"
In a context where material durability is essential for the safety of infrastructures and the promotion of a sustainable energy transition, mastering corrosion phenomena represents a major challenge for key sectors such as decarbonized energy transport through buried pipelines and civil engineering (hydrogen, nuclear, underground infrastructures). The CORPORE project addresses this issue by proposing the development of advanced numerical simulation models to study corrosion in porous media using COMSOL Multiphysics.
The main scientific and technological objective is to establish an integrated multiphysics modeling approach for the electrochemical and transport mechanisms within porous materials: studying the coupled influence of chemistry, pore network properties, and material–environment interactions on the initiation and propagation of corrosion.
This approach will help optimize anticorrosion protection strategies, reduce maintenance costs, and extend the service life of structures. From a state-of-the-art perspective, most current models focus on homogeneous media and compartmentalized approaches. Our project stands out by integrating a multi-scale mechanistic modeling framework combined with the use of archaeological data for long-term validation.
"
This research proposal focuses on the study and implementation of polytopal methods for solving the equations of fluid mechanics. These methods aim to handle the most general meshes possible, overcoming geometric constraints or those inherited from CAD operations such as extrusions or assemblies that introduce non-conformities. This work also falls within the scope of high-performance computing, addressing the increase in computational resources and, in particular, the development of massively parallel computing on GPUs.
The objective of this thesis is to build upon existing polytopal methods already implemented in the TRUST software, specifically the Compatible Discrete Operator (CDO) and Discontinuous Galerkin (DG) methods. The study will be extended to include convection operators and will investigate other methods from the literature, such as Hybrid High Order (HHO), Hybridizable Discontinuous Galerkin (HDG), and Virtual Element Method (VEM).
The main goals are to evaluate:
1. The numerical behavior of these different methods on the Stokes/Navier-Stokes equations;
2. The adaptability of these methods to heterogeneous architectures such as GPUs.
MRI scanners are invaluable tools for medicine and research, whose operation is based on exploiting the properties of atomic nuclei immersed in a very intense static magnetic field. In almost all MRI scanners, this field is generated by a superconducting electromagnet.
The design of electromagnets for MRI must meet very demanding requirements in terms of the homogeneity of the field produced. In addition, as the magnetic field becomes more intense, the forces exerted on the electromagnet increase, raising the issue of the mechanical strength of the windings. Finally, the “manufacturability” of the electromagnet imposes constraints on the shapes of acceptable solutions. The design of superconducting electromagnets for MRI therefore requires a meticulous effort to optimize the design, subject to constraints based on magneto-mechanical multiphysics modeling.
A new innovative multiphysics topological optimization methodology has been developed, based on a density method (SIMP) and a finite element code. This has made it possible to produce magnet designs that meet the constraints on the homogeneity of the magnetic field produced and on the mechanical strength of the windings. However, the solutions obtained are not feasible in practice, both in terms of the manufacturability of the coils (cable windings) and their integration with a supporting structure (coils held in place by a steel structure).
The objective of this thesis is to enhance the topological optimization method by formalizing and implementing manufacturing constraints related to the winding method, residual stresses resulting from pre-tensioning the cables during winding, and the presence of a structural material capable of absorbing the forces transmitted by the coils.
Until recently, CO2 capture technologies were developed separately from CO2 utilization technologies, even though coupling the CO2 desorption stage with the chemical transformation of CO2, which is generally exothermic, would yield significant energy savings.
The first coupled solutions have recently been proposed, but they are mainly at moderate temperatures (100-180°C) [1], or even recently close to 225°C [2].
The objective of this doctoral thesis is to study, both experimentally and theoretically, a coupled system in the 250-325°C temperature range that allows via Fischer-Tropsch-type catalytic hydrogenation the direct production of higher value-added products
Reinforcing steel plays a major role in the behavior of reinforced concrete structures. Nevertheless, significant conservatisms may sometimes be imposed by design codes, raising questions about the feasibility of construction or the viability of the structure (economic, environmental, etc.). It is within this context that the doctoral research takes place. Building on recent developments, the work aims to propose an innovative design approach relying on the use of nonlinear finite element calculations, combined with topological optimization algorithms (defining reinforcement directions and bar cross-sections) and evolutionary optimization algorithms (determining the placement of bars with fixed cross-sections).
The method should, through an iterative process, yield solutions that meet an optimal design configuration. Considering the multiple, potentially conflicting objectives to minimize (such as cost, feasibility, strength, and carbon footprint), the approach will guide the configuration of input parameters based on an analysis of the relevant output results.
Applying the method to complex, practice-based case studies (for example, beam-column junctions) will demonstrate its relevance compared with more conventional design methods. By the end of the thesis, the doctoral candidate will have developed advanced skills in the use and development of state-of-the-art tools, ranging from nonlinear finite element simulation to modern optimization techniques based on artificial intelligence.
Operating nuclear reactors are subject to a variety of perturbations. These can include vibrations of the fuel pins and fuel assemblies due to fluid-structure interactions with the moderator, or even vibrations of the core barrel, baffle, and pressure vessel. All of these perturbations can lead to small periodic fluctuations in the reactor power about the stable average power level. These power fluctuations are referred to as “neutron noise”. Being able to simulate different types of in-core perturbations allows reactor designers and operators to predict how the neutron flux could behave in the presence of such perturbations. In recent years, many different research groups have worked to develop computational models to simulate these sources of neutron noise, and their resulting effects on the neutron flux in the reactor. The primary objective of this PhD thesis will be to bring Monte Carlo neutron noise simulations to the scale of real-world industry calculations of nuclear reactor cores, with a high-fidelity continuous-energy physics representation. As part of this process, the student will add novel neutron noise simulation capabilities to TRIPOLI-5, the next-generation production Monte Carlo particle-transport code jointly developed by CEA and ASNR, with the support of EDF.
As part of its study of progressive deformations in fuel assemblies within PWR cores, the CEA has developed two simulation tools. The first, Phorcys [1], calculates the flow of coolant in and around slightly deformed assemblies using a network of parametric pressure drops, then deduces the fluid forces acting on the structures. The second, DACC [2], uses finite element simulation to analyze thermomechanical behavior under irradiation and the interaction between assemblies during power cycles. Finally, fluid-structure interaction is analyzed using numerical coupling of these two tools, within which uncertainties can be propagated and analyzed [3].
The nuclear revival program (SMR, 4th generation reactors, PN, etc.) is providing new technologies and new core and fuel assembly topologies that need to be analyzed in terms of the risks associated with quasi-static deformations of core assemblies. With a view to both capitalizing on and extending the possibilities of simulation, the aim is to enable these two tools to handle the flow and deformation of slender structures in a more generic way in order to cover a wide range of nuclear technologies efficiently and quickly.
To do this, it will be necessary to identify, classify, and then model in a reduced but predictive manner the main flow structures that may occur within a fluid volume cluttered with slender structures with a large exchange surface area. The complete hydraulic model of the core will thus be created by concatenating elementary models that comply with strict interfacing conditions. A method for analyzing the overall flow obtained will then enable the quantification of the force field contributing to the deformations. A similar logic of classification and scaling would also be implemented with regard to the evaluation of reversible and irreversible deformations of a slender structure subjected to external stresses and severe irradiation. One difficulty is that the fine topology of a fuel assembly can exhibit nonlinearities at small scales that propagate in part to the macroscopic scale. Ultimately, a robust, cost-effective partitioned coupling will have to be implemented between the coolant flow and these individual structures, which deform and interact in a constrained environment.
The modeling framework thus constructed will make it possible to study the progressive deformations of assemblies and the associated risks for a wide range of nuclear reactor technologies.
Neutronics is the study of the behavior of neutrons in matter and the reactions they induce, particularly the generation of power through the fission of heavy nuclei. Modeling the steady-state neutron flux in a reactor core relies on solving a generalized eigenvalue problem of the form:
Find (phi, keff) such that A phi=1/keff B phi and keff is the eigenvalue with the largest magnitude, where A is the disappearance matrix which is assumed invertible, B represents the production matrix, phi denotes the neutron flux, and keff is called the multiplication factor.
The neutronics code APOLLO3® is a joint project of CEA, Framatome, and EDF for the development of a next-generation code for reactor core physics to meet both R&D and industrial application needs [4].
The MINOS solver [2] is developed within the framework of the APOLLO3® project. This solver is based on the mixed finite element discretization of the neutron diffusion model or the simplified transport model. The strategy for solving the aforementioned generalized eigenvalue problem is iterative; it involves applying the inverse power method [6].
The convergence speed of this inverse power method algorithm depends on the spectral gap. In the context of large cores such as the EPR reactor, it is observed that the spectral gap is close to 1, which degrades the convergence of the inverse power method algorithm. It is necessary to apply acceleration techniques to reduce the number of iterations [7]. In neutron transport, the preconditioning called Diffusion Synthetic Acceleration is very popular for the so-called inner iteration [1] but has also recently been applied to the so-called outer iteration [3]. A variant of this method was introduced in [5] for solving a source problem. It is theoretically shown that this variant converges in all physical regimes.
[1] M. L. Adams, E. W. Larsen, Fast iterative methods for discrete-ordinates particle transport calculations, Progress in Nuclear Energy, Volume 40, Issue 1, 2002.
[2] A.-M. Baudron and J.-J. Lautard. MINOS: a simplified PN solver for core calculation. Nuclear Science and Engineering, volume 155(2), pp. 250–263 (2007).
[3] A. Calloo, R. Le Tellier, D. Couyras, Anderson acceleration and linear diffusion for accelerating the k-eigenvalue problem for the transport equation, Annals of Nuclear Energy, Volume 180, 2023.
[4] P. Mosca, L. Bourhrara, A. Calloo, A. Gammicchia, F. Goubioud, L. Mao, F. Madiot, F. Malouch, E. Masiello, F. Moreau, S. Santandrea, D. Sciannandrone, I. Zmijarevic, E. Y. Garcia-Cervantes, G. Valocchi, J. F. Vidal, F. Damian, P. Laurent, A. Willien, A. Brighenti, L. Graziano, and B. Vezzoni. APOLLO3®: Overview of the New Code Capabilities for Reactor Physics Analysis. Nuclear Science and Engineering, 2024.
[5] O. Palii, M. Schlottbom, On a convergent DSA preconditioned source iteration for a DGFEM method for radiative transfer, Computers & Mathematics with Applications, Volume 79, Issue 12, 2020.
[6] Y. Saad. Numerical methods for large eigenvalue problems: revised edition. Society for Industrial and Applied Mathematics, 2011.
[7] J. Willert, H. Park, and D. A. Knoll. A comparison of acceleration methods for solving the neutron transport k-eigenvalue problem. Journal of Computational Physics, 2014, vol. 274, p. 681-694.