AECL-5852

ATOMIC ENERGY m j & & L'ÉNERGIE ATOMIQUEOF CANADA LIMITED ^ K j r DU CANADA LIMITÉE

"FLOW-INDUCED VIBRATION OF

NUCLEAR POWER STATION COMPONENTS"

by

M.J. PETTIGREW

Presented at the 90th Annual Congress of the Engineering

Institute of Canada, Halifax, Nova Scotia, October 4-8, 1976

Chalk River Nuclear Laboratories

Chalk River, Ontario

September 1977

"FLOW-INDUCED VIBRATION OF NUCLEARPOWER STATION COMPONENTS"*

by

M.J. Pettigrew, H.C.S.M.E.

^Presented at the 90th Annual Congress of theEngineering Institute of Canada, Halifax,Nova Saotia, October 4-8, 1976.

Atomic Energy of Canada LimitedChalk River Nuclear Laboratories

Chalk River, OntarioKOJ 1J0

Se-pterriber 1977

AECL-5852

"VIBRATIONS ENGENDREES PAR L'ECOULEMENT DES F.LUIDES DANSLES COMPOSANTS DES CENTRALES ELECTRONUCLEAIRES"*

parM.J. Pettigrew

Plusieurs composants des centrales électronucléaires CANDU** sont sujetsà des vitesses d'écoulement des fluides relativement grandes en régimeliquide ou biphasé (eau/vapeur). Le combustible nucléaire dans les canauxde combustible et les faisceaux de tubes dans les générateurs de vapeursont des composants typiques. Souvent on augmente les vitesses d'écoule-ment pour améliorer le rendement des composants, par example, pour obtenirun meilleur échange calorifique dans les canaux de combustible. Pour desraisons économiques on préférerait spécifier des composants plus petits ouéliminer des éléments de structure, par example, on utilise des tubes depetits diamètres pour réduire l'inventaire d'eau lourde. De grandes vitessesd'écoulement et une réduction des éléments de structure peuvent causer desproblèmes de vibrations. CetL? communication traite des problèmes et analysesde vibrations des composants des centrales électronucléaire engendrées parles écoulements.

L'usure par frottement, la fatigue, le bruit acoustique et les difficultéesopérationelles sont les problèmes causés par les vibrations. On examine derécents problèmes comme l'usure de tubes de générateur de vapeur.

Les écoulements dans les composants nucléaires peuvent être parallèles ou trans-versaux. Dans les canaux à combustible l'écoulement est surtout par-allèle. L'écoulement est transversal et liquide au travers des faisceauxde tubes d'échangeurs de chaleur tandis qu'il est aussi transversal maisbiphasé dans la région des générateurs de vapeur où les tubes sont coudésen U. On discute des mécanismes d'excitation dominants en écoulementparallèle et transversal. Eh écoulement parallèle on considère deuxméchanismes principaux qui sont l'excitation aléatoire due à la turbulencede l'écoulement et l'instabilité fluidelastique. En écoulement transversalon considère en plus le détachement périodique des tourbillons. Notre méthoded'analyse des composants nucléaires est présentée. L'analyse des vibrationsdes générateurs de vapeur est donnée en example.

Nos études courrantes sur les vibrations engendrées par les écoulements sontdécrites. Ceci inclus l'étude du comportement vibratoire des éléments decombustible nucléaire dans un réacteur expérimental.

On conclu que, même si le travail de recherches n'est pas encore terminé,la plupart des problèmes de vibrations peuvent être évités, pourvu que lescomposants nucléaires sont analyses au stage de la conception et que cesanalyses sont appuyées par des études expérimentales au besoin. On n'a pasencore rencontré de situations où les vibrations ont sérieusement limitél'ingénieur au stage de la conception.

* Cormuniaation présentée au BOieme congrès annuel de l'Institut canadiendes ingénieurs, Halifax, Nouvelle-Eaosse, octobre 4-8, 1976.

** CANDU - CANada Deuterium Uranium.

L'Energie Atomique duCanada, LimitéeChalk River, OntarioCanada, KOJ 1J0 AECL-5852Septembre 1977

"FLOW-INDUCED VIBRATION OF NUCLEAR POWER STATION COMPONENTS"*

by M.J. Pettigrew, M.C. S.M.E.Atomic Energy of Canada LimitedChalk River Nuslear Laboratories

ABSTRACT

Several components of CANDU** nuclear power stations are subjected to relativelyhigh flow velocities in either liquid or two-phase (steam/water) flow. Typicalof such components are the nuclear fuel in the fuel channels and tube bundlesin the steam generators. Often higher component performance, requires higherflow velocities, for instance, to improve heat transfer in fuel channels.Economics sometimes dictates smaller components or minimum structural constraints,for example small diameter tubes are used in steam generators to minimize heavywater inventory. High flow velocities and decreased structural rigidity couldlead to problems due to excessive flow-induced vibration. This paper generallytreats the problems and the analyses related to flow-induced vibration of nuclearpower station components.

Fretting-wear, fatigue, acoustic noise and operational difficulties are the problemscaused by flow-induced vibration. Some recent problems such as fretting of Jteamgenerator tubes are reviewed.

Flow in nuclear components may be parallel or transverse. In fuel channels theflow is mainly parallel to the fuel elements. Liquid cross-flow exists in heatexchanger tube bundles and U-bend tube regions of steam generators are sub-jected to two-phase cross-flow. The vibration excitation mechanisms predominantin parallel and transverse flow are discussed and formulated. In parallel flowtwo basic vibration excitation mechanisms are considered, namely random excitationdue to flow turbulence and fluidelastic instability. The above and periodic wakeshedding are considered in cross-flow.

