Numerical investigation of Fluid – Structure interaction (FSI) on sodium leakage accident at prototype fast breeder reactor monju
Nuclear Science and Technology, Vol.10, No. 2 (2020), pp. 15-25
Numerical Investigation of Fluid – Structure Interaction (FSI) on
Sodium Leakage Accident at Prototype Fast Breeder Reactor Monju
Hoang Tan Hung, Bui Thi Hoa, Hoang Minh Giang
Institute for Nuclear Science and Technology, 179 Hoang Quoc Viet, Nghia Do, Cau Giay, Ha Noi
(Received 28 February 2020, accepted 21 April 2020)
Abstract: This study presents a numerical investigation of fluid-structure interaction about sodium
leakage accident at prototype fast breeder reactor Monju. The dynamic forces of sodium liquid flow
acting on the thermowell are the main cause of fatigue failure, which leads to the occurrence of
thermowell cracking due to intense stresses and high fatigue-cycle. Since the location and magnitude
of these stresses are unknown, an analysis of the vibrational characteristics and stresses caused by FSI
was performed by using ANSYS to prevent similar accidents in the future. The most dangerous case
was found for FSI analysis by comparisons between the natural frequency of thermowell and vortex
shedding frequency at several operating conditions. The results showed that a stress concentration
location is similar to the location of broken thermowell, and the amplitude of stress is large enough for
fatigue damage.
Keywords: Monju, Sodium leakage accident, FSI, ANSYS.
was to study the interaction between water and
circular cylinder structure under the
operational conditions of the Monju reactor.
I. INTRODUCTION
Monju is a fast breeder reactor (FBR)
that has been developed in Japan for a long –
term research, development, and utilization
program in nuclear energy. On 8th December
1995, the reactor suffered a serious accident
with sodium leaked through a temperature
sensor due to a break of thermowell inside a
secondary pipe resulting from intense vibration.
A study on sodium leakage at Monju was
performed in [1] to investigate the causes and
consequences of the accident. From the results,
it was concluded that the breakage of the
thermowell was caused by high cycle fatigue
of the well tube tip due to Vortex-Induced
Vibration (VIV) phenomenon.
On the other hand, to prevent the sodium
leakage accident, the improvement of
thermowell design was obtained by means of
an analytical study using the finite element
method (FEM) [3]. Various designs of
thermowell were taken into account. The
results showed that the design of thermowell
with a continuous low-gradient slope and no
neck could avoid the effects of VIV.
It can be seen that, after the sodium
leakage accident at the Monju reactor, many
studies were performed to find the cause of the
accident and also to prevent the accident from
happening again. This prevention could be
done by the thermowell design and its working
condition improvement. However, the number
of studies on thermowell stress concentration
prediction under the operational condition still
limited. Therefore, it is necessary to perform a
In the study of Ref. [2], it was found that
vortex-induced vibration depends on the
specific range of reduced velocity. Therefore, a
range of the reduced velocity was created using
the experimental facility to avoid that
phenomenon. The purpose of this experiment
©2020 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
NUMERICAL INVESTIGATION OF FLUID – STRUCTURE INTERACTION (FSI)…
study on the prediction of the stress
concentration of thermowell. On the other hand,
the Monju accident happened due to the VIV
phenomenon as a consequence of FSI. One
study on the consequence of FSI using ANSYS
has done [4] to predict thermowell stress
concentration on the steam temperature sensor.
Base on this paper, our work focus on ANSYS
simulation to predict the stress concentration of
Monju’s thermowell.
generating capacity of 280 MW. Liquid
sodium is used in the primary and secondary
cooling systems. An accident occurred due to
the failure of a thermowell located in the
secondary cooling system in the course of
power
thermowell was broken apart by high cycle
fatigue failure. Figure shows the
buildup
test
programs.
