Fluid Structure Interaction for Tubes Bundles: Presentation of a Linear Equivalent Model

2017 ◽  
Author(s):  
Daniel Broc ◽  
Gianluca Artini
Keyword(s):  
Dynamic Behavior ◽  
Fast Reactor ◽  
Stokes Equations ◽  
Nuclear Industry ◽  
Equivalent Model ◽  
Free Fluid ◽  
Inertial Effects ◽  
Primary Coolant ◽  
Dissipative Effects ◽  
Reactor Cores

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.

Fluid Structure Interaction for Tubes Bundles: Different Homogenization Methods

2017 ◽  
Author(s):  
Daniel Broc ◽  
Gianluca Artini
Keyword(s):  
Fluid Flow ◽  
Dynamic Behavior ◽  
Fast Reactor ◽  
Free Fluid ◽  
Inertial Effects ◽  
The Core ◽  
Dissipative Effects ◽  
Numerical Tools ◽  
Reactor Cores ◽  
Theoretical Analyses

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.

Fluid Structure Interaction Modelling for the Vibration of Tube Bundles: Part I—Analysis of the Fluid Flow in a Tube Bundle

2011 ◽  
Author(s):  
Quentin Desbonnets ◽  
Daniel Broc
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Tube Bundle ◽  
Nuclear Industry ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Navier Stokes Equations ◽  
Dissipative Effects ◽  
Tube Bundles ◽  
Interaction Modelling

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.

Physical and Numerical Methods for the Dynamic Behavior of the Fast Reactor Cores

2014 ◽  
Author(s):  
Daniel Broc ◽  
Jérome Cardolaccia ◽  
Laurent Martin
Keyword(s):  
Numerical Methods ◽  
Dynamic Behavior ◽  
Fast Reactor ◽  
Computer Code ◽  
Point Of View ◽  
Liquid Sodium ◽  
Primary Coolant ◽  
The Core ◽  
Safety Studies ◽  
Reactor Cores

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 Interactions for Tube Bundles: Physical Meaning of a Rayleigh Damping

2010 ◽  
Author(s):  
Daniel Broc ◽  
Jean Franc¸ois Sigrist
Keyword(s):  
Fluid Flow ◽  
Numerical Simulations ◽  
Physical Meaning ◽  
Dynamic Behaviour ◽  
Stokes Equations ◽  
Tube Bundle ◽  
Inertial Effects ◽  
Rayleigh Damping ◽  
Dissipative Effects ◽  
Tube Bundles

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, small 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 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. Important developments have been made in the last years to develop homogenization methods for the dynamic behaviour of tube bundles. The numerical size of the problem is reduced, and it is possible to make numerical simulations on large tube bundles with reasonable computer times. These methods consider that the fluid movement is governed by the Euler equations for the fluid. They are based on an analysis on an elementary cell, corresponding to one tube, and on an expression of the forces applied by the fluid to the structure. This force only depends on the fluid’s and tube’s acceleration. Only “inertial effects” will theoretically take place, with globally lower frequencies. A research program is under progress to take into account dissipative effects also, with a homogenization of the Navier-Stokes equations in the tube bundle. It is common, in numerical simulations, to add a damping for the structures by using a global Rayleigh damping. The paper deals with the physical meaning of this Rayleigh damping in the Euler homogenized equations. It can be demonstrated that this damping corresponds to a force applied by the fluid to the structure depending not only on the acceleration, but on the fluid and structure velocity also. This Rayleigh damping is a first step to take into account the dissipative effects for FSI in tube bundles.

Core Mechanical Dynamics Experiment in the Phénix Reactor

2015 ◽  
Author(s):  
Daniel Broc ◽  
Jérome Cardolaccia ◽  
Laurent Martin ◽  
Jean Louis Portier
Keyword(s):  
Dynamic Behavior ◽  
Fast Reactor ◽  
Early Stage ◽  
Response Characteristic ◽  
Point Of View ◽  
Primary Coolant ◽  
The Core ◽  
Safety Studies ◽  
Numerical Tools ◽  
Dynamic Response Characteristic

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.

Fluid Structure Interaction Modelling for the Vibration of Tube Bundles: Part II—Homogenization Method Based on the Navier Stokes Equations

2011 ◽  
Author(s):  
Daniel Broc ◽  
Quentin Desbonnets
Keyword(s):  
Fluid Flow ◽  
Dynamic Behaviour ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Navier Stokes Equations ◽  
Dissipative Effects ◽  
Tube Bundles ◽  
Homogenization Methods ◽  
Physical Phenomena

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.

Fast Reactor Cores: Seismic Excitation in the Vertical Direction — Numerical Methods

2018 ◽  
Author(s):  
Daniel Broc ◽  
Gianluca Artini ◽  
Jérome Cardolaccia ◽  
Laurent Martin
Keyword(s):  
Numerical Methods ◽  
Dynamic Behavior ◽  
Nonlinear Model ◽  
Fast Reactor ◽  
Vertical Direction ◽  
Seismic Excitation ◽  
Fluid Structure ◽  
The Core ◽  
Fuel Assemblies ◽  
Reactor Cores

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.

Fluid Structure Interaction Homogenization for Tube Bundles: Significant Dissipative Effects

2018 ◽  
Author(s):  
Gianluca Artini ◽  
Daniel Broc
Keyword(s):  
Stokes Equations ◽  
Tube Bundle ◽  
Thermal Power ◽  
Fluid Structure Interaction ◽  
Coupled System ◽  
Nuclear Industry ◽  
Dynamical Analysis ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Dissipative Effects

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.

Advances in Structural Materials for Fast-Reactor Cores

Atomic Energy ◽  
2016 ◽  
Vol 119 (5) ◽  
pp. 362-371 ◽  
Author(s):  
A. A. Nikitina ◽  
V. S. Ageev ◽  
M. V. Leont’eva-Smirnova ◽  
N. M. Mitrofanova ◽  
I. A. Naumenko ◽  
...  
Keyword(s):  
Fast Reactor ◽  
Structural Materials ◽  
Reactor Cores

An Experimental Study on Insulating Property of Helium in High Temperature Gas Cooled Reactor

2014 ◽  
Author(s):  
Shan Yue ◽  
Xingnan Liu ◽  
Zhengang Shi
Keyword(s):  
High Temperature ◽  
Electrical Equipment ◽  
Structure Design ◽  
Nuclear Industry ◽  
Parallel Plane ◽  
Primary Coolant ◽  
Experimental Platform ◽  
Insulating Properties ◽  
High Temperature Gas ◽  
Better Than

HTGR, short for high temperature gas cooled reactor, has gained a lot of attention in nuclear industry. Gas helium, 7MPa in pressure, is used as primary coolant of HTR-PM in where there are a lot of electrical equipment. Insulating property of helium is worse than that of air according to Paschen curves and there are very few articles or related standards about insulating property of high pressure gas helium, which makes the electrical equipment structure design lack of basis. In this study, an experimental platform for testing insulating performance is designed, based on which the experiments of testing the withstanding voltages of penetration assemblies and the breakdown voltages of parallel plane electrodes at different pressures are carried out. The results show that for both the penetration assemblies and the parallel plane, their breakdown voltages in helium are far lower than in air under the same condition of 15°C /0.1MPa. For the penetration assemblies, their insulating properties in helium at 150°C/7MPa are better than those in air at 15°C/0.1MPa.

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