Our approach to the vibration analysis of nuclear components is presented. Thisis illustrated by the vibration analysis of steam generator designs.

Current investigations related to flow-induced vibration are outlined. Thisincludes the experimental study of the in-reactor vibration behaviour of fuelelements.

It is concluded that, although there are still areas of uncertainty, most flow-induced vibration problems can be avoided provided that nuclear components areproperly analysed at the design stage and that the analyses are supported byadequate testing and development work when required. There has been no caseyet where vibration considerations have seriously constrained the designer.

* Presented at the 90th Annual Congress of the Engineering Institute ofCanada, Halifax, Nova Saotia, Ootobev 408, 1976.

** CANDU - CANada Deuterium Uranium.

Chalk River, Ontario KOJ 1J0

September 1977 AECL-5852

CONTENTS

Page

1. INTRODUCTION 2

2. FLOW-INDUCED VIBRATION PROBLEMS 3

3. FLOW CONSIDERATIONS IN NUCLEAR STATIONCOMPONENTS 5

4. VIBRATION EXCITATION MECHANISMS IN AXIAL FLOW ... 8

Fluidelastic Instability 8

Forced Vibration . 10

5. VIBRATION EXCITATION MECHANISMS IN CROSS-FLOW ... 17

1) Forced Vibration 17

2) Fluidelastic Instability 18Periodic Wake Shedding Resonance 20

6. VIBRATION ANALYSIS OF NUCLEAR COMPONENTS 21

7. CURRENT VIBRATION STUDIES

Vibration Behaviour of Nuclear Fuel in Reactor .. 25

Vibration Damping and Support Dynamics of HeatExchanger Tubes 26

Other Vibration and Related Studies CurrentlyUnderway 27

8. CONCLUDING REMARKS 28

REFERENCES 30

FIGURES , 35

-2-

1. INTRODUCTION

Several components of CANDU* nuclear power stations are

subjected to relatively high flow velocities. Typical

of such components are the nuclear fuel bundles in the

fuel channels and the tube bundles of steam generators

and heat exchangers. Often higher component performance

requires higher flow velocities, for instance, to improve

heat transfer in fuel channels. Economics sometimes

dictates smaller components or minimum structural con-

straints, for example small diameter tubes are used in

steam generators to minimize the inventory of expensive

heavy water. High flow velocities and decreased struc-

tural rigidity could lead to problems due to excessive

flow-induced vibration. Such problems could seriously

affect the performance and reliability of nuclear power

stations.

The above is best illustrated by an example. Fretting-

wear due to vibration of one of the many tubes in a

steam generator could result in leakage of heavy water

primary coolant into the secondary system. A station

shut-down lasting a few days would be required for repairs,

This is very undesirable in terms of lost production and

of radiation exposure limitation of maintenance personnel.

Although an effective tube plugging technique has been

developed1'2 in preparation for the unlikely event of a

tube failure, it is much preferable to avoid vibration

problems altogether. This can be achieved by proper

flow-induced vibration analysis of nuclear station com-

ponents at the design stage.

This paper is a general outline of our work in the area

of flow-induced vibration. Some recent vibration

* CANDU (CANada Deuterium Uranium)

-3-

problems are reviewed. Flow-induced vibration excitation

mechanisms are discussed. The paper outlines our approach

and techniques to analyse nuclear power station components

from a flow-induced vibration point of view. The

prevention of flow-induced vibration problems is emphasized.

Some current vibration studies are described.

FLOW-INDUCED VIBRATION PROBLEMS

The problems related to flow-induced vibration are gener-

ally fretting-wear, fatigue, acoustic noise and operational

difficulties. Figures la and b show a case of steam gene-

rator tube fretting-wear which occurred in the Douglas

Point nuclear power station3. The "U" bend tubes near

the outlet are subjected to high velocity two-phase

(steam/water) flow. In a few of the Douglas Point steam

generators the "U" bend tubes were not supported at the

top and vibrated with sufficient amplitude to contact

each other resulting in the fretting-wear shown on Fig. la.

Vibration of the "U" bend tubes also caused fretting at

the location of nearby supports. In one tube the fretting

was extensive enough to cause leakage as shown on Figure, lb.

In most of the steam generators the "U" bend tubes were

supported at the top and no fretting problem occurred.

This problem could have been prevented simply by providing

for adequate tube supports.

A case of heat exchanger tube fretting-wear is shown in

Figure 2. He.e the fretting-wear occurred at the location

of lacing metal strips which were added to provide addi-

tional support near the inlet where flow velocities are

relatively high. The problem was attributed to the com-

bination of excessively loose lacing of the metal strips

and partial blockage of the inlet which resulted in much

-4-

hlgher than expected flow velocities in the region of

the damage". Avoidance of inlet blockage and the

replacement of the lacing strips by proper support plates

were the corrective actions taken in this case.

Fretting-wear was observed on the top fuel bundles in

40% of the high flow fuel channels of the Gentilly-1

nuclear power station. Figure 3 is a photograph of

typical fretting damage taken through an optical magnifier

during "hot cell" examination. Figure 4 is a simplified

flow diagram of the Gentilly-1 station which is of the

CANDU-BLW* type. The fuel bundles (Fig. 5) are assembled

in the form of a string held together with a central sup-

porting tube. The latter is terminated at the top by a

flux suppressor and at the bottom by a spring assembly.

