Assessment of new models for the investigation of hypothetical accidents in GEN4 fast reactors.
Multi-component two-phase flows in conjunction with fluid-structure interaction (FSI) problems can occur in a very large variety of engineering applications; amongst them, the hypothetical severe accidents postulated in Generation IV sodium and lead fast-breeder reactors (respectively SFR and LFR).
In SFRs, the worst postulated severe accident is the so-called hypothetical core disruptive accident (HCDA), in which the partial melt of the core of the reactor interacts with the surrounding sodium and creates a high-pressure gas bubble, the expansion of which generates shock waves and is responsible of the motion of liquid sodium, thus eventually damaging internal and surrounding structures.
The LFR presents the advantage that, unlike sodium, lead does not chemically react with air and water and, therefore, is explosion-proof and fire-safe. On the one hand, this allows a steam generator inside the primary coolant. On the other hand, the so-called steam generator tube ruptures (SGTR) should be investigated to guarantee that, in the case of this hypothetical accident the structure integrity is preserved. In the first stage of a SGTR, it is supposed that the steam-generator high-pressure high-temperature water penetrates inside the primary containment, thus generating a BLEVE (boiling liquid expanding vapor explosion) with the same behavior and consequences as the high-pressure gas bubble of a HCDA.
In both HCDA and STGR, there are situations in which the multi-component two-phase flows is in low Mach number regime which, when studied with classical compressible solver, presents problems of loss of accuracy and efficiency. The purpose of this PhD is
* to design a multiphase solver, accurate and robust, to investigate HCDA STGR scenarios.
* to design a low Mach number approach for bubble expansion problem, based on the artificial compressibility method presented in the recent paper "Beccantini et al., Computer and fluids 2024".
The aspect FSI will be also taken into account.
Code Development and Numerical Simulation of Gas Entrainment in Sodium-Cooled Fast Reactors
In sodium-cooled fast reactors (SFRs), the circulation of liquid sodium is ensured by immersed centrifugal pumps. Under certain conditions, vortices can develop in recirculation zones, promoting the entrainment of inert gas bubbles (typically argon) located above the free surface. If these bubbles are drawn into the primary circuit, they can damage pump components and compromise the safety of the installation. This phenomenon remains difficult to predict, particularly during the design phase, as it depends on numerous physical, geometrical, and numerical parameters.
The objective of this PhD work is to contribute to a better understanding and modeling of gas entrainment in free-surface flows typical of SFRs, through Computational Fluid Dynamics (CFD) simulations using the open-source code TrioCFD, developed by the CEA. This code includes an interface-tracking module (Front Tracking) that is particularly well-suited for simulating two-phase phenomena involving a deformable free interface.
Effect of gravity on agitation within a turbulent bubbly flow in a channel
Understanding two-phase flows and the boiling phenomenon is a major challenge for the CEA, for both the design and safety of nuclear power plants. In a Pressurized Water Reactor (PWR), the heat generated by the nuclear fuel is transferred to the water in the primary circuit. Under accident conditions, the water in the primary circuit can enter a nucleate boiling regime, or even evolve to a boiling crisis. While the phenomenon of boiling is the subject of numerous studies, the dynamics of the generated bubbles also receive special attention at the CEA. This thesis will focus on the coupling between the turbulence generated by a shear flow and the agitation induced by the bubbles. Its originality lies in the study of the effect of gravity, achieved by tilting the channel, a parameter that can generate complex flow regimes.
This experimental work will be based on the new CARIBE facility at CEA Saclay. The PhD student's mission will be to characterize the different flow regimes and then to conduct a detailed study of the flow by implementing specific metrology (including Particle Image Velocimetry (PIV), hot-film anemometry, and optical probes). Conducted within the LE2H laboratory, the project will benefit from a close collaboration with the LDEL (CEA Saclay) and the IMFT (Toulouse). The PhD student will work in a dynamic environment with other PhD students and will present their work at national and international conferences.
We are looking for a candidate with a background in fluid mechanics and a strong interest in experimental work (a Master's thesis internship is possible). This PhD offers the opportunity to develop expertise in instrumentation, data analysis, and turbulent two-phase flows—skills that are highly valued in the energy, industrial, and academic research sectors.
Localised solidifications in Molten Salt Reactors
In a Molten Salt Reactor (MSR), the nuclear fuel is a liquid, high-temperature salt which acts as its own coolant. Some accidental transients (over-cooling of the fuel, leak) may cause localised solidifications of the fuel salt in the core. These solidifications will have in turn an impact on the salt flow in the core, as well as its neutronic behavior, and could lead to a localised over-heating of the core vessel. Such transients are not well studied, although they have a major impact on the safety and design of an MSR.