The
1
configuration of thermowell before and after
the accident. The tip of the well-tube was
lost and the thermocouple was bent
approximately 45 degrees from the original
position. Thermowell is a type of step-shank
with its whole length of 185.5 mm and its
thickness of 3 mm as shown in Figure 1. It is
made of 304 stainless steel, which is 8000
kg/m3 in density, Young modulus, E, is in the
range of 193 – 200 GPa, and the Poisson
ratio equal to 0.29 [5].
In this study, following the study as
mentioned in [4], an analysis of FSI between
sodium liquid and Monju’s thermowell will be
performed by using ANSYS. Two approaches
of one-way FSI and two-way FSI are applied to
investigate the VIV phenomenon to find the
stress concentration location and the stress
amplitude acting on Monju’s thermowell.
II. EXPERIMENTAL FACILITY AND
CALCULATING METHODS
From the operation history of the
secondary loop of the Monju fast breeder
reactor [6] and thermodynamic and transport
properties of sodium liquid [7], the
characteristics of sodium liquid flow depend on
the history of the secondary heat transport
system operation is presented in Table I.
A. Overview of Monju facility
The Monju fast-breeder reactor is a
sodium-cooled reactor operating at a thermal
output of 714 MW and has an electrical
Fig. 1. Thermowell configuration before and after the accident [8]
Table I. Characteristics of sodium liquid flow in the secondary heat transport system
Temperature
(
Velocity
(m/s)
5.20
2.08
2.08
Dynamic viscosity
Density (kg/m3)
Reynold number
(10-4 Pa.s)
4.52
Case 1
Case 2
Case 3
Case 4
200
200
450
485
903.0352
903.0352
846.2525
838.1427
1.04x105
4.15x104
6.92x104
7.23x104
4.52
2.55
2.41
2.08
16
HOANG TAN HUNG et al.
phenomenon could lead to large amplitude
B. Calculation Method
The VIV phenomenon is the main cause
vibrations of structure, which in turn causes
fatigue damage. However, this situation occurs
in a range of frequencies, not a single value of
frequency as the normal resonance. The
following condition is given to avoid fatigue
damage [10]:
of damaging the thermowell of the Monju
reactor. Vortices were formed and detached
periodically from either side of cylindrical
bodies causes an unsteady oscillating flow. An
asymmetrical flow pattern develops around the
body because of the periodic shedding and
changes in the pressure distribution behind the
body. Vortex shedding occurs at a certain
frequency, which is called vortex shedding
frequency (fS). This frequency depends on flow
velocity U and the cylinder diameter D,
Strouhal number (St) and formulated as [9]:
fS < 0.4 fN
(2)
Because the Monju reactor was operated
under several conditions, it is necessary to find
the most dangerous case to perform FSI
analysis by using the criteria of equation (2).
Firstly, Modal analysis was applied to
determine the natural frequency (fN) and the
mode shape of the structure. Secondly, 2D
flow analysis in Fluent was conducted to
determine the vortex shedding frequency of
different flow conditions. A comparison
between the natural frequency of structure (fN)
and vortex shedding frequency (fS) could show
the most dangerous case to perform FSI
analysis. Finally, the FSI calculation was
performed to analyze the location and value of
stress concentration on the thermowell tube.
The value of stress concentration was
compared with the endurance limit of material
(SE). The diagram of the analysis process is
shown in Figure 2.
(1)
As a result of the periodic change of the
vortex shedding, the pressure distribution on
the cylinder outer surface may also change
periodically, thereby generating a periodic
force on the cylinder surface. Each cylindrical
body has its natural frequencies (fN). If the
vortex shedding frequency (fS) is close to one
of the natural frequencies (fN), resonance could
have happened. Then, as a result, the
cylindrical bodies start to vibrate with the same
frequency as the vortex shedding frequency,
called the lock-in phenomenon. This lock-in
Fig. 2. Analysis process
17
NUMERICAL INVESTIGATION OF FLUID – STRUCTURE INTERACTION (FSI)…
it may lead to the resonance which causes the
failure of the structure. Therefore, it is an
essential process to find out the natural
frequencies and mode shapes of a structure to
find the most dangerous case of flow operation
of the Monju reactor.