The strings are inserted in upward flow vertical fuel

channels as shown on Figure 6. They are attached at the

bottom and free at the top of the fuel channels. The

flow gradually becomes two-phase as boiling occurs along

the fuel and reaches i 16% steam quality near the top.—2 —1The mass flux is typically 4400 kg.m .s . The fretting

problem was attributed to transverse flow-induced vibra-

tion of the fuel strings. Unexpectedly some of the flux

suppressors were assembled eccentrically. This caused

the fuel strings to be bent and promoted fretting-wear.

The corrective measures taken were to as-.ure the concentric

assembly of the fuel and to increase fuel string flexural

rigidity to reduce vibration.

We now consider an example where flow-induced vibration

could have lead to operational difficulties. In the

Gentilly-1 station, control absorber guide tubes are

cantilevered and suspended vertically in the calandria as

* BLW -(Boiling Light Water)

- "5-

shown on Figure 7. They extend past the horizontal

booster fuel rods. The absorber guide tubes were

directly exposed to the submerged jet flow emerging

from the booster rod outlet. During prototype testing

the absorber guide tubes vibrated severely. In the

reactor core this would have resulted in local reactivity

disturbances which could have caused operational problems.

The designers avoided the problems altogether by providing

a protective shroud attached to four adjacent calandria

tubes as shown on Figure 7a.

We have encountered other problems such as excessive

acoustic noise due to flow control valve dynamics and

fatigue cracking due to noise-induced vibration of

steam discharge nozzles. So far all our flow-induced

vibration problems have been solved by simple design

modifications or changes in operational conditions.

3. FLOW CONSIDERATIONS IN NUCLEAR STATION COMPONENTS

Consider the simplified flow diagram of a typical CANDU-

PHW* nuclear power station as shown on Figure 8. Most

stations in Canada are of that type. Starting at the

primary pumps, the heavy water coolant flows in the

headers, into the feeder pipes leading to each fuel

channel. The fuel channels are horizontal. The flow

in the channels is essentially axial to the fuel bundles.

Flow velocities in the order of 9 m/s are typical. The

bundles are held down in the channel by gravity forces.

They are not held together by me.chanical means although

they are pushed together against a downstream stop by

hydraulic forces. This is different than the string

type fuel bundle assembly of vertical CANDU-BLW fuel

channels.

* PHW - (Pressurized Heavy Water)

-6-

The fuel bundles may be partly subjected to cross-flow

during refuelling operations when they .are moved past

the inlet or outlet feeders. In Pickering and earlier

stations, the flow remains liquid throughout the fuel

channels. In post Bruce stations and to some extent

in Bruce the coolant is allowed to boil and downstream

fuel bundles and outlet feeders are subjected to some two-

phase (steam/water) flow. For example in Gentilly-2 and

Point Lepreau, the average channel outlet quality is

expected to be around 4%. These stations are sometimes

called CAFDU-BHW*.

The outlet feeders are coupled to main headers which

lead to the steam generators. Figure 9 shows a typical

recirculating type steam generator. All flow situations

are possible in this component. Heavy water flows in the

tubes at varying conditions from 5% steam quality to

subcooled liquid. The tubes are subjected to liquid

cross—flow in the preheater section and in the recirculated

water entrance region near the tubesheet. The saturated

water then flows up and gradually boils, to reach 15 - 20%

steam quality at the top. Thus liquid and two-phase

axial flow exists along the tubes. Two-phase cross-

flow is predominant at the top of the "U" tube region

where the mass flux is typically 300 kg m~*.s .

There are many heat exchangers in a nuclear station, e.g.

the moderator heat exchangers. The tubes of heat exchangers

are mostly subjected to cross-flow particularly near inlets

and outlets. The steam produced by the steam generators is

* CANDU-BHW - (Boiling Heavy Water)

-7-

condensed after going through the turbine. The condenser

is an enormous heat exchanger whose tubes are exposed to

high velocity steam flow. The immersion heaters located

at the bottom of the pressurizer are another category of

interesting components. The heater elements are exposed to

incoming liquid or two-phase flow during station start-up

and out going liquid flow during shutdown. Flow-induced

vibration of the calandria tubes may also be possible. They

are subjected to some moderator cross-flow and may be exposed

to submerged jet for example near the effluent of booster

fuel rods.

Thus from a flow-induced vibration point of view, nuclear

station components are essentially cylindrical structures

or bundles of cylinders subjected to axial or transverse

flow. "The flow may be internal or external to the cylinders

and it may be liquid, vapour or two-phase. This is outlined

on Table 1. The first task in any flow-induced vibration

analysis is to define the flow conditions prevailing in the

nuclear component under study.

TABLE 1: Possible Flow Conditions in Nuclear Power Stations

STATION COMPONENTS

Fuel Channel

Feeder Pipe

Fuel (Normal lyI During Loading

Calandria Tube

Control Rod

SteamGenera-tors

Entrance

"U" tube

Ptehee'—r

Elseirhere

Heat Exchangers

Condenser

%

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/

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g(H

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1Sl/

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our

1 a azzJj

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iisa tu

Yes

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-8-

VIBRATION EXCITATION MECHANISMS IN AXIAL FLOW

In axial flow we consider two flow-induced vibration

excitation mechanisms, namely: fluidelastic instability

and forced vibration response to random excitation due

to flow turbulence. Other excitation mechanisms such

as self-excited vibration5 and parametric vibration1"7

have been suggested. However we have not yet needed to

consider them. For a comprehensive review of this topic,

the reader is referred to Paldoussis8.

Fluidelastio Instability

Fluidelastic instabilities result from the interaction

between hydrodynamic forces and the motion of structures.

