Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop

Licun Wu Daogang Lu and Yu Liu

Nuclear Science and Engineering North China Electric Power University Beijing 102206 China

Correspondence should be addressed to Licun Wu wlc121126com

Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014

Academic Editor Jiejin Cai

Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration

1 Introduction

The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature

of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper

In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432

2 Science and Technology of Nuclear Installations

R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator

Test sectionwith 4 fuel rods

Figure 1 Concept of the active channel for SCWR fuel qualification

Low pressurecoolant injection

Recir-culationpump

Emergency pump

Depressurizationsystem

Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-p

ower

Active channel

Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test

Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach

Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the

flutter instability will happen when the flow rate is larger thanthe critical flow rate

Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence

Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode

Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration

2 Theoretical Models

Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as

1198641198681205974

119906

1205971199114+ 120578119868

1205975

119906

1205971199051205971199114+ 11989811988611988021205972

119906

1205971199112minus 1205741198790

1205972

119906

1205971199112

minus1

2119862119879

1198981198861198802

119863[(1 minus

1

2120574) 119897 minus 119911]

1205972

119906

1205971199112

minus1

2(1 minus 120574)119862

1015840

119879

11989811988611988021205972

119906

1205971199112+ 21198981198861198801205972

119906

120597119911120597119905

+1

2119862119873

1198981198861198802

119863

120597119906

120597119911+1

2119862119873

119898119886119880

119863

120597119906

120597119905

+ 119862119881

120597119906

120597119905+ (119898 + 119898

119886)1205972

119906

1205971199052= 119892 (119909 119905)

(1)

where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898

119886is the added mass 119879

0is the initial axial tension

1198621015840

119879

is the form drag coefficient at the free end 119862119881is the

effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is

Science and Technology of Nuclear Installations 3

Table 1 Natural frequency of the fuel rod

Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz

y

z U

l

c1 c2

k2k1

Figure 3 Schematic diagram of the fuel rod in axial flow

unsupported or elastically supported 119862119879is equal to 119862

119873and

defined as

119862119873= 119862119879=

4119862119891

120587119862119898

(2)

where 119862119891is the drag coefficient due to shear forces and 119862

119898is

added mass coefficientThe appropriate boundary conditions associated with the

equation of motion are as followsFor 119911 = 0

1198961119906 + 119864119868

1205973

119906

1205971199113= 0 119888

1

120597119906

120597119911minus 119864119868

1205972

119906

1205971199112= 0 (3)

and for 119911 = 119897

1198962119906 minus 119864119868

1205973

119906

1205971199113= 0 119888

2

120597119906

120597119911+ 119864119868

1205972

119906

1205971199112= 0 (4)

where 1198961and 1198962are displacement spring constants and 119888

1and

1198882are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions

(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions

3 Details of Experiment

31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with

Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection

Figure 4 Schematic diagram of experimental loop

Table 2 Experimental conditions and geometry parameters of thetest section

Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm

water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide

The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5

In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the

4 Science and Technology of Nuclear Installations

A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm

Figure 5The collocation and geometry of the fuel assembly and testsection

Hole Clearance

Fuel rod

(a)

Spacer

(b)

Figure 6 Schematic diagram of two types of spacers

top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo

32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it

projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data

However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment

Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows

The thickness of the container 1198891is the same as the

thickness of channel 11988910158401

in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889

2is equal to that from fuel rod to the inner wall

of the channel 11988910158402

Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909

119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )

The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as

119910 = 072582119909 minus 1790196 (5)

where 119909 is the actual position of the micrometer and 119910 is themeasured position

Assuming the actual position is 1199091 themeasured position

is 1199101 then (5) becomes

1199101= 072582119909

1minus 1790196 (6)

Moreover if the actual position is 1199092and the measured

position is 1199102 (5) becomes

1199102= 072582119909

2minus 1790196 (7)

Subtracting (7) to (6) gives

1199102minus 1199101= 072582 (119909

2minus 1199091) (8)

Noting (1199092minus1199091) is the actual displacement of micrometer

Δ119909 and (1199102minus1199101) is the correspondingmeasured displacement

Δ119910 so (8) becomes

Δ119910 = 072582 sdot Δ119909 (9)

Science and Technology of Nuclear Installations 5

Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d9984002

d9984001

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )

Figure 7 Measurement calibration device

350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)

Actual position of micrometer (120583m)

Experimental valueLinear fit curve

Figure 8 Measurement calibration curve

From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)

