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This article was downloaded by: [200.4.253.2]On: 30 June 2015, At: 06:26Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK
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Evaluation of Acoustic- and Flow-Induced Vibration
of the BWR Main Steam Lines and DryerRyo MORITA
a, Shiro TAKAHASHI
b, Keita OKUYAMA
b, Fumio INADA
a, Yukio OGAWA
c&
Kazuhiro YOSHIKAWAc
aCentral Research Institute of Electric Power Industry , 2-11-1 Iwado Kita, Komae-shi,
Tokyo , 201-8511 , JapanbHitachi Ltd., Energy & Environmental Systems Laboratory , 7-2-1 Omika-cho, Hitachi-
shi, Ibaraki , 319-1221 , JapancHtachi-GE Nuclear Energy, Ltd. , 1-1-3 Saiwai-cho, Hitachi-shi, Ibaraki , 317-0073 ,
JapanPublished online: 05 Jan 2012.
To cite this article:Ryo MORITA , Shiro TAKAHASHI , Keita OKUYAMA , Fumio INADA , Yukio OGAWA & Kazuhiro YOSHIKAWA(2011) Evaluation of Acoustic- and Flow-Induced Vibration of the BWR Main Steam Lines and Dryer, Journal of Nuclear
Science and Technology, 48:5, 759-776
To link to this article: http://dx.doi.org/10.1080/18811248.2011.9711759
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Evaluation of Acoustic- and Flow-Induced Vibration
of the BWR Main Steam Lines and Dryer
Ryo MORITA1;, Shiro TAKAHASHI2, Keita OKUYAMA2, Fumio INADA1,
Yukio OGAWA3 and Kazuhiro YOSHIKAWA3
1Central Research Institute of Electric Power Industry, 2-11-1 Iwado Kita, Komae-shi, Tokyo 201-8511, Japan2Hitachi, Ltd. Energy & Environmental Systems Laboratory, 7-2-1 Omika-cho, Hitachi-shi, Ibaraki 319-1221, Japan
3Htachi-GE Nuclear Energy, Ltd., 1-1-3 Saiwai-cho, Hitachi-shi, Ibaraki 317-0073, Japan
(Received February 14, 2010 and accepted in revised form October 23, 2010)
The boiling water reactor (BWR-3) steam dryer in the Quad Cities (QC) Unit 2 Nuclear Power Plant
was damaged by high-cycle fatigue due to acoustic-induced vibration. The cause of the dryer failure was
considered as flow-induced acoustic resonance at the stub pipes of the safety relief valve (SRV) in themain steam lines (MSLs). The acoustic resonance was considered to be generated by the interaction
between the sound field and an unstable shear layer across the closed side branches of SRVs. We have
started a research program on BWR steam dryers to develop methods of evaluating the loading. Moreover,
it is necessary to evaluate the dryer integrity of BWR-5 plants, which are the main type of BWR in Japan.
In the present study, we conducted 1/10-scale BWR model tests and analysis to investigate the flow-
induced acoustic resonance and acoustic characteristics in MSLs. The test apparatus consisted of a steam
dryer, a steam dome, and 4 MSLs with 20 SRV stub pipes. Computational fluid dynamics (CFD) analysis
was conducted to evaluate the acoustic source in MSLs. Finite element method (FEM) was applied to
calculate the three-dimensional wave equations for acoustic analysis. We demonstrated that large fluctu-
ating pressure occurred in the high- and low-frequency regions. The high-frequency fluctuating pressure
was generated by the flow-induced acoustic resonance in the SRV stub pipes. We evaluated the acoustic
source (that is, the fluctuating pressure) in MSLs by unsteady CFD calculations, and we evaluated the
pressure propagation by acoustic analysis. These results were verified by comparison with the results of
scale-model tests, and they showed good agreement with the experimental results. The effects of the
difference between the properties of air and steam were numerically investigated, and it was found that the
effects on the acoustic resonance in the SRV stub pipes were not significant.
KEYWORDS: boiling water reactor, power uprate, main steam lines, dryer, safety relief valve,
acoustic vibration, flow-induced acoustic resonance, computational fluid dynamics analysis,
acoustic analysis
I. Introduction
As a method of obtaining higher electric power from
existing nuclear power stations, power uprate has been wide-ly used in many countries. Power uprate involves increasing
the thermal power output from a nuclear power reactor to
above the rated power. In the United States, more than 120
power uprate applications up to 120% power level have been
approved since the 1970s, and more than 5,700 MWe of
electricity has been generated by power uprate. In European
power plants, a significant power uprate has often been
implemented as part of a plant modernization program to
improve plant performance. In Japan, power uprate has re-
cently been considered as an effective method of increasing
the amount of electric power from existing nuclear power
plants and reducing greenhouse gas emissions. Therefore, it
is expected that power uprate will be introduced and widely
carried out here in the near future, so that it will be necessary
to evaluate the dryer integrity of BWR-5 plants, which arethe main type of BWR in Japan.
In recent years, extended power uprate (EPU) has been
implemented in many BWRs (Fig. 1) in the US. The boiling
water reactor (BWR-3) in the Quad Cities (QC) Unit 2
Nuclear Power Plant experienced a significant increase in
steam moisture in the main steam lines (MSLs) while oper-
ating under EPU conditions.1) Inspection revealed that the
BWR-3 steam dryers in QC-2 had been damaged by high-
cycle fatigue due to acoustic-induced vibration under 117%
EPU conditions. In actual plant tests in QC-2 with measure-
ment sensors installed in the reactor vessel, it was observed
that the acoustic loading of the steam dryers increased sig-nificantly with the implementation of EPU. It was also ob-
served that the fluctuating pressure was significantly increas-
2011 Atomic Energy Society of Japan, All Rights Reserved.
Corresponding author, E-mail: [email protected]
Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 48, No. 5, p. 759776 (2011)
759
ARTICLE
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ed along with increased flow velocity in MSLs due to EPU
implementation. The principal cause of the dryer failure was
considered as flow-induced acoustic resonance in the safety
relief valve (SRV) stub pipes. After investigation, it was
concluded that significant loading on the dryer was caused
by the fluctuating pressure generated in the SRV stub pipesthat propagated to the dryers through MSLs (Fig. 2).
From the dryer failure experience in QC-2, it became
apparent that the quantitative evaluation of dryer loading is
important for BWRs for which power uprate is planned. As a
practical method of confirming dryer integrity under EPU
operation, the fluctuating pressure in the MSLs was meas-
ured with strain gages on the MS pipes in actual US plants.
Dryer loading was evaluated using the strain data obtained
through acoustic analysis, and the integrity of the dryer
against acoustic load under actual plant operation conditions
could be evaluated. However, to assess the dryer integrity in
the planning process of power uprate, it would be more
desirable to predict the dryer loading using scale tests orby analysis before implementing the uprate conditions in the
actual plant. For this purpose, we made trial analyses using
computational fluid dynamics (CFD) and finite element
method (FEM) approaches to predict dryer loading, and
we have started a research program to develop evaluation
methods of BWR dryer loading. Our evaluation research
program is shown in Fig. 3. The fluctuating pressure gener-
ated in SRV stub pipes was calculated through CFD analysis.