For cylinders in axial flow, the pertinent hydrodynamic

forces9 are the frictional forces, the fluid acceleration

forces and in some cases the drag forces (e.g., cylinders

with one free end). Instabilities appear in the form of

either buckling or flutter-like oscillations. Figure 10

shows a flexible cylinder experiencing fourth mode

buckling while being subjected to confined liquid flow.

Fluidelastic instabilities are possible with both internal

and external liquid flow. In spite of some experimental

efforts10, we have not yet confirmed that instabilities

are possible in two-phase axial flow. To be conservative

we assume they exist in our analyses.

The fluidelastic behaviour of cylindrical structures in

axial flow has been formulated by Paldoussis8'9. The

dynamic response y at a time t of a uniform cylinder of

diameter D, length L, flexural rigidity £1, mass and

hydrodynamic mass m and M respectively, subjected to

an axial velocity U is governed by:

-9-

- î C T ^ Hl-f6)L-x} â_I _ {6To + i(1_ô)e;MU2} ^

3x 3x*

iîj =0.3x 2 D D 3t c

In this equation, x is a point along the cylinder, y is

an internal damping coefficient, €„ is the axial

frictional force coefficient, T is an externally

imposed tension, C' is a downstream end base drag

coefficient, C is the normal frictional force coefficient

and CD represents a viscous damping coefficient at zero

flow velocity. Finally, 6 = 0 corresponds to the case

where the downstream end Is free to move axially and S «

1 when it is not. For U^ 0, solution of this equation yields

the eigenvalues and eigenfunctions of the system, which are

complex. By varying U one may determine the critical flow

velocities for fluidelastic instabilities and the corres-

ponding mode shapes associated with these instabilities.

In a very approximate way, critical velocities for fluid-

elastic instability may be formulated in terms of the

non-dimensional velocity

u - OL /MTU ... (2)

For a given mode it is desirable to keep u much lower

than the critical value to avoid instability. In general

if u is lower than unity there should be no problem8'11.

In a nuclear component where M and V may be fixed for

-10-

other considerations, instability problems may be avoided

by increasing the flexural rigidity El or increasing the

number of support points (e.g., decreasing L).

Fortunately, critical velocities for fluidelastic insta-

bilities are much higher than the axial flow velocities

normally encountered in nuclear components. For instance

the critical velocity of a typical steam generator tube is

in the order of 100 m/s. The relatively long, very

flexible and heavy fuel strings of CANDU-BLW fuel channel

are the exception for which the possibility of fluid-

elastic instabilities must be considered11.

Forced Vibration

Nuclear components may respond to 1) excitation forces

that are of mechanical origin and are structurally trans-

mitted, or 2)boundary layer pressure fluctuations

that are generated by the fluid. Structurally transmitted

forces may be generated by rotating machinery such as

pumps or the turbine-generator or by other components

with moving parts such as control valves and fuelling

machines. It is also possible that the flow-induced

vibration response of other components such as the feeder

pipes be structurally transmitted to for example the

fuel bundles. It is very difficult to evaluate structur-

ally transmitted forces as they are not characterized

by the component under consideration. They depend on the

overall system to which the component is integrated.

Fortunately we have not experienced vibration problems

due to structurally transmitted vibration.

Fluid-borne pressure fluctuations may be divided in two

groups, namely: far field and near field. Far field

disturbances are generated by upstream components such

-li-

as pumps, valves, elbows and headers and are transmitted

by the fluid. Pressure fluctuations due to far field

sources would generally be broadband in nature except

for those generated by pumps. These would be at a fre-

quency related to the pump speed times the number of impeller

vanes. Such forces are again very difficult to formulate

as the fluid dynamic behaviour of the overall system needs

to be understood. Far field disturbances are insignificant

in two-phase flow as they are quickly attenuated by the

inherently high damping of two-phase mixtures. This is

fortunate since two-phase flow induced vibrations are

generally more severe.

Near field disturbances are generated locally by the fluid

as it flows around the component of interest. They may

be generated in a number of ways such as general turbulence,

swirl, cross-flow components, flow regime changes and

nucleate boiling. The result is a broadband random

pressure field acting at the surface of cylindrical com-

ponents. At a given time, the pressure is not uniform

around the periphery of a component. This results in a

net time varying force which excites the component to

vibrate. It may be shown with the assistance of

References 12, 13 and 14, that the mean square response~2

y (x) of a uni-dimensional continuous uniform cylindrical

structure to distributed random forces g(x,t) may be

expressed by:

-12-

y2(x) = E E T ^ 7 7 V ^ ) / |Hr(f)||Hs(f)|cos[er(f)-es(f)]r s r s m

J J 4>r(x)J J r f>s(x') R(x,x',f) dx dx' df ..(3)

where: 1) the spatial correlation density function

R(x,x',f) is defined by

R(x,x',f) = 2 f T->a |^ /" i(x,t) g(x',t+T) dt e"j(2irf) dT ..(4)

2) the frequency response function is

a ' < f > - ? — A r ••

Çr is the damping ratio at the r mode and 6 is the argumentof Hr(f).

r

3) (x) and (x) represent the normal mode ofr s i . .,

vibration of the structure for the r and s mode, and

4) x and x* are points on the structure and T is

a uifference in time t.

For the above derivation we assume that the damping is small

and that it does not introduce coupling between modes to

justify modal analysis. The natural modes are normalized

so that

m _2(x) dx = 1 ..(6)

where the total mass per unit length m = m + M.

