Assimilation of transient data and calibration of simulation codes using time series

In the context of scientific simulation, some computational tools (codes) are built as an assembly of (physical) models coupled in a numerical framework. These models and their coupling use data sets fitted on results given by experiments or fine computations of “Direct Numerical Simulation” (DNS) type in an up-scaling approach. The observables of these codes, as well as the results of the experiments or the fine computations are mostly time dependent (time series). The objective of this thesis is then to set up a methodology to improve the reliability of these codes by adjusting their parameters through data assimilation from these time series.
Work on parameter fitting has already been performed in our laboratory in a previous thesis, but using scalars derived from the temporal results of the codes. The methodology developed during this thesis has integrated screening, surrogate models and sensitivity analysis that can be extended and adapted to the new data format. A preliminary step of transformation of the time series will be developed, in order to reduce the data while limiting the loss of information. Machine learning /deep learning tools could be considered.
The application of this method will be performed within the framework of the nuclear reactor severe accident simulation. During these accidents, the core loses its integrity and corium (fuel and structure elements resulting from the reactor core fusion) is formed and can relocate and interact with its environment (liquid coolant, vessel’s steel, concrete from the basemat…). Some severe accident simulation codes describe each step / interaction individually while others describe the whole accident sequence. They have in common that they are multiphysic and have a large number of models and parameters. They describe transient physical phenomena in which the temporal aspect is important.
The thesis will be hosted by the Severe Accident Modeling Laboratory (LMAG) of the IRESNE institute at CEA Cadarache, in a team that is at the top of the national and international level for the numerical study of corium-related phenomena, from its generation to its propagation and interaction with the environment. The techniques implemented for data assimilation also have an important generic potential which ensures important opportunities for the proposed work, in the nuclear world and elsewhere.

Multi-block and non-conformal domain decomposition, applied to the 'exact' boundary coupling of the SIMMER-V thermohydraulics code

This thesis is part of the research required for the sustainable use of nuclear energy in a decarbonized, climate-friendly energy mix. Sodium-cooled 4th generation reactors are therefore candidates of great interest for saving uranium resources and minimizing the volume of final waste.

In the context of the safety of such reactors, it is important to be able to precisely describe the consequences of possible core degradation. A collaboration with its Japanese counterpart JAEA allows the CEA to develop the SIMMER-V code dedicated to simulating core degradation. The code calculates sodium thermohydraulics, structural degradation and core neutronics during the accident phase. The objective is to be able to represent not only the core but also its direct environment (primary circuit) with precision. Taking this topology into account requires partitioning the domain and using a boundary coupling method. The limitation of this approach generally lies in the quality and robustness of the coupling method, particularly during fast transients during which pressure and density waves cross boundaries.

A coupling method was initiated (Annals of Nuclear Energy 2022, Implementation of multi-domains in SIMMER-V thermohydraulic code https://doi.org/10.1016/j.anucene.2022.109338) at LMAG, which consists of merging the different decompositions of each of the domains, with the aim of constituting a unique decomposition of the overall calculation. This method was developed in a simplified framework where the (Cartesian) meshes connect in a conformal manner at the boundary level. The opportunity that opens up is to extend this method to non-conform meshes by using the MEDCoupling library. This first step, the feasibility of which has been established, will make it possible to assemble components to constitute a 'loop' type system. The second step will consist of extending the method so that one computational domain can be completely nested within another. This nesting will then make it possible to constitute a domain by juxtaposition or by nesting with non-conforming domain meshes and decompositions. After verifying the numerical qualities of the method, the last application step will consist of building a simulation of the degradation of a core immersed in its primary tank ('pool' configuration) allowing the method followed to be validated.

This job will enable the student to develop knowledge in numerical techniques and modeling for complex physical systems with flows. He or she will apply techniques ranging from method design to validation, as part of a dynamic, multidisciplinary team at CEA Cadarache.

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.

CFD development and modeling applied to thermal-hydraulics of hydrogen storage in salt caverns

A PhD thesis is available at LMSF lab of CEA in collaboration with Storengy, a world specialist in natural gas storage in salt caverns. Measurements carried out in the cavity showed that gas is in convective motion in the upper part of the cavity and is not necessarily in thermodynamic equilibrium with the brine at the bottom of the cavity, leading to gas stratification phenomena. The different flow regimes (convective or not) will strongly influence, on the one hand, mass exchanges between the gas and the brine and therefore the evolution of the gas composition (in moisture and other components) at the cavity exit and, on the other hand, thermal exchanges between the gas and the rock mass surrounding the cavity. In this context, CFD-based prediction tools are highly beneficial for understanding these phenomena and will contribute to a better interpretation of the physical measurements made in the cavity, to the design improvment of surface installations and to monitoring storage facilities, particularly for hydrogen storage. In this doctoral project, the aim is to develop a thermal-hydraulics model based on TrioCFD software for gas storage in realistically-shaped cavities and under cavity operating conditions (injection and withdrawal phases). To this end, the operation of storage salt cavities will be modeled, initially for a real geometry and in single-phase flow, then in two-phase flow, taking into account mass exchanges between the brine and the gas in the cavity.

