Calculating the dynamic response of equipment mounted on submarine hulls to the underwater explosions require handling a "coupled" model, composed of the equipment and the hull immersed in a fluid in order to represent the physic involved, namely fluid/structure interactions and mechanical interactions between the equipment and the hull. For various industrial applications, it is necessary to describe the response of equipment with masses and frequencies spanning over a wide range of values. The task may become cumbersome and time consuming when using "coupled" simulations – and may even become out of reach with classical finite element codes. The present paper proposes a versatile method to efficiently and accurately calculate the dynamic response of hull-mounted equipment to underwater explosions, without performing "coupled" calculations. The method, grounded on the calculation of "transfer functions" representing the mechanical interactions at stake (fluid/structure and structure/structure coupling), is presented and applied to various situations representative of shock problems (for 1D, 2D, 3D geometries).

In the frame of the GEN IV Forum and of the ASTRID Project, a program is in progress in the CEA (France) for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (or FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fuel Assemblies. The FA and the NS are slender structures, inserted in a grid plate, which may be considered as beams form a mechanical point of view. The dynamic behavior of this system has to be understood, for design and safety studies. This dynamic behavior of the core is strongly influenced by the sodium and by contacts between the beams at the pads level and at the top. The fluid leads to complex interactions between the structures in the whole core. The contacts between the beams limit the relative displacements. Two main movements have been considered so far: global horizontal movements under a seismic excitation, and opening of the core. Physical and numerical methods and tools have been developed to describe and simulate the dynamic behavior. These methods are integrated in CAST3M, general computer code developed at the CEA Saclay. The assemblies are modeled as beams. The impacts at the pads between the assemblies are taken into account by using a nonlinear model. The Fluid Structure Interaction is taken into account by using homogenization methods. This paper is devoted to the improvement of these methods to take into account the vertical component of a seismic excitation. The key points are: - the fluid structure coupling in the vertical direction, - the modification of the description of the impacts to take into account the vertical displacements of the assemblies, - the modification of the boundary condition at the foot of the assembly, in order to take into account the uplift with a nonlinear model.

In the nuclear industry, tube arrays immersed in dense fluid are often encountered. These systems have a large amount of tubes necessary to increase the thermal power exchanged and their dynamical analysis for safety assessment and in life operation is one of the major concern of the nuclear industry. The presence of the fluid creates a strong coupling between tubes which must be taken into account for complete dynamical analysis. However, the description of fluid's effects on oscillating structures demands great numerical efforts, especially when the tube number increases making any direct numerical simulations impossible to achieve. In this framework, homogenization methods are a possible solution in order to deal with tube bundle Fluid-Structure Interaction (FSI) problems; in fact, it gives the possibility to analyze the dynamics of the global coupled system in large domain with reasonable degree of detail and faster simulations times. At the CEA of Saclay a method based on the linearized Euler equations has been developed. It was presented in a previous PVP conference and its main goal is to assess the effect of spatial deformations of the tube bundle displacement field on the dynamic behavior. In the present paper, after an analysis on the modeling of fluid force where dissipative effects are significant, a homogenized model based on the Navier-Stokes equations is introduced. Simulations in bi-dimensional configurations for different excitations are performed.