-13-

"lonsider now the fundamental mode only of a lightly

lamped simply supported cy

sin (TTX/A). If we assume:

lamped simply supported cylinder (i.e., (x) = (2/£m)

1) that the random force field is homogeneous, the power

spectral density function of the force S(g) is independent

of location, i.e.,

R(x,x',f) =• R'(x.x') S(g) -'(7)

and 2) that both S(g) and the spatial correlation R'(x,x')

are fairly independent of frequency near the fundamental

frequency of the cylinder, we can show that the space and

frequency term» in Equation 3 may be separated and that:

|Hg(f)j cos U ( f ) - es(f)| df = Ïïfx/4Ç ..(8)

substituting Equation 6, 7 and 8 in 3 we get for x = 1/2

(i.e., midspan):

2

7 (ft/2) = L ..(9)16 m f 1 ir Ç

where ipt is a ratio of effective cylinder length over

actual length and is a measure of the spatial correlation

of the forcing function. \p is defined as:

*L " lï f f *1 < X ) *1

-14-

Equation 9 is very similar to that derived by Gorman15'16

and Reavis . Similarly if we define a peripheral spatial2 2

correlation ratio IJJ such that D î S(p) = S(g), the

response may be expressed in terms of the power spectral

density S(p) of the random pressure field p(x,t).

If we further assume that the random excitation forces

are completely spatially correlated (i.e., R'(x,x') = 1)

we obtain from Equation 6, 9 and 10:

-, S(g)y (H/2) = —, 3 2 ..(11)

4TT fxJ in ^

This equation may be useful to make a first outside guess

at forced random vibration response. Obviously if the

random forces are not well correlated, the vibration

response would be much less.

The main difficulty here is to determine the statistical

properties of the forcing function,that is its spatial

correlation density function R(x,x',f) for all the

configurations of interest. Gorman has measured values

of tyT , (f»_ and S(p) for some typical fuel element con-

figurations15'16'18 . Using the above measured values,

he has had remarkable success in predicting the vibration

response of a fuel element in axial two-phase flow simulated

by air/water mixtures16. Predicted and measured vibration

amplitudes are compared on Figure 11.

As shown on Figure 11 the vibration response is maximum

at a simulated steam quality of approximately 15%. We

have done further testing in steam/water flow where much

higher qualities were achieved19. The results on Figure 12

show two maxima in the vibration response vs steam quality

curves. This is explained in terms of two-phase flow

-15-

regime changes as follows: At low steam quality, bubbly/slug

flow regime exists and the vibration amplitude increases

with increasing quality until it reaches a maximum. This

is reasonable since higher vibration amplitudes are expected

at the higher velocities related to higher steam qualities.

The maximum amplitude corresponds to the start of the

transition between bubbly/slug and annular flow regime.

As the quality is increased, annular flow regime is estab-

lished. This flow regime is presumably less turbulent

and the vibration amplitude reaches a minimum. As the

quality is increased further, the flow velocity and con-

sequently the vibration amplitude increases again to reach

another maximum. This maximum corresponds to the transition

between annular flow and dispersed/fog flow regime. The

vibration amplitude decreases again to a minimum as fog

flow regime is established.

We have studied the effect of subcooled and bulk nucleate

boiling at the surface of a cylinder on its vibration response19.

Nucleate boiling does not contribute significantly to

vibration excitation for typical cylindrical structures.

It should be apparent by now that predicting the vibration

response of nuclear components subjected to random pressure

fields is not always simple. Several researchers have

developed semi-empirical expressions which may be useful

for some axial liquid flow problems. The expression developed

by Païdoussis8 is relatively successful as shown on Figure 13

where it is compared to experimental data. Paldoussis'

expression converted te dimen&ional form is:

.65-,

Y -A

^ - 5x10 K-4a V 2 5(l .2.2

M1.47 , 0.67M /m

1 + 4M/m..(12)

-16-

where Y is defined as the "maximum" amplitude, K is a

proportionality constant, a- is the dimensionless first

mode eigenvalue, V is the kinematic viscosity of the

fluid and D, the hydraulic diameter. K = 1 for laboratory

controlled conditions with minimum far field disturbances.

For nuclear power station components K = 5 is more realistic,

In Equation 12 the velocity exponent is 1.85. This is

reasonable since fluid forces are generally related to

velocity squared. The vibration amplitude is directly

related to L * /(El)' . Again this makes sense as it is

comparable to the deflection of beams under distributed

loading. The latter depends on L /El. We have found in

many practical cases in liquid flow that vibration is

roughly proportional to velocity squared. The above is

not much affected by the non-dimensional velocity term2 2 2u = ML U /El in the denominator of Equation 12. As

seen earlier, the velocity in most nuclear components

is much lower than the critical velocity for instability,2

thus U

-17-

5. VIBRATION EXCITATION MECHANISMS IN CROSS-FLOW

Generally in cross-flow induced vibration problems, we

consider three basic flow-induced vibration excitation

mechanisms: 1) forced vibration, where the cylinders are

forced to vibrate by random excitation due to flow turbulence;

2) fluidelastic instability, where the fluid forces are

related to the relative motion between cylinders in such

a way that coupling and instability results; and, 3) reso-

nance, where the natural frequency of the cylinders coin-

cides with the frequency of periodic wake shedding.

We have observed the first two excitation mechanisms in

both liquid and two-phase cross-flow. Periodic wake

shedding resonance is possible in liquid flow but has

not been observed in two-phase flow. Either it does not

exist or it is dominated by the response to random flow

excitation. Hence we do not consider it.