The objective of the PhD is to study different accidental transients that would lead to localised solidifications, and to study their impact on the neutronics and thermal-hydraulics of the core. These analyses will require the use of multiphysics, MSR-adapted numerical tools, such as the CFD code TrioCFD and its extensions TRUST-NK (neutronics) and Scorpio (reactive transport), as well as the deterministic neutronic code APOLLO3. In order to balance precision and computation time, different models will be tested, depending on the transient studied: 1D/ turbulent 3D (RANS, LES) models for thermal-hydraulics ; diffusion / SPn transport / Sn transport for neutronics.
Numerical modelling of large ductile crack progagation and assessment of margins comparing to engineering approach
Predicting failure modes in metal structures is an essential step in analyzing the performance of industrial components where mechanical elements are subjected to significant stress (e.g., nuclear power plant components, pipelines, aircraft structural elements, etc.). To perform such analyses, it is essential to correctly simulate the behavior of a defect in ductile conditions, i.e., in the presence of significant plastic deformation before and during propagation.
Predictive numerical simulation of ductile tearing remains an open scientific and technical issue despite significant progress made in recent years. The so-called local approach to fracture, notably the Gurson model (and its modified version GTN), is widely used to model ductile tearing. However, its use has limitations: significant computation time, simulation stoppage due to the presence of completely damaged elements in the model, and non-convergence of the result when the mesh size is reduced.
The aim of this thesis is to develop the ductile tear simulation model used at LISN so that it can be applied to large crack propagation on complex structures. It also aims to compare the results obtained with engineering methods that are simpler to implement.
Fatigue crack growth modelling with residual stress - Improvement of the Gtheta method
Residual stresses are self-balanced stress fields found in certain mechanical components in the absence of external loading. Caused by welding, for example, these stresses can potentially affect the behaviour of the structure and its resistance to fracture. When demonstrating the integrity of a mechanical component, particularly in the context of nuclear safety, it is crucial to precisely understand the role of these stress fields on the component's resistance. In the case of fatigue crack propagation, to accurately model all the phenomena involved (stress redistribution, evolution of plasticity, closure effect), it will be necessary to improve numerical tools, such as meshing and crack propagation methods (AMR, X-FEM...) and the J-integral interpolation in the case of through-cracks (Gtheta method). The thesis will consist of two complementary parts: (a) numerical development aimed at improving the Gtheta method in Castem FE code, associated with a 3D crack propagation modelling using AMR, and (b) continuation of component scale tests on fatigue crack propagation in different configurations of residual stress fields.
Numerical simulation of turbulence models on distorted meshes
Turbulence plays an important role in many industrial applications (flow, heat transfer, chemical reactions). Since Direct Simulation (DNS) is often an excessive cost in computing time, Reynolds Models (RANS) are then used in CFD (computational fluid dynamics) codes. The best known, which was published in the 70s, is the k - epsilon model.
It results in two additional non-linear equations coupled to the Navier-Stokes equations, describing the transport, for one, of turbulent kinetic energy (k) and, for the other, of its dissipation rate (epsilon). ). A very important property to check is the positivity of the parameters k and epsilon which is necessary for the system of equations modeling the turbulence to remain stable. It is therefore crucial that the discretization of these models preserves the monotony. The equations being of convection-diffusion type, it is well known that with classical linear schemes (finite elements, finite volumes, etc ...), the numerical solutions are likely to oscillate on distorted meshes. The negative values of the parameters k and epsilon are then at the origin of the stop of the simulation.
We are interested in nonlinear methods allowing to obtain compact stencils. For diffusion operators, they rely on nonlinear combinations of fluxes on either side of each edge. These approaches have proved their efficiency, especially for the suppression of oscillations on very distorted meshes. We can also take the ideas proposed in the literature where it is for example described nonlinear corrections applying on classical linear schemes. The idea would be to apply this type of method on the diffusive operators appearing in the k-epsilon models. In this context it will also be interesting to transform classical schemes of literature approaching gradients into nonlinear two-point fluxes. Fundamental questions need to be considered in the case of general meshes about the consistency and coercivity of the schemes studied.
During this thesis, we will take the time to solve the basic problems of these methods (first and second year), both on the theoretical aspects and on the computer implementation. This can be done in Castem, TrioCFD or Trust development environments. We will then focus on regular analytical solutions and application cases representative of the community.
Staggered schemes for the Navier-Stokes equations with general meshes
The simulation of the Navier-Stokes equations requires accurate and robust numerical methods that
take into account diffusion operators, gradient and convection terms. Operational approaches have
shown their effectiveness on simplexes. However, in some models or codes
(TrioCF, Flica5), it may be useful to improve the accuracy of solutions locally using an
error estimator or to take into account general meshes. We are here interested in staggered schemes.
This means that the pressure is calculated at the centre of the mesh and the velocities on the edges
(or faces) of the mesh. This results in methods that are naturally accurate at low Mach numbers .