The fluctuating pressure propagated from SRV stub pipes to
the dryer was evaluated through acoustic analysis. By input-
ting the dryer loading in the structural analysis, the dryer
stress was evaluated and its integrity was verified. Theseanalysis methods have been verified by comparison with
scale tests using a 1/10-scale model of BWR-5 plants.
Acoustic resonance is produced by the interaction be-
tween the sound field and an unstable shear layer across
the closed stub pipes of SRVs (Fig. 4). Fluctuating pressure
or sound is generated by the unsteady motion of vortices.
The resonance of the quarter-wavelength mode is excited by
the vortex sound in the SRV stub pipes. If the vortex shed-
ding frequency is close to the resonance frequency, the
vortex shedding frequency is locked at the resonance fre-
quency. Through this feedback mechanism, highly intense
fluctuating pressure occurs in the SRV stub pipes.The phenomenon of flow-induced acoustic resonance in
the SRV stub pipes has been investigated by many research-
ers. The acoustic resonance frequency can be evaluated us-
ing the geometry of SRV stub pipes and the speed of sound,
and the prediction of acoustic resonance is considered to be
possible.2) The occurrence of acoustic resonance can be
judged by the relation between acoustic resonance frequency
and vortex shedding frequency or Strouhal number (St). It
seems that peak excitation occurs around St: 0.40.45.24)
Weaver and MacLeod2) investigated the effects of the radius
of the stub pipe entrance, and they suggested guidelines for
designing SRV stub pipes including a suitable entrance
radius to prevent the flow-induced vibration. Boldwin andSimmons5) measured the pulsation and vibration at SRVs
in actual power plants and identified the threshold of the
resonance. However, as these studies were based on air flow
rather than steam flow, which is used in actual nuclear power
plants, the effects of fluids (differences between air flow and
steam flow) are not clear. Moreover, the pressure propaga-
tion to the MSLs and the stress on the dryer are unknown
under the resonance condition. Therefore, in this study, we
made flow calculations under the resonance condition and
carried out the acoustic and structure analysis of MSLs and
the dryer using the calculation results.
The quantitative prediction of fluctuating pressure has alsobeen performed using scale tests. The scaling law is very
important for the quantitative evaluation of actual plants
Steam Dryer
Steam Separator
PLR Pump
Reactor Core
Jet Pump
Fig. 1 Boiling water reactor (BWR)
Nozzle
Dryer
MSL
SteamDome
SRV Stub Pipe
Flow
AcousticSource
Propagatio
n
Loading
Upper View
Acoustic Wave
Fig. 2 BWR steam dome, dryer, and MSLs
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from scale test results. Weaver, MacLeod,
2)
and Ziada
3)
applied u2=2 (, density; u, velocity) to normalize the
fluctuating pressure. Howe6) showed that the fluctuating
pressure was proportional to u3=a(a, speed of sound) when
there was a dipole acoustic source. Sommerville7) applied
the scale model to investigate flow-induced acoustic reso-
nance at SRV stub pipes and showed that the fluctuating
pressure was proportional to a2 under the resonance con-
dition.7) In this study, u2=2 was applied to normalize the
fluctuating pressure.
Many SRV stub pipes are mounted on the MS pipes in
BWR main steam systems (MSSs). Acoustic characteristics
are affected by these multiple SRV stub pipes. The intensity
of the fluctuating pressure and the acoustic characteristicsare different from those in the case of a single SRV stub
pipe,8) and the fluctuating pressure for multiple SRV stub
pipes should be investigated for the BWR MSSs.
Acoustic vibration is excited by the intense source of
acoustic resonance of SRVs. Howe6) showed that the sound
power of the acoustic source is generated by vortices con-
vecting in a sound field, as well as the fluid velocity and
other factors. The steam velocity in the MSLs is so high that
intense turbulent energy related to the vortices is generated
throughout MSLs. Therefore, we must focus on the location
where acoustic resonance would be induced. Acoustic reso-
nance is caused by the configuration of the sound field andthe properties of fluids. A change in flow channel geometry
causes reflection of the sound. MSLs have flow channels that
expand, diffuse, or change their flow area. Moreover, the
arrangement and configuration of MSLs and branches de-
pend on the nuclear power plant. It is possible that anotheracoustic resonance may be induced by branches of MSLs.
The probability of occurrence of those other acoustic res-
onances must be investigated to confirm the integrity of the
dryer.
In the present study, we demonstrated the cause of dryer
failure by using numerical analysis and scale tests. We
visualized a region of intense vorticity, which became the
acoustic source (Sec. IV-1), at the SRV stub tube opening.
We also verified the acoustic resonance in the SRV stub
pipe (Sec. IV) and the propagation of fluctuating pressure to
the dryer (Secs. V and VI).
We also developed methods of evaluating the acousticsource (see Sec. IV). In-house CFD codes were applied,
and air and steam calculations were conducted to evaluate
the acoustic source in the MSLs. We clarified the effects of
the difference between the properties of air and steam, and
the effects of multiple stub pipes and the intensity of acoustic
pressure on actual power plant conditions. Analysis methods
were verified by comparison with scale tests.
Finally, the integrity of BWR-5 dryer in Japan was eval-
uated. This type of MSS was modeled for analysis and tests.
The acoustic characteristics of multiple SRVs and dead legs,
which are closed side branches, were also investigated
(Sec. IV-2).
II. BWR Main Steam Lines
A typical BWR MSS is illustrated in Fig. 5. It mainly
consists of a steam dome and 4 MSLs. BWR MSLs have two
geometrically different lines referred to as MSL 1 and MSL
2 in the present paper. MSL 1 and MSL 2 are downstream
from the steam dome and around the SRVs as illustrated in
Fig. 6. MSL 1 has 3 SRVs and MSL 2 has 7 SRVs. In MSL
2, 4 SRVs (numbered SRV 47) are at the piping where the
main steam flow crosses and 3 (SRV 13) are at the piping
where flow stagnates. The SRV stub pipes where the main
steam flow crosses (SRV 47) form the acoustic source. TheSRV stub pipes where the flow stagnates (SRV 13) cause
the acoustic influence.