1) Foraed Vibration

We treat the problem of forced vibration response due

to random cross-flow turbulence in the same manner as

for axial flow. The vibration response may be estimated

using Equation 3. Here again the difficulty is to deter-

mine the statistical properties of the forcing function

due to cross-flow turbulence. Gorman20 has done this in

some typical configurations of heat exchanger tube bundles

by direct measurements. We have also deduced the forcing

function from the vibration response21'22. Much more

information is needed in this area. However in cases

where forcing function information is lacking, the analy-

tical techniques to predict vibration response may still

be used advantageously. For instance the vibration

response of a prototype component may be compared to that

-18-

of an existing nuclear station component exposed to

similar flow conditions.

Vibration response to random flow turbulence is usually

not a serious problem in liquid cross-flow. Other flow-

induced vibration excitation mechanisms are generally

the limiting criteria. This is not true however in two-

phase cross-flow where the turbulence is inherently much

stronger.

As in axial flow, the random vibration response in cross-

flow is approximately related to velocity in two-phase

flow and to velocity squared in liquid flow21'22.

2) Fluide las tic Instability

The fluidelastic instability phenomena is somewhat different

in cross-flow than in axial flow. In a bundle of cylinders,

the hydrodynamic forces on one cylinder are affected by

the motion of neighbouring cylinders. This creates an

interaction between hydrodynamic forces and the motion

of cylinders. When the energy absorbed by the cylinders

from the unsteady part of the hydrodynamic forces exceeds

that dissipated by damping during one cycle of motion,

fluidelastic instabilities occur. This situation is

possible when the flow velocity is sufficiently high.

Theoretically the motion of the cylinders should increase

indefinitely. However in practice it is limited by non-

linearities such as the presence of neighbouring cylinders.

This results in severe rattling and possible damage. For

an isolated circular cylinder there is no interaction and

hence no instability of this type. This is not true for

a non-circular body as interaction between fluid forces

and torsional motion may occur. We have found22 that

fluidelastic instabilities are possible in both liquid

and two-phase cross-flow.

-19-

The critical velocity Vrc at which fluidelastic insta-

bility occurs in the s vibration mode of a cylinder may

be expressed as:

- ->1/2V = K e f /(2pm f 2 c|> 2 (x)dx)I S J S J ..(13)J

Xl

where c is the viscous damping coefficient, K, is a factor

determined experimentally, p is the fluid density and

x1, x. define the length over which the cylinder is

subjected to flow.

Equation (13) is a generalized expression derived from

Connor's formulation23 of fluidelastic instability in a

single -array of cylinders. V is the reference critical gap

velocity and is equal to V a c p/(p-D) in which V is the

free stream velocity (i.e., velocity taken as if there

were no cylinders), p is the pitch of the tube bundle

and D the cylinder outside diameter. If the cylinders

are exposed to cross-flow over their entire length,

knowing that c = Airmfç, Equation 13 reduces to Connors'

expression

Vrc/fD = K(m6/pD2)Js ..(14)

in which the logarithmic decrement

-20-

'Peviodio Wake Shedding Résonance

The periodic formation of vortices downstream of an

isolated cylinder in cross-flow is a Classical phenomena

called Karman vortex shedding. The frequency of vortex

formation is defined in terms of a Strouhal Number S ~

FD/V where S is usually ^ 0.2. What happens in closely

packed bundles of cylinders is not so well understood.

Three mechanisms which could lead to periodic forces

may be postulated as shown on Figure 16, namely:

1) Vortex shedding25; The formation of vortices should,

however, be much affected by the close proximity of adjacent

and particularly downstream cylinders. 2) Buffeting;

Periodic forces may arise on a given cylinder a:, it is being

subjected to the vortices generated by the upstream cylinder.

3) Turbulent theory26; The argument here is that the scale

of turbulence is controlled by the geometry of the cylinder

bundle configuration. For a given flow velocity, same

scale turbulence leads to narrow band turbulent forces and

to some degree of periodicity.

Whatever the mechanism, periodic wake shedding forces could

result in a resonance problem if their frequencies coincide

with one of the natural frequencies of the cylinders.

The peak vibration amplitude Y. . at resonance for the r

mode of vibration of a cylindrical structure is given by:

Airfrc /

•/o

C T p D V2 ( x ) ( x ) dx . . . ( 1 5 )

L r

where: CT is the dynamic lift coefficient attributed toLi

periodic wake shedding and V(x) is the flow velocity dis-

tribution at any point along the cylinder.

-21-

We normally assume for conservatism that at resonance the

periodic forces are spatially correlated.

In our experience we have not observed periodic wake

shedding resonance for tubes inside a tube bundle. We

have mostly encountered it for upstream tubes20, that is

in the first and to a lesser extent in the second tube

row (see Figure 17). We have found the lift coefficient C^

based on the free stream velocity V to be generally less

than unity. We have not yet been able to correlate the wake

shedding frequency in terms of a predictable criterion such

as the Strouhal No., fd/V. Thus we assume resonance in the

analysis whenever this mechanism appears possible.

6. VIBRATION ANALYSIS OF NUCLEAR COMPONENTS

The first step in the vibration analysis of a nuclear

component is to define its dynamic parameters, that is:

stiffness or flexural rigidity, mass including the hydro-

dynamic mass and both structural and viscous damping.

Oncfc these are known the natural frequencies f . and mode

shapes .(x) may be calculated. Then the vibration

response may be predicted.

Take for example the case of a nuclear steam generator.

A typical steam generator tube and the flow conditions

to which it is subjected is shown on Figure 18. From

a mechanical dynamics point of view "U" tubes are simply

multi-span beams clamped at the tubesheet and held at

the baffle-supports with varying degree of constraint.

The latter is dependent on support geometry and parti-

cularly tube-to-support clearance. To be conservative

we assume the intermediate supports to be essentially

hinged. We do not yet take into account the clearance

between tube and support to keep our analysis linear.

