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Journal of Pressure Vessel Technology | Volume 129 | Issue 1 | Research Paper
RESEARCH PAPERS

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

[+] Author and Article Information
Jean-François Sigrist

Service Technique et Scientifique,  DCN Propulsion, 44620 La Montagne, Francejean-francois.sigrist@dcn.fr

Daniel Broc

Service d’Etude Mécanique et Sismique,  CEA Saclay, 91191 Gif-Sur-Yvette, France

Christian Lainé

Service Technique et Scientifique,  DCN Propulsion, 44620 La Montagne, France

J. Pressure Vessel Technol 129(1), 1-6 (Mar 17, 2006) (6 pages) doi:10.1115/1.2389025 History: Received October 17, 2005; Revised March 17, 2006
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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.
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References

1
Makerle, J., 1999, “Fluid-Structure Interaction Problems, Finite Element Approach and Boundary Elements Approaches. A Bibliography,” Finite Elem. Anal. Design, 31 , pp. 231–240.
2
Morand, H. J.-P., and Ohayon, R., 1995, "Fluid Structure Interaction", Wiley, New York.
3
Sigrist, J. F., Broc, D., and Lainé, C., 2005. “A Homogenization Method for the Analysis of a Coupled Fluid-Structure Interaction Problem with Inner Solid Structures,” European Nuclear Conference , Versailles.
4
Axisa, F., 2001, "Interactions Fluide Structure", Hermès, London.
5
Rajakumar, C., and Rogers, C. G., 1991, “The Lanczos Algorithm Applied to Unsymmetric Generalized Eigenvalue Problem,” Int. J. Numer. Methods Eng.  [CrossRef], 32 , pp. 1009–1026.
6
Boujot, J., 1987, “Mathematical Formulation of Fluid-Structure Interaction Problems,” Model. Math. Anal. Numer., 21 , pp. 239–260.
7
Gibert, R. J., 1986, "Vibrations des structures. Interaction avec les fluides. Sources d’excitation aléatoires", Collection de la Direction des Etudes et Recherches d’Electricté de France, vol. 69 , Eyrolles.
8
Sigrist, J. F., Broc, D., and Lainé, C., 2005, “Seismic Analysis of a Nuclear Reactor with Fluid-Structure Interaction,” Pressure Vessel and Piping, Denver, CO.
9
Brochard, D., and Hammami, L., 1998, “Non-Linear Analysis of Nuclear Reactor Cores by an Homogenization Method,” Pressure Vessel and Piping, San Diego, CA.
10
Cheval, K., 2001, “Modélisation du comportement sismique de structures multitubulaires baignées par un fluide dense,” Ph.D. Thesis, Université d’Evry.
11
Planchard, J., and Ibnou-Zahir, M., 1983, “Natural Frequencies of a Tube Bundle in an Incompressible Fluid,” Comput. Methods Appl. Mech. Eng.  [CrossRef], 41 , pp. 47–68.
12
Conca, C., Planchard, J., Thomas, B., and Vanninathan, M., 1994, "Problèmes mathématiques en couplage fluide∕structure. Applications aux faisceaux tubulaires", Collection de la Direction des Etudes et Recherches d'Electricité de France, Vol. 85 , Eyrolles.
13
Broc, D., Queval, J. C., and Viallet, E., 2003, “Seismic Behaviour of PWR Reactor Cores: Fluid-Structure Effects,” 17th Conference on Structural Mechanic in Reactor Technology , Prague.
14
Broc, D., 2004, “Seismic Behaviour of PWR Reactor Cores: Whole Core Model with Fluid-Structure Interaction Effects,” Flow Induced Vibrations , Paris, July 6–9, Vol. 1 , pp. 283–288.
15
Verpeaux, P., 1989, “A Modern Approach of Computer Codes for Structural Analysis,” 10th Conference on Structural Mechanics in Reactor Technology , Anaheim, CA.
16
Cheng, F. Y., 2001, "Matrix Analysis of Structural Dynamics", Marcel Dekker, New York.

Figures

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+Axisymmetric model of the nuclear pressure vessel
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Axisymmetric model of the nuclear pressure vessel
Figure 1

Axisymmetric model of the nuclear pressure vessel

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+Fluid problem mesh with and without inner structures modeling
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Fluid problem mesh with and without inner structures modeling
Figure 2

Fluid problem mesh with and without inner structures modeling

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+Elementary fluid cell mesh
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Elementary fluid cell mesh
Figure 3

Elementary fluid cell mesh

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+Axisymmetric finite element model of the nuclear pressure vessel
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Axisymmetric finite element model of the nuclear pressure vessel
Figure 4

Axisymmetric finite element model of the nuclear pressure vessel

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+Fluid and structure finites elements, coupling and interface elements
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Fluid and structure finites elements, coupling and interface elements
Figure 5

Fluid and structure finites elements, coupling and interface elements

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+Uncoupled eigenmode of the reactor (without fluid)
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Uncoupled eigenmode of the reactor (without fluid)
Figure 6

Uncoupled eigenmode of the reactor (without fluid)

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+Coupled eigenmodes of the reactor (with fluid, without inner pressure, without inner structures)
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Coupled eigenmodes of the reactor (with fluid, without inner pressure, without inner structures)
Figure 7

Coupled eigenmodes of the reactor (with fluid, without inner pressure, without inner structures)

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+Stiffness forces from correction terms Kπ and Kσ
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Stiffness forces from correction terms Kπ and Kσ
Figure 8

Stiffness forces from correction terms Kπ and Kσ

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+Cumulated modal masses for the coupled eigenmodes calculated with the homogenization technique
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Cumulated modal masses for the coupled eigenmodes calculated with the homogenization technique
Figure 9

Cumulated modal masses for the coupled eigenmodes calculated with the homogenization technique

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