1. Modal analysis
The vibrational characteristics of the
structure were determined using Modal
analysis. These characteristics which contain
natural frequencies and mode shapes of the
structure are important in designing a
structure subjected to a dynamic load. The
basic equation used in the Modal analysis for
free, undamped vibration which is given [11]
as followings:
2. 2D Fluent analysis
The 2D Fluent analysis was performed
with a typical cross-section of thermowell.
2D model of thermowell and mesh is showed
in Figure 3. As it can be seen in Table I, all
of the cases have Reynold numbers greater
([ ]
[ ]{
}
{ }
=
(3)
[ ]
[ ]
Where and are the stiffness and
than 104 so the standard k - (k is the
,
mass matrix; is a mode shape vector
turbulence kinetic energy (m2/s2) and is
the specific rate of dissipation (m2/s3))
turbulence model for near-wall interactions
model was chosen for simulation. By using a
Fast Fourier Transformation (FFT) of
velocity, the vortex shedding frequency of
different flow conditions was found and
compared with natural frequencies from
Modal analysis.
(Eigenvector) of mode i and is a natural
frequency of mode i.
Dynamic response of structures could
occur under the harmonically varying load,
whose frequencies are used to determine
whether the resonance occurs or not. If the
frequency of vortex shedding (fs) is close to
one of the natural frequencies (fi) of structures,
D1 = 0.01 m = D
D2 = 0.14 m = 14 D
D3 = 0.16 m = 16 D
D4 = 0.15 m = 15 D
Fig. 3. Model of 2D Fluent analysis at the typical cross-section of thermowell
the fluid and solid domain should be
3. FSI analysis
From the previous results, the most
continuous. A set of coupling boundary
conditions, therefore, is introduced. The
dangerous case was selected for FSI analysis.
An interface surface between the solid and
the fluid domain always existed in FSI
analysis. At this interface, both the governing
equations and the boundary conditions from
interface
conditions
of
displacement
continuity, Eq. 4, and traction equilibrium
(momentum transfer), Eq. 5 must be satisfied
along the fluid-structure boundary [9].
18
HOANG TAN HUNG et al.
df = ds
Pf = Ps
(4)
(5)
data is transferred from Fluent solver to the
Structure solver. In contrast, the two-way FSI
approach uses both the traction equilibrium, Eq. 5,
and the displacement continuity condition, Eq. 4.
Through the two-way FSI process using both
Eq. 4 and 5, displacement values are updated to
the fluid mesh.
Where df and ds are the deformations of
fluid and structure domain; Pf and Ps are the
pressure of the fluid and structure domain.
The analysis in this study was divided
into two simulations, one-way FSI and two-
way FSI, to compare the structural response to
static and dynamic load.
C. Verification of the Modal and FSI
calculation models
To demonstrate further the validity of
the Modal and FSI calculation models with
oscillation problems, the oscillation of an
exemplary vertical plate in a cavity filled
with fluid was investigated. Figure 4 shows
a schematic diagram of the oscillation
problem [12].
In the one-way FSI simulation, the focus
is on the effect of sodium flow to the
thermowell, so the pressure load data only
transferred from Fluent solver to the Structure
solver as mentioned in equation 5. However,
the solid displacement is not transferred back
to the Fluent solver. Therefore, pressure data
taken from the Fluent solver is imported to the
Structure solver.
A thin plate is anchored to the bottom
of a closed cavity filled with fluid. There is no
friction between the plate and the side of the
cavity. During the first 0.5 seconds, a
uniformly distributed load of 30 N/m is
applied to distort it. Once this load is released,
the plate oscillates back and forth to regain its
equilibrium, and the surrounding air damps
this oscillation. The flexible plate has
Young’s modulus of E = 2.5 MPa, a Poisson’s
ratio of = 0.35, and a density of 2550 kg/m3.
The one-way FSI simulation is one-way
data transport. Nevertheless, the two-way FSI
simulation is more complicated because of
their interaction between both solvers. The
motion of thermowell simulation is solved in
the Transient structure, while the motion of
flow is solved in Fluent. The System Coupling
controls the solution process as well as data
transfers between the two analysis systems.
Force data from the motion of flow is received
by the Transient structure as mentioned in
equation 5. After finishing the Structural
solving process, the displacement data from the
motion of thermowell is received by the Fluent
as mentioned in equation 4 then the Fluent
solves the fluid behavior over time. As a
consequence, the mesh is deformed according
to the response of the structure. Displacement
values are interpolated to the fluid mesh which
results in deformation of the fluid domain.
The simulation with fluid density is =
1kg/m3, and three different dynamic viscosities
of the fluid = 0.2, 1.0, and 5.0 Pa.s are
considered for the flow conditions.
In summary, the one-way FSI approach
Fig. 4. Geometry of oscillating plate
uses only the traction equilibrium, Eq. 5, and the
(not drawn to scale)
19
NUMERICAL INVESTIGATION OF FLUID – STRUCTURE INTERACTION (FSI)…
In Modal analysis, a fixed support
constraint is needed to hold the bottom of the
thin plate in place and the set up to find the
first natural frequency and mode shape of the
plate. The result of Modal analysis showed that
the value of the first natural frequency of the
plate is 0.317Hz.
exist slight discrepancies in the frequency and
the amplitude of oscillation. A different mesh
model could be the leading cause of these
discrepancies. Sodium liquid is the fluid domain
with specific viscosity and density in FSI
analysis of Monju’s thermowell. If its density
and viscosity change, its behavior could be
different. In four different cases listing in Table
I, lower viscosity of sodium liquid in the range
of 2.41 – 4.52×10-4 Pa.s causes a lower damping
coefficient; it may take a longer time for the
plate to reach the equilibrium state.
An interface between the solid domain
and the fluid domain was created for data
transferring, as mentioned in the previous
section of FSI analysis. Displacement values of
the plate are interpolated to the fluid mesh using
two-way FSI. Figure 5 (a, b, c) shows the
horizontal displacement of the free end of the
plate comparisons between our calculation
From the analytical calculation, the first
natural frequency of the simplified of a
clamped beam is defined as follows [12]:
results with that of Gl
viscosities of fluid. Our results have the same
tendency as Gl ck: the higher the viscosity of
̈ck [12] at three different
(6)
√
̈
the fluid, the faster the plate is damped and
reaches the equilibrium state. However, there
Where I is the polar moment of inertia
and m is the total mass.
(a) = 0.2 Pa.s
(b) = 1.0 Pa.s
(c) = 5.0 Pa.s
Fig. 5. Comparison of the displacements of the free end of the beam form three different fluid viscosities
with Gl
̈
ck et al (2001) [12]
20
HOANG TAN HUNG et al.
However, our result only showed the
Therefore, the Modal and FSI calculation
models can be applied for fundamental analysis
of the oscillation of thermowell.
displacement of the plate in time. Therefore,
FFT is used to find the frequency of the plate to
compare it with the analytical calculations.
Applying the FFT of the displacements to the
case of the dynamic viscosity of 0.2 Pa.s, the
first natural frequency of the plate can be found,
III. RESULTS AND DISCUSSION
Because the lock-in can occur when the
frequency of vortex shedding (fs) is close to
one of the natural frequencies (fi) of structures,
the Modal simulation set up to find the first six
natural frequencies of thermowell. Table II
shows the results of Modal analysis, the value
of frequencies are nearly equal in pair because
of the symmetry characteristic of the geometry
model of y and z-direction.
f= 0.319 Hz. The analytical value of = 0.300
Hz is approximately equal to the simulation
value of Modal analysis 0.317 Hz (5.6%
difference) and FSI analysis 0.319 Hz (6.3 %
difference). It can be seen that the characteristic
of the oscillation of the plate is nearly the same
with the thermowell on the Monju reactor.