-22-

The tube dynamics is completely defined by knowing m,

c, El, H and the boundary conditions (i.e., the support

locations). We assume that either the damping coefficient

c or the damping ratio Ç be independent of frequency.

Typical values for c are 0.04-0.07 kg rad/cm.s and 0.25-

0.5 kg rad/cm«s in liquid and two-phase flow respectively.

These correspond roughly to Ç = 0.02 and Ç = 0.08 at

typical tube frequencies.

Based on Equations 3, 13 and 15 we have developed a computer

program called "PIPEAU" to predict the vibration response

of multispan tube bundles. The program first calculates

the mode shapes .(x.) and the natural frequencies f.

(i.e., eigenvalue solution) using a method similar to that

suggested by Darnley27. Then the response and the critical

velocities for fluidelastic instability are estimated.

For the example shown on Figure 18 the threshold velocity

for instability in the U-bend region (between supports 6

and 12) where m = 0.42 kg/m and Ç = 0.08 is calcualted to

be 3.3 times the actual velocity. A similar calculation

for the inlet region (between supports 0 and 4) where m =

0.53 kg/m and t, = 0.028 shows that instability would be

entered from a high mode oscillation, at a threshold

velocity more than 5 times the actual velocity.

Calculations of tube response to random excitation are

shown on Figure 19. Two sections of the tube described

on Figure 18 are subjected to different flow conditions

and thus to forcing functions of different power spectral

densities and spatial correlations. The first few modes

are considered in the response.

-23-

Ideally our approach to the vibration analysis of heat

exchanger and steam generator designs should be that out-

lined on Figure 20. That is: starting from an initial

design, given the flow conditions (1); the flow distribution

and velocities are calculated (2); this indicates the

excitation mechanisms and permits the formulation of the

forcing function g(x,t) (3); the latter is the input to

the system (tube bundle) which needs to be defined in

terms of f , .(x), ç (4); then the response is calculated

in the form of y(x,f), the dynamic stresses cr(x,f) and

the forces at the supports F(x,f) (5); the next step

is to predict fatigue and fretting damage (6); this

leads to the last step which is to either accept (7)

or modify the design depending on whether or not there are

problems. The response calculation technique described

earlier essentially links (3) to (5). We are not yet at

this ideal stage. It is sometimes difficult to determine

flow velocities in complex three-dimensional flow path

particularly in two-phase flow. We do not yet have enough

information to formulate the forcing function in all cases.

We would like more tube damping numbers. It is desirable

to express the tube-to-tube support dynamics in terms of

the statistical properties of the impact forces. This

will likely prove to be the criterion governing the vibration-

fretting relationship. Finally we need to understand

better the vibration-fretting relationship for different

materials in various relevant environments.

Our practical approach to design analysis is as follows:

1) avoid fluidelastic instabilities; 2) make sure the

tube response to random excitation is low enough to avoid

fretting or fatigue problems; and 3) avoid periodic

wake shedding resonance or demonstrate it is not a problem.

-24-

When our response calculation technique is not sufficient

to satisfy the above specifications we can use it to

compare the design under study to that of an existing

satisfactory design. The calculation technique is then

used as a normalization tool. Alternately we can test a

model of the region in doubt21. It is also possible to

conduct a fretting endurance test on a single tube sub-

jected to the vibration response we estimate using our

response calculation technique. If the heat exchanger

component is easily accessible after installation in the

reactor system, we can measure its vibration behaviour

and take corrective action subsequently if necessary.

For this purpose we have developed in collaboration with

a manufacturer a very sensitive biaxial accelerometer

probe that can be inserted in the tubes during operation

(see Figure 21).

A similar approach may be used to analyse other nuclear

station components. For instance we have developed a

comprehensive computer model for the dynamics of CANDU-BLW

type fuel strings in collaboration with Paidoussis18 . The

model analyses the stability of a fuel string and predicts

its forced vibration response. The model is based on a

matrix type formulation analogous to Equation 1 to suit

the system of discrete fuel bundles. Currently a dynamic

model for CANDU-PHW fuel bundles in horizontal fuel channels

is being developed at the Whiteshell Nuclear Research

Establishment28'29.

-25-

CURRENT VIBRATION STUDIES

Vibration Behaviour of Nuclear Fuel in Reactor

Vibration studies of nuclear fuels are usually conducted

in out of reactor adiabatic test facilities. Under actual

reactor conditions, the mechanical characteristics of the

fuel are affected by thermal expansion of, in particular,

the U0_ fuel pellets. Also, under diabatic conditions,

additional flow-induced vibration excitation sources are

possible, e.g. enhanced cross-flow between fuel bundle

subchannels due to possible enthalpy imbalance. We have

studied the effect of in-reactor conditions on typical

CANDU-BLW fuel bundles in the experimental reactor NRU

at the Chalk River Nuclear Laboratories38.

A string of five fuel bundles was inserted in a two-

phase test loop simulating a CANDU-BLW fuel channel as

shown on Figure 22. Fuel vibrations were measured with in-

tegral lead weldable strain gauges installed on seven

typically located fuel elements. Figure 23 shows a typical

strain gauge installation on a fuel bundle. Measurements

were taken over a wide range of flow conditions, i.e.,

from 0 to 100% fuel power (0 to 100 W/cm2 heat flux),

from 70 C of subcooling to 25% steam quality, at pressures— 2—1of 28 to 90 bars, and at mass fluxes up to 4600kg-m ŝ .

Steam was generated by the fuel and/or added at the inlet of

the test section from external boilers.

