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The flow in fuel assemblies of PWRs with mixing grids has been analyzed with CFD calculations by numerous authors. The comparison between calculation and experiment has often shown an insensitivity of the calculated cross flow velocity on the turbulence modeling. The study presented here was carried out to confirm this result. The comparison between measurements in the AGATE facility (5 × 5 tube bundle) and Trio_U calculations with a linear eddy viscosity turbulence model (k–e) and Large Eddy Simulations (LES) is presented. The AGATE experiments have originally not been designed for CFD validation but to characterize different types of mixing grids. Nevertheless, the quality of the experimental data allows the quantitative comparison between measurement and calculation. The test section of the AGATE facility has been discretized for the LES calculation on 300 million control volumes by using a staggered grid approach on tetrahedral meshes. 20 days of CPU on 4600 cores of the HPC machine CURIE of the TGCC was necessary to calculate the statistics of the turbulent flow, in particular the mean velocity and the RMS of the turbulent fluctuations. The parallelism of Trio_U was tested up to 10,000 processor cores using strong scaling and has shown a good efficiency up to about 6000 cores, i.e., 40,000 control volumes per core. For various distances from the mixing grid, calculated horizontal profiles of the cross flow velocity and of the axial velocity are compared to measurements. It seems that the flow patterns directly downstream of the grid are insensitive to the used turbulence model. Inertia forces related to the geometry of the mixing vanes are dominant in this region. Thus, the application of turbulence models should not be tested close to mixing grids.

The flow in fuel assemblies of Pressurized Water Reactors (PWR) with mixing grids has been analysed with Computational Fluid Dynamics (CFD) by numerous authors. The comparisons between calculation and experiment are mostly focused on the flow in the near wake of the mixing grid, i.e. on the flow in the first 5 to 10 hydraulic diameters ( d h ) downstream of the grid. In the study presented here, the comparison between the measurements in the AGATE facility (5 × 5 tube bundle) and Trio_U calculations is done for the whole distance between two successive mixing grids that is up to about 50 d h downstream of the grid. The AGATE experiments have originally not been designed for CFD validation but to characterize different types of mixing grids. Nevertheless, the quality of the experimental data allows the quantitative comparison between measurement and calculation. The conclusions of the comparison are summarized below: • Linear turbulent viscosity models seem to work rather well as long as the cross flow velocity in the rod gaps is advection controlled, that is directly downstream of the mixing grid, • Further downstream, when the cross flow velocity is reduced and anisotropic turbulence becomes a more and more important mixing phenomena, linear viscosity models can fail, • The mixing grid affects the cross flow velocity up to the successive grid. The flow in fuel assemblies is never similar to that in undisturbed rod bundles. The test section of the AGATE facility has been discretized on 300 million control volumes by using a staggered grid approach on tetrahedral meshes. 20 days of CPU on 4600 cores of the High Performance Computer (HPC) cluster CURIE of the Centre de Calcul, Recherche et Technologie (CCRT) were necessary to converge the statistics of the turbulent fluctuations, completely converge the mean velocity and incompletely converge the RMS of the turbulent fluctuations.

Sodium cooled fast reactors (SFRs) have been developed in France for nearly 50 years with successively Rapsodie, Phenix and Superphenix plants. Nowadays, the so-called Astrid prototype is developed in France in the frame of Generation IV deployment. The Astrid project requires thermal hydraulic inputs to support the design and the safety analysis. This paper deals with some thermal hydraulic concerns in the primary circuit: the subassembly, the core, the hot plenum and the cold plenum. The so-called TRIO_U Computational Fluid Dynamic (CFD) code developed at CEA has been progressively adapted to these Astrid concerns. The paper presents the recent improvements, the present status and the remaining challenges for TRIO_U code on each topic. For the subassembly, refined modelling and sub-channel modelling have been developed in parallel. The validation process based on existing experimental data is in progress. A global core modelling including the inter-wrapper region and the connection to the hot plenum is depicted. The need of experimental validation is pointed out. The core outlet region requires refined Large Eddy Simulation computations to predict temperature fluctuations which can induce thermal fatigue. Validation based on sodium experimental data is briefly presented. Thermal stratification in the plenum is a key point for thermal stress analysis on the structures. Validation process includes the comparison to reactor data. Special developments using a Front Tracking method are carried out to deal with free surface and gas entrainment. A methodology including local and global modelling is developed and the validation process is in progress. For decay heat removal situations and especially in natural convection cases, the whole primary vessel – except at the moment the intermediate heat exchangers and the pumps – is modelled with TRIO_U code. Phenix ultimate tests performed in 2009 will be used for the qualification of these particular situations.