ASTRID is a project for an industrial prototype of a 600 MWe sodium cooled Fast Reactor, led by CEA. An important program is in progress for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (of FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fluid Assemblies. The FA and the NS are slender structures, which may be considered as beams, form a mechanical point of view. The dynamic behavior of this system has to be understood, for design and safety studies. Two main movements have to be considered: global horizontal movements under a seismic excitation, and opening of the core. The fluid leads to complex interactions between the structures in the whole core. The dynamic behavior of the core is also strongly influenced by contacts between the beams and by the sodium, which limit the relative displacements. Numerical methods and models are built to describe and simulate this dynamic behavior. The validation of the numerical tools is based on the results of different experimental programs, already performed or in progress. The paper is mainly devoted to the modeling of the Fluid Structure Interaction phenomena in the Fast Reactor cores. Tubes bundles immersed in a dense fluid are very common in the nuclear industry (reactor cores and steam generators). In the case of an external excitation (earthquake or shock) the presence of the fluid leads to "inertial effects" with lower natural frequencies, and "dissipative effects", with higher damping. The geometry of a tubes bundle is complex, which may lead to very huge sizes for the numerical models. Many works have been made during the last decades to develop homogenization, in order to simplify the problem. Theoretical analyses are presented on different simplifications and assumptions which can be made in the homogenization approach. The accuracy of the different assumptions depends of the conditions of the system: fluid flow or fluid at rest, small or large displacements of the structure. In the general case, it is theoretically necessary to consider the Navier Stokes equations: the fluid flow is fully nonlinear. Models have been developed during the last years, based on the Euler linear equations, corresponding to a fluid at rest, with small displacements of the structure. Only the inertial effects are theoretically described but the dissipative effects may be taken into account by using a Rayleigh damping. Different theoretical analyses show that, even in the case of a nonlinear fluid flow, the linear potential flow models may be used as linear equivalent models. In the cases with an important head loss in the fluid flow through the tubes, the fluid movement is mainly driven by the important forces exchanged with the structure and by the pressure gradient. The global equations of the system are close to the equations used for porous media, like the Darcy equations. An important condition to get a relevant model is to describe globally the energy balance in the system. The energy given to the fluid by the solid correspond to a variation of kinetic energy in the fluid and to energy dissipation in the fluid. Attention will be paid to the cases where the tubes bundle is in interaction with free fluid, without tubes. The global equation of the system has to be accurate for the tubes bundle and for the free fluid also.

ASTRID is a project for an industrial prototype of a 600 MWe sodium cooled Fast Reactor, led by CEA. An important program is in progress for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (of FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fluid Assemblies. The FA and the NS are slender structures, which may be considered as beams, form a mechanical point of view. The analysis of the dynamic behavior of tubes bundles immersed in a dense fluid is a major challenge in the nuclear industry (reactor cores, steam generators). In some cases, the excitation is given by the fluid flow, with a complex behavior which may lead to instabilities. The paper only considers the case of an external excitation (earthquake or shock). The fluid leads to two main effects: "inertial effects" with lower vibration frequencies and "dissipative effects" with a higher damping. In the general case the fluid has to be described by the Navier-Stokes equations. It is possible to use the Euler linear equations in the case of vibrations of the tubes in a globally stagnant fluid. In all cases the modeling of the system could lead to huge numerical problems if each tube is described explicitly. Homogenization technics allow to limit the size of the problem. Homogenization methods taking into account the Euler equations for the fluid have been developed, and widely used for analyses of the dynamic behavior of reactor cores. Only the inertial effects are theoretically described but the dissipative effects may be roughly taken into account by using a Rayleigh damping. The paper presents an improvement of the method, allowing a better description of the dissipative effects, with a more general form of the expression of the forces exchanged between the fluid and the tubes. The theoretical basis of the numerical model are presented, as well as illustrations of the interest of the method: a better physical description is obtained for the dynamic behavior of the tubes bundle, particularly in the case of interactions with free fluid, without tubes.

A research program is ongoing at CEA in the framework of ASTRID project, for developing and validating tools for the analysis of the mechanical dynamic behaviour of Fast Breeder Reactor (FBR) cores. In this context, Fluid Structure Interaction is a recurring problem, especially in case of tube bundles in nuclear reactor cores or steam generators. The large number of elements makes modelling difficult to perform and any direct numerical simulation at whole core scale unachievable. In order to overcome this limitation, we resort to homogenisation techniques which allow to describe the global dynamic behaviour of the whole fluid-structure system. The purpose of this study is to better understand the effects of the spatial variation of the tube displacement field on the whole bundle dynamics. Thanks to multiple scales, a complete development of the problem is conducted. An analysis of the effects of spatial variations of the long scale displacement field on the tube bundle’s dynamics is led. As a first step we consider the homogenisation of Euler linear equations that gives us the possibility to make a thorough assessment of the problem with the extension to follow to Navier-Stokes equations.