We investigated in particular the effect of fuel power.

The natural frequency of fuel elements increases rapidly

by roughly 50% during the first reactor start-up as shown

on Figure 24. During the first shut-down it decreases

quickly down to 75% power and remains essentially constant

at lower power. The second start-up and serond shut-down.

-26-

are somewhat similar to the first shut-down. This behaviour

is explained in terms of fuel rigidity increase due to

fuel pellet expansion with power. During the first shut-

down and subsequent cycles the frequency vs power relation-

ship is different than during the first start-up because

then the fuel sheath has already been deformed plastically

by the first start-up. Then it takes a higher reactor

power for the fuel to expand firmly in the sheath and to

increase its rigidity.

The fuel element vibration behaviour is much dependent on

fuel history. This is attributed to change in rigidity,

internal damping and boundary conditions due to UO. pellets

expansion inside the -Fuel sheath, element bowing and other

geometrical changes. This is shown on Figure 25 where

vibration spectra taken at different times under essentially

similar conditions are compared for a typical fuel element.

We have found that fuel element vibration amplitudes were

generally small being less than 10 vim RMS under normal

CANDU-BLW operating conditions.

Vibration Damping and Support Dynamias of Heat Exchanger

Tubes

We are currently studying the damping behaviour of heat

exchanger tubes. The experiments are done on tubes of

different diameters ranging from 0.75 to 2.5 mm. The tubes

are installed in the trough shown on Figure 26 where they

can be immersed in water or in any other fluids to study

the effect of viscosity. Single and multispan tubes are

tested with both idealized or realistic heat exchanger

supports. The effect of frequency is explored by

varying span length. To obtain the damping values, we

use both the simple logarithmic decrement technique and

the frequency response method.

-27-

Typical vibration damping results are shown on Figure 27

for a simply supported 12.7 mm diameter heat exchanger

tube. The net viscous damping due to water decreases

with frequency.

We are now preparing tests to study the dynamics of the

tube-to—tube support interaction. This is particularly

important when the tube-to-support clearance is significant.

Our intentions are to measure the statistical properties

of the impact forces generated by the tubes at the tube

supports when realistic vibration amplitudes are

simulated. We plan to use this information to correlate

vibration response and fretting-wear data.

Other Vibration and Related Studies Currently Underway

We have discussed above two typical vibration studies

related to nuclear components. Other experimental and

analytical investigations are underway, such as:

1) Vibration vs Fretting Relationship: This is the

subject of an extensive program for both nuclear fuel

and heat exchanger materials31'32. The effects of several

parameters such as frequency, clearance, amplitude and

impact forces are investigated in both laboratory and

realistic environments.

2) Analytical Modelling of the Dynamics of Tube-to-

Support Interaction: An analytical model is being deve-

loped to treat the problem of tube-to-tube support

impacting in heat exchangers33. It takes into considera-

tion the non-linearity due to tube-to-tube support clea-

rance.

3) Vibration of Heat Exchanger Tube in Liquid Cross-Flow:

This work21* is continuing. Several different triangular

and square heat exchanger tube bundle geometries have

-28-

been studied. We are now investigating the effect of

irregularities such as the presence of sealing strips,

sealing rods and tube free lanes on neighbouring tube

vibration response.

4) Vibration of Tube Bundles in Two-Phase Cross-Flow:

We are preparing further experiments in support of steam

generator designs. Air-water mixtures will be used to

simulate steam/water two-phase flow.

5) Dynamics of Flexible Cylinder in Confined Flow:

Further experiments are underway particularly to explore

the dynamics and stability of flexible cylinders

subjected to two-phase axial flow.

6) Nuclear Fuel Dynamic Parameters: Tests have been

done to determine fuel bundle and fuel string dynamic

parameters such as dynamic stiffness, viscous damping,

hydrodynamic mass and structural damping. We are

preparing further tests particularly to study hydrodynamic

mass and damping in two-phase flow.

8. CONCLUDING REMARKS

It is concluded that, although there are still areas of

uncertainty, most flow-induced vibration problems can be

avoided. This requires that nuclear components be properly

analysed at the design stage and that the analyses bd

supported by adequate testing and development work.

There has been no case yet where vibration considerations

have seriously constrained the designer. Although some-

times difficult to analyse, vibration problems usually

require simple solutions.

-29-

ACKNOWLEDGEMENT: Many people have contributed to the

work discussed in this paper. Among those are R.I. Hodge,

R.B. Turner, A.O. Campagna, P. Tiley, Y. Sylvestre, J. Platten

and P.L. Ko of the Chalk River Nuclear Laboratories;

I. Oldaker of the Whiteshell Nuclear Research Establishment;

M.P. Paldoussis of McGill University; D.G. Gorman of the

University of Ottawa and C.F. Forrest and N.L. Carlucci of

Westinghouse Canada Ltd. The author is very grateful to all.

- 3 0 -

REFERENCES

1. R . I . Hodge, J .E . LeSurf, J.W. Hi lborn,"Steam Generator R e l i a b i l i t y , The Canadian Approach",Presented at the XIX Nuclear Congress of Rome, March1974, a l s o Atomic Energy of Canada Limited ReportAECL-4471 ( 1 9 7 4 ) .

2 . D.G. Dalrymple, "Current Canadian Use of Explos iveWelding for Repair and Manufacture of Nuclear SteamGenerators", AECL Research and Development inEngineer ing , Atomic Energy of Canada Limited ReportAECL-4427, Winter 1972.

3. R.T. Har t l en , "Recent F i e l d Experience with Flow-inducedVibrat ion of Heat Exