Simulation of the Fluid-Structure Interaction Involving Two-Phase Flow and Hexagonal Structures in a Nuclear Reactor Core

In order to enhance safety assessments of Sodium Fast Reactors (SFR), some scenarios involving transient Fluid-Structure Interactions (FSI) are investigated using numerical simulation tools. SFRs are indeed quite sensible to mechanical deformations regarding their nuclear power (see [1] for more details). The originality of the scenario presented in the paper is to consider sufficient large mechanical interactions involving a large pressure decrease in the fluid domain. This decrease leads to vaporization of the fluid and then to a different impact on the structures. By means of the open-source software Code Saturne developed by EDF [2], this scenario is investigated in 2D using a 3-equation model derived from the Navier-Stokes equations while an harmonic model is applied for the mechanical structures. The code coupling is managed using the Newmark algorithm for the mechanical part and a damped fixed point algorithm in order to get a converged coupled FSI problem

Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density $\rho_a$ on the negative axis and with density $\rho_b$ on the positive axis. All the cumulants of $Q_t$ grow like $\sqrt{t}$. In the range where $Q_t \sim \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities recently derived by Tracy and Widom for exclusion processes on the infinite line.Comment: 2 figure

The new wave of university researchers and libraries

This paper examines changes in attitudes and behaviours of the new wave of researchers (early career researchers) regarding the academic library and its functions in seven coun-tries around the world. It documents trends and establishes the direction in which things are heading. Data were collected from over 100 researchers from the sciences and social sciences through interviews, repeated annually for 3 years. Findings show that attitudes to-wards libraries and their use have barely changed over the years and they remain largely invisible to ECRs, although in the case of China, attitudes are distinctly negative and use declined and in Poland sentiment appears to be rock bottom. Libraries, when used are really mainly used for one purpose only, which is to get hold of the full text of papers. The danger is that ECRs are decoupling from libraries

Towards More Efficient Implementations of Multiscale Thermal-Hydraulics

International audienceOver the past decade, the need to supplement system-scale simulations of reactor transients with the results of finer simulations (subchannel or CFD) has increased continuously. In many cases, the local phenomena predicted at these scales (such as flow patterns in the core or within inlet/outlet plenums) can affect the overall transient: in that case, then all codes should be run concurrently in a consistent manner in order to obtain a single, "multi-scale" simulation of the transient of interest.Because their subchannel/CFD components tend to require meshes beyond the capabilities of the 3D modules present in modern system codes, most multiscale simulations can only be performed by coupling different codes together. The strategy used to implement this coupling can have a crucial impact on both the solution accuracy and on the numerical cost of the calculation : in particular, algorithms which require small time steps or large number of iterations between the codes can multiply the numerical cost of multiscale compared to an (already expensive) standalone CFD simulation.This paper discusses a range of algorithms suitable for coupling thermal-hydraulics codes at either thermal or hydraulic boundaries. These algorithms are grouped into four broad classes of increasing complexity (fixed-point, improved fixed-point, quasi- Newton and Newton): the more complex variants are more difficult to implement, but have been observed to significantly decrease the numerical overhead of multi-scale coupling

Développement de schémas numériques pour la résolution d'écoulements multiphases sur maillages généraux

International audienceEuler-Euler simulations of two-phase flows, such as the 6-equations model adopted in many systemthermal-hydraulics (STH) codes, becomes more challenging as the gas-liquid density ratio ρl/ρg increases. On structured meshes, the association of a staggered ”MAC” numerical scheme with a semiimplicit ”ICE” solution algorithm has proven particularly robust, and is currently used in the 3D modules of the TRACE, CATHARE or RELAP codes.However, structured meshes are too restrictive to cover a number of potential applications : apart fromthe CFD scale, unstructured, polyhedral meshes are also encountered at the component scale when modelling SFR subassemblies. This later case is the focus of the TrioMC code developed at CEA. In 2019, this code was reimplemented using a new numerical scheme (”PolyMAC”) designed to generalise to arbitrary meshes the main properties of the MAC staggered numerical scheme [1]. In 2020-2021, this scheme, originally designed to solve the single-phase Navier-Stokes and energy equations, was extended to multiphase flows: physical models dedicated to sodium boiling were then implemented in TrioMC, and preliminary validation was carried out against a benchmark sodium boiling test (the KNS-37 L22 test provided by the ESFR-SMART H2020 project).L'analyse de sûreté des réacteurs nucléaires nécessite dans de nombreux cas de résoudre la dynamique d'écoulements diphasiques liquide-vapeur, décrits par le modèle ``Euler-Euler'' à 6 équations (conservation de la masse, de la q.d.m. et de l'énergie de chacune des phases). La plupart des codes de thermohydraulique développés dans le domaine nucléaire (TRACE, RELAP, CATHARE...) résolvent ce système à l'aide d'une discrétisation spatiale décalée de type MAC et d'un schéma en temps semi-implicite de type ICE : ce choix offre une robustesse importante (absence de modes parasites, faible sensibilité aux forces irrotationelles) et un coût numérique attractif (le système linéaire résolu à chaque itération de Newton ne porte que sur la pression), mais ne s'applique qu'aux maillages cartésiens structurés. Ainsi, les codes industriels capables de résoudre le modèle Euler-Euler sur des maillages plus généraux (Neptune_CFD, CUPID) ont recours à une discrétisation spatiale colocalisée : ils peuvent cependant souffrir d'une perte de robustesse, en particulier lorsque le rapport des densités des deux phases $\rho_l/\rho_g$ est très élevé.Afin de traiter des écoulements diphasiques de sodium ($\rho_l/\rho_g \sim$ 2000), le CEA a entrepris de développer une famille de schémas numériques, dénommées ``PolyMAC'', généralisant le schéma MAC à des maillages généraux et compatibles avec une résolution de type ICE. Pour les équations scalaires, ces schémas, dénommés ``P0P1nc'', ``P0'' et ``P1'' se rapprochent respectivement des schémas ``Hybrid Mixed Mimetic'', ``MPFA-O'' et N-MFD. Cette communication décrira ces trois schémas, détaillera les difficultés rencontrées pour les appliquer à l'échelle industrielle($\gtrsim 10^6$ mailles, $\gtrsim 10^3$ cœurs), et enfin présentera les résultats obtenus sur le benchmark du mini-symposium ainsi que quelques exemples applicatifs