Study of fracture toughness - microstructure relationships of new high performance oxide dispersion strengthened steels

ODS steels are considered for the development of components for fourth generation reactors. They offer high tensile and creep strength and good resistance to irradiation [1-3]. This high level of reinforcement is accompanied by a reduction in ductility and toughness. Tube shaping changes the microstructure, so the properties of the material in its final form should be evaluated. The work of B. Rais [4] made it possible to compare the different tests and to develop a test and an analysis method for measuring toughness on thin tubes.

This present PhD will use this new test to evaluate the toughness of various ODS grades. Varied microstructures from historical and recent productions will assessed to identify the mechanisms, the key parameters driving toughness and to identify the microstructural parameters which drive the response of the material. In this work we will be interested in ferritic / martensitic grades, some of which come from a manufacturing process which is the subject of a patent application [5-6] and for which we observe for the first time remarkable properties in resilience, associated with good hot mechanical properties.

The study will be based on a comparison of experience and finite element modeling. This applied research work will allow the student to acquire solid skills in fracture mechanics and fine characterization of materials (SEM, EBSD, etc.). A good understanding of the mechanical properties/microstructure relationships will make it possible to understand the origin of the observed properties and to propose new optimizations on the microstructures to improve the mechanical behavior and/or the shaping of the material.

Student profile: Engineer or M2 Mechanics/Materials

On the role of the elastic deformation field on the formation of irradiation defects in pure metals

In the context of extending the operational lifetime of nuclear power plants (NPPs), currently operating in France, a materials ageing surveillance strategy is in place. It is essential for ensuring their mechanical properties. During the operation of the plant, materials are subjected to irradiation. Under this exposure, the internal structure of materials evolves, leading to the creation of numerous defects that degrade macroscopic properties and may result in a limitation of the long-time operation (LTO) of components. The proposed work is a fundamental study conducted on model materials, aiming to better understanding the behavior under irradiation of metallic alloys. It will contribute to the predictive modelling of materials, covering defects created at the nanoscale up to the level of nuclear components.

The irradiation of materials with high-energy particles such as neutrons, ions, or electrons generates a large number of defects called point defects (PD). These mobile PDs can migrate and aggregate to form 2D or 3D-objects like prismatic loops or cavities respectively. They can also be eliminated at PD sinks. The system is then submitted to PDs flows directed towards these sinks. These flows are then responsible for phenomena such as radiation-induced segregation (RIS) or precipitation (RIP) of solute atoms [1] [2]. The presence of clusters of PDs and of PD flows alters the microstructure and can deteriorate the physical response of the irradiated materials. In particular, the formation of prismatic loops degrades the mechanical properties of materials as they can impede dislocations and induce embrittlement [3]. In a previous study, we focused on vacancy defects in the form of cavities and investigated the facetting of defects formed in a weakly anisotropic metal, aluminum, using in-situ irradiations in a high-resolution transmission electron microscope (HRTEM).
The work aims to go further in the role of the elastic deformation field on the morphology of irradiation defects. More precisely, it aims to carry out a systematic study on different metals with different anisotropy coefficients. We have chosen reference metals with body-centered cubic (BCC) and face-centered cubic (FCC) structures with low or high anisotropy coefficients. The study will concern Cr and Fe with a BCC structure, and Al and Cu with a FCC structure and may be extrapolated to alloys of higher complexity such as high entropy alloys (HEA). The work will be mainly experimental but will also include a theoretical part. The effects of the crystal anisotropy on the morphology of prismatic loops will be carried out by phase field modelling [4]. The spatial arrangement of the loops will be studied by Object Kinetic Monte-Carlo (OKMC) simulations [5], as recently done in aluminium.
The work will be mainly experimental. We will studied [100]-oriented single crystals to avoid any surface effect on the shape of the objects formed. They will be irradiated with heavy ions at temperatures normalized with respect to their melting temperature either in-situ within the Jannus Orsay platform, or ex-situ within the Jannus Saclay platform [6]. Loops will be imaged by conventional TEM or STEM with a FEI Tecnai and Jeol NeoARM type microscopes. The latter is equipped with a double spherical aberration corrector. The work will be carried out within the framework of the joint research laboratory (LRC) MAXIT.
The work will also include a modelling part. The effects of crystallographic anisotropy on the morphology of prismatic loops will be investigated using a phase-field code [4]. The spatial arrangement of the loops will be studied using Object Kinetic Monte Carlo (OKMC) [5], as recently done in aluminum.
This work follows a 2-year postdoctoral fellowship scheduled to conclude in December 2023, during which deep learning (DL) approaches were developed to accelerate the automatic detection of defects created under irradiation [7]. The utilization of these approaches will significantly enhance the statistical robustness and precision of the results.