Since a long time, the Large Eddy Simulation (LES) concept is considered as a very promising candidate for advanced thermal hydraulic modeling in Nuclear Reactor Safety. This paper shows how LES is successfully applied in an industrial framework to free shear flows at high Reynolds numbers and to the associated transport of scalars (e.g. boron). Extensive verification and validation attempts towards this objective have already been performed for the Trio_U code ( Hohne et al., 2006 , Bieder et al., 2007 , Bieder and Graffard, 2007 ). In the first part, this paper presents a short overview of what has been done for predicting the boron concentration at the core inlet under accident conditions. These calculations are then related to the demands of Best Practice Guidelines (BPG), which have been discussed by Mahaffy et al. (2007) . It is shown, that high quality LES simulations for free sheer flows can be performed on tetrahedral meshes, what significantly simplifies the mesh generation procedure in topologically complex geometries. Guidelines specifically devoted to the LES framework are proposed to analyse the capability of numerical schemes to treat correctly the scalar transport.

We will try to present herein the main issues of our investigation in numerical methods for two-phase flow modeling, within the framework of the NEPTUNE project, which benefits from both contributions of CEA and EDF. These may be recast in five work packages. The first two are devoted to the mathematical and numerical modeling of two-phase flows with interfaces and the two-fluid two pressure approach. This in particular includes investigation of relaxation methods in order to establish correct links with standard two-fluid models, which are the core of the third work package. Computations of the interaction of shock waves with bubbles will be presented. Some new results concerning two-fluid and three-field flow modeling will also be briefly presented. Part of the work in the third work package concerns benchmarking, and comparison with several hyperbolic solvers, but also improvement of numerical treatment of source terms, multi-field models and suitable boundary conditions. The fourth one, which deals with the interfacial coupling of codes, is probably the most important one since it requires connecting all models together. Since little attention has been paid to this crucial point, part of the focus will be given in this paper on the coupling of equations of state, one-dimensional and three-dimensional codes, porous approach and free medium approach, but also on ongoing work concerning relaxed and unrelaxed hyperbolic two-phase flow models. The fifth work package gathers all classical contributions in numerical methods, including: recent applications of fictitious domain methods ; preconditioning of so-called “low Mach number” two-phase flows (with applications to the motion of rising bubbles in water) ; parallel and multigrid techniques (with applications to steam generators in nuclear power plants) ; Finite Volume Element methods (with applications to the standard two-fluid models) ; construction and validation of new exact or approximate Riemann solvers (in order to cope with vanishing phases). The latter five obviously aim at improving accuracy, stability and also at reducing CPU time. A few examples will enable to highlight the main advantages and possible drawbacks of these new developments, and the impact of the current and future increasing computational facilities. Main past achievements, and key points of current and future work on all these issues will be discussed. All available references will be given in order to help the reader getting a more accurate insight on these various contributions. The whole has clearly benefited from contributions of several PhD students : Thomas Fortin, Vincent Guillemaud, Olivier Hurisse, Angelo Muronne, Isabelle Ramiere, Jean-Michel Rovarch and Nicolas Seguin.

Resume Un modele de turbulence compressible propose dans une precedente note est applique au cas d'un champ isotrope statistiquement stationnaire. Le modele est d'abord valide par confrontation avec une simulation numerique directe. Les resultats sont ensuite analyses pour des nombres de Reynolds plus grands. A bas Mach, deux regimes sont detectes: un regime pseudo-son, apparaissant dans la gamme des echelles turbulentes, et un regime acoustique, se manifestant a des echelles beaucoup plus grandes. Dans la zone pseudo-son, le spectre de la partie dilatationnelle du champ de vitesse est trouve en K −3 , tandis que dans la zone acoustique, les resultats sont en accord avec ceux des modeles d'emission acoustique. Une analyse des comportements relatifs a de plus forts Mach est egalement presentee et les differences entre la presente fermeture et un modele EDQNM (quasi normal Markovien a amortissement tourbillonnaire) precedemment developpe sont brievement discutees.

Resume A partir d'une extension de l'approximation des interactions directes (DIA) precedemment proposee par Marion et al. pour la turbulence faiblement compressible, un modele en deux points et en un temps est derive. Ce modele differe de la theorie EDQNM (quasi normale Markovienne a amortissement tourbillonnaire) pour ce qui est des hypotheses retenues pour exprimer les correlations en deux temps. La structure du systeme d'equations fermees obtenu est identique a celle resultant de la demarche EDQNM, cependant les temps caracteristiques sont modifies. Les deux fermetures conduisent a des resultats tres semblables dans le cas d'un champ incompressible, tandis que dans le cas de la turbulence compressible, elles donnent lieu a des resultats profondement differents, comme il sera montre dans une prochaine note.