1 Copyright © 2011 by ASME Proceedings of the ASME 2011 Pressure Vessels & Piping Division Conference PVP2011 July 17-21, 2011, Baltimore, Maryland,… [628156]

1 Copyright © 2011 by ASME Proceedings of the ASME 2011 Pressure Vessels & Piping Division Conference
PVP2011
July 17-21, 2011, Baltimore, Maryland, USA
PVP2011-57534
PIPE RUPTURE ANALYSIS CONSIDERING FLUID-STRUCTURE INTERACTION

Yuk
ari Hamamoto
IHI Corporation
Yokohama, Japan Makoto Toyoda
IHI Corporation
Yokohama, Japan

ABSTRACT
Global warming is caused by the emission of greenhouse
gases, like CO2. Nuclear energy is one of the main sources of
low-carbon energy. In the events of serious accidents, a nuclear
power plant may emit radioactivity that is harmful to human
health. Nuclear power should be used after enough evidence of
its safety is provided.
Measures for safety of nuclear power plants, such as
autogenous control and LBB, have been developed. Moreover,
there is requirement with respect to the design, safety,
equipments components and systems of nuclear plant. For
example, it is necessary to place components that restrain pipe
whip behavior, and to design peripheral equipments that may be
affected by high-pressured fluid in pipe rupture accidents [1],
[2].
In the case of pipe rupture that occurs to structures such as
nuclear plants and steam generators, a pipe deforms releasing
its inner high-pressured fluid.
In previous studies, the pipe whip behavior analyses have
been performed by using blowdown thrust force that is
estimated by fluid analysis.
In this study, we simulate pipe whip behavior and
reduction of blowdown thrust force by releasing inner fluid to
the atmosphere. The analysis model is an elbow pipe and high-
pressure fluid running inside. We considered fluid-structure
interaction effect in the analysis because ovalization of the
cross-section of the elbow part as well as a change of the elbow
torus radius affects fluid flow blowing out from the ruptured
part of the pipe.

INTRODUCTION
When a high-pressure pipe which is in nuclear power
plants, boilers, and compressors breaks, the pipe is dynamically
deformed with releasing its internal fluid. In the design of the
nuclear power plant, it is necessary to calculate the pipe
movement for safety at the pipe rupture accident. On the other hand, when the pipe rupture accident of the compressor occurs,
it is necessary to explain the behavior of the broken pipe.
In past studies, simulations of structural analysis for the
movement of a broken pipe have been carried out. A thrust load
applied in those simulations has been obtained from fluid
dynamic analyses of fluid release from pipe. In other cases, the
structural analyses have been done by using a simplified thrust
load obtained from design safety limits. So, there is a possibility
of doing a conservative design compared with an actual thrust
load.
In the present study, a dynamic deformation of a pipe and
the decrease of the thrust load with the releasing internal fluid
are simulated simultaneously. The analytical model is a pipe
which has an elbow part and high-pressure fluid flow inside. If
such a pipe breaking takes place, the elbow part ovalization and
the elbow torus radius change is expected [3]. It is thought that
flow of the fluid that is released from pipe changes every
second with the deformation of this pipe. Moreover, it is
thought that the pipe is deformed in proportion to the reaction
force of the releasing fluid. Therefore, it is thought that the pipe
behavior when pipe is broken can be simulated more accurately
by using the technique of the present study: the movement of
the fluid and pipe is solved simultaneously.
In the pipe rupture in the present study, instantaneous
crack propagation in the circumferential direction of the pipe is
assumed. Therefore, the crack initiation and propagation are not
considered. Momentary break of a pipe is assumed when the
hydrogen detonation is caused in a nuclear power plant.

NOMENCLATURE
LBB = Leak Before Break
SPH = Smoothed Particle Hydrodynamics (Method)
AUTODYN = An explicit analysis software for impact
analysis
Abaqus = a finite element program software for structure
and heat-defer analysis Proceedings of the ASME 2011 Pressure Vessels & Piping Division Conference
PVP2011
July 17-21, 2011, Baltimore, Maryland, USA
PVP2011-57534
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2 Copyright © 2011 by ASME ANALYTICAL METHOD
Analytical model
The main conditions of the calculation are shown below.
Figure 1 shows the pipe model.
・ pipe internal radius: 315[mm]
・ pipe thickness: 35[mm]
・ inner pressure: 7.24[MPa]
・ temperature: 550[K]
・ fluid initial velocity: 0[m/s2]
・ pi
pe material:
Young’s modulus: 182401[MPa]
Poisson ratio: 0.3
Density: 7.85E-09[ton/mm3]

FIGURE 1: PIPE MODEL

Analysis code and Solver
The analytical code used in this study is AUTODYN-3D
Version12.0.01i. Shell elements are used for the pipe and SPH
particles are used for internal fluid. Figure 2 shows an analytical
model for AUTODYN. In some plants, a valve shuts
automatically the moment inner pressure decreases. In the
AUTODYN analysis, the tank size is adjusted so that the
amount of the fluid from the valve to the base of the pipe
becomes equivalent to the tank volume. The fluid running
inside the pipe is also modeled. It is assumed that the tank is a
rigid body and the pipe is an elastic body. In the initial state, the
pressure of the fluid is 7.24MPa.
To compare with the calculation of the present study, the
pipe rupture simulation that uses analytical code Abaqus is
performed. For the Abaqus analysis model, three kinds of
elements (beam element, elbow element and shell element) are
used to model a pipe. The pipe rupture simulation that uses
beam elements is done in actual designs though the cross-
sectional deformation of pipe is not considered in beam
elements. On the other hand, the stiffness decrease due to pipe
ovalization is considered in elbow elements. It is thought that a
computation result that uses shell elements gives the nearest
behavior to real behavior. Figure 3 shows the Abaqus analysis
model. The pipe boundary is assumed to be completely fixed. The thrust load by an internal fluid, defined as pipe sectional
area × fluid pressure ≒2.3×106 N, is applied to the pipe
br
eaking point as a concentrated load. Damping is not
considered and the initial thrust force keeps acting to assume
the design of the safety side. Figure 4 shows the time history of
simplified thrust force used for the analysis. The directional
change of the thrust load (follower force) in accordance with the
deformation of pipe is considered.

FIGURE 2: AUTODYN ANALYSIS MODEL

FIGURE 3: ABAQUS ANALYSIS MODEL

1600mm1400mm350mm
fixed
1600mm1400mm350mm
1600mm1400mm350mm
fixed
SPH particles
tank：rigid body
piping：elastic body
SPH particles
tank：rigid body
piping：elastic body

固定点
推力荷重
推力荷重Shell要素 Beam・Elbow要素
固定点fixedfixed
thrust loadthrust loadBeam ・Elbow element Shell element
固定点
推力荷重
推力荷重Shell要素 Beam・Elbow要素
固定点fixedfixed
thrust loadthrust loadBeam ・Elbow element Shell element
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3 Copyright © 2011 by ASME

FIGURE 4: TIME HISTORY OF THRUST FORCE
AMPLITUDE
CALCULATION RESULTS
Pipe rupture simulation results by Abaqus
Figure 5 shows the time history of displacement of pipe
breaking position obtained by the pipe rupture simulation by
Abaqus. The calculation results show that simulation with beam
elements that does not take deformation of the cross-section
into account results in stiff pipe. On the other hand, simulation
with shell or elbow elements to include cross-sectional
deformation effect results in less stiff pipe. It can be said that
there is an influence due to the pipe section ovalization. The
deformation calculated from beam elements is shown in Figure
6. In Figure 6, the deformation is exaggerated to 5 times of real
deformation. It can be seen that the elbow is expanded from
Figure 6. The deformation in the computational result of shell
elements is shown in Figure 7. In Figure 7, the ovalization of
the pipe elbow part is seen.

FIGURE 5: DISPLACEMENT HISTORY OF PIPE
BREAKING POSITION (ABAQUS)

FIGURE 6: DEFORMATION CALCULATED FROM THE
BEAM ELEMENTS

FIGURE 7: CROSS SECTION OV ALIZA TION

Computational results of pipe rupture by AUTODYN
Figure 8 shows diffusion of an internal fluid. Figure 9 and
10 show the time history of the thrust load with the releasing
fluid calculated by the pipe breaking simulation by AUTODYN.
The load is obtained by momentum derivation of the fluid (SPH
particles). At the beginning a sharp large load appears, then
the load gradually decreases. If it is assumed that load
continuance time is 0.15s, the mean value of the thrust load is
about 9.93×105 N. Compared with the thrust force 2.3×105 N
as
sumed in Abaqus analysis, it would appear that the load
obtained by AUTODYN analysis is excessively large. Figure 11
shows the time history of displacement of breaking position. At
0.075 seconds of Figure 11, the breaking point passes by the
original position. Large displacement is obtained compared with
Figure 5. In the next chapter, the influence of the difference of
the load is discussed.

AA
変形前
変形後
変形前
変形後afterbefore
変形前
変形後
変形前
変形後afterbefore
00.20.40.60.811.2
0 0.2 0.4 0.6 0.8 1
Time[s]Nondimensional force
020406080100
0 0.05 0.1 0.15 0.2 0.25
Time[s]Total displacement[mm]Beam element
Elbow element
Shell element
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4 Copyright © 2011 by ASME

FIGURE 8: APPEARANCE OF THE DIFFUSION OF AN
INTERNAL FLUID

FIGURE 9: FLUID REACTION FORCE (0-0.004[s])

FIGURE 10: FLUID REACTION FORCE (0-0.23[s])

FIGURE 11: DISPLACEMENT TIME HISTORY OF
BREAKING POINT (AUTODYN)

Pipe rupture results by Abaqus with the thrust load obtained by
AUTODYN analysi s
To confirm the influence of the difference of the load, pipe
ru
pture simulation by Abaqus with the thrust load is obtained by
AUTODYN analysis (Fig. 9,10) is calculated. The applied force
is shown in Figure 12 and 13.
Figure 14 shows displacement time history of pipe
breaking position. Compared with the results of the simplified
load (Fig.5), the maximum displacement of both calculations is
almost the same, but it seems that the frequency of Figure 14 is
the twice as high as Figure 5. In Abaqus analysis, the structural
damping is not considered. Therefore, the pipe of Abaqus
model with the load obtained by AUTODYN keeps vibrating at
eigen frequency even if the thrust load is lost. As Figure 14
shows the total displacement, the actual frequency is 1/2 of
values that can be read from figure 14. So, the frequency of
Figure 5, 11 and 14 are almost the same.
Compared with the AUTODYN analysis result (Fig.11),
sm
aller displacement is obtained from the Abaqus analysis. The
di
fference of the maximum value may be given by the difference
of formulations of elements, fluid-structure interaction effects
an
d load condition. To confirm the influence of the difference of
the formulations, the AUTODYN analysis in which load is applied
to
the pipe breaking point as a concentrated load without inner
fluid is required. Moreover, it is necessary to compare two load
conditions indetail.

0.0005[s] 0.0015[s]
0.0025[s] 0.0125[s]
0.0005[s] 0.0015[s]
0.0025[s] 0.0125[s]
020406080100120140160180
0.00 0.05 0.10 0.15 0.20 0.25
time[s]Total displacement[mm]
0.0E+002.0E+064.0E+066.0E+068.0E+061.0E+071.2E+071.4E+071.6E+071.8E+072.0E+07
0.000 0.001 0.002 0.003 0.004
time[s]Fluid reaction force[N]
0.0E+005.0E+051.0E+061.5E+062.0E+062.5E+063.0E+063.5E+064.0E+064.5E+06
0.000 0.050 0.100 0.150 0.200 0.250
time[s]Fluid reaction force[N]
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5 Copyright © 2011 by ASME

FIGURE 12: THRUST LOAD AMPLITUDE (0-100[%])

FI
GURE 13: THRUST LOAD AMPLITUDE (0-1[%])

FIGURE 14: DISPLACEMENT TIME HISTORY OF PIPE
BREAKING POSITION (ABAQUS ANALYSIS, THE
THRUST LOAD IS OBTAINED BY AUTODYN ANALYSIS)

CONCLUSIONS
In this study, both pipe deformation and inner fluid
releasing are calculated simultaneously by AUTODYN. It is
expected that the force which deforms the pipe is closer to the
real force with this method. In this calculation, cross-section
ovalization of a pipe and directional change of inner fluid can
be considered.
Compared with the maximum displacement about 110mm of
Abaqus analysis, the AUTODYN analysis result about 170mm
is larger. So, it is possible that the displacement is calculated
small by the Abaqus pipe rupture simulation results.
It is important to compare the AUTODYN analysis with
ex
perimental results. To confirm the validity of AUTODYN an
analysis, an experiment that imitates the pipe rupture is
scheduled.

REFERENCES
[1] Ueda, S., “Dynamic Behavior of Pipe under Loss of Coolant
Accident”, JAERI-M 87-027, 1987. (in Japanese)
[2] Miyazaki, N., “Analytical Studies of Blowdown Thrust
Force and Dynamic Response of Pipe at Pipe Rupture
Accident” The Japan Society of Mechanical Engineers A,
V ol. 51(461), pp.98-106, 1985. (in Japanese)
[3] Hosokawa, N., Yatabe, H., Watanabe, T., ‘‘In-plane bending
behavior of a large diameter steel elbow for gas pipeline’’
Journal of Structure Engineering of Japan A, V ol. 46A(1),
pp17-24, 2000. (in Japanese)

020406080100120
0.00 0.05 0.10 0.15 0.20 0.25
time[s]Nondimensional force[%]input load
0.00.51.0
0.00 0.05 0.10 0.15 0.20 0.25
time[s]Nondimensional force[%]input load
020406080100120
0 0.05 0.1 0.15 0.2 0.25
Time[s]Total displacement[mm]Beam element
Elbow element
Shell element
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