Simulation of Structural Deformations of Flexible Piping Systems by Acoustic Excitation

[+] Author and Article Information
Matthias K. Maess

Institute of Applied and Experimental Mechanics, Department of Mechanical Engineering, University of Stuttgart, 70550 Stuttgart, Germanymaess@iam.uni-stuttgart.de

Lothar Gaul

Institute of Applied and Experimental Mechanics, Department of Mechanical Engineering, University of Stuttgart, 70550 Stuttgart, Germanygaul@iam.unl-stuttgart.de

J. Pressure Vessel Technol 129(3), 363-371 (Oct 02, 2006) (9 pages) doi:10.1115/1.2748819 History: Received December 30, 2005; Revised October 02, 2006

Valve actuation and pump fluctuation in piping systems generate propagating sound waves in the fluid path which in turn can lead to undesired excitation of structural components. This vibro-acoustic problem is addressed by studying the propagation dynamics as well as the excitation mechanism. Fluid-structure interaction has a significant influence on both hydroacoustics and on structural deformation. Therefore, pipe models are generated in three dimensions by using finite elements in order to include higher-order deflection modes and fluid modes. The acoustic wave equation in the fluid is hereby fully coupled to the structural domain at the fluid-structure interface. These models are used for simulating transient response and for performing numerical modal analysis. Unfortunately, such 3D models are large and simulation runs turn out to be very time consuming. To overcome this limitation, reduced pipe models are needed for efficient simulations. The proposed model reduction is based on a series of modal transformations and modal truncations, where focus is placed on the treatment of the nonsymmetric system matrices due to the coupling. Afterwards, dominant modes are selected based on controllability and observability considerations. Furthermore, modal controllabilities are used to quantify the excitation of vibration modes by a white noise acoustic source at the pipe inlet. The excitation of structural elements connected to the piping system can therefore be predicted without performing transient simulations. Numerical results are presented for a piping system consisting of straight pipe segments, an elbow pipe, joints, and a target structure. This example illustrates the usefulness of the presented method for vibro-acoustic investigations of more complex piping systems.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

FE model of a fluid-filled pipe segment with elastic supports and flanges

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Figure 2

Bending mode shape (circumferential order n=2) of a fluid-filled supported pipe segment as part of the circuit piping system

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Figure 3

Fluid wave propagation in the elbow pipe

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Figure 4

Acoustic pressure at cross section B1-B2: top (p1 – – –), bottom (p2–∙–), and pressure gradient (pz —)

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Figure 5

Pressure input mobility uz∕p at point B1 reveals Bernoulli beam-type mode at 920.5Hz

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Figure 6

Substructuring and model reduction steps

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Figure 7

Transient simulation of hydroacoustics in a longitudinal pipe segment: excitation at left end (top), result by full model (middle). Simulation errors (bottom) by the modal truncated model (er, 141 DOFs —) and by the further reduced model (et, 26 DOFs – – –) are almost identical.

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Figure 8

Hankel singular values (HSV) for the first 140 modes

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Figure 9

Hankel singular values (HSV) for the first 100 modes

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Figure 10

Transient simulation of structural deflection of an elbow pipe due to acoustic excitation in the fluid (top): result by full model (middle) simulation errors (bottom) by modal truncated model (101 DOFs —) and by further reduced model (22 DOFs – ∙ –)

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Figure 11

Pressure input mobility at point B (ux∕p) compared to HSVs

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Figure 12

Piping system with target structure

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Figure 13

Input mobilities ux∕p at points B (—), C (– – –) and HSVs at points B (◇) and C (+)

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Figure 14

Modal controllabilities wcj(o) correspond to modal input mobilities ξ∕p (top). Modal observabilities woj (bottom) depend upon receiver point B (◇) or C (+).

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Figure 15

Mode shapes 4 (28.7Hz, left) and 5 (33.0Hz, right) with deformation ux at points B and C




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