 results are very close thus confirming the correct integration of ALCYONE models in PLEIADES V2 architecture. Agreement between ALCYONE V14 and V2 is also very good for external corrosion thickness and fraction gas release and has also been checked on internal pressure, free volumes. Among these results, discrepancies are more significant for cladding external diameter and fuel and clad elongation but still in rather good agreement. These discrepancies are a consequence of code corrections, improvements in the coupling scheme and integration of new models and constitutive laws. Fig. 2. Cladding external diameter variation at the end of base irradiation for V1.4_trunk vs V2 (2.a) and V1.4 vs V2 (2.b). 4

5 Fig. 3. Fuel elongation at the end of base irradiation for V1.4_trunk vs V2 (3.a) and V1.4 vs V2 (3.b). Fig. 4. Clad elongation at the end of base irradiation for V1.4_trunk vs V2 (4.a) and V1.4 vs V2 (4.b). 5

6 Fig. 5. External corrosion thickness at the end of base irradiation for V1.4_trunk vs V2 (5.a) and V1.4 vs V2 (5.b). Fig. 6. Fraction gas release at the end of base irradiation for V1.4_trunk vs V2 (6.a) and V1.4 vs V2 (6.b). Fig. 7 to 10 show comparisons between ALCYONE 2.0 results and measurements. Acceptable errors due to uncertainties are plotted with dot lines. For fraction gas release, corrosion thickness, free volumes and internal pressure, ALCYONE 2.0 accuracy is equivalent to the one of ALCYONE 1.4. However, accuracy of ALCYONE 2.0 has been improved for fuel and clad elongations. It has also been improved for external cladding diameter except for a high burnup rod. 6

7 Fig. 7. Fraction gas release (7.a) and cladding external diameter variation (microns) (7.b) at the end of base irradiation: ALCYONE 2.0 vs measures. Fig. 8. Fuel (8.a) and cladding (8.b) elongation at the end of base irradiation: ALCYONE 2.0 vs measures. 7

8 Fig. 9. External corrosion thickness (9.a) and internal pressure (bar) (9.b) at the end of base irradiation: ALCYONE 2.0 vs measures. Fig. 10. Free volume at the end of base irradiation: ALCYONE 2.0 vs measures. As for base irradiations, ALCYONE 2.0 results for PCI power ramps are in good agreement with ALCYONE 1.4 results and showed an improvement in code robustness: 2 ramp calculations could not be completed with ALCYONE 1.4 while no convergence problems were encountered with the new version. Fig. 11 gives the ALCYONE 2.0 comparison with measurements for fraction gas release and external cladding diameter variation. When compared to measurements, ALCYONE 2.0 accuracy is equivalent to the one of ALCYONE 1.4 for external cladding diameter variation and MOX fraction gas release. However, for UO 2 fuels, fraction gas release calculated with ALCYONE 2.0 is slightly higher than with ALCYONE 1.4 even though it was already overestimated with ALCYONE 1.4. A new calibration of ALCYONE with the fission gas model CARACAS is needed. 8

9 Fig. 11. Fraction gas release (11.a) and cladding external diameter variation (microns) (11.b) after power ramp: ALCYONE 2.0 vs measures. Finally, ALCYONE results on analytical experiments are not presented in this article but they allowed fuel internal temperature comparison with in-pile thermocouple and fission gas release comparison during irradiation in addition of usual post irradiation examination comparisons. They confirmed previous conclusions. IV. COMPUTATION TIME Code optimization has been performed in new PLEIADES V2 architecture to speed up computation. For instance, access to field values is now more efficient. Thanks to these improvements, most sequential computation times have been significantly reduced in ALCYONE 2.0 (more than 50 % in average) in spite of the addition of a new convergence criterion on internal pressure which can increase iterations number. Moreover, development of parallelism in PLEIADES V2 architecture gives the opportunity to reduce computation time again for 1D multi-slices schemes where each axial slice is calculated on a different processor. Fig. 12 and 13 show speedup obtained in base irradiation calculations with 30 slices and in PCI power ramps with 5 or 8 slices. Speedup is significant for a number of processors up to the axial slice number plus 1 (master node). Fig. 12. Speedup vs. processors number for base irradiations with ALCYONE

10 Fig. 13. Speedup vs. processors number for PCI power ramps with ALCYONE 2.0. V. CONCLUSIONS Non-regression of validation versus previous version has been checked for ALCYONE 2.0 calculation schemes: 1D, 1D MARGARET, 1D RACHEL, 2D, 3D, LOCA and RIA. Validation base used for this verification includes more than 350 rods up to 80 GWd/t with different fuels (UO 2 and MOX), cladding (Zy4 and M5) and irradiation conditions (base irradiation, PCI power ramp, LOCA and RIA). Comparisons with measurements have shown a good accuracy in ALCYONE results but a new global calibration of ALCYONE models is needed to improve specific results such as fission gas release in UO 2 fuels during PCI power ramps. Moreover code robustness has been increased and comptuation time have been significantly reduced thanks to code optimization and parallelism used in PLEIADES V2 architecture. ACKNOWLEDGMENTS This research was conducted in the framework of the PLEIADES project, which is supported financially by the CEA (Commissariat à l Energie Atomique et aux Energies Alternatives), EDF (Electricité de France) and AREVA-NP. REFERENCES 1. V. MARELLE, P. GOLDBRONN, S. BERNAUD, E. CASTELIER, J. JULIEN, K. NKONGA, L. NOIROT and I. RAMIERE, New developments in ALCYONE 2.0 fuel performance code, Proceedings of Top Fuel 2016, Boise, ID, September 11-15, B. MICHEL, J. SERCOMBE, C. NONON, F. MICHEL and V. MARELLE, Simulation of Pellet-Cladding Interaction with the PLEIADES Fuel Performance Software Environment, Nuclear Technology, 182, (2013). 3. J. SERCOMBE, R. MASSON and T. HELFER, Stress concentration during pellet cladding interaction: Comparison of closed-form solutions with 2D(r, ) finite element simulations, Nuclear Engineering and Design, 260, (2013). 4. B. MICHEL, J. SERCOMBE, G. THOUVENIN and R. CHATELET, 3D fuel cracking modelling in pellet cladding mechanical interaction, Engineering Fracture Mechanics, 75, (2008). 5. F. FEYEL and J.L. CHABOCHE, FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, 183, (2000). 10