Shape optimization for innovation in nuclear fuels
Nuclear industry is currently developping enhanced Accident Tolerant Fuels" (ATF) [1]. These fuels feature enhanced physical properties; in particular, thanks to the addition of thermal conductors inside the fuel, they tend to be colder in standard as well as in accident conditions.
This thesis aims at developping numerical strategies (that will be programmed into a semi-industrial code) in order to propose new "shapes" of fuels (by "shape", we mean internal structures or microstructures), and to optimze already existing concepts. It will take advantage of recent numerical and mathematical techniques related to the so-called "shape optimization" [2]. Based on the previous work [3], more and more complex physical phenomena will be taken into account : first, thermal conductivity and mechanical behaviour in standard conditions, then gaz diffusion... Discussion with experts and modelization will be necessay in order to reformulate these physical behaviours into forms amenable to numerical simulation.
This thesis will take place at the CEA center of Cadarache in the fuel research department, in a laboratory devoted to modelling and numerical methods. The latter is affiliated to the Institute IRESNE for the research low-carbon energy production.
This project will be in collaboration with Nice University offering so an environment both academic and connected to application.
It also takes part in the PEPR DIADEM called Fast-in-Fuel, a national research project.
We search for excellent candidates with a solid background in scientific computing, analysis and numerical analysis of partial differential equations, as well as in optimization. Skills in physics (mechanics and thermics) will also be considered. The proposed subject aims at a concrete application at the intersection of various scientific fields, and it is largely exploratory. Hence, curiosity and creativity will also be highly appreciated.
[1] Review of accident tolerant fuel concepts with implications to severe accident progression and radiological releases, 2020.
[2] G. Allaire. Shape optimization by the homogenization method, volume 146 of Applied Mathematical Sciences. Springer-Verlag, New York, 2002.
[3] T. Devictor. PhD Manuscript, 2025 (in preparation)
Constrained geometric optimization of immersed boundaries for thermal-hydraulic simulations of turbulent flow in a finite-volume approach
The technical issue underpinning this thesis topic is the mitigation of the consequences of a loss of primary coolant accident in a pressurized water reactor with loops. It is of the utmost importance to minimize the flow of water leaving the vessel and to manage the available cold water reserves for safety injections as effectively as possible, in order to prevent or delay core flooding, overheating, and possible core degradation. To this end, the use of passive devices operating on the principle of hydraulic diodes, such as vessel flow limiters or advanced accumulators, is being considered. The subject of this thesis is the geometric optimization of this type of device, described by an immersed boundary, in order to maximize its service efficiency.
Several recent theses have shown how to introduce the Penalized Direct Forcing (PDF) immersed boundary method into the TRUST/TrioCFD software, under various spatial discretizations and for laminar and turbulent regimes. Similarly, they have ruled on the possibilities of deterministic geometric optimization in the finite-element context during simulations, based on the use of the PDF method.
After a bibliographic study of this kind of method, we will focus on the possibilities of implementation in finite volume discretization, the consideration of constraints, and the comparison to reference calculations. The latter will be carried out on academic and industrial configurations (accumulators and flow limiters).
The doctoral student will work in a R&D unit on innovative nuclear system within the IRESNE Institute (CEA Cadarache. He will develop skills in fluid mechanics and numerical methods.
Development of an autonomous module for glass alteration modeling and its coupling with reactive transport codes
In the context of the sustainable and safe use of nuclear energy within a carbon-free energy mix that addresses the climate emergency, managing radioactive waste inventory is a priority concern. The alteration of nuclear glass therefore directly affects the long-term assessment of the safety of geological storage of this waste. Understanding and simulating these processes is therefore a major scientific, industrial, and societal challenge. Existing models, such as GRAAL2 [1] developed at the CEA, capture the passivation mechanisms governing glass alteration, bridging nanometric processes to mesoscopic scale through mesoscopic-scale kinetic laws used in reactive transport codes (RTC).
