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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

760 R. MORITAet al.

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY


4/19

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

Evaluation of Acoustic- and Flow-Induced Vibration of the BWR Main Steam Lines and Dryer 761

VOL. 48, NO. 5, MAY 2011


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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

762 R. MORITAet al.



6/19

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


VOL. 48, NO. 5, MAY 2011


7/19

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.



8/19

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)


VOL. 48, NO. 5, MAY 2011


9/19

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)

766 R. MORITAet al.



10/19

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.


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


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


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)


VOL. 48, NO. 5, MAY 2011


11/19

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

768 R. MORITAet al.



12/19

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


VOL. 48, NO. 5, MAY 2011


13/19

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


770 R. MORITAet al.



14/19

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.


(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


VOL. 48, NO. 5, MAY 2011


15/19

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

772 R. MORITAet al.



16/19

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-


(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)


VOL. 48, NO. 5, MAY 2011


17/19

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

774 R. MORITAet al.



18/19

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


VOL. 48, NO. 5, MAY 2011


19/19

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.

References

1) G. DeBoo, K. Ramsden, R. Gesior, Quad Cities unit 2 main

steam line acoustic source identification and load reduction,

Proc. ICONE14, Miami, Florida, USA, Jul. 1720, 2006,

89903 (2006).2) D. S. Weaver, G. O. MacLeod, Entrance port rounding

effects on acoustic resonance in safety relief valves, ASME

PVP, 389, 291297 (1999).

3) S. Ziada, A flow visualization study of flow-acoustic cou-

pling at the mouth of a resonant side-branch, ASME PVP,

258, 3559 (1993).

4) B. D. Knotts, A. Selamet, Suppression of flow-acoustic cou-

pling in sidebranch ducts by interface modification,J. Acoust.

Soc., 265[5], 10251045 (2003).5) R. M. Boldwin, H. R. Simmons, Flow-induced vibration in

safety relief valves, J. Pressure Vessel Technol., 108, 267

272 (1986).

6) M. S. Howe, Theory of Vortex Sound, Cambridge Univ. Press,

Cambridge (2003).

7) D. V. Sommerville, Scaling laws for model test based BWR

steam dryer fluctuating load definitions, Proc. ASME PVP

2006-ICPVT-11, Vancouver, Canada, Jul. 2327, 2006, 93703

(2006).

8) S. Ziada, S. Shine, Strouhal number of flow-excited acoustic

resonance of closed side branches, J. Fluids Struct.,13, 127

142 (1999).

9) R. Morita, F. Inada, M. Mori, K. Tezuka, Y. Tsujimoto, CFD

simulations and experiments of flow fluctuations around a

steam control valve, J. Fluids Eng., 129[1], 4854 (2007).

10) R. Morita, Development of MATIS-SC code for high

speed steam flow with non-equilibrium condensation, Proc.

ICCFD4, Ghent, Belgium, Jul. 1014, 2006 (2006).

11) Y. Takakura, S. Ogawa, T. Ishiguro, Turbulence models for

3D transonic viscous flows, Collection of Tech. Papers AIAA

9th Com. Fluid Dynamics Conf., Buffalo, NY, USA, Jun. 13

15, 1989, 240248 (1989).

12) S. Yoon, A. Jameson, Lower-upper symmetric-Gauss-Seidel

method for the Euler and Navier-Stokes equations, AIAA J.,

26[9], 10251026 (1988).

13) W. Wagner, J. R. Cooper, A. Dittmann, The IAPWS indus-

trial formulation 1997 for the thermodynamic properties ofwater and steam, J. Eng. Gas Turbines Power, 122[1], 150

(2000).

14) W. G. England, J. C. Firey, O. E. Trapp, Additional velocity

of sound measurements in wet steam, Ind. Eng. Chem. Proc-

ess Des. Dev., 5[2], 198202 (1966).

15) S. Yamamoto, H. Daiguji, Higher-order-accurate upwind

schemes for solving the compressible Euler and Navier-Stokes

equations, Comput. Fluids, 22, 259270 (1993).

16) S. Takahashi, K. Okuyama, A. Tamura, M. Ohtsuka, M.

Tsubaki, Y. Mabuchi, T. Kubota, Y. Ogawa, F. Inada, R.

Morita, Fluctuating pressure generating in BWR main steam

lines acoustic excited by safety relief valve stub pipes and

dead legs, Proc. ICONE18, Xian, China, May 1721, 2010,

29361 (2010).

776 R. MORITAet al.


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