# Study of the behaviour of volatile fission products in nuclear fuels under temperature transients

The quantity of radioactive fission products, which can be released out of irradiated nuclear fuel in accidental conditions, is a key data for the design of safety components of a Nuclear power plant. This release was largely studied in the case of severe accidents but less is known for temperature below 1400°C. The aim of the Ph.D. Work will consist in using new in-situ characterization tools that are now available on MERARG furnace at the IRESNE institute in CEA-Cadarache in order to improve the characterization of volatiles PFs in this temperature range. The Ph.D. Student will have to design and run thermal treatment on irradiated nuclear fuel making use of in and ex-situ gamma spectrometry, in-situ optical sighting device and measurement of the PO2 of the furnace atmosphere. This work will be performed with the support of experimental team at IRESNE. The Ph.D. Student will also participate to the interpretation of the results in close collaboration with experimental and modeling teams at IRESNE. In order to test the proposed mechanism, the Ph.D. Student can also perform separate-effects experiments on simulating materials in collaboration with team at university. This work will be valued both in industrial context with technical notes and in academic context with paper in journals and attending scientific conferences.

# Multiphysics coupling algorithms for black-box solvers in an HPC framework

This research work is proposed as part of the NumPEx (from French, Numerical Methods for Exascale) research priority program and equipment (PEPR). It belongs with the Exa-MA Project (Methods and Algorithms for Exascale) and is jointly proposed by researchers from CEA (IRESNE Institute, Cadarache center) and Inria (Bordeaux). It takes place in a work package dedicated to discretization methods and aims to build efficient numerical methods for solving Multiphysics problems, i.e., problems in which different physics interact.

Numerical simulation of phenomena involving different physics can be carried out using either a monolithic or partitioned approach.

The monolithic approach consists in representing the different physics by solving a single matrix system containing all the unknowns. This system is often ill-conditioned and requires adapted techniques to be solved. It is also important to note that the algebraic system to be solved is often very large, reaching or even exceeding the maximum capacity of current solvers.

The partitioned approach relies on efficient solvers already developed and adapted to each of the Physics considered separately. The difficulty then lies in coupling these different solvers to obtain the converged Multiphysics solution.

The aim of this thesis is to develop an efficient and generic numerical method for coupling different physics solvers used in black-box way. In addition, this approach needs to be scalable to Exascale.

The relevance and generalizability of the proposed approach will be verified on electromagnetic/acoustic/seismic and thermo-mechanical couplings. In addition, the efficiency of the numerical method will be compared with that of a monolithic resolution considered as a reference numerical approach, but including physical modeling that is often degraded. Experimental validations will also be possible.

# HPC Parallel Integrodifferential Solver for Dislocation Dynamics

Context : Understanding the behavior of metals at high deformation rate [4] (between 104 and 108 s-1) is a huge scientific and technologic challenge. This irreversible (plastic) deformation is caused by linear defects in the crystal lattice : these are called dislocations, which interact via a long-range elastic field and contacts.

Nowadays, the behavior of metals at high deformation rate can only be studied experimentally by laser shocks. Thus, simulation is of paramount importance. Two approaches can be used : molecular dynamics and elastodynamics simulations. This thesis follows the second approache, based on our recent works [1, 2], thanks to which the first complete numerical simulations of the Peierls-Nabarro Equation (PND) [5] was performed. The latter equation describes phenomena at the scale of the dislocation.

PND is a nonlinear integrodifferential equation, with two main difficulties : the non-locality in time and space of the involved operators. We simulated it thanks to an efficient numerical strategy [1] based on [6]. Nevertheless, the current implementation is limited to one CPU –thus forbidding thorough investigations on large-scale systems and on long-term behaviors.

Thesis subject : There are two main objectives :

- Numerics. Based on the algorithmic method of [1], implement a HPC solver (High Performance Computing) for the PND equation, parallel in time and space, with distributed memory.

- Physics. Using the solver developped, investigate crucial points regarding the phenomenology of dislocations in dynamic regime. For exploiting the numerical results, advanced data-processing techniques will be employed, potentially enhanced by resorting to AI techniques.

Depending on the time remaining, the solver might be employed for investigating dynamic fractures [3].

Candidate profile : The proposed subject is multidisciplinary, between scientific computing, mechanics, and data-processing. The candidate shall have a solid background in scientific computing applied to Partial Differential Equations. Mastering C++ with OpenMP and MPI is recommended. Moreover, interest and knowledge in physics –especially continuum mechanics- will be a plus.

The PhD will take place at the CEA/DES/IRESNE/DEC in Cadarache (France), with regular journeys to Paris, for collaboration with CEA/DAM and CEA/DRF.

[1] Pellegrini, Josien, Shock-driven motion and self-organization of dislocations in the dynamical Peierls model, submitted.

[2] Josien, Etude mathématique et numérique de quelques modèles multi-échelles issus de la mécanique des matériaux. Thèse. (2018).