This PhD aims to develop an autonomous glass module (GM) based on the GRAAL2 model, capable of computing glass alteration kinetics and interfacing with different reactive transport codes (HYTEC, CRUNCH…). The main objectives are: (i) to design and implement a kinetic module, (ii) to develop a coupling interface managing information exchange with RTC, (iii) to define and carry out numerical validation campaigns on reference test cases for both the GM and the coupler, and (iv) to perform sensitivity and uncertainty analyses to identify the key parameters controlling glass behavior in a multi-material context (glass, iron, clay).
The PhD will take place at the Laboratory for Environmental Transfer Modeling (LMTE), within the IRESNE Institute (CEA, Cadarache site, Saint-Paul-lès-Durance). The project will provide the PhD candidate with cross-disciplinary skills in geochemistry, multiphysics coupling, and scientific software development, opening career opportunities in both academic research and nuclear/environmental engineering.
References:
[1] M. Delcroix, P. Frugier, E. Geiger, C. Noiriel, The GRAAL2 glass alteration model: initial qualification on a simple chemical system, Npj Mater Degrad 9 (2025) 38. https://doi.org/10.1038/s41529-025-00589-4.
Proximal primal-dual method for joint estimation of the object and of unknown acquisition parameters in Computed Tomography.
As part of the sustainable and safe use of nuclear energy in the transition to a carbon-free energy future, the Jules Horowitz research reactor, currently under construction at the CEA Cadarache site, is a key tool for studying the behaviour of materials under irradiation. A tomographic imaging system will be exploited in support of experimental measures to obtain real-time images of sample degradation. This imaging system has extraordinary characteristics due to its geometry and to the size of the objects to be characterized. As a result, some acquisition parameters, which are essential to obtain a sufficient image reconstruction quality, are not known with precision. This can lead to a significant degradation of the final image.
The objective of this PhD thesis is to propose methods for the joint estimation of the object under study and of the unknown acquisition parameters. These methods will be based on modern convex optimization tools. This thesis will also explore machine learning methods in order to automate and optimize the choice of hyperparameters for the problem.
The thesis will be carried out in collaboration between the Marseille Institute of Mathematics (I2M CNRS UMR 7373, Aix-Marseille University, Saint Charles campus) and the Nuclear Measurement Laboratory of the IRESNE institute of the French Alternative Energies and Atomic Energy Commission (CEA Cadarache, Saint Paul les Durance). The doctoral student will work in a stimulating research environment focused on strategic questions related to non-destructive testing. He or she will also have the opportunity to promote his or her research work in France and abroad.
Modeling of Critical Heat Flux Using Lattice Boltzmann Methods: Application to the Experimental Devices of the RJH
LBM (Lattice Boltzmann Methods) are numerical techniques used to simulate transport phenomena in complex systems. They allow modeling fluid behavior in terms of particles moving on a discrete grid (a "lattice"). Unlike classical methods, which solve the differential equations of fluids directly, LBM simulate the evolution of the fluid particle distribution functions in a discrete space using propagation and collision rules.
The choice of lattice in LBM is a crucial step, as it directly affects the accuracy, efficiency, and stability of the simulations. The lattice determines how fluid particles interact and move through space, as well as how the discretization of space and time is performed.
LBM methods exhibit a natural parallelism because the computations at each grid point are relatively independent. Compared to classical CFD methods, LBM can better capture certain complex phenomena (such as multiphase, turbulent, or porous media flows) because they rely on a mesoscopic modeling of the fluid, directly derived from particle kinetics, rather than on a macroscopic resolution of the Navier–Stokes equations. This approach allows for a finer representation of interfaces, nonlinear effects, and local interactions, which are often difficult to model accurately using classical CFD methods. LBM therefore enables the capture of complex phenomena at a lower computational cost. Recent studies have notably shown that LBM can reproduce the Nukiyama boiling curve (pool boiling) and, consequently, accurately calculate the critical heat flux. This flux corresponds to a bulk boiling, known as a boiling crisis, which results in a sudden degradation of heat transfer.
