Fluid-Structure Interaction Effects Modeling for the Modal Analysis of a Nuclear Pressure Vessel

2006 ◽  
Vol 129 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Jean-François Sigrist ◽  
Daniel Broc ◽  
Christian Lainé
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Pressure Vessel ◽  
Nuclear Reactor ◽  
Fluid Structure Interaction ◽  
Added Mass ◽  
Interaction Effects ◽  
Element Discretization ◽  
Fluid Structure ◽  
Structure Interaction

The present paper deals with the modal analysis of a nuclear reactor with fluid-structure interaction effects. The proposed study aims at describing various fluid-structure interaction effects using several numerical approaches. The modeling lies on a classical finite element discretization of the coupled fluid-structure equation, enabling the description of added mass and added stiffness effects. A specific procedure is developed in order to model the presence of internal structures within the nuclear reactor, based on periodical homogenization techniques. The numerical model of the nuclear pressure vessel is developed in a finite element code in which the homogenization method is implemented. The proposed methodology enables a convenient analysis from the engineering point of view and gives an example of the fluid-structure interaction effects, which are expected on an industrial structure. The modal analysis of the nuclear pressure vessel is then performed and highlights of the relative importance of FSI effects for the industrial case are evaluated: the analysis shows that added mass effects and confinement effects are of paramount importance in comparison to added stiffness effects.

A Homogenization Method for the Modal Analysis of a Nuclear Reactor With Fluid-Structure Interaction

2006 ◽  
Author(s):  
Jean-Franc¸ois Sigrist ◽  
Daniel Broc
Keyword(s):  
Modal Analysis ◽  
Nuclear Reactor ◽  
Mass Operator ◽  
Fluid Structure Interaction ◽  
Homogenization Method ◽  
Theoretical Point ◽  
Element Discretization ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Internal Structures

The present paper exposes a homogenization method developed in order to perform the modal analysis of a nuclear reactor with fluid-structure interaction effects. The homogenization approach is used in order to take into account the presence of internal structures within the pressure vessel. A homogenization method is proposed in order to perform a numerical calculation of the frequencies and modal masses for the eigenmodes of the coupled fluid-structure problem. The technique allows the use of a simplified fluid-structure model that takes into account the presence of internal structures: the theory bases are first recalled, leading to a new formulation of the fluid-structure coupled problem. The finite element discretization of the coupled formulation leads to the modification of the classical fluid-structure interaction operators. The consistency of the formulation is established from a theoretical point of view by evaluating the total mass of the coupled system with the fluid and structure mass operator, and the modified added mass operator. The method is tested and validated on a 2D case (two concentric cylinders with periodical rigid inclusions within the annular space) and applied on the industrial case. A complete modal analysis (calculation of frequencies and modal masses) is performed on a simplified geometry of a nuclear reactor with and without internal structures. Numerical results are then compared and discussed, and the influence of the internal structures on the fluid-structure coupled phenomenon is highlighted.

Seismic Analysis of a Nuclear Reactor With Fluid-Structure Interaction

2005 ◽  
Author(s):  
Jean-Franc¸ois Sigrist ◽  
Daniel Broc ◽  
Christian Laine
Keyword(s):  
Internal Structure ◽  
Pressure Vessel ◽  
Nuclear Reactor ◽  
Seismic Analysis ◽  
Mass Operator ◽  
Fluid Structure Interaction ◽  
Added Mass ◽  
Operating Conditions ◽  
Fluid Structure ◽  
Structure Interaction

The present paper is related to a seismic analysis of a naval propulsion ground prototype nuclear reactor with fluid-structure interaction modeling. Many numerical methods have been proposed over the past years to take fluid/structure phenomenon into account [14] in various engineering domains, among which nuclear engineering in seismic analysis [15]. The purpose of the present study is to apply general methods on a global approach of the nuclear reactor. A simplified design of the pressure vessel and the internal structure is presented; fluid-structure interaction is characterized by the following effects: • added mass effects are highlighted with the calculation of an added mass operator, obtained from a finite element discretisation of the coupled problem. The numerical model is developed within the CASTEM code using an axi-symmetric model of the industrial structure; • coupling effects between the external and internal structure via the confined inner fluid are also illustrated and numerically described with the added mass operator; • added stiffness effects are taken into account with an added stiffness matrix describing pre-stress effects due to a static pressure loading simulating the actual operating conditions of the reactor. The expected fluid-structure interaction effects on the nuclear pressure vessel and their numerical modeling leads to the definition of a global coupled model which can be used to perform a seismic analysis. A modal analysis is first performed and classical linear methods (static, spectral and temporal) are then applied on the studied structure with taking fluid-structure into account.