In this paper we focus on of Sodium Fast Reactor core undergoing several mechanical scenarios. The mechanical full-core model in Cast3M code is described using finite elements method and Fluid Structure Interaction is taken into account. We consider several system excitations: fluid injection, seismic excitation and compressive/opening forces applied to the bundle of assemblies. The geometry deformation is next applied for transient neutron transport simulations using a diffusion tool built in Cast3M code, named Cast3M Neutron Transport Tool (CNTT). We expose and analyze variation of power, change of fissile zone volume and assembly displacements. CNTT succeeded in code-to-code comparison using TRIPOLI-4 (a Monte Carlo code) and APOLLO3 (a deterministic code). The novelty of CNTT is the use of remeshing to take into account core distortion. The validity of assumptions applied in our approach and prospects for the future are discussed as well. The developed methodology may serve as a general tool for analysis of fast reactor systems under various mechanical excitation. Cast3M based tools provide new possibilities for safety assessments, fundamental for current and upcoming nuclear designs. (C) 2016 Elsevier Ltd. All rights reserved.

ASTRID is a project for an industrial prototype of a 600 MWe sodium cooled Fast Reactor, led by CEA. A consequent program is in progress for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (or FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fluid Assemblies. The FA and the NS are slender structures, which may be considered as beams, from a mechanical point of view. The dynamic behavior of this system has to be understood, for design and safety studies. Two main movements have to be considered: global horizontal movements under the effect of a seismic excitation, and a radial opening of the core. The fluid presence leads to complex interactions between the structures at a distance. The dynamic behavior of the core is strongly influenced by contacts between the beams and by the interactions with the sodium, which both limit their relative displacements. Numerical methods and models are built to describe and simulate this dynamic behavior. The validation of the numerical tools is based on the results of different experimental programs, already performed or in progress. The paper presents the interpretation of tests performed in 2013 in the Phénix reactor. The French Phénix reactor was definitively shutdown in 2009 and is currently at an early stage of the decommissioning process. Before unloading the core, it has been decided to perform one last experimental campaign aimed at testing the mechanical dynamic behavior of the core. The interpretation of the tests highly contributes to the validation of the simulation methods. Relatively good comparisons have been obtained between the theoretical and experimental results, for the static excitation (stiffness of the bundle) and for the dynamic response (characteristic times). The tests confirm that the fluid leads to a significant decrease of the frequencies. Uncertainties remain on the significant damping which seems to be present, and may be due to the fluid or to the structures.

In the frame of the GEN IV Forum and of the ASTRID Project, a program is in progress in the CEA (France) for the development and the validation of numerical tools for the simulation of the dynamic mechanical behavior of the Fast Reactor cores, with both experimental and numerical parts. The cores are constituted of Fuel Assemblies (of FA) and Neutronic Shields (or NS) immersed in the primary coolant (sodium), which circulates inside the Fluid Assemblies. The FA and the NS are slender structures, which may be considered as beams, form a mechanical point of view. The dynamic behavior of this system has to be understood, for design and safety studies. Two main movements have to be considered: global horizontal movements under a seismic excitation, and opening of the core. The dynamic behavior of the core is strongly influenced by contacts between the beams and by the sodium. The contacts between the beams limit the relative displacements. The fluid leads to complex interactions between the structures in the whole core. The paper presents the physical and numerical methods and tools used to describe and simulate the phenomena. A key point is the Fluid Structure Interaction (or FSI): the interactions between the beams and the liquid sodium. The fluid movement is assumed to be described by the equations of a perfect fluid. Simple and efficient homogenization methods may be used to reduce the size of the problem. These methods are integrated in a general computer code, CAST3M developed at the CEA Saclay. This computer code allows to take into account the impacts between the beams. Some applications are presented.

