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Research Papers: Fluid-Structure Interaction

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

[+] Author and Article Information
Jean-François Sigrist

Service Technique et Scientifique, DCNS Propulsion, 44620 La Montagne, Francejean-francois.sigrist@dcnsgroup.com

Daniel Broc

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

In the elementary case depicted by Fig. 8, it could have been of some practical as well as theoretical interest to account for the various symmetries in the bundle and therefore reduce the size of the problem. In the industrial case, which is concerned by the application of the method, the complexity of the bundle geometry makes is difficult to efficiently account for symmetries. Therefore, the possibility of using symmetries has been discarded on purpose in the present analysis.

This assumption has some restrictions only in the high frequency range; complete homogenization of the tubes-fluid system must indeed account for acoustic wave propagation and dispersion within the bundle. In the industrial applications of the presented method, the tube characteristics are such that the frequencies of interest are below 100 Hz, so that fluid compressibility effects can safely be discarded in the analysis. However, fluid equations presented here will take into account constant fluid compressibility. For the application example proposed in the present section, acoustic wave velocity in the fluid will be set at a high but finite value, which is consistent with the modeling of a nearly incompressible fluid.

The cumulated mass represented in the graph is related to the tube motions and does not take into account the mass of the surrounding fluid, which represents the other 50% of the total mass.

Figure 1 indicates that a second mode at frequency ratio $β∼92.5%$ has also a non-negligible contribution in the seismic response of the tube bundle (although less significant than the so-called “dominant mode” represented in Fig. 1). It is checked in the same manner that the modal characteristics of this mode (frequency ratio, effective masse, shape) is correctly predicted by the homogenization method.

This remark remains physically consistent only in linear analysis; when the level of the imposed acceleration is high enough to generate large motions of the tubes and shocks between the tubes, all modes are likely to be involved in the dynamic response of the tube bundle. Further investigation and validation of the method in the nonlinear case is therefore required to deal with such complex interaction and will be dealt with in future applications.

The pitch-to-diameter ratio is in this case $p/2R=75%$, but the other tube characteristics are the same as those defined in Fig. 8.

J. Pressure Vessel Technol 131(3), 031302 (Feb 11, 2009) (11 pages) doi:10.1115/1.3062940 History: Received August 17, 2007; Revised February 08, 2008; Published February 11, 2009

## Abstract

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, , 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.

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## Figures

Figure 1

Periodic arrays of square/circle structures embedded in fluid

Figure 2

Compact steam generator for naval nuclear propulsion

Figure 3

Coupled and homogenized tube bundle modeling with FSI

Figure 4

Elementary cell ΩT: elementary tube ΩS immersed in fluid elementary domainΩF

Figure 5

Homogenized cell with adjacent homogenized, nonhomogenized an structure cells

Figure 7

Fluid and structure, fluid and tube finite element coupling

Figure 8

Figure 9

Finite element discretization of the 2D 10×10 tube bundle with coupled and homogenization methods

Figure 10

Elementary cell calculation

Figure 11

Effective mass and number of modes versus frequency ratio: comparison of coupled and homogenized methods

Figure 12

Eigenmode calculation with coupled and homogenization methods

Figure 13

Mesh refinement in the elementary cell

Figure 6

Homogenized fluid-and-coupled with an elastic structure

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