33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889

1to be larger than the actual

displacement 1198892 That has a substantial influence on the

result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of

fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840

1

is the same as the actualdisplacement 1198891015840

2

34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)

4 The Experimental Results and Analysis

41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases

Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider

119865 prop 120588 sdot 1198812 (10)

119865 prop 120588 sdot (119876

119904)

2

(11)

Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of

6 Science and Technology of Nuclear Installations

Position 1

Position 2

X

Y

d2d1

SensorO

(a) Original structure 1198891gt 1198892

d9984002d9984001

Sensor

(b) Improved structure 11988910158401

=

119889

1015840

2

3m

m

3mm

05

mm

(c) Size of metal sheet

Figure 9 Schematic of improved structure

Displacement of the

Displacement

Correctionmodule

sensor

Final displacementsignals signals signals

Digital signalsComputer

Initial displacement Initial voltage

Analog signalsinstrument

Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)

Figure 10 Schematic diagram of data acquisition system

supercritical water according to (10) it can be noted thatthe average value of fluid exciting force 119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop

42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process

43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]

As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from

Science and Technology of Nuclear Installations 7

Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

2 Science and Technology of Nuclear Installations

R145 R17

R285

Pressure tube

Guidetubes

Fuelrods

Assembly box

OutletInletCooler

Recuperator

Test sectionwith 4 fuel rods

Figure 1 Concept of the active channel for SCWR fuel qualification

Low pressurecoolant injection

Recir-culationpump

Emergency pump

Depressurizationsystem

Pressurizerand

accumulator

Primary pump

Accumulator

Reactor building

Cooler

Fuel

rods

120574-p

ower

Active channel

Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test

Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach

Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the

flutter instability will happen when the flow rate is larger thanthe critical flow rate

Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence

Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode

Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration

2 Theoretical Models

Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as

1198641198681205974

119906

1205971199114+ 120578119868

1205975

119906

1205971199051205971199114+ 11989811988611988021205972

119906

1205971199112minus 1205741198790

1205972

119906

1205971199112

minus1

2119862119879

1198981198861198802

119863[(1 minus

1

2120574) 119897 minus 119911]

1205972

119906

1205971199112

minus1

2(1 minus 120574)119862

1015840

119879

11989811988611988021205972

119906

1205971199112+ 21198981198861198801205972

119906

120597119911120597119905

+1

2119862119873

1198981198861198802

119863

120597119906

120597119911+1

2119862119873

119898119886119880

119863

120597119906

120597119905

+ 119862119881

120597119906

120597119905+ (119898 + 119898

119886)1205972

119906

1205971199052= 119892 (119909 119905)

(1)

where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898

119886is the added mass 119879

0is the initial axial tension

1198621015840

119879

is the form drag coefficient at the free end 119862119881is the

effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is

Science and Technology of Nuclear Installations 3

Table 1 Natural frequency of the fuel rod

Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz

y

z U

l

c1 c2

k2k1

Figure 3 Schematic diagram of the fuel rod in axial flow

unsupported or elastically supported 119862119879is equal to 119862

119873and

defined as

119862119873= 119862119879=

4119862119891

120587119862119898

(2)

where 119862119891is the drag coefficient due to shear forces and 119862

119898is

added mass coefficientThe appropriate boundary conditions associated with the

equation of motion are as followsFor 119911 = 0

1198961119906 + 119864119868

1205973

119906

1205971199113= 0 119888

1

120597119906

120597119911minus 119864119868

1205972

119906

1205971199112= 0 (3)

and for 119911 = 119897

1198962119906 minus 119864119868

1205973

119906

1205971199113= 0 119888

2

120597119906

120597119911+ 119864119868

1205972

119906

1205971199112= 0 (4)

where 1198961and 1198962are displacement spring constants and 119888

1and

1198882are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions

(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions

3 Details of Experiment

31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with

Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection

Figure 4 Schematic diagram of experimental loop

Table 2 Experimental conditions and geometry parameters of thetest section

Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm

water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide

The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5

In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the

4 Science and Technology of Nuclear Installations

A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm

Figure 5The collocation and geometry of the fuel assembly and testsection

Hole Clearance

Fuel rod

(a)

Spacer

(b)

Figure 6 Schematic diagram of two types of spacers

top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo

32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it

projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data

However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment

Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows

The thickness of the container 1198891is the same as the

thickness of channel 11988910158401

in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889

2is equal to that from fuel rod to the inner wall

of the channel 11988910158402

Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909

119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )

The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as

119910 = 072582119909 minus 1790196 (5)

where 119909 is the actual position of the micrometer and 119910 is themeasured position

Assuming the actual position is 1199091 themeasured position

is 1199101 then (5) becomes

1199101= 072582119909

1minus 1790196 (6)

Moreover if the actual position is 1199092and the measured

position is 1199102 (5) becomes

1199102= 072582119909

2minus 1790196 (7)

Subtracting (7) to (6) gives

1199102minus 1199101= 072582 (119909

2minus 1199091) (8)

Noting (1199092minus1199091) is the actual displacement of micrometer

Δ119909 and (1199102minus1199101) is the correspondingmeasured displacement

Δ119910 so (8) becomes

Δ119910 = 072582 sdot Δ119909 (9)

Science and Technology of Nuclear Installations 5

Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d9984002

d9984001

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )

Figure 7 Measurement calibration device

350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)

Actual position of micrometer (120583m)

Experimental valueLinear fit curve

Figure 8 Measurement calibration curve

From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)

33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889

1to be larger than the actual

displacement 1198892 That has a substantial influence on the

result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of

fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840

1

is the same as the actualdisplacement 1198891015840

2

34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)

4 The Experimental Results and Analysis

41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases

Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider

119865 prop 120588 sdot 1198812 (10)

119865 prop 120588 sdot (119876

119904)

2

(11)

Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of

6 Science and Technology of Nuclear Installations

Position 1

Position 2

X

Y

d2d1

SensorO

(a) Original structure 1198891gt 1198892

d9984002d9984001

Sensor

(b) Improved structure 11988910158401

=

119889

1015840

2

3m

m

3mm

05

mm

(c) Size of metal sheet

Figure 9 Schematic of improved structure

Displacement of the

Displacement

Correctionmodule

sensor

Final displacementsignals signals signals

Digital signalsComputer

Initial displacement Initial voltage

Analog signalsinstrument

Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)

Figure 10 Schematic diagram of data acquisition system

supercritical water according to (10) it can be noted thatthe average value of fluid exciting force 119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop

42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process

43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]

As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from

Science and Technology of Nuclear Installations 7

Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Science and Technology of Nuclear Installations 3

Table 1 Natural frequency of the fuel rod

Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz

y

z U

l

c1 c2

k2k1

Figure 3 Schematic diagram of the fuel rod in axial flow

unsupported or elastically supported 119862119879is equal to 119862

119873and

defined as

119862119873= 119862119879=

4119862119891

120587119862119898

(2)

where 119862119891is the drag coefficient due to shear forces and 119862

119898is

added mass coefficientThe appropriate boundary conditions associated with the

equation of motion are as followsFor 119911 = 0

1198961119906 + 119864119868

1205973

119906

1205971199113= 0 119888

1

120597119906

120597119911minus 119864119868

1205972

119906

1205971199112= 0 (3)

and for 119911 = 119897

1198962119906 minus 119864119868

1205973

119906

1205971199113= 0 119888

2

120597119906

120597119911+ 119864119868

1205972

119906

1205971199112= 0 (4)

where 1198961and 1198962are displacement spring constants and 119888

1and

1198882are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions

(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions

3 Details of Experiment

31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with

Pressuregauge

Flow meter

Flow meterPump

Water tank

Dirt separator

Valve

Valve Valve

Testsection

Figure 4 Schematic diagram of experimental loop

Table 2 Experimental conditions and geometry parameters of thetest section

Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm

water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide

The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5

In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the

4 Science and Technology of Nuclear Installations

A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm

Figure 5The collocation and geometry of the fuel assembly and testsection

Hole Clearance

Fuel rod

(a)

Spacer

(b)

Figure 6 Schematic diagram of two types of spacers

top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo

32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it

projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data

However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment

Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows

The thickness of the container 1198891is the same as the

thickness of channel 11988910158401

in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889

2is equal to that from fuel rod to the inner wall

of the channel 11988910158402

Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909

119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )

The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as

119910 = 072582119909 minus 1790196 (5)

where 119909 is the actual position of the micrometer and 119910 is themeasured position

Assuming the actual position is 1199091 themeasured position

is 1199101 then (5) becomes

1199101= 072582119909

1minus 1790196 (6)

Moreover if the actual position is 1199092and the measured

position is 1199102 (5) becomes

1199102= 072582119909

2minus 1790196 (7)

Subtracting (7) to (6) gives

1199102minus 1199101= 072582 (119909

2minus 1199091) (8)