Fluid–structure interaction (FSI) is of major importance when describing the dynamic behaviour of nuclear pressure vessels, since the presence of confined fluid strongly influences the response of structures when subjected to external loadings, such as a seismic loading. Accounting for FSI when performing the seismic analysis of nuclear reactors or steam generators can be done through the description of inertial effects, which are predominant in the low frequency domain. Finite element techniques are now of common use in design office to model coupled (quiescent) fluid–structure systems, using standard non-symmetric (u,p) or symmetric (u,p,φ) coupled formulations. When considering complex systems such as a tube bundle in steam generators, producing a finite element model which includes tubes, fluid and structures is a tedious task which is out of reach in many practical applications. A homogenisation method has been proposed which allows FSI modelling of tube bundles: it has been successfully applied to a complex structure. In the aforementioned developments, focus was put on the mathematical and numerical aspects of the method, leaving out some questions regarding the physical interpretation of the calculations. In the present paper, a new insight on the homogenisation approach is exposed with the objective of proposing a formulation of the method based on physical considerations, leading to a correction of the homogenised problem. Enhancement of the method is discussed from an engineering standpoint: it allows for a wider range of applications in the nuclear industry.

The present paper deals with the dynamic analysis of a tube bundle with Fluid Structure Interaction (FSI) modeling using a structural acoustic homogenized method. Such a coupled problem leads to many degrees of freedom [a system of very large matrices] to compute tube displacements and pressure in the acoustic domain, it is therefore irrelevant to use standard coupled methods in industrial cases. Instead, specific modelings have to be used, such as structural acoustic homogenized method. Implementation and applications of such a technique within the general finite element code ABAQUS are performed using the so-called UEL Fortran subroutine. Firstly, general theoretical aspects on the homogenized method proposed by Broc & Sigrist are revisited. Then, subroutines developments are validated comparing results from the homogenized method to those of a standard approach on the representative case of a 10×10 tube bundle in two-dimensional and three-dimensional configurations subjected to seismic loadings. Results show that: (i) homogenized elements can easily be used as standard elements from the ABAQUS elements library, (ii) the homogenized approach is accurate on a physical point of view and (iii) considerably reduces modeling effort and computational time compared to a standard structural acoustic method.

In 1989 and 1990, four very fast and high amplitude decreases of the measured neutron flux, known as 'AURN' events, occurred in the Phenix fast neutron reactor and were not well explained despite a significant investigation program carried out in the 90 s. The perspective of the Phenix end of life led the French Nuclear Energy Div. to reinitiate AURN studies in particular with dedicated Phenix tests. It comes out from simulations with improved fluid-structure interaction model of the core movement that an outward movement of the sub-assemblies can generate a power variation consistent with the AURN signals. 'AURN' Phenix tests confirm the abnormal thermal behavior of an experimental sub-assembly, a new A URN scenario has been proposed on this basis. (authors)

Cet article presente les aspects theorique, numerique et pratique d’une methode de calcul pour la description du comportement vibratoire de faisceaux tubulaires avec interaction fluide/structure (IFS). Il s’agit en particulier de rendre compte des effets inertiels caracteristiques de l’IFS dans la gamme des « basses frequences ». La methode proposee repose sur une description globale de la dynamique du faisceau ; elle est fondee sur un modele equivalent de l’interaction entre les tubes et le fluide, deduit a partir d’une analyse locale de la vibration du tube confine dans le faisceau. Cette methode d’homogeneisation peut etre mise en œuvre avec tout code de calcul elements finis proposant les operateurs « standards » de l’interaction fluide/structure (operateurs d’energie cinetique et potentielle fluide et structure ; operateurs de couplage fluide/structure). Deux exemples de validation pour des problemes elementaires sont proposes dans l’article sous forme d’une comparaison entre les approches « couplee » et « homogeneisee » ; un exemple d’application conclut l’expose et permet d’illustrer le caractere general de la methode.