Fluid-Structure Interaction Effects Modeling for the Modal Analysis of a Steam Generator Tube Bundle

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Jean-François Sigrist ◽  
Daniel Broc
Keyword(s):  
Modal Analysis ◽  
Steam Generator ◽  
Pressure Vessel ◽  
Seismic Analysis ◽  
Tube Bundle ◽  
Fluid Structure Interaction ◽  
Interaction Effects ◽  
Homogenization Method ◽  
Fluid Structure ◽  
Structure Interaction

Seismic analysis of steam generator is of paramount importance in the safety assessment of nuclear installations. These analyses require, in particular, the calculation of frequency, mode shape, and effective modal mass of the system eigenmodes. As fluid-structure interaction effects can significantly affect the dynamic behavior of immersed structures, the numerical modeling of the steam generator has to take into account FSI. A complete modeling of heat exchangers (including pressure vessel, tubes, and fluid) is not accessible to the engineer for industrial design studies. In the past decades, homogenization methods have been studied and developed in order to model tubes and fluid through an equivalent continuous media, thus avoiding the tedious task to mesh all structure and fluid subdomains within the tube bundle. Few of these methods have nonetheless been implemented in industrial finite element codes. In a previous paper (Sigrist, et al., 2007, “Fluid-Structure Interaction Effects Modeling for the Modal Analysis of a Nuclear Pressure Vessel,” J. Pressure Vessel Technol., 123, pp. 1–6), a homogenization method has been applied to an industrial case for the modal analysis of a nuclear rector with internal structures and coupling effects modeling. The present paper aims at investigating the extension of the proposed method for the dynamic analysis of tube bundles with fluid-structure interaction modeling. The homogenization method is compared with the classical coupled method in terms of eigenfrequencies, eigenmodes, and effective modal masses.

Modal Analysis of a Nuclear Reactor With Fluid-Structure Interaction: Influence of Fluid Compressibility

2006 ◽  
Author(s):  
Jean-Franc¸ois Sigrist ◽  
Daniel Broc
Keyword(s):  
Modal Analysis ◽  
Compressible Fluid ◽  
Nuclear Reactor ◽  
Fluid Structure Interaction ◽  
Low Frequency ◽  
Operating Pressure ◽  
Fluid Structure ◽  
Displacement Potential ◽  
Structure Interaction ◽  
Temperature Conditions

The present paper deals with the modal analysis of a nuclear with fluid-structure interaction effects. In a previous study, added mass and added stiffness effects due to fluid-structure interaction were modeled and studied. A dynamic analysis was performed for a seismic excitation, i.e. in the low frequency range. The present study deals with high frequency analysis, i.e. taking into account compressibility effects in the fluid problem. Elasto-acoustic coupling phenomena are studied and described in the industrial case. The elasto-acoustic coupled problem is formulated using the displacement/pressure-displacement potential coupled formulation which yields symmetric matrices. A modal analysis is first performed on the fluid problem alone, with a calculation of acoustic eigenfrequencies and the corresponding modal masses. A modal analysis is then performed for the coupled fluid-structure problem in the case of an incompressible fluid and a compressible fluid at standard pressure and temperature conditions and for a compressible fluid at the operating pressure and temperature conditions. Elasto-coupling effects are then highlighted and discussed.

Investigation of Numerical Methods for Modal Analysis of a Tube Bundle With Fluid-Structure Interaction

2007 ◽  
Author(s):  
Jean-Franc¸ois Sigrist ◽  
Daniel Broc
Keyword(s):  
Modal Analysis ◽  
Pressure Vessel ◽  
Seismic Analysis ◽  
Tube Bundle ◽  
Fluid Structure Interaction ◽  
Homogenization Method ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Internal Structures ◽  
Homogenization Methods

Seismic analysis of tube bundle is of paramount importance in the safety assessment of nuclear installations. These analyses require in particular the calculation of frequency, mode shape and effective mass of the system eigenmodes. As fluid-structure interaction effects can significantly affect dynamic behaviour of immersed structures, the numerical modeling of the tube bundle has to take into account FSI. A complete modeling of heat exchangers (including pressure vessel, tubes and fluid) is not accessible to the engineer for industrial design studies. In the past decades, homogenization methods have been studies and developed in order to model tubes and fluid through an equivalent continuous media, thus avoiding the tedious task to mesh all structure and fluid sub-domains within the tube bundle. Few of these methods have nonetheless been implemented in industrial finite element codes. In previous papers (Sigrist & Broc, Pressure Vessel and Piping, Vancouver, July 2006), a homogenization method has been developed and applied to an industrial case for the modal analysis of a nuclear rector with internal structures and coupling effects modeling. The present paper aims at investigating the application of the proposed method for the dynamic analysis of tube bundle. The homogenization method is compared with direct and indirect fluid-structure coupled methods for the calculation of eigenmode frequencies, shapes and modal masses.

Analysis and finite element discretization for optimal control of a linear fluid–structure interaction problem with delay

2018 ◽  
Vol 40 (1) ◽  
pp. 140-206
Author(s):  
Gilbert Peralta ◽  
Karl Kunisch
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Fluid Structure Interaction ◽  
Interaction Model ◽  
Necessary Optimality Conditions ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Fluid Structure ◽  
Delay Term ◽  
Structure Interaction

Abstract An optimal control problem for a linearized fluid–structure interaction model with a delay term in the structural damping is analyzed. A distributed control acting on the fluid domain, structure domain or both is considered. The necessary optimality conditions are derived both for rough and smooth initial data. A parabolic regularization of the problem and its convergence are investigated. Finite element discretization for the regularized problem and error estimates are provided. Piecewise linear elements with bubble functions for the fluid and a discontinuous Galerkin scheme for the spatial and temporal discretizations are utilized respectively. Numerical experiments illustrating the theoretical results are given.

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