Fluctuations de courant hors d'équilibre

thèse effectuée en 2008-2012; rédaction décembre 2011Out-of-equilibrium systems are often associated with the presence of a current, of energy or of particles, which breaks detailed balance. In these systems, the usual tools of statistical mechanics, such as the free energy, are unavailable. New methods, inspired by the theory of dynamical systems, can describe these models from their macroscopic properties : they are joined by the microscopic methods available in some specific cases, such as integrable systems. We studied the current Qt which crosses such systems during the time t. Since Qt is a random variable, we have considered its full counting statistics, through its large deviation function or its cumulants. In the first class of systems we studied, diffusive sys- tems with one conserved quantity on the infinite line, we were able to compute the latter exactly; we also compared the predictions of macroscopic and microscopic approaches in this case. We then studied one-dimensional mechanical models, which are known to exhibit a departure from Fourier's law in one dimension : we were able to determine nu- merically that this anomalous behavior extends to the higher cumulants of Qt. Finally, we studied a system, the ABC model, which exhibits an out-of-equilibrium phase tran- sition. Away from the transition, current flutcuations obey Fourier's law; however, they become anomalous close to the critical point, with a behavior reminiscent of mechanical models.Les systèmes hors d'équilibre sont souvent caractérisés par la présence d'un courant, d'énergie ou de particules, qui brise le bilan détaillé. Dans ces systèmes, les outils tradi- tionnels de la physique statistique, telles la fonction de partition ou l'énergie libre, ne sont pas définies. De nouvelles méthodes, issues de la théorie des systèmes dynamiques, ont été introduites au cours des vingt dernières années afin de décrire ces systèmes à partir de leurs propriétés macroscopiques : elles viennent s'ajouter aux méthodes microscopiques disponibles dans certains cas, comme les systèmes intégrables. Nous nous sommes intéressés au courant Qt traversant un tel système pendant une durée t. Qt étant une grandeur fluctuante, nous avons cherché à obtenir sa statistique (fonction de grandes déviations, cumulants). Dans la première classe de systèmes que nous avons étudiée, les systèmes diffusifs conservant une quantité sur la ligne infinie, nous avons pu calculer ces cumulants exactement ; nous avons aussi pu confronter les résultats des approches microscopiques et macroscopiques. Notre intérêt s'est ensuite porté sur une seconde classe de systèmes, les systèmes mécaniques, qui présentent un écart à la loi de Fourier en dimension 1 : numériquement, nous avons pu généraliser cette propriété aux cumulants supérieurs de Qt. Enfin, nous avons étudié les fluctuations du courant d'un système, le modèle ABC, présentant une transition de phase hors d'équilibre. Les fluctuations, qui respectent la loi de Fourier loin de la transition, deviennent anormales près du point critique, leur comportement se rapprochement alors qualitativement de celui observé dans les systèmes mécaniques

Multiscale and Multiphysics Simulation of Sodium Fast Reactors: From Model Development to Safety Demonstration

International audienceThe safety justification for the Sodium Fast Reactors (SFR) built in the 1970s and 1980s (such as PHENIX and SUPERPHENIX in France) relied, for its thermal-hydraulic component, on a system-scale analysis similar to those developed for LWRs at the time. This tried-and-true approach, relying on the coupling of a 0D/1D network of hydraulic elements to a point-kinetic neutronic model, starts to show its limitations when applied to contemporary SFR designs. These designs often integrate new safety features, such as passive decay heat removal systems or a negative void-effect core: these systems, though responsible for major safety improvements, tends to induce new, hard-to-model physical phenomena.For instance, DHR systems at the top of a pool-type SFR tend to cool the core via a several competing natural convection paths; meanwhile, boiling in a low-void effect core leads to both global and local power fluctuations, the latter of which can only be modelled through 3D neutron transport.The challenges posed by these new designs have given rise to new modelling strategies. These include multi-scale thermal hydraulics, where a system-scale calculation is augmented, in relevant areas, with finer (subchannel or CFD) models in order to better predict natural convection flow in the primary pool;multi-physics models, coupling thermal-hydraulics to 3D neutron transport codes, were similarly developed in order to apprehend coupled 3D effects between neutronics and thermal-hydraulics. More recently, efforts have been made to support these methods with a comprehensive validation databaserelying, as for system codes, on experiments at the separate-effects, combined-effect and integral scales.For multi-scale methods, large steps have been taken towards this goal, to the extent that several SFR projects now intend to rely on multi-scale simulations to predict natural convection; multi-physics approaches have not yet achieved this level of maturity, but important new efforts should help improve itin the next few years

Reconstruction for models on random graphs

Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given ‘far away ’ observations. Several theoretical results (and simple algorithms) are available when their joint probability distribution is Markov with respect to a tree. In this paper we consider the case of sequences of random graphs that converge locally to trees. In particular, we develop a sufficient condition for the tree and graph reconstruction problem to coincide. We apply such condition to colorings of random graphs. Further, we characterize the behavior of Ising models on such graphs, both with attractive and random interactions (respectively, ‘ferromagnetic ’ and ‘spin glass’). 1. Introduction an