Fig. 4 Flow-induced acoustic resonance of SRVs in MSL
MSL StrainMeasurement
Stress
AcousticSource
Propagation
Stress
Loading
Comparison
Fluctuating Pressure
CFDAnalysisCFD
Analysis
AcousticAnalysisAcousticAnalysis
StructuralAnalysisStructuralAnalysis
Dryer VibrationMeasurement
Dryer PressureMeasurement
Evaluationof Integrity
SourceTests
PropagationTests
Actual Plant Analysis Scale Tests
Fig. 3 Evaluation flow chart
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III. Test and Calculation Methods
1. Single SRV Side Branch Tests
The experimental apparatus, consisting of a compressor,
accumulator, pressure-reducing valve, flow regulator, silenc-
ers, and test section, is shown in Fig. 7. Air at room temper-
ature and almost atmospheric pressure provided by a large
compressor was used as a fluid instead of steam. The test
section was composed of a main pipe and a stub pipe, which
was made of transparent acrylic to allow visualization of the
velocity fields inside the mouth of the stub pipe (Fig. 8). TheT-joint bifurcation had a sharp edge. All the cross sections of
the main and stub pipes were circular with inner diameters D
and d of 40 and 16 mm, respectively. The length of the
entrance before the bifurcation was 62:5D. Silencers
(50:0D long) were installed upstream and downstream from
the test sections to reduce the noise from the compressor and
pressure-regulating valve. The velocity of the main pipe flow
was corrected by measuring the pressure, temperature, and
flow rate of the main pipe flow with a pressure transducer
(accuracy: 1%), T-type thermocouple (accuracy: 0:5 K),
and flow cell flowmeter (accuracy: 2%), respectively. A
series of experiments was performed by varying the velocityof the main pipe flow (580 m/s). The Mach number was the
same as that of actual BWR plants and was approximately
0.010.24. The two-dimensional velocity fields inside the
mouth of the stub pipe were also measured using a particle
image velocimetry (PIV) system, which is a nonintrusive
measurement technique. In the PIV system, a high-speed
camera captured the positions of flow-tracing particles at
two known times by illuminating the particles using a laser
sheet. In this visualization experiment, we used a double-
pulse YAG laser (output: 120 mJ at 532 nm) and a high-
speed CCD camera. The camera resolution was
1;024 1;024pixels and the interrogation window was 32
32pixels. To reduce the refraction due to the acrylic pipe atthe mouth of the side branch, we adopted the Scheimpflug
condition for the stereoscopic-imaging configuration meth-
od. In this method, the object plane, lens plane, and image
plane intersected at one point (Fig. 8). Sequences of 200
images were recorded with a temporal distance between two
consecutive images, for which the time interval (t) was
0.125 s. The velocity vector was evaluated in the interrog-
ation window as the ratio between the average displacement
of the particles and t. Particle displacement within the
interrogation window was evaluated by applying a cross-
correlation scheme. The tracer particles were a polypropy-
lene glycol mist, and had an average particle diameter ofapproximately 1mmand a density of 1.34 kg/m3, almost the
same as air. Therefore, the effects of the fluid viscosity/
Steam DomeTurbine
MSL
(50m)
Upper View
MSL2
MSL1
Fig. 5 Typical BWR main steam system
SRV Stub Pipe
Steam Dome
Turbine
Dead LegFlow
MSL1
FlowMSL2
SRV5 SRV6
SRV4
SRV1
SRV3
SRV2
SRV7
MSL MeasurementLocation
Fig. 6 MSL 1 and MSL 2 downstream from the steam dome and
around SRVs
Compressor
Accumulator
Pressure-
reducing valveSilencer
50D
(2,000 mm)
Test section
Atmospheric
emission
T PFlow regulator
Q
Straight62.5D
(2,500 mm)
Straight62.5D
(2,500 mm)
Silencer50D
(2,000 mm)
Fig. 7 Test apparatus of single SRV
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density change caused by the tracer were negligible. The
tracer particle concentration was optimized as necessary
depending on the flow state.
2. BWR MSL Test
We investigated the flow-induced acoustic resonance in
the MSS using the 1/10-scale test apparatus illustrated in
Fig. 9. The 1/10-scale BWR test apparatus was made withreference to a typical Japanese BWR-5. The test apparatus
consisted of a dryer, a steam dome, and 4 MSLs with 20
SRV stub pipes indicated by red points. The MSLs were
modeled from the steam dome to the turbine stop valves.
Silencers were installed upstream and downstream from the
test sections to reduce the noise from the compressor, and
the flow- and pressure-regulating valves. Air at room tem-
perature and almost atmospheric pressure provided by a
large compressor was used as a fluid instead of steam. The
compressor capacity was 3,000 m3/h, and a velocity of more
than 60 m/s and St of less than 0.32 could be maintained
constantly. The flow velocity in the MSLs was varied toinvestigate the effects ofSton the fluctuating pressure. The
Mach number of the 1/10-scale tests was the same as that of
actual BWR plants and was approximately 0.1. Fluctuating
pressures were measured with pressure sensors flush-mount-
ed on the wall surface and having a minimum resolution of
0.34 Pa. Fluctuating pressures were measured on the top of
the SRV stub pipes, at the MSLs, on the inner surface of the
steam dome, and on the outer dryer hoods. The pressures,
temperatures, and flow rates in the steam dome and MSLs
were measured with sensors for the accurate determination
of flow conditions. Tests results of a single SRV and multi-
ple SRVs were compared with each other for the fluctuating
pressure at the top of the SRV stub pipe.
3. CFD Calculations
CFD calculations were done using in-house 3D compres-
sible flow codes, MATIS-C9) for air flow and MATIS-SC10)
for steam flow. These codes adopt large eddy simulation
(LES) methodology to perform precise turbulent calcula-
tions. In this study, a modified Smagorinsky model11) was
applied. This model is optimized for a compressible high-
speed flow. Also, because high-accuracy unsteady calcula-
tions are required in this research, the 2nd-order temporal
precision scheme with Newton iterative procedure and LU-
SGS algorithm12) were applied.
The MATIS-C code uses the equation of state (EOS) forthe calculations of state quantities assuming an ideal gas.
On the other hand, the steam flow code MATIS-SC can be
used for the steam flow with phase change and is applicable
to the wet steam region under the assumption of a homoge-
neous flow. For the calculation of state quantities, an ap-
proximate EOS is usually applied. However, as the relation-
ship between the state quantities is very complex and the
assumption of an ideal gas cannot be applied, an approxi-
mate EOS does not have a high enough accuracy for the state
quantities calculation (O(101)). Thus, we used a look-up
table based on IAPWS-IF9713) for the calculation of state
quantities. In this model, density () and internal energy ("),which are calculated from N-S equations, are assigned as
independent variables in the look-up table, and state quanti-
Tracer generator
Air Flow(5-80 m/s)
Laser Sheet
Visualization Area
Main pipe
Pressure sensor
CCD
camera
Side branch pipe
Double-pulse YAG Laser
D
d
(a) Horizontal sectional view
(b) Vertical sectional view
Len
splate
Image
plate
Objectplate
Intersection point
Main pipe
Side branch pipe
Camera lens
CCD senser
Double-pulse
YAG Laser
Fig. 8 Detail of test section
SteamDome
SRV StubPipe
MSL
Header
Compressor(3,000 m3/h)
FTP
FTP 4
Dryer
Silencer
Dryer
PressureSensor
PT
Silencer
Dead Leg
RegulatingValve
AirEmission
T
P
Fig. 9 Test apparatus of BWR dryer and MSLs
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ties are derived from the these values. This model has a high
accuracy (O(107)). Figure 10 shows the applicable range
of the look-up table for the MATIS-SC code. The look-up
table covers a wide range of steam conditions including
those in the steam turbine of nuclear and thermal powerplants.