[3] Geubelle, Rice. J. of the Mech. and Phys. of Sol., 43(11), 1791-1824. (1995).

[4] Remington et coll., Metall. Mat. Trans. A 35, 2587 (2004).

[5] Pellegrini, Phys. Rev. B, 81, 2, 024101, (2010).

[6] Lubich & Schädle. SIAM J. on Sci. Comp. 24(1), 161-182. (2002).

# Role of surface properties of UO2 powder particles on their agglomeration suitability and rheological behaviour

This study aims to predict the powder flow behavior in the context of nuclear fuel fabrication. This issue is common to many industrial fields because poor powder flow can lead to process problems such as pipe clogging, reduced rates, or the presence of heterogeneities in the final product. The first objective of this PhD thesis is, on the one hand, to provide a more accurate description of the powder agglomerates and, on the other hand, to characterize their surface. Based on these surface and structural data of UO2 powder particles, the second objective of this work is to achieve a better understanding of the agglomeration/desagglomeration properties in order to correlate them with the flow properties.

The future PhD student will need to use and develop experimental methods (particle characterization tools, surface characterization analyzers, phenomenological modeling) at the IRESNE institute (CEA-Cadarache) in the fuel study department (DEC), specifically within a team dedicated to experiments on nuclear fuel.

This study, applied to UO2 powders, has a generic nature because it is suitable for the study of all granular media. At the end of the PhD, the doctoral candidate will communicate the results through publications and conference presentations. An expertise in granular media will be acquired, which is an attractive and valuable skill in many industrial fields such as agri-food, pharmaceutical industries, metallurgy, or building materials.

# Simulation and measurement of thermomechanical behaviour of granular bed into a fluid media

For several applications, granular media deals with complex physical phenomena. The multi-scale aspect of their microstructure they contains makes the prediction and modeling of heat transfer and its properties non-trivial to compute. In the case of ceramic powders, highly polydisperse powders with grain size extending over several orders of magnitude, are commonly employed. The different pore sizes and the large amount of heat transfer surfaces make the evaluation and simulation of the thermal properties of powders complex to compute.

Homogenized empirical laws are commonly used for this purpose. They allow fast and cheap computation of equivalent properties but rely on a number of empirical parameters which limit their application domain. Explicit simulation tools like DEM/FFT method [1], provide a more detailed description of the microstructure of the granular shape and packing, with higher computational costs. We use this method to tackle the models and better understand the competition between the different modes of heat transfer in the packed beds (heat conduction in gas, heat conduction in grains, conductance at contact between grains, radiation, etc.).

In order to test and improve the simulations and the models, a previous phD thesis was carried out on the effect of grain size and atmosphere on the equivalent thermal conductivity [2]. It gave a better understanding of the competition between heat transfers of different porosity scales and the effect of gas penetration in the microstructure, and to the proposal of new equivalent thermal conductivity models.

The aim of this thesis consists in pursuing this work to study the influence of grain size distribution on the conductivity of the packed bed. It will involve experimental measurements to acquire reliable and controlled data, and a simulation/modeling work to better understand and model the thermal properties of these media. The thesis will involve a collaboration between the Departement of Nuclear Fuels (IRESNE institute, CEA Cadarache) and IUSTI institute in Marseille. The experimental part will take place at IUSTI in Marseille, and the simulations in CEA Cadarache. Specific attention will concern the analysis of measurement and simulation uncertainties.

This subject has applications to many industrial fields such as energy production and transformation, heat exchangers and process engineering. It will gives to the candidate skills at the end of the thesis which might be of a great interest whether in industry or in academic research.

[1] Calvet, T., Vanson, J. M., & Masson, R. (2022). A DEM/FFT approach to simulate the effective thermal conductivity of granular media. International Journal of Thermal Sciences, 172, 107339.

[2] Letessier, J., Gheribi, A. E., Vanson, J. M., Duguay, C., Rigollet, F., Ehret, N., ... & Gardarein, J. L. (2023). Thermal transport-porosity-microstructural characteristics: unpicking the relationship in ultra-porous a-Al2O3 powder. International Journal of Heat and Mass Transfer, 205, 123898.

# Fragmentation metamodel for the simulation of the powder grinding process

The grinding process, used since antiquity to crush seeds and nuts, is vital across various industries, such as mining, civil engineering, and pharmacy. Current research aims to optimize this procedure by enhancing the properties of powders while reducing energy costs. Experimental methods for studying grinding face complexities due to dynamic forces and the continual changes in materials. Fortunately, recent advancements in simulation, using the Discrete Element Method (DEM), offer a perspective to investigate these mechanisms, especially in the context of co-grinding for nuclear fuel manufacturing.

This thesis topic specifically aims to accelerate the simulation of these mechanisms for industrial use. The objective is to develop a fragmentation metamodel based on artificial intelligence. To achieve this, it will be necessary to create a database simulating particle fragmentation and to define the essential features of the process. The approach will encompass several phases, including predicting a particle's fragmentation and learning the fragmentation mode using advanced techniques, such as neural networks.