It is well known that a fluid may strongly influence the dynamic behaviour of a structure. Many different physical phenomena may take place, depending on the conditions: fluid flow, fluid at rest, little or high displacements of the structure. Inertial effects can take place, with lower vibration frequencies, dissipative effects also, with damping, instabilities due to the fluid flow (Fluid Induced Vibration). In this last case the structure is excited by the fluid. Tube bundles structures are very common in the nuclear industry. The reactor cores and the steam generators are both structures immersed in a fluid which may be submitted to a seismic excitation or an impact. In this case the structure moves under an external excitation, and the movement is influence by the fluid. The main point in such system is that the geometry is complex, and could lead to very huge sizes for a numerical analysis. Homogenization models have been developed based on the Euler equations for the fluid. Only inertial effects are taken into account. A next step in the modelling is to build models based on the homogenization of the Navier-Stokes equations. The papers presents results on an important step in the development of such model: the analysis of the fluid flow in a oscillating tube bundle. The analysis are made from the results of simulations based on the Navier-Stokes equations for the fluid. Comparisons are made with the case of the oscillations of a single tube, for which a lot of results are available in the literature. Different fluid flow pattern may be found, depending in the Reynolds number (related to the velocity of the bundle) and the Keulegan Carpenter number (related to the displacement of the bundle). A special attention is paid to the quantification of the inertial and dissipative effects, and to the forces exchanges between the bundle and the fluid. The results of such analysis will be used in the building of models based on the homogenization of the Navier-Stokes equations for the fluid.

The safety of vitrified radioactive waste disposal in granite is based on the concept of multiple barriers, which include an engineered clay barrier placed between the waste package and the granite. The mechanical properties of the swelling clays used were studied with a view to practical application for storage facility dimensioning. This involved a macroscopic examination of the clays swelling capacities (for sealing of storage boreholes) and fracture criteria (mechanical stability).

Flow dynamics, in-line and transverse forces exerted on an oscillating circular cylinder in a fluid initially at rest are studied by numerical resolution of the two-dimensional Navier–Stokes equations. The Keulegan–Carpenter number is held constant at KC=10 and Re is increased from 40 to 500. For the different flow regimes, links between flow spatio-temporal symmetries and force histories are established. Besides simulations of long duration show that in two ranges of Re, forces exhibit low frequency fluctuations compared to the cylinder oscillation frequency. Such observations have been only mentioned in the literature and are more deeply examined here. In both ranges, force fluctuations correspond to oscillations of the front and rear stagnation points on the cylinder surface. However, they occur in flow regimes whose basic patterns (V-shaped mode or diagonal mode) have different symmetry features, inducing two distinct behaviors. For 80≤Re≤100, fluctuations are related to a spectral broadening of the harmonics and to a permutation between three vortex patterns (V-shaped, transverse and oblique modes). In the second range 150≤Re≤280, amplitude fluctuations are correlated to the appearance of low frequency peaks interacting with harmonics of the cylinder frequency. Fluctuations are then a combination of a wavy fluctuation and an amplitude modulation. The carrier frequency corresponding to the wavy fluctuation depends on Re and is related to a fluid characteristic time; the modulation frequency is independent of Re and equal to 1/4 of the cylinder oscillation frequency.

It is well known that a fluid may strongly influence the dynamic behaviour of a structure. Many different physical phenomena may take place, depending on the conditions: fluid at rest, fluid flow, little or high displacements of the structure. Inertial effects can take place, with lower vibration frequencies, dissipative effects also, with damping, instabilities due to the fluid flow (Fluid Induced Vibration). In this last case the structure is excited by the fluid. The paper deals with the vibration of tube bundles in a fluid, under a seismic excitation or an impact. In this case the structure moves under an external excitation, and the movement is influenced by the fluid. The main point in such system is that the geometry is complex, and could lead to very huge sizes for a numerical analysis. Many works has been made in the last years to develop homogenization methods for the dynamic behaviour of tube bundles. The size of the problem is reduced, and it is possible to make numerical simulations on wide tubes bundles with reasonable computer times. These homogenization methods are valid for "little displacements" of the structure (the tubes), in a fluid at rest. The fluid movement is governed by the linear Euler equations (without the convective term). In this case, only "inertial effects" will take place, with globally lower frequencies. It is well known that dissipative effects due to the fluid may take place, even if the displacements of the tube are no so high, or if the fluid is not still. Such effects may be described in the homogenized models by using a Rayleigh damping, but the basic assumption of the model remains the "perfect fluid" hypothesis. It seem necessary, in order to get a best description of the physical phenomena, to build a more general model, based on the general Navier Stokes equation for the fluid. The homogenization of such system will be much more complex than for the Euler equations. The paper presents the first step in the building of a method based on the homogenization of the Navier Stokes equations.