New schemes have recently been presented in this context and have shown their
robustness and accuracy. However, these discretisations can be very costly in terms of memory and
computation time compared with MAC schemes on regular meshes
We are interested in the "gradient" type methods. Some of them are based on a
variational formulation with pressure unknowns at the mesh centres and velocity vector unknowns on
the edges (or faces) of the cells. This approach has been shown to be effective, particularly in terms of
robustness. It should also be noted that an algorithm with the same degrees of freedom as the
MAC methods has been proposed and gives promising results.
The idea would therefore be to combine these two approaches, namely the "gradient" method with the same degrees of freedom as MAC methods. Initially, the focus will be on recovering MAC schemes on regular meshes. Fundamental
questions need to be examined in the case of general meshes: stability, consistency, conditioning of
the system to be inverted, numerical locking. An attempt may also be made to recover the gains in
accuracy using the methods presented in for discretising pressure gradients.
During the course of the thesis, time will be taken to settle the basic problems of this method (first and
second years), both on the theoretical aspects and on the computer implementation. It may be carried
out in the Castem, TrioCFD, Trust or POLYMAC development environments. The focus will be on
application cases that are representative of the community.
Radiative heat transfer: efficient numerical resolution of associated problems in Beerian or non-Beerian media for the validation of simplified models
This research proposal focuses on the study, through modeling and numerical simulation, of heat transfer within a heterogeneous medium composed of opaque solids and a transparent or semi-transparent fluid. The considered modes of transfer are radiation and conduction.
Depending on the scale of interest, the radiance is the solution of the Radiative Transfer Equation (RTE). In its classical form, the RTE describes heat transfer phenomena at the so-called local scale, where solids are explicitly represented in the domain. At the mesoscopic scale of an equivalent homogeneous medium, however, the radiance is governed by a generalized RTE (GRTE) when the medium no longer follows the Beer–Lambert law. In this work, we focus on the numerical resolution of the RTE in both configurations, ultimately coupled with the energy conservation equation for temperature.
In deterministic resolution of the RTE, a standard approach for handling the angular variable is the Discrete Ordinates Method (Sn), which relies on quadrature over the unit sphere. For non-Beerian media, solving the GRTE is a very active research topic, with Monte Carlo methods often receiving more attention. Nevertheless, the GRTE can be linked to the generalized transport equation, as formulated in the context of particle transport, and a spectral method can be applied for its deterministic Sn resolution. This is the direction pursued in this PhD project.
The direct application of this work is the numerical simulation of accidents in Light Water Reactors (LWR) with thermal neutrons. Modeling radiative heat transfer is crucial because, in the case of core uncovering and fuel rod drying, radiation becomes a major heat removal mechanism as temperatures rise, alongside gas convection (steam). This topic is also relevant in the context of the nuclear renaissance, with startups developing advanced High Temperature Reactors (HTR) cooled by gas.
The goal of this thesis is the analysis and development of an innovative and efficient numerical method for solving the GRTE (within a high-performance computing environment), coupled with thermal conduction. From an application standpoint, such a method would enable high-fidelity simulations, useful for validating and quantifying the bias of simplified models used in engineering calculations.
Successful completion of this thesis would prepare the student for a research career in high-performance numerical simulation of complex physical problems, beyond nuclear reactor physics alone.
Hybrid CPU-GPU Preconditioning Strategies for Exascale Finite Element Simulations
Exascale supercomputers are based on heterogeneous architectures that combine CPUs and GPUs, making it necessary to redesign numerical algorithms to fully exploit all available resources. In large-scale finite element simulations, the solution of linear systems using iterative solvers and algebraic multigrid (AMG) preconditioners remains a major performance bottleneck.
The objective of this PhD is to study and develop hybrid preconditioning strategies adapted to such heterogeneous systems. The work will investigate how multilevel and AMG techniques can be structured to efficiently use both CPUs and GPUs, without restricting computations to a single type of processor. Particular attention will be paid to data distribution, task placement, and CPU–GPU interactions within multilevel solvers.
From a numerical point of view, the research will focus on the analysis and construction of multilevel operators, including grid hierarchies, intergrid transfer operators, and smoothing procedures on avalible GPU's and CPU's. The impact of these choices on convergence, spectral properties, and robustness of preconditioned iterative methods will be studied. Mathematical criteria guiding the design of efficient hybrid preconditioners will be investigated and validated on representative finite element problems, e.g., regional-scale earthquake analysis.
These developments will be coupled with domain decomposition and parallelization strategies adapted to heterogeneous architectures. Particular attention will be paid to CPU–GPU data transfers, memory usage, and the balance between compute-bound and memory-bound kernels. The interaction between numerical choices and hardware constraints, such as CPU and GPU memory hierarchies, will be designed and developed to ensure scalable and efficient implementations.