In this study, despite the steam in the BWR MSLs being
within a low wetness region, i.e., slightly dry steam condi-
tions, we applied the condition under which the enthalpy was
slightly (about 10 kJ/kg) larger than that of saturated steam.
As mentioned above, MATIS-SC can be used for the wet
steam region and the phase change under the assumption of
homogeneous flow, and the sound speed is very different for
saturated steam and wet steam. This change occurs discon-
tinuously according to theoretical and MATIS-SC calcula-
tions. However, in the experiments by England et al.,14) the
sound speed changed moderately with increasing wetness of
the steam. Because the sound speed in the low wetness
region is almost the same as that in saturated or dry steam,
and the sound speed has a strong effect on the resonance
frequency, we applied slightly dry steam conditions so that
the resonance frequency was the same as that observed in
actual BWRs.
These codes have already been validated through some
benchmark tests.9,10) In particular, for the MATIS-SC code,
some steam experiments were made to validate the code
(Fig. 11). However, we could not observe the fluctuating
pressure at the stub pipe under the resonance conditions
because of the inadequate spatial precision. MATIS codes
usually apply the 2nd-order TVD scheme. This is unsatisfac-
tory for resolving the fluctuating pressure using a practicable
mesh number. Thus, we attempted to increase the spatialprecision. As a result of this approach, we found that the
calculations with the following higher order scheme showed
good agreement with experiments conducted in this paper
and provided sufficient accuracy to observe the fluctuating
pressure.
Convective term: 5th-order upwind scheme (for air flow)
and 4th-order MUSCL-TVD scheme15) (for steam flow)
5th-order upwind:
fx
ji
fi3 9fi2 45fi1 45fi1 9fi2 fi3
60
jaij
fi3 6fi2 15fi1 20fi 15fi1 6fi2 fi3
60
4th-order MUSCL:
fxji fui1=2 fui1=2
fui1=2 1
2ffuRi1=2 fu
Li1=2g
1
2jajuRi1=2 u
Li1=2
uLi1=2 ui1
6D ~~uu~uui1=2
1
3D ~uui1=2
Fig. 10 Applicable range of MATIS-SC (green- and pink-colored
regions) and steam condition in steam turbine
(b) Comparison of Pressure
Distributions(a) Flow Distributions
Fig. 11 Validation of MATIS code10) (Comparison of steam flow experiments)
764 R. MORITAet al.
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uRi1=2 ui11
6D ~uui3=2
1
3D ~~uu~uui1=2
D ~uu;D ~~uu~uu: limiter function ofDu
Dui1=2 ui1=21
62 ~uui1
2 ~~uu~uui
Viscous term: 6th-order central difference
6th-order central:
fxji fi3 9fi2 45fi1 45fi1 9fi2 fi3
60x
Table 1 summarizes the features of MATIS-C and
MATIS-SC.
4. Acoustic Analysis Methods
Acoustic analysis was used to calculate the acoustic res-
onance mode in the MSLs and the steam dome. FEM was
applied to calculate the three-dimensional wave equations
used in the acoustic analysis. In the present study, the steam
dome, dryer, and MSLs in the 1/10-scale BWR test appa-ratus (Fig. 8) were included in the FEM model as illustrated
in Fig. 12. All the boundaries were set to complete reflec-
tion. The properties of air at room temperature were used as
the fluid conditions.
IV. Acoustic Source Evaluation
1. Test and Calculation Results in Single SRV Stub Pipe
(1) Test Results
More than one SRV stub pipe is installed in BWR MSLs.
This makes the acoustic characteristics complex because
acoustic waves generated at SRV stub pipes interact witheach other.24) In this section, we investigate the flow-in-
duced acoustic resonance in a single SRV stub pipe from
acoustic and fluidonics perspectives.
(a) Acoustic perspective: A significantly large fluctuating
pressure generated by flow-induced acoustic resonance was
obtained over the range of Strouhal numbers (St) of 0.3
0.6.24) Stis defined in terms of the inner diameter of the stub
pipe (d), the flow velocity of the main pipe (U), and the
resonance frequency (fn) as shown in Eq. (1):
St fnd
U: 1
The acoustic pressure reaches a maximum at the top of the
stub pipe because standing waves are excited inside the stub
pipe. Therefore, we measured the fluctuating pressures at the
Table 1 Features of MATIS-C and MATIS-SC
3D-FDM-based LES
Fluid Compressible flow
Governing /Mass conservation
equations /Momentum conservation
/Energy conservation
State quantity /Equation of state (Air)
calculation /Look-up table constructed
by IAPWS-IF 97 (Steam)
/Convective term:
Discretization 5th-order upwind
/Viscous term:
4th-order central
Time marching
2nd-order backward diff.
with Newton iteration
/Implicit method: LU-SGS12
Turbulence
model Modified Smagorinsky11
Steam Dome
MSL
SRV Stub Tube
Dead Leg
0.6mSteam Dome
MSL
Dryer
0.6m
Fig. 12 Computational grids for acoustic analysis (1/10-scale BWR test size)
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top of the stub pipe under various St conditions (Fig. 13).
Pressure was normalized by the dynamic pressure of the
main pipe flow. In the cases of high (St 0:35) and low
(St0:69
) flow velocity, the fluctuating pressures weresmall and random, and were caused by turbulence. On
the other hand, when the flow velocity was approximately
50 m/s (St 0:44), the fluctuating pressure was almost com-
pletely caused by acoustic resonance, and was as large as the
dynamic pressure of the main flow. From the above, we
conducted a significantly large fluctuating pressure at the
top of the stub pipe, which was generated under certain St
conditions.
To analyze the fluctuating pressure in detail, we calculated
their power spectrum density (PSD) as shown in Fig. 14.
PSD was normalized by the square of the dynamic pressure
of the main pipe flow. The abscissa shows the sound fre-
quency normalized by the resonance frequency of the 1st
mode resonance (n 1) given by Eq. (2):
fn a2n 1
4LLen 1; 2; 3; ; 2
where a is the sound speed and L is the length of the side
branch. Le is the end correction, 0:425d corresponding to
Rayleighs upper limit. A significantly high peak was ob-
served at the resonance frequency, and this peak could be
used to clarify the flow-induced acoustic resonance.
The effects ofSton the pressure amplitude are shown in
Fig. 15. The root-mean-square (R.M.S.) of the fluctuating
pressure was normalized by the dynamic pressure of themain pipe flow. In theStrange from 0.3 to 0.6, a significantly
large fluctuating pressure was generated. This result indicat-
ed that the significantly large fluctuating pressure originated
from flow-induced acoustic resonance at the bifurcation.
(b) Acoustic fluidonics: Vortex sound, which is a part of
aerodynamic sound, is caused by unsteady fluid motion.