The critical heat flux is a crucial issue for the experimental devices (DEX) of the Jules Horowitz Reactor, as they are cooled by water either via natural convection (fuel capsule-type devices) or forced convection (loop-type devices). Thus, to ensure the proper cooling of the DEX and reactor safety, it is essential to verify that the critical heat flux is not reached within the studied parameter range. It must therefore be determined with precision. Previous studies conducted on a fuel-capsule-type DEX using the NEPTUNE-CFD code (classical CFD methods) have shown that modeling is limited to regions far from the critical heat flux. In general, flows with high void fractions (greater than 10%) cannot be easily resolved using classical CFD approaches.
The student will first define a lattice to apply LBM to a RJH device under natural convection. They will consolidate the results obtained for the critical heat flux on this configuration by comparing them with available data. Finally, exploratory calculations under forced convection (laminar to turbulent regime) will be conducted.
The student will be hosted at the IRESNE institute.
Electrical impédanceTomography for the Study of Two-Phase Liquid Metal/Gas Flows
As part of the sustainable use of nuclear energy within a carbon-free energy mix in combination with renewable energies, fourth-generation fast neutron reactors are crucial for closing the fuel cycle and controlling uranium resources. Ensuring the safety of such a sodium-cooled reactor relies for a significant part on the early detection of gas voids in their circuits. In these opaque and metallic environments, optical imaging methods are ineffective, making it necessary to develop innovative techniques.
This PhD project is part of the development of Electrical Impedance Tomography (EIT) applied to liquid metals, a non-intrusive approach enabling the imaging of local conductivity distributions within a flow.
The work will focus on the study of electromagnetic phenomena in two-phase metal/gas systems, in particular the skin effect and eddy currents generated by oscillating fields.
Artificial-intelligence approaches, such as Physics-Informed Neural Networks (PINNs), will be explored to combine numerical learning with physical constraints and will be compared with purely numerical simulations.
The objective is to establish refined physical models adapted to metallic environments and to design inversion methods robust against measurement noise.
Experiments on Galinstan will be conducted to validate the models and demonstrate the feasibility of detecting gas inclusions in a liquid metal.
This research, carried out at IRESNE Institute of CEA Cadarache, will open new perspectives in electromagnetic imaging for opaque, highly conductive media.
Towards a new iterative approach for the efficient modeling of mechanical contact
As part of the modeling and simulation of nuclear fuel behavior across different reactor types, the Institute for Research on Nuclear Energy Systems for Low-Carbon Energy Production (IRESNE) at CEA Cadarache, in partnership with various industrial and academic stakeholders, is developing the PLEIADES software platform for fuel behavior simulation. In this context, the interaction between the fuel and its cladding, the first containment barrier, is a key phenomenon for understanding and predicting the behavior of fuel elements.
The modeling and numerical simulation of mechanical contact phenomena represent a major scientific and technological challenge in solid mechanics, due to the intrinsic complexity of the problem, characterized by its highly nonlinear and non-smooth nature.
To overcome the limitations of classical approaches, such as the penalty or Lagrange multiplier methods, new contact resolution strategies based on iterative fixed-point schemes are currently being explored at the CEA. These approaches offer several advantages: they avoid the direct solution of complex and ill-conditioned systems, significantly improve numerical efficiency, and exhibit very low sensitivity to algorithmic parameters, making them particularly well suited for high-performance computing (HPC) environments.
The objective of this PhD work is to extend these strategies to more complex and realistic situations, by taking into account nonlinear material behaviors and incorporating more sophisticated contact laws, such as friction. Depending on the progress of the work, the final phase will focus on transferring the developments to a high-performance computing (HPC) environment, using a parallel finite element solver.
The project will benefit from internationally recognized expertise in mechanics, applied mathematics, and nuclear fuel simulation, with supervision from CEA researchers and additional academic collaborations (CNRS).
[1] P. Wriggers, "Computational Contact Mechanics", Springer, 2006. doi:10.1007/978-3-540-32609-0.
[2] V. Yastrebov, "Numerical Methods in Contact Mechanics", ISTE Ltd and John Wiley & Sons, 2013. doi: 10.1002/9781118647974
[3] I. Ramière and T. Helfer, “Iterative residual-based vector methods to accelerate fixed point iterations”, Computers & Mathematics with Applications, vol. 70, no. 9, pp. 2210–2226, 2015. doi: 10.1016/j.camwa.2015.08.025.