Table II. Natural frequency of thermowell
Mode
1
2
3
4
5
6
Natural
frequency
fN (Hz)
261.15 261.22 1611.70 1612.00 4327.20 4327.50
Four cases of 2D Fluent analysis were
performed to find the frequency of vortex
shedding (fs) of each flow condition with a
typical cross-section of thermowell. The
velocity of sodium flow is 5.20 m/s and 2.08
m/s, corresponding to the 100% and 40% flow
operation. Figure 6 shows that the vortex
shedding appears behind the thermowell, and
the change of drag and lift forces coefficient is
periodical in Case 1. The frequency of vortex
shedding (fs) of each case is found by using
FFT. A detailed comparison between the
average natural frequency of structure (fN) and
vortex frequency fo fluid (fS) for Mode 1 and
Mode 2 is shown in Table III. From Eq. 2, it can
be seen that the safe cases could be reached if
the frequency ratio, f, is smaller than 0.40, and it
could be dangerous in reverse situations. Except
for Mode 1 and 2, it can be seen that f is much
smaller than 0.40 in other modes with higher
frequencies. The most dangerous case could
occur in Mode 1 and 2. Therefore, higher
natural frequency comparisons are not necessary.
The results show that the most dangerous case
of flow condition can lead to fatigue damage is
Case 1 with ratio f = fS/ fN = 0.65. The obtained
result in Case 1 was in good agreement with that
in [1].
Table III. Comparison of natural frequency of thermowell and vortex shedding frequency
Vortex shedding
frequency fS (Hz)
Average natural frequency fN
(Mode 1 and mode 2) (Hz)
Ratio f = fS/ fN
Case 1
Case 2
Case 3
Case 4
170.94
64.10
64.10
64.10
261.185
261.185
261.185
261.185
0.65
0.25
0.25
0.25
21
NUMERICAL INVESTIGATION OF FLUID – STRUCTURE INTERACTION (FSI)…
a) Appearance of vortex shedding behind the
typical cross-section of thermowell
b) Lift coefficient and drag coefficient variations
of thermowell
Fig. 6. 2D Fluent vortex shedding (case 1)
According to the previous result, the
selected Case 1 was chosen for FSI analysis to
find the location and value of stress
concentration on the thermowell tube. Figure 7
shows the vortex shedding appears behind the
thermowell in both scenarios of FSI analysis.
The changes in the diameter from the root to
the top of the thermowell resulted in the
differences in size and time of vortex
shedding’s appearance. In the case of one-way
FSI, the flow pressure will be mapped on the
deformation and stress concentration. However,
no reversed feedback process on the flow field
could occur. In the case of two-way FSI, the
deformation information will be feedback to
the flow field to calculate the influence of
deformation on the flow. Because of the
intensive interaction between sodium flow and
thermowell, the lift force and drag force are
changed. Their change makes the thermowell
oscillated around the equilibrium position. As a
result, the thermowell was bent by these forces
that similars to thermowell configuration [8].
thermowell
surface
to
calculate
the
a) One-way FSI
b) Two-way FSI
c) Thermowell configuration [8]
Fig. 7. Appearance of vortex shedding behind the thermowell
Figure 8 shows that the location of stress
value of stress concentration is very different
between the two types of FSI analysis. The
maximum equivalent stress of 18.6 MPa in
one-way FSI is much smaller than that in the
case of two-way FSI. The results show a big
difference between the structural response of
concentration on the thermowell in FSI
analysis is found in the place of the notch
which is the same broken location of
thermowell in the accident [8] for both cases
one-way FSI and two-way FSI. However, the
22
HOANG TAN HUNG et al.
static and dynamic load. The one-way FSI
load in two-way FSI in which the resonance
could lead the system to oscillate with larger
amplitude and maximum stress. In one-way
FSI simulation, the fluid domain was not
updated when the thermowell deformation
happened. Differences in the pressure field
lead to more conservative deflection values,
whereas two-way FSI simulations updated the
fluid domain related to the thermowell
deformation at each time step. However, this
approach needs a higher computational cost.
could not lead to fatigue damage because the
endurance limit of structural steel is 86.2 MPa.
