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Research Papers: Fluid-Structure Interaction

# Harmonic Analysis of a Cylinder Cluster in Square Confinement With Position-Dependent Fluid Damping

[+] Author and Article Information

Westinghouse Electric Company, 5801 Bluff Road, Columbia, SC 29209

J. Pressure Vessel Technol 130(4), 041303 (Aug 22, 2008) (10 pages) doi:10.1115/1.2967755 History: Received May 03, 2006; Revised February 13, 2007; Published August 22, 2008

## Abstract

The vibration of cylinder clusters in axial flow is a classical engineering problem, with applications to nuclear fuel rods and steam generator tubes. The classical method of solution to this problem consists in development of modal analysis of the entire cluster including structural characteristics and fluid-elastic effects due to the presence of the dense medium in the space between cylinders, followed by a forced-vibration analysis. It is shown here that the out-of-phase fluid-elastic effects (added damping) are dependent on the position of cylinders within the bundle, not unlike the already proven in-phase effects (added mass). A two-dimensional arbitrary Lagrangian Eulerian (ALE) finite-element analysis is used to compute the hydrodynamic coupling effects in a $5×5$ rod cluster subject to single-phase parallel flow. These motion-dependent effects are subsequently embedded into the equations of motion for scaled-down array of nuclear fuel rods, which are structurally modeled as variable-mass Euler–Bernoulli beams on elastic supports. The modal and harmonic analyses developed on the basis of these equations shows that the rod response is affected by the rod position within the cluster, relative to the confinement.

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## Figures

Figure 1

(a) Short fuel rod; (b) infinitesimal element

Figure 2

Bundle geometry and confinement

Figure 3

Equivalent angle of incidence

Figure 4

CFD mesh detail

Figure 5

Bundle modes at 6.7m∕s: (a) 58.6Hz, and (b) 61.8Hz

Figure 6

Complex natural bundle frequencies for modal expansion using the first three single-rod modes

Figure 7

First natural frequency stability

Figure 8

Power spectral density of Cylinders 3, 8, and 13, upon harmonic excitation of Cylinder 13

Figure 9

PSD of Cylinders 3, 8, and 13, upon harmonic excitation of Cylinder 3

Figure 10

Spectral response for Rods 1 and 3, with and without position-specific damping

Figure 11

Fluid forces in the x and y directions, due to harmonic motion of ROD 13 in the x direction: (a) 13, x; (b) 8, x; (c) 13, y; (d) 8y.

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