Figure 16 shows the instantaneous velocity map obtained
from PIV analysis at the mouth of the stub pipe when Stwas
0.44 (Fig. 13). The left side of the figure corresponds to the
upstream region of the main pipe flow. The X and Y axes
show the main pipe flow direction and axial direction per-
pendicular to the main pipe flow, respectively. An anticlock-
wise vortex separated from the leading edge of the pipe
bifurcation. Therefore, this vortex was expected to exciteacoustic standing waves at the pipe bifurcation.
The R.M.S. of the fluctuating vorticity near the trailing
edge of the cavity was calculated as shown in Fig. 17. The
results were averaged for 200 vorticity fields. The vorticity
ofSt 0:4 and 0.9 conditions was normalized by the max-
imum vorticity. High-vorticity amplitude appeared near the
trailing edge of the bifurcation under the resonance condition
(St 0:4). It was noteworthy that the intensity of the vor-
ticity for each value ofStcorresponded to that of the pres-
sure amplitude.
The shear layer departing the leading edge of the bifurca-
tion was unstable and generated a vortex that excited acous-tic standing waves. These acoustic waves are reflected at the
top of the stub pipe, and the oscillations on the shear layer
St=0.44
-2
-1
0
1
2
0 0.01
Time [ s ]
Pressure[-]
St=0.69
St=0.35
Fig. 13 Fluctuating pressures at the top of stub pipe under various
Stconditions
0 0.5 1 1.5Frequency [ - ]
St=0.44
St=0.69
St=0.35
FluctuatingPressure[-]
10-8
10-610
-4
10-2
100
102
Fig. 14 Power spectrum density (PSD)
IncreasingVelocity
0 0.5 1.0 1.5 2.0St
0
0.5
1.0
1.5BWR OperatingCondition
FluctuatingPressure[]
Fig. 15 Influence of St on pressure amplitude, frequency, and
maximum vorticity amplitude near the trailing edge of bifurca-
tion
X/ d
Y/d
Stub pipe
Main pipe Flow direction
0
70
Velocity[m/s]
0 0.2 0.4 0.6 0.8 1.0
0.3
0.0
-0.3
Vortex
Fig. 16 Instantaneous velocity maps at the mouth of the stub pipe
(St 0:44)
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were enhanced. In the Strange from 0.3 to 0.6, this process
was regenerative.24) Therefore, large coherent (same fre-
quency and phase) vortices on the shear layer developed anda large fluctuating pressure was generated. Thus, a signifi-
cantly large fluctuating pressure was generated by flow-in-
duced acoustic resonance over the range ofSt from 0.30.6.
(2) CFD Results
(a) Computational Conditions
Figure 18 shows the computational domain and mesh
used to model MS piping with the single SRV stub pipe.
The MS pipe length is about 5.45 times longer than the MS
pipe diameter (D), and the stub pipe diameter (d) and length
(h) were about 0:3Dand 1:03D, respectively. The curvature
radius of the connection between the MS pipe and the stub
pipe was set at 0 to simplify the phenomena.
As the calculations with air were done under ordinarytemperature and pressure conditions, and those with steam
were done under typical BWR main steam conditions, the
Reynolds numbers (Re) in the steam calculations were dif-
ferent from those in the air calculations. Therefore, 2 types
of mesh were prepared with mesh numbers of about 2 mil-
lion (normal mesh) and 4 million (fine mesh). The fine mesh
was applied for steam flows with high Re. The boundary
conditions were as follows.
Air
- Ordinary temperature and pressure conditions (about
300 K, 0.1 MPa) were applied.
- Inlet total pressure and temperature were provided, andvelocity and density were extrapolated.
- Exit static pressure was provided and velocity and density
were extrapolated.
- A nonslip adiabatic wall was assumed.
Steam
- Typical BWR main steam conditions (about 558 K,7.0 MPa) were applied.
- Inlet static pressure and enthalpy were provided, and ve-
locity and density were extrapolated.
- Exit static pressure was provided, and velocity and density
were extrapolated.
- A nonslip adiabatic wall was assumed.
In both cases, the inlet velocity was varied as a parameter
using the ratio of the inlet pressure to the exit pressure. The
pressure amplitude and flow conditions were normalized by
Stand normalized pressure amplitude (p0 2p=Uin2),
respectively.
(b) Results
Figure 19 shows the R.M.S. amplitude of fluctuatingpressure around the stub pipe for air of St 0:42. Large
fluctuations were observed around the stub pipe, particularly
at the top of the stub pipe.
Figure 20 shows the time histories of the static pressure
and the results of FFT analysis at the top of the stub pipe
under several conditions. The frequency is shown as the
frequency ratio, f=fn. Periodic fluctuating pressure was ob-
served at the stub pipe under specific conditions. Large-
amplitude and periodic fluctuating pressure was observed
for both St 0:42 in air (Fig. 19(a)) and St 0:439 in
steam (Fig. 19(c)). As the peak frequency ratio of this fluc-
tuation was almost 1.0, we considered it to be the 1st
moderesonance at the stub pipe. However, this phenomenon was
hardly observed under St 0:57condition. It is well known
X/ d
Y/d
Stub pipe
Main pipe Flow direction
0
1.0
Vorticity[-]
0 0.2 0.4 0.6 0.8 1.0
0.3
0.0
-0.3
(a) St = 0.4
X/ d
Y/d
Stub pipe
Main pipe Flow direction
0
1.0
Vor
ticity[-]
0 0.2 0.4 0.6 0.8 1.0
0.3
0.0
-0.3
(b) St = 0.9
Fig. 17 Time-averaged vorticity maps at the mouth of the stub
pipe
MS Pipe(:D)Stub Pipe
L:5.45D
L:5.45D
Flow
Fig. 18 Computational domain of MS pipe with single stub pipe
Fig. 19 R.M.S. amplitude of fluctuating pressure (Air,St 0:42)
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that the resonance strongly depends on the inlet velocity and
occurs for a specific range of inlet velocities (or St). There-
fore, we thought that the St0:57
condition was outside theresonance range.
Figure 21 compares the pressure amplitude for severalSt
conditions. Figure 21(a) shows the comparison between air
experiments and calculations, and Fig. 21(b) shows the com-
parison of calculated results for air flow and steam flow. The
resonance peak obtained from the air calculations was ob-
served at about St 0:42, and the corresponding peak ob-
tained from experiments was at about St 0:44. Both results
had good qualitative agreement. Weaver and MacLeod2)
found that the peak of the resonance amplitude occurred at
St 0:44, and Ziada3) found that it occurred at about
St 0:4. Our computational and experimental results were
in agreement with both these studies.However, some difference was observed in the low-reso-
nance region (St> 0:5). In this region, the calculation results
underestimated the peak amplitude. We thought that the
pressure fluctuation by turbulence (pressure fluctuation with
no peak frequency) was dominant in this region. However,
the inlet turbulent intensity was not considered in the calcu-
lation because it could not be measured in the experiments,
and we attributed this to the underestimation of the turbu-
lence in the calculations.