On the other hand, in two-way FSI, the
absolute value of the maximum equivalent stress
curve shows almost harmonic behavior (Figure
9). Although the time of simulation is short,
which is enough time to observe the thermowell
oscillating a few times. It is seen that only the
first thermowell oscillating period is unstable, but
the maximum equivalent stress of other periods is
still greater than the endurance limit which could
cause fatigue damage. The obtained result of
two-way FSI gives a similar phenomenon that
happened in the Monju accident.
Although the calculation value of
maximum equivalent stress two-way FSI is
higher than the endurance limit, this study does
not provide a complete picture of the
assessments due to limitations in the
computational resources. Therefore, further
analysis for observing the behavior of stress
concentration on thermowell need to be done
in the future.
The difference of results between one-
way FSI and two-way FSI can be caused by
pressure load. The static load in one-way FSI
could not have resonance effects like dynamic
a) One-way FSI
b) Two-way FSI
Fig. 8. Stress concentration on thermowell
Fig. 9. Maximum equivalent stress (two-way FSI)
23
NUMERICAL INVESTIGATION OF FLUID – STRUCTURE INTERACTION (FSI)…
VIETNAM ATOMIC ENERGY INSTITUTE
(VINATOM) through the R&D Project: "Fluid –
Structure Interaction (FSI) of sodium leakage
incident at prototype fast breeder reactor Monju
by ANSYS".
IV. CONCLUSIONS
In this study, two approaches of one-way
FSI and two-way FSI using for analysis were
performed
to
investigate
the
VIV
phenomenon and the stress concentration
location and the stress amplitude acting on
Monju’s thermowell. The flow condition
with maximum stress was chosen for FSI
analysis to find the most severe case leading
to thermowell fatigue damage. The obtained
result shows that fatigue damage initiated at
an early stage of the 100% flow operation.
REFERENCES
[1]. H. Mikami, A. Shono and H. Hiroi, “Sodium
Leak at Monju (I) - Cause and Consequences”,
Tech. Committee Meeting on Evaluation of
Radioactive Materials Release and Sodium
Fires in Fast Reactors, Oaria, Ibaraki, Japan,
International Atomic Energy Agency, Vienna,
Austria, 1996.
- In both approaches, the vortex
shedding appears behind the thermowell. The
changes in the diameter from the root to the top
of the thermowell resulted in the differences in
size and time of vortex shedding’s appearance.
[2]. Masaya Kondo, Yoshinari Anoda, “Water
Flow Simulation Test on Flow – Induced
Oscillation of Thermowell in Prototype Fast
Breeder Reactor MONJU”, JSME International
Journal, Serires B, Vol.4, No.4, 2001.
- The one-way FSI approach predicts
well the stress concentration location. However,
the value of the maximum equivalent stress at
that location is not predicted with enough
accuracy. In opposite, for the two-way FSI, it
could predict both the stress concentration
location and the value of the maximum
equivalent stress at that location. Therefore, a
two-way FSI approach for the evaluation of the
stress on the thermowell of the Monju reactor
is suitable.
[3]. Hideki Aoi, Yue Zhao, Tamotsu Hayase,
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higher than the endurance limit. This condition is
reached in our analysis using two-way FSI.
However, it is needed a longer time of simulation
to observe the change in the stress amplitude for
the overall fatigue damage process.
[5]. AISI Type 304 Stainless Steel, [online]
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[6]. Masaki Morishita, Yusaku Wada, “Fatigue
analysis of thermowell due to flow – induced
vibration”, Flow – Induced Vibration and
ACKNOWLEDGMENTS
The authors of this paper wish to express
Transient Thermal
– Hydraulics, ASME
their appreciation for the financial support from
International, p. 120, 1998.
24
HOANG TAN HUNG et al.
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