Advantage for the student: The PhD is situated in a laboratory composed by 25 researchers and approximately 25 students (PhD, postdoctoral fellows), creating a simulating scientific environment. The activities involve both experimental and simulation sides, offering the opportunity to interact with experts from both sides.

[1] M. Nastar, L. T. Belkacemi, E. Meslin, et M. Loyer-Prost, « Thermodynamic model for lattice point defect-mediated semi-coherent precipitation in alloys », Communications Materials, vol. 2, no 1, p. 1-11, mars 2021, doi: 10.1038/s43246-021-00136-z.
[2] L. T. Belkacemi, E. Meslin, B. Décamps, B. Radiguet, et J. Henry, « Radiation-induced bcc-fcc phase transformation in a Fe3%Ni alloy », Acta Materialia, vol. 161, p. 61-72, 2018, doi: https://doi.org/10.1016/j.actamat.2018.08.031.
[3] M. Lambrecht et al., « On the correlation between irradiation-induced microstructural features and the hardening of reactor pressure vessel steels », Journal of Nuclear Materials, vol. 406, no 1, p. 84-89, 2010, doi: http://dx.doi.org/10.1016/j.jnucmat.2010.05.020.
[4] A. Ruffini, Y. Le Bouar, et A. Finel, « Three-dimensional phase-field model of dislocations for a heterogeneous face-centered cubic crystal », Journal of the Mechanics and Physics of Solids, vol. 105, p. 95-115, août 2017, doi: 10.1016/j.jmps.2017.04.008.
[5] D. Carpentier, T. Jourdan, Y. Le Bouar, et M.-C. Marinica, « Effect of saddle point anisotropy of point defects on their absorption by dislocations and cavities », Acta Materialia, vol. 136, p. 323-334, sept. 2017, doi: 10.1016/j.actamat.2017.07.013.
[6] A. Gentils et C. Cabet, « Investigating radiation damage in nuclear energy materials using JANNuS multiple ion beams », Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 447, p. 107-112, mai 2019, doi: 10.1016/j.nimb.2019.03.039.
[7] T. Bilyk, A. M. Goryaeva, E. Meslin, M.-C. Marinica, Quantification of radiation damage in high entropy alloys by deep learning approach, 2-7/10/2022, MMM2022, Baltimore, USA

Impact of irradiation parameters on the alpha’ phase formation in oxide dispersion strengthened steels

Ferritic-martensitic oxide dispersion strengthened steels (ODS steels) are materials of great interest in the nuclear industry. Predominantly composed of iron and chromium, these materials can become brittle due to the precipitation of a chromium-rich phase, called a', under irradiation. This phase, known to be sensitive to irradiation conditions, provides an ideal topic for a deeper exploration of the capability to emulate neutron irradiation with ions. Indeed, while ion irradiations are frequently used to understand phenomena observed during neutron irradiations, the question of their representativeness is often raised.

In this thesis, we aim to understand how the irradiation parameters can affect the characteristics of the a' phase in ODS steels. To do so, various ODS steels will be irradiated under different conditions (flux, dose, temperature, and type of particles, such as ions, neutrons, electrons), and subsequently analyzed at the nanoscale. The a' phase (size, chromium content) obtained for each ion irradiation condition will be compared to the one after neutron irradiation.