Multi-physics modelling of a light water nuclear reactor operating under natural convection: study of innovative solutions for startup and power control
Among the most recent designs of water-moderated Small Modular Reactors (SMR), several concepts are characterized by natural convection in the primary circuit during normal and abnormal operation, with the aim of increasing the inherent safety of the design. The absence of primary pumps in this type of SMRs significantly complicates the start-up and power increase ramps. This requires the development of specific start-up procedures to heat up the primary water circuit and enable the reactor to reach its nominal conditions, in accordance with safety requirements. These kinds of procedures rely on simulations using validated models to understand the reactor behavior during these phases and define the accessible parameters domain.
The goal of this PhD project is to develop a numerical model capable of simulating the startup of an SMR operating in natural convection, and to contribute to the validation of this model. The PhD study also aims at developing a methodology for reactor control systems optimization, to attain a fast startup while remaining within the prescribed safety criteria.
The analysis of the reactor startup procedure entails two disciplines: thermal-hydraulics and neutronics, which requires the development of multi-physics coupled simulation tools. Three scientific calculation tools in particular will be coupled in the framework of the PhD study: CATHARE3 (reactor system thermal-hydraulics), FLICA5 (core thermal-hydraulics) and APOLLO3 (neutronics).
The PhD student will work in a team of neutron physicists and thermohydraulic engineers at the IRESNE Institute (CEA Cadarache). He/she will develop skills in nuclear reactor physics and modeling.
Simulation of crack initiation and propagation in random heterogeneous materials
This PhD thesis is concerned with cracking in nuclear fuels at the microstructure level, a phenomenon that is essential to understand in order to model the behavior of materials under irradiation. Indeed, crack initiation and propagation can lead to the release of fission gases and the formation of fragments inducing fissile matter displacement. Current industrials models are based on simplified representations of the porous microstructure and empirical fracture criteria, which limits their physical accuracy and validation by separate effects.
To overcome these limitations, the proposed thesis work consists of using multi-scale approaches and high-performance computing (HPC) finite element simulations. The main objectives are to define a Representative Volume Element (RVE) for crack initiation in materials with random porosity, improve the failure criteria used in legacy codes and define their uncertainties, and finally establish the domain of validity for analyzing crack propagation in the RVE.
The first line of research consists of rigorously defining the size of the RVE based on local physical variables such as the maximum principal stress. Variance reduction methods will be used to optimize the number of calculations required and estimate the associated errors.
In a second step, simulations performed to determine the RVE size will be used to improve industrial models. The approach will seek to separate the mechanical effects of an isolated bubble from those resulting from interactions between neighboring bubbles. Machine learning techniques may be used to develop this new model. Validation will be based on indirect measurements of cracking, such as gas release observed during thermal annealing, particularly for high burn-up structure (HBS) fuels, where legacy models fail to predict the kinetics of cracking.
Finally, crack propagation within the RVE will be studied using 3D phase field simulations, which allow for detailed representation of the various stages after the crack initiation. The influence of boundary conditions on the RVE will be examined by comparison with simulations on larger domains.
The thesis will be carried out at the Institute for Research on Nuclear Systems for Low-Carbon Energy Production (IRESNE) of the CEA Cadarache, within the PLEIADES platform development team, which is specialized in fuel behavior simulation and multiscale numerical methods. It will be conducted in collaboration with the CNRS/LMA as part of the MISTRAL joint laboratory, notably on aspects relating to the analysis of random medium representativeness and micromechanical simulation of crack propagation.
Numerical Simulation of Fluid–Structure Interactions with Contact under Flow Using a Penalized Direct Forcing Method
This PhD work is part of the study of the dynamics of fuel assemblies subjected to axial flow and external mechanical excitation, particularly of seismic type. The objective is to develop an innovative numerical approach capable of accurately predicting the three-dimensional dynamic response of one or several assemblies, while accounting for the coupled effects between the fluid flow and mechanical loads. This problem is particularly complex due to the need to consider large displacements, potential contacts between structures, and strong interactions with the surrounding fluid.