The resonance peak obtained from the steam calculations
was observed at around St 0:4 with both a normal mesh
and a fine mesh. The amplitude obtained from the fine meshcalculations was larger than that obtained from the normal
mesh calculations, but the shapes of the peak curve and the
peakStwere almost the same. Also, although the amplitudeof the steam calculations (fine mesh) was slightly larger than
that obtained from the air calculations and experiments, we
saw good agreement regarding the peak Strouhal number
and the resonance region between the results of air and
steam flow calculations. Therefore, we considered that the
differences between the results of the air and steam calcu-
lations for the resonance at the stub pipe were not significant
if an appropriate normalization is adopted. In other words,
the results of the air calculations and experiments are useful
for predicting the pressure under resonance conditions in
actual power plants.
2. Characteristics of Fluctuating Pressure Generated inBWR MSLs
(1) Test Results
The R.M.S. amplitudes of the fluctuating pressure meas-
ured at the top of the SRV stub pipes are plotted in Fig. 22
(The locations where the fluctuating pressure were measured
(SRV 1 to SRV 7) are indicated in Fig. 6). The fluctuating
pressure of a single SRV is also plotted as a reference. The
fluctuating pressure was normalized by the peak fluctuating
pressure of a single SRV. The fluctuating pressure is plotted
for different values of St using Eq. (1). Frequency fn was
calculated using the following equation,
fn a4LLe
; 3
(a) St = 0.42, Air
(b) St = 0.57, Air
(c) St = 0.439, Steam
(d) St = 0.568, Steam
Fig. 20 Time histories of static pressure at the top of the stub pipe(b) Comparison of calculation results
between air flow and steam flow
(a) Comparison between experiments and calculations
(air flow)
Fig. 21 Comparison of R.M.S. amplitude
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whereLe is the end correction in air and it is approximately
equal to 0:425d.
As shown in Fig. 22, whenStwas less than approximately
0.6, the fluctuating pressure at the SRV stub pipes increased
significantly and reached a maximum whenStwas from 0.3
to 0.4. The fluctuating pressure of multiple SRVs was much
higher than that of a single SRV when acoustic resonance
occurred. The range of St in which acoustic resonance oc-
curred was wider in the case of multiple SRVs than that for a
single SRV. This was caused by the interaction between
SRV stub pipes and the multiple acoustic resonance modes.
Reflections in the MSLs also affected the intensity of the
fluctuating pressure in the case of the multiple SRVs. Acous-tic resonance was not clearly observed when Stwas above
0.7. Under the operating conditions of BWR-5 plants in
Japan, Stis more than 0.7; thus, intense acoustic resonance
is unlikely to occur.
The PSD of fluctuating pressure is shown in Fig. 23 under
the condition ofSt 0:35. Frequency was normalized by the
calculated resonance frequency of a single SRV stub pipe
using Eq. (3). The fluctuating pressure was normalized by
the peak of the fluctuating pressure generated in the SRV
stub pipes. The fluctuating pressure was measured at the MS
pipes near the steam dome as shown in Fig. 6.
For MSL 1, a strongly dominant peak was obtained at theresonance frequency of the SRV stub pipe (f 1:0). In
contrast, large peaks were also observed at low frequencies
of 0.13 and 0.21 for MSL 2. These peaks were not observed
in the results for MSL 1. This difference was caused by the
dead leg, because the only difference between the configu-
rations of MSL 1 and MSL 2 was the existence of the dead
leg in MSL 2. A strong peak was also confirmed at the
resonance frequency of the SRV stub pipe in MSL 2. We
investigated the acoustic resonance at low frequencies later
using acoustic analysis.(2) CFD Results for the Model with 3 Stub Pipes
(a) Computational Conditions
Figure 24 shows the computational domain and mesh
used to investigate the effects of MS piping with the 3
SRV stub pipes. The MS pipe length was about 18 times
longer than its diameter (D), and the MS pipe diameter and
the stub pipe diameter and length were the same as those for
a single stub pipe.
The calculations with air were done for the mesh number
of about 5.5 million. The boundary conditions were the same
as those in Sec. IV-1.
(b) ResultsFigure 25 shows the R.M.S. amplitude of the fluctuating
pressure around the stub pipe obtained under the condition of
0
1
2
3
4
5
6
0 0.5 1 1.5St [ - ]
Fluctuating
Presssure
[-
]
SRV1SRV2
SRV3
Single SRV
BWR OperatingCondition
0
1
2
3
4
5
6
0 0.5 1 1.5St [ - ]
Fluctuating
Presss
ure
[-
]
SRV4
SRV5
SRV6
SRV7
Single SRV
BWR OperatingCondition
Fig. 22 Characteristics of fluctuating pressure in multiple SRVs
(a) MSL1
(b) MSL2
0 0.5 1.0Frequency f []
FluctuatingPre
ssureP
rms
[]
St=0.35
f=1.0
0.0
0.5
1.0
1.5
0.13
0.21
St=0.35
0
Frequency f []
0.0
0.5
FluctuatingPressureP
rms
[] 1.0
0.5 1.0 1.5
Fig. 23 PSD of fluctuating pressure
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St 0:35, and Fig. 26 shows the time histories of static
pressure and the results of FFT analysis at the top of the
stub pipes under several conditions. When St 0:35, large-
amplitude fluctuations were observed at all stub pipes with
phase differences between each stub pipe. As the peak fre-
quency ratio was almost 1.0, we thought that the sameresonance as that for the single stub pipe occurred under
this condition. However, the amplitude was much larger than
that for a single stub pipe (SRV 1> SRV 2 > SRV 3). The
resonance at each pipe was enlarged through the fluctuating
pressure in the MS pipe. Hardly any resonance was observed
when St 0:59.
Figure 27 compares the pressure amplitude obtained by
experiments and single SRV calculations, andFig. 28 shows
the distribution and profile of the R.M.S. pressure amplitude
around the MSLs under theSt 0:35condition. The profile
was obtained along the center of the main pipe.
The calculated results had qualitative agreement withthose of experiments in terms of the descending order of
amplitude at 3 SRVs (fluctuating mode) when St 0:35
(SRV 1> SRV 2> SRV 3). However, the calculated fluc-
tuating mode forSt 0:42was different from that of experi-
ments. This was because of the difference in the boundary
conditions at the inlet and the exit. The reflecting boundary
condition was applied in CFD calculations. However, in
experiments, acoustic absorption materials were added at
the inlet and exit, and the boundary was partially reflecting.
The pressure amplitude in the case of 3 SRVs was several
times larger than that in the case of the single SRV. Experi-ments by Ziada and Shine8) showed the same phenomenon
and it was also observed in actual BWR model experiments
(see Fig. 22). The fluctuating pressure on each SRV was
considered to enhance that on other SRVs, through the
fluctuating pressure mode in the MSLs. The nodes of the
fluctuating pressure (antinodes of the velocity) in the MSLs
were observed at the positions of the SRVs in Fig. 28, and
this pressure mode in the MSLs enhanced the acoustic res-
onance at the SRVs.