The research will build upon previous works, notably those of D.-C. Vu (CEA thesis 2020-2023), and will be validated using experimental data associated with other academic endeavors. The doctoral candidate will have access to significant simulation resources, with access to the computing resources of the IRESNE Institute (CEA-Cadarache) and other platforms. In essence, this thesis project aims to merge expertise in grinding with artificial intelligence techniques to innovate in the field of particle fragmentation.

# Manufacturing of a UO2 fuel from granules: study of the influence of granules characteristics on microstructure and properties of the fuel

In UO2 fuel manufacturing, granules may be used as raw materials. This study aims at determining the influence of granules characteristics on final microstructure of sintered pellets. This study is mainly based on experiments in a CEA laboratory (CEA Cadarache).

# Calculation of the thermal conductivity of UO2 nuclear fuels and the influence of irradiation defects

Atomistic simulations of the behaviour of nuclear fuel under irradiation can give access to its thermal properties and their evolution with temperature and irradiation. Knowledge of the thermal conductivity of 100% dense oxide can now be obtained by molecular dynamics and the interatomic force constants[1] at the single crystal scale, but the effect of defects induced by irradiation (irradiation loop, cluster of gaps) or even grain boundaries (ceramic before irradiation) remain difficult to evaluate in a coupled way.

The ambition is now to include defects in the supercells and to calculate their effect on the force constants. Depending on the size of the defects considered, we will use either the DFT (Density Functional Theory) or an empirical or numerical potential to perform the molecular dynamics. AlmaBTE allows the calculation of phonon scattering by point defects and the calculation of phonon scattering by dislocations and their transmission at an interface have also recently been implemented. Thus, the chaining atomistic calculations/AlmaBTE will make it possible to determine the effect of the polycrystalline microstructure and irradiation defects on the thermal conductivity. At the end of this thesis, the properties obtained will be used in the existing simulation tools in order to estimate the conductivity of a volume element (additional effect of the microstructure, in particular of the porous network, Fast Fourier Transform method), data which will finally be integrated into the simulation of the behavior of the fuel element under irradiation.

The work will be carried out at the Nuclear Fuel Department of the CEA, in a scientific environment characterised by a high level of expertise in materials modelling, in close collaboration with other CEA teams in Grenoble and in the Paris region who are experts in atomistic calculations. The results will be promoted through scientific publications and participation in international congresses.

# Study of restructuring phenomena in UO2 fuel using High Resolution Electron Back Scatter Diffraction

Electron BackScatter Diffraction (EBSD) has helped to highlight microstructural changes in UO2 fuel pellets, such as the subdivision of grains into weakly disoriented sub-grains, either after compression tests at high temperature or after irradiation. However, the analyses carried out to date by this method present several limitations.

The main objective of this thesis is to improve their angular and spatial resolution. To this end, high-resolution EBSD (HR-EBSD) and Transmission Kikuchi Diffraction (HR-TKD) will be developed and applied to different restructured fuels. The new data acquired by these methods will improve our knowledge of the defect population (dislocations) and the local mechanical state of the fuel. They will be used in crystalline plasticity models.

This subject will enable the PhD student to acquire skills in advanced microstructural characterisation of materials, exploitation of experimental data and micromechanical modelling, which will be applicable to a wide range of materials.

The thesis work will mainly take place at the Fuel Research Department (IRESNE INstitute, CEA Cadarache) in a laboratory for the characterisation and study of the properties of fresh and irradiated fuels. It will also take place over a shorter period of time at the LEM3 laboratory of the University of Loraine based in Metz, which supervises this thesis in collaboration with the CEA and which has internationally recognized experience in the characterization of materials using the considered techniques in this study.

# which thermomechanical coupling is required to describe nuclear fuel fragmentation ?

When subjected to a temperature ramp, irradiated nuclear fuel undergoes fragmentation, which increases with increasing temperature ramp. This intuitive result cannot, however, be described by the fuel behavior codes existing at the CEA, because the latter calculate the stress state of the fuel pellet statically, that is to say with equations, which do not depend on the time. The aim of the thesis is to go beyond this limitation by proposing a modeling, in elastic mechanics, which can account for the effect of the speed of temperature rise. To do this, we will adopt a thermodynamic approach, using the Onsager formalism. The thesis work will consist of writing a theoretical model of mechanical thermal coupling based on time-dependent equations, then applying it to a simplified simulation of the fuel pellet. The candidate must have knowledge of mechanics and thermodynamics, ideally in the thermodynamics of irreversible processes. He will benefit from a high-level scientific environment with skills on thermomechanical codes and the behavior of the fuel pellet during a thermal transient at the Fuel Research Department (IRESNE Institute, CEA Cadarache) and skills on the Onsager formalism with his thesis director.