Noting (1199092minus1199091) is the actual displacement of micrometer

Δ119909 and (1199102minus1199101) is the correspondingmeasured displacement

Δ119910 so (8) becomes

Δ119910 = 072582 sdot Δ119909 (9)

Science and Technology of Nuclear Installations 5

Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d9984002

d9984001

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )

Figure 7 Measurement calibration device

350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)

Actual position of micrometer (120583m)

Experimental valueLinear fit curve

Figure 8 Measurement calibration curve

From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)

33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889

1to be larger than the actual

displacement 1198892 That has a substantial influence on the

result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of

fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840

1

is the same as the actualdisplacement 1198891015840

2

34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)

4 The Experimental Results and Analysis

41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases

Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider

119865 prop 120588 sdot 1198812 (10)

119865 prop 120588 sdot (119876

119904)

2

(11)

Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of

6 Science and Technology of Nuclear Installations

Position 1

Position 2

X

Y

d2d1

SensorO

(a) Original structure 1198891gt 1198892

d9984002d9984001

Sensor

(b) Improved structure 11988910158401

=

119889

1015840

2

3m

m

3mm

05

mm

(c) Size of metal sheet

Figure 9 Schematic of improved structure

Displacement of the

Displacement

Correctionmodule

sensor

Final displacementsignals signals signals

Digital signalsComputer

Initial displacement Initial voltage

Analog signalsinstrument

Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)

Figure 10 Schematic diagram of data acquisition system

supercritical water according to (10) it can be noted thatthe average value of fluid exciting force 119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop

42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process

43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]

As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from

Science and Technology of Nuclear Installations 7

Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

4 Science and Technology of Nuclear Installations

A-A

B-B

A-A

B-B

Local view

Displacementsensor

45mm

45mm

710

mm

02mm

Figure 5The collocation and geometry of the fuel assembly and testsection

Hole Clearance

Fuel rod

(a)

Spacer

(b)

Figure 6 Schematic diagram of two types of spacers

top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo

32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it

projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data

However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment

Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows

The thickness of the container 1198891is the same as the

thickness of channel 11988910158401

in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889

2is equal to that from fuel rod to the inner wall

of the channel 11988910158402

Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909

119899(119899 = 1 2 3 4 ) and Δ119910

119899(119899 = 1 2 3 4 )

The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as

119910 = 072582119909 minus 1790196 (5)

where 119909 is the actual position of the micrometer and 119910 is themeasured position

Assuming the actual position is 1199091 themeasured position

is 1199101 then (5) becomes

1199101= 072582119909

1minus 1790196 (6)

Moreover if the actual position is 1199092and the measured

position is 1199102 (5) becomes

1199102= 072582119909

2minus 1790196 (7)

Subtracting (7) to (6) gives

1199102minus 1199101= 072582 (119909

2minus 1199091) (8)

Noting (1199092minus1199091) is the actual displacement of micrometer

Δ119909 and (1199102minus1199101) is the correspondingmeasured displacement

Δ119910 so (8) becomes

Δ119910 = 072582 sdot Δ119909 (9)

Science and Technology of Nuclear Installations 5

Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d9984002

d9984001

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )

Figure 7 Measurement calibration device

350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)

Actual position of micrometer (120583m)

Experimental valueLinear fit curve

Figure 8 Measurement calibration curve

From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)

33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889

1to be larger than the actual

displacement 1198892 That has a substantial influence on the

result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of

fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840

1

is the same as the actualdisplacement 1198891015840

2

34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)

4 The Experimental Results and Analysis

41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases

Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider

119865 prop 120588 sdot 1198812 (10)

119865 prop 120588 sdot (119876

119904)

2

(11)

Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of

6 Science and Technology of Nuclear Installations

Position 1

Position 2

X

Y

d2d1

SensorO

(a) Original structure 1198891gt 1198892

d9984002d9984001

Sensor

(b) Improved structure 11988910158401

=

119889

1015840

2

3m

m

3mm

05

mm

(c) Size of metal sheet

Figure 9 Schematic of improved structure

Displacement of the

Displacement

Correctionmodule

sensor

Final displacementsignals signals signals

Digital signalsComputer

Initial displacement Initial voltage

Analog signalsinstrument

Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)

Figure 10 Schematic diagram of data acquisition system

supercritical water according to (10) it can be noted thatthe average value of fluid exciting force 119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop

42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process

43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]

