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Research Papers: Fluid-Structure Interaction

Godunov’s Method for Simulatinons of Fluid-Structure Interaction in Piping Systems

[+] Author and Article Information
Janez Gale1

Reactor Engineering Division, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Sloveniajanez.gale@ijs.si

Iztok Tiselj

Reactor Engineering Division, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Sloveniaiztok.tiselj@ijs.si

1

Corresponding author.

J. Pressure Vessel Technol 130(3), 031304 (Jul 11, 2008) (12 pages) doi:10.1115/1.2937758 History: Received September 27, 2006; Revised March 27, 2007; Published July 11, 2008

Constant coefficient one-dimensional linear hyperbolic systems of partial differential equations (PDEs) are often used for description of fluid-structure interaction (FSI) phenomena during transient conditions in piping systems. In the past, these systems of equations have been numerically solved with method of characteristics (MOCs). The MOC method is actually the most efficient and accurate method for description of the single-phase transient in the cold liquid where the constant coefficient mathematical model describes phenomenon with sufficient accuracy. In energy production systems where hot pressurized liquid is used for heat transfer between the heat source and the steam generator, more complex and nonlinear mathematical models are needed to describe transient flow and these models cannot be solved with MOC method because the models are not constant. In addition, the MOC method can be used for pipes having discontinuities like elbows, geometrical changes, material properties changes, etc., but only with some extra numerical modeling. An interesting alternative is explicit characteristic upwind numerical method, known as Godunov’s method that is frequently used for nonlinear systems or systems where properties change with position. In the present study, applicability of the Godunov’s method for the FSI analyses is tested with eight first order PDEs mathematical model. The conventional linear mathematical model is improved with convective term that makes the system nonlinear and additional terms that enable simulations of the FSI in arbitrarily shaped piping systems located in a plane. Two PDEs describe pressure waves in the single-phase fluid and six PDEs describe axial, lateral, and rotational stress waves in the pipe. The applied system of equations has stiff source terms. This numerical problem is solved introducing implicit iterations. The proposed model is verified with a rod impact experiment that is carried out on single-elbow pipe hanging on wires. Godunov’s method is found as a very promising numerical method for simulations of the FSI problems.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry and nodalization of the smooth input model

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Figure 2

Pressure history in P1

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Figure 3

Pressure history in P3

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Figure 4

Pressure history in P5

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Figure 5

Axial force history in P2

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Figure 6

Axial velocity history in P2

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Figure 7

Momentum history in P2

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Figure 8

Momentum history in P4

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Figure 9

Pressure history in P1—grid refinement study

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Figure 10

Geometry and nodalization of the sharp input model

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Figure 11

Pressure history in P5—comparison of smooth and sharp model

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Figure 12

Momentum history in P4—comparison of smooth and sharp model

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Figure 13

Pressure history in P5—different difference schemes

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Figure 14

Pressure history in P5—CFL factor influence

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Figure 15

Flexibility factor along the pipe for rod impact experiment (smooth model)

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Figure 16

Momentum history in P4—influence of the flexibility factor

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Figure 17

Eigenvalues along the pipe for rod impact experiment (variable thickness)

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Figure 18

Pressure history in P5—influence of the variable thickness

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Figure 19

Eigenvalues history in Point P4—rod impact experiment (nonlinear system)

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Figure 20

Pressure history in P5—influence of the nonlinearity in fluid momentum equation

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