Synthesis, characterization and modeling of (Mn,Co)3O4 thin films applied to corrosion layers and spintronics

Spinel-type transition metal oxides (AB2O4) appear spontaneously during the generalized corrosion of steels or alloys in aqueous or gaseous environments at high temperatures. This spinel phase forms a continuous corrosion layer and thus regulates corrosion processes by controlling conductivity and material transport between the material and the oxidizing medium. They are also applied voluntarily as protective coatings against degradation phenomena. In particular, the Mn-Co-O spinel system is very promising as protective conductive layers on ferritic stainless steel used to fabricate interconnects in solid oxide fuel cells for green hydrogen production. The composition of the spinel phase determines the protective performance of the coatings. This feature is particularly delicate for materials used in high-temperature electrolyzers, as electronic transport must be optimal (high electrolysis), but must not be accompanied by material transport (low cation diffusion).
In contrast, electronic transport properties of spinel-type transition metal oxides are generally not well understood. Measurements are made on complex corrosion layers (or coatings) of variable composition, low crystallinity, complex microstructure and low thickness. Furthermore, spinel oxides exhibit magnetic properties and composition-dependent cationic disorder that are usually ignored, even though they have a strong impact on electronic transport. The properties highlighted here are the ones that also hold significant importance within the field of spintronics. Thus, tuning the chemical composition of these spinel-structured oxides (normal, inverse or mixed) offers a wide range of magnetic (ferrimagnetic, antiferromagnetic) and electronic (semimetallic, semiconductor, insulator) properties. In particular, CoMn2O4 is expected to exhibit a complex magnetic configuration [1], mainly related to the arrangement of Co2+ and Mn3+ cations in interstitial sites, which needs to be analyzed in detail. Unlike corrosion layers, these physical studies require the synthesis of thin films of well-controlled composition and high crystallinity.
The aim of the thesis is to build up knowledge of physicochemical and structural properties of (Mn,Co)3O4 in order to contribute to the elaboration of Mn-Co-O phase diagrams and electronic transport models based on the relationship between order/disorder, magnetic properties and resistivity of (Mn,Co)3O4. Eventually, the whole (Fe,Cr,Mn,Co)3O4 system will be also considered. The study will be carried out on thin films of perfectly controlled composition and high crystallinity, and will be enhanced by numerical simulations. The experimental and theoretical work will be based on the results of previous studies on (Ni,Fe,Cr)3O4 epitaxial thin films [2,3].
The thesis will be divided as follows:
- Growth of thin films and multilayers by MBE (Molecular Beam Epitaxy) (J.-B. Moussy)
- Spectroscopic characterization using XPS (X-ray photoemission spectroscopy) (F. Miserque)
- Fine structure characterization by DRX and X-ray absorption (XMCD) (P. Vasconcelos)
- Modeling of core-level spectra (XPS, XAS and XMCD) and atomistic modeling (A. Chartier)
- Magnetic characterization by SQUID/VSM magnetometry and electric transport characterization (J.-B. Moussy)

[1] Systematic analysis of structural and magnetic properties of spinel CoB2O4 (B= Cr, Mn and Fe) compounds from their electronic structures, Debashish Das, Rajkumar Biswas and Subhradip Ghosh, Journal of Physics: Condensed Matter 28 (2016) 446001.
[2] Stoichiometry driven tuning of physical properties in epitaxial Fe3-xCrxO4 thin films, Pâmella Vasconcelos Borges Pinho, Alain Chartier, Denis Menut, Antoine Barbier, Myrtille O.J.Y. Hunault, Philippe Ohresser, Cécile Marcelot, Bénédicte Warot-Fonrose, Frédéric Miserque, Jean-Baptiste Moussy, Applied Surface Science 615 (2023) 156354.
[3] Elaboration, caractérisation et modélisation de films minces et multicouches à base d’oxydes (Ni,Fe,Cr)3O4 appliquées à la corrosion et à la spintronique, A. Simonnot, thèse en cours.

High-Performance Computing (HPC) resolution of "point-saddle" problems arising from the mechanics of contact between deformable structures

In the field of structural mechanics, simulated systems often involve deformable structures that may come into contact. In numerical models, this generally translates into kinematic constraints on the unknown of the problem (i.e. the displacement field), which are dealt with by the introduction of so-called dual unknowns that ensure the non-interpenetration of contacting structures. This leads to the resolution of so-called "saddle-point" linear systems, for which the matrix is "indefinite" (it has positive and negative eigenvalues) and "sparse" (the vast majority of terms in this matrix are zero).

In the context of high-performance parallel computing, we're turning to "iterative" methods for solving linear systems, which, unlike "direct" methods, can perform well for highly refined numerical models when using a very large number of parallel computing processors. But for this to happen, they need to be carefully designed and/or adapted to the problem at hand.

While iterative methods for solving "positive definite" linear systems (which are obtained in the absence of kinematic constraints) are relatively well mastered, solving linear point-saddle systems remains a major difficulty [1]. A relatively abundant literature proposes iterative methods adapted to the treatment of the "Stokes problem", emblematic of incompressible fluid mechanics. But the case of point-saddle problems arising from contact constraints between deformable structures is still a relatively open problem.

The proposed thesis consists in proposing iterative methods adapted to the resolution of linear "saddle-point" systems arising from contact problems between deformable structures, in order to efficiently handle large-scale numerical models. The target linear systems have a size of several hundred million unknowns, distributed over several thousand processes, and cannot currently be solved efficiently, either by direct methods, or by "basic" preconditioned iterative methods. In particular, we will validate the approach proposed by Nataf and Tournier [2] and adapt it to cases where the constraints do not act on all the primal unknowns.

The work carried out can be applied to numerous industrial problems, particularly in the nuclear industry. One example is the case of fuel pellets, which expand under the effect of temperature and the generation of fission products, and come into contact with the metal cladding of the fuel rod, which can lead to cladding failure [3].

This thesis is in collaboration with the LIP6 laboratory (Sorbonne-université).

An internship can be arranged in preparation for thesis work, depending on the candidate's wishes.

[1] Benzi, M., Golub, G. H., & Liesen, J. (2005). Numerical solution of saddle point problems. Acta numerica, 14, 1-137. (https://page.math.tu-berlin.de/~liesen/Publicat/BenGolLie05.pdf)
[2] Nataf, F., & Tournier, P. H. (2023). A GenEO Domain Decomposition method for Saddle Point problems. Comptes Rendus. Mécanique, 351(S1), 1-18. (https://doi.org/10.5802/crmeca.175)
[3] Michel, B., Nonon, C., Sercombe, J., Michel, F., & Marelle, V. (2013). Simulation of pellet-cladding interaction with the pleiades fuel performance software environment. Nuclear Technology, 182(2), 124-137. (https://hal.science/hal-04060973/document)

Implicit/explicit transition for numerical simulation of Fluid-Structure Interaction problems treated by immersed boundary techniques

In many industrial sectors, rapid transient phenomena are involved in accident scenarios. An example in the nuclear industry is the Loss of Primary Coolant Accident, in which an expansion wave propagates through the primary circuit of a Pressurized Water Reactor, potentially vaporizing the primary fluid and causing structural damage. Nowadays, the simulation of these fast transient phenomena relies mainly on "explicit" time integration algorithms, as they enable robust and efficient treatment of these problems, which are generally highly non-linear. Unfortunately, because of the stability constraints imposed on time steps, these approaches struggle to calculate steady-state regimes. Faced with this difficulty, in many cases, the kinematic quantities and internal stresses of the steady state of the system under consideration at the time of occurrence of the simulated transient phenomenon are neglected.

Furthermore, the applications in question involve solid structures interacting with the fluid, undergoing large-scale deformation and possibly fragmenting. A immersed boundary technique known as MBM (Mediating Body Method [1]) recently developed at the CEA enables structures with complex geometries and/or undergoing large deformations to be processed efficiently and robustly. However, this coupling between fluid and solid structure has only been considered in the context of "fast" transient phenomena treated by "explicit" time integrators.

The final objective of the proposed thesis is to carry out a nominal regime calculation followed by a transient calculation in a context of fluid/immersed-structure interaction. The transient phase of the calculation is necessarily based on "explicit" time integration and involves the MBM fluid/structure interaction technique. In order to minimize numerical disturbances during the transition between nominal and transient regimes, the calculation of the nominal regime should be based on the same numerical model as the transient calculation, and therefore also rely on an adaptation of the MBM method.

Recent work defined an efficient and robust strategy for calculating steady states for compressible flows, based on "implicit" time integration. However, although generic, this approach has so far only been tested in the case of perfect gases, and in the absence of viscosity.

On the basis of this initial work, the main technical challenges of this thesis are 1) to validate and possibly adapt the methodology for more complex fluids (in particular water), 2) to introduce and adapt the MBM method for fluid-structure interaction in this steady-state calculation strategy, 3) to introduce fluid viscosity, in particular within the framework of the MBM method initially developed for non-viscous fluids. At the end of this work, implicit/explicit transition demonstration calculations with fluid-structure interaction will be implemented and analyzed.

An internship can be arranged in preparation for thesis work, depending on the candidate's wishes.

[1] Jamond, O., & Beccantini, A. (2019). An embedded boundary method for an inviscid compressible flow coupled to deformable thin structures: The mediating body method. International Journal for Numerical Methods in Engineering, 119(5), 305-333.