(3) CFD Results for the Actual BWR MSL with 3 Stub
Pipes
(a) Computational ConditionsTo investigate the pressure amplitude of SRVs under
actual BWR conditions, we did a steam calculation under
(a) Experimental Setup
( 2.5D )( 2D )
D
SRV Stub PipeMSL
Pressure Sensor
MS Pipe Stub Pipes
L:18D
SRV1
SRV2
SRV3
Flow
(b) Computational Domain
Fig. 24 Schematics of MS piping with 3 stub pipes
Fig. 25 R.M.S. amplitude of fluctuating pressure (Air,St 0:35)
(a) St = 0.35, Air
(b) St = 0.59, Air
Fig. 26 Time histories of static pressure at the top of the stub
pipes
Fig. 27 Comparison of R.M.S. amplitude
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the rated power (100% power) condition using a model of
the actual BWR MSLs. Figure 29 shows the computational
domain. The full-scale MSL with 3 stub pipes and a shape
similar to that of the MSL without a dead leg in Fig. 12
(MSL 1) is modeled. The mesh number was about 5.6
million. The boundary conditions were as follows.
- Actual BWR steam conditions under the rated power
(100% power) were applied.- Inlet static pressure and enthalpy are provided, and veloc-
ity and density were extrapolated.
- Exit static pressure was provided, and velocity and density
were extrapolated.
- A nonslip adiabatic wall was assumed.
(b) Results
Figure 30 shows the average velocity and pressure dis-
tributions along the flow direction. The velocity and pressure
were normalized by the inlet velocity and pressure. Flow and
pressure drift were observed at the elbows, and this drift
reached the straight section of the piping. Figure 31 shows
the distribution of R.M.S. pressure amplitude around SRVs;Figs. 32 and 33 show the pressure time histories and the
results of FFT analysis at points A and B (see Fig. 29) and
the top of the SRVs (SRV 13); Fig. 34 compares the
R.M.S. amplitude of fluctuating pressure at SRVs.At points A and B, pressure oscillations with a peak
frequency of approximately 10 were observed. These were
thought to be caused by the flow disturbance at the elbows.
At the top of the SRVs, periodic pressure fluctuation with a
small amplitude and a peak frequency of about 1.0 was
observed. This was considered to be the second peak reso-
nance (the resonance caused by a row of two vortices cross-
ing the SRV stub pipe) observed in the experiments by
Takahashi et al.16) However, as the amplitude of this peak
and the overall R.M.S. amplitude observed in Fig. 34 were
small, it seemed that flow-induced acoustic resonance did
not occur in SRVs under the rated power condition.
V. Propagation of Fluctuating Pressure to Dryer
1. Propagation of Fluctuating Pressure
The fluctuating pressure in the BWR MSLs was also
investigated by 1/10-scale BWR tests. The time variation
of the fluctuating pressure in MSL 1 is shown in Fig. 35
under the condition ofSt 0:34. The flow velocity increas-
ed excessively compared with that under actual BWR con-
ditions. The fluctuating pressure was normalized by the
dynamic pressure in the MSLs. This fluctuating pressure
was measured on the top of the SRV stub pipes, in the MSLs
near the nozzle, and at the center of the outer dryer hood(Fig. 35). Flow-induced acoustic resonance occurred when
St 0:34. The fluctuating pressure with the resonance fre-
(a) Pressure Distribution
(b) Pressure Profile along the Center
of the Main Piping
0
0.05
0.1
0.15
0.2
0.25
0.3
-0.4 -0.2 0 0.2 0.4 0.6
R.M.S.pressureamp.[
-]
distance from SRV1
SRV1 SRV2 SRV3
Fig. 28 Distribution and profile of R.M.S. pressure amplitude
(Air, St 0:389)
inlet
exit
A
B
SRV1SRV2 SRV3
Fig. 29 Computational domain of actual BWR MS piping with 3
stub pipes
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quency was obtained throughout the steam dome and MSLs.
As shown in Fig. 35(a), the fluctuating pressure became an
intense pure tone at the top of the SRV stub pipes. As
pressure fluctuating with the SRV resonance frequency
could be seen on the MSL and dryer hood, acoustic reso-
nance occurred in the SRV stub pipes at a higher velocity
flow than that in the normal operation, and the fluctuating
pressure propagated from the SRVs to the dryer through the
MSLs. The amplitude of the fluctuating pressure observed atthe top of the stub pipes was reduced significantly in the
MSLs and in the steam dome.
The PSD of the fluctuating pressure is shown in Fig. 36
for St 0:34. The frequency was normalized by the reso-
nance frequency, and the PSD was normalized by the square
of the dynamic pressure of the MSL flow. The PSD of the
fluctuating pressure was evaluated at the top of one SRV, at
the MSLs near the dome nozzle, and at the center of the
outer dryer hood. An especially high peak was observed at
the resonance frequency for every PSD, confirming the oc-currence of flow-induced acoustic resonance. As shown in
Fig. 36(c), periodic fluctuating pressure with low frequen-
cies of less than 0.25 was also observed on the dryer hood.
The low-frequency fluctuating pressure that occurred from
turbulent flow in the dome and MSLs also acted on the dryer
hood.
The variation of the amplitude of the fluctuating pressure
is shown in Fig. 37. The fluctuating pressure in the MSLs
propagated from the SRVs was less than 5% of that observed
in SRV stub pipes, and its amplitude on the dryer hood was
less than 2% of that in SRV. (The fluctuating pressure in the
MSLs was about 7.5% of that at SRV1 in the calculation (seeFig. 28)). This was a reasonably conservative value com-
pared with that obtained in the experiments.
Fig. 31 R.M.S. pressure amplitude distributions
(a) Average Velocity Distribution
(b) Pressure Distribution
Fig. 30 Average velocity (a) and pressure (b) distributions along
flow direction
(a) SRVs Upstream and Downstream
(Point A and B in Fig.31)
(b) Top of SRVs
Fig. 32 Pressure time history
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2. Acoustic Mode in MSLsThe acoustic characteristics in multiple SRVs varied with
changes in St. The acoustic analysis of multiple SRV stub
pipes was conducted to investigate the variation of acoustic
modes in MSLs. MSL 1 was selected for analysis. Reso-
nance modes and frequency were calculated through mode
analysis. Two typical resonance modes are shown in Fig. 38.
The resonance mode in which the resonance in SRV 3
became stronger was dominant in Fig. 38(a). On the other
hand, the resonance in SRV 3 was weak and that in SRV 1
became stronger in Fig. 38(b). These were multiple reso-
Fig. 34 Comparison of R.M.S. amplitude
(a) SRVs Upstream and Downstream
(Point A and B in Fig.31)
(b) Top of SRVs
Fig. 33 FFT analysis of pressure fluctuations at SRVs
0.4
0.2
0
0.2
0.4
0
0.005 0.01
Pressure[]
Time [s]
0.4
0.2
0
0.2
0.4
0
0.005 0.01
Pressure[]
Time [s]
(a) Top of evaluated SRV stub pipe
(b) Main steam line
(c) Center of evaluated outer dryer hood
8
4
0
4
8
0 0.005 0.01
Time [s]
Pressure[]
SRV1 SRV2 SRV3
Center of OuterDryer Hood
Main SteamLines
Top of SRV Stub
Flow Flow
Fig. 35 Fluctuating pressure (St 0:34)
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nance modes in multiple SRV stub pipes because the reso-
nance mode was affected by the standing wave in the MSpipe, which changed the locations of the node and antinode
when the frequency changed.