As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from

Science and Technology of Nuclear Installations 7

Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

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International Journal of

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FuelsJournal of

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Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CombustionJournal of

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Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

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Nuclear InstallationsScience and Technology of

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Science and Technology of Nuclear Installations 5

Micrometer

Water

Container

Sensor

Channel wall

Fuel rod

d2

d1

d9984002

d9984001

Δxn(n = 1 2 3 )

Δyn(n = 1 2 3 )

Figure 7 Measurement calibration device

350

300

250

200

150

100

50

0

300 350 400 450250200150100500

Mea

sure

d po

sitio

n by

sens

or (120583

m)

Actual position of micrometer (120583m)

Experimental valueLinear fit curve

Figure 8 Measurement calibration curve

From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)

33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889

1to be larger than the actual

displacement 1198892 That has a substantial influence on the

result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of

fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840

1

is the same as the actualdisplacement 1198891015840

2

34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)

4 The Experimental Results and Analysis

41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases

Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider

119865 prop 120588 sdot 1198812 (10)

119865 prop 120588 sdot (119876

119904)

2

(11)

Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of

6 Science and Technology of Nuclear Installations

Position 1

Position 2

X

Y

d2d1

SensorO

(a) Original structure 1198891gt 1198892

d9984002d9984001

Sensor

(b) Improved structure 11988910158401

=

119889

1015840

2

3m

m

3mm

05

mm

(c) Size of metal sheet

Figure 9 Schematic of improved structure

Displacement of the

Displacement

Correctionmodule

sensor

Final displacementsignals signals signals

Digital signalsComputer

Initial displacement Initial voltage

Analog signalsinstrument

Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)

Figure 10 Schematic diagram of data acquisition system

supercritical water according to (10) it can be noted thatthe average value of fluid exciting force 119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop

42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process

43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]

As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from

Science and Technology of Nuclear Installations 7

Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

6 Science and Technology of Nuclear Installations

Position 1

Position 2

X

Y

d2d1

SensorO

(a) Original structure 1198891gt 1198892

d9984002d9984001

Sensor

(b) Improved structure 11988910158401

=

119889

1015840

2

3m

m

3mm

05

mm

(c) Size of metal sheet

Figure 9 Schematic of improved structure

Displacement of the

Displacement

Correctionmodule

sensor

Final displacementsignals signals signals

Digital signalsComputer

Initial displacement Initial voltage

Analog signalsinstrument

Data acquisition

Filter module

Arithmetic module

fuel rod

(below 30Hz)

Figure 10 Schematic diagram of data acquisition system

supercritical water according to (10) it can be noted thatthe average value of fluid exciting force 119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop

42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process

43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]

As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from

Science and Technology of Nuclear Installations 7

Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Science and Technology of Nuclear Installations 7

Table 3 Root mean square displacement of the fuel rod in through hole case

Flow rate (m3h)Root mean square displacement (120583m)

1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 11 Displacement power spectral density of the fuel rod inthrough hole case

6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz

Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration

It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency

0 5 10 15 20 25Frequency (Hz)

30 35

minus120

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

q = 362m3hq = 288m3hq = 139m3h

Figure 12 Displacement power spectral density of the fuel rod inblind hole case

0 5 10 15 20 25Frequency (Hz)

30 35 40

minus120

minus125

minus130

minus135

minus140

Pow

er sp

ectr

a (dB

)

Through hole caseBlind hole case

Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

8 Science and Technology of Nuclear Installations

0 5 10 15 20 25Frequency (Hz)

Through hole caseBlind hole case

30 35minus150

minus125

minus130

minus135

minus140

minus145

Pow

er sp

ectr

a (dB

)

Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h

at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value

44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On

0030

0025

0020

0015

0010

0005

0000

Prob

abili

ty d

ensit

y fu

nctio

np(x)

minus100 100minus75 75minus50 50minus25 0 25

Statistic of experimental dataNormal distribution curve

Displacement x (120583m)

Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h

Through hole caseBlind hole case

20

18

16

14

12

1010 15 20 25 30 35 40

Flow rate (m3h)

Rms d

ispla

cem

ent (120583

m)

05

Figure 17 Root-mean-square displacement changing with flow ratein two cases

the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well

45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Science and Technology of Nuclear Installations 9

Left Right

Spacer

Fuel rod

V

Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability

that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop

5 Conclusions

An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows

(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that

(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of

boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly

(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977

[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982

[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987

[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983

[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985

[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998

[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002

[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006

[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007

[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984

[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984

[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014