As shown in Fig. 23(b), significant peaks in the fluctuating
pressure were observed at frequencies of 0.13 and 0.21 in
MSL 2. On the other hand, no distinguishing peak was
observed below a frequency of 1.0 in MSL 1. From the
difference in the MS pipe configurations between MSL 1
and MSL 2 shown in Fig. 6, these low frequencies were
considered to be caused by the dead leg; only MSL 2 had a
dead leg (the long closed side branch). To clarify the cause
of the low frequency, we did an acoustic analysis that fo-
cused on the dead leg in MSL 2. The results are shown inFig. 39. Three resonance modes were observed in the low-
frequency region. The resonance mode in Fig. 39(a) was
caused by the reflection from the root of the dead leg to
the inlet of the steam dome. The resonance mode in
Fig. 39(b) was induced by the reflection from the top of
the dead leg to the inlet of the steam dome and that in
Fig. 39(c) was induced by the reflection from the top to
the root of the dead leg or from the top of the dead leg to
the lower end of the steam dome. We confirmed that low-
frequency resonance modes were generated by the reflection
at the top and root of the dead leg. The inlet and lower end of
the steam dome caused the other reflections.
VI. Dryer LoadingAcoustic analysis was also carried out to evaluate the
propagation of fluctuating pressure and dryer loading. Cal-
culation conditions were the same as those in the 1/10-scale
BWR tests. The results of the acoustic analysis are illustrated
in Fig. 40. A fluctuating pressure was input into the MSLs
fromt 0 ms. The fluctuating pressure was propagated from
the MSLs to the steam dome while slightly decreasing in
amplitude. Larger fluctuating pressures were observed at
the dome surface near the dryer skirt and nozzles and acted
on the dryer hoods; thus, these locations were particularly
focused on in the present study.
The results of the analysis on the dryer hood were com-pared with those of 1/10-scale BWR tests. The pressure
obtained from the analysis is shown in Fig. 41(a) for three
0.0000
0.0002
0.0004
0.0006
0 0.5 1 1.5
PSD
[]
Frequency [ ]
0.0000
0.0004
0.0008
0.0012
0.0016
0 0.5 1 1.5
PSD[]
Frequency [ ]
(a) Top of evaluated SRV stub pipe
(c) Center of evaluated outer dryer hood
0
1
2
3
0 0.5 1 1.5
PSD[]
Frequency [ ]
(b) MSLs near steam dome nozzle
Fig. 36 PSD of fluctuating pressure (St 0:34)
0
20
40
60
80
100
SRV StubFluctu
atingPressure[%]
St =0.34
Dryer HoodMSL
Fig. 37 Variation of intensity of fluctuating pressure
(a) Resonance in SRV3 (b) Resonance in SRV1
SRV1SRV3
High (+)
High ()0
High (+)
High ()
FluctuatingPressure []
0
FluctuatingPressure []
Fig. 38 Resonance mode in multiple SRV stub pipes
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different times. The fluctuating pressure at the dryer hood
obtained from scale-model tests is also shown in Fig. 41(b).
The fluctuating pressure was normalized by the average
fluctuating pressure in the four MSLs (100%). The fluctuat-
ing pressure decreased by approximately one-third from the
MSLs to the dryer hood. In the analysis results, the fluctuat-
ing pressure was calculated at the same locations as those
measured in the tests and was also normalized. The fluctu-
ating pressure was the largest at the lower left of the dryer
hood in test and analysis results. Although the fluctuating
pressures at the upper left and center of the dryer hood inanalysis were smaller than those in the test results, the dis-
tribution of the fluctuating pressure was almost the same for
both. A quantitative comparison between the test and analy-
sis results is also given in Table 2. The average difference
between the fluctuating pressure in the analysis and test
results was only 7.5%.
VII. Conclusions
We carried out 1/10-scale BWR-5 model tests, CFD cal-
culations, and acoustic analysis to evaluate the flow-induced
acoustic resonance in SRV stub pipes and the propagation ofthe fluctuating pressure from the SRV stub pipes to the dryer
through the MSLs. The following conclusions were obtained.
1. The intense vorticity, which became a source of acoustic
resonance, was generated and resonated with quarter-
wavelength acoustic modes in the SRV stub pipes, andthe generated fluctuating pressure propagated from the
SRVs to the dryer.
Table 2 Comparison between test and analysis results
Item Test Analysis
Fluctuating pressure
on dryer hood 39.9% 32.4%
Fluctuating pressure in MSLs was 100% on average.
(c)f = 0.21
0
High (+)
High ()
FluctuatingPressure [-]
(a)f = 0.12 (b)f = 0.13
Fig. 39 Resonance mode in MSLs
t = 5 ms t = 10 ms
t = 15 ms t = 20 ms
Fig. 40 Pressure distribution on steam dome
+High
Low
Pressure []
0
20.1%
59.6% 34.5%
32.6%15.3%
t=0
t=/4
t=/2
39.6%
65.9%
28.8%
33.4%
31.6%
Evaluated Location
Dryer
(a) Analysis (b) Tests
Fig. 41 Pressure distributions on dryer hood
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2. CFD calculations were used to evaluate the acoustic
source (= fluctuating pressure) in the MSLs. Concern-
ing the resonance amplitude and the effects of multiple
SRVs, CFD calculations were verified by experiments.
3. The effect of the difference between the properties of air
and steam on the resonance on the stub pipe was not
significant. In other words, the results of air calculations
and experiments are useful for predicting the resonance
in actual power plants.
4. According to the results of calculations and scale-model
tests, the resonance amplitude of multiple SRVs was
several times larger than that of a single SRV. The
fluctuating pressure on each SRV was thought to en-
hance that on other SRVs, through the fluctuating pres-
sure mode in the MSLs.
5. Significant fluctuating pressures occurred in the high-
and low-frequency regions. The low-frequency fluctuat-
ing pressure appeared in the MSL with the dead leg.
This low frequency almost coincided with the natural
frequency of the MSL caused by the reflection at thedead leg.
6. Under actual power plant conditions, periodic pressure
fluctuations with a peak frequency of about 1.0 were
observed. However, as the amplitude of these fluctua-
tions was quite small, it was thought that flow-induced
acoustic resonance did not occur under the rated power
condition of a typical Japanese BWR-5.
7. Results of the 1/10-scale tests were compared with
those of acoustic analysis. The acoustic analysis could
well predict the dryer loading. The difference in fluctu-
ating pressure between analysis and test results was only
7.5% on average.As the above summarized results demonstrated, we have
developed CFD calculations and acoustic analysis ap-
proaches that were useful for evaluating the flow-induced
acoustic resonance in SRV stub pipes and the propagation of
the fluctuating pressure from the SRV stub pipes to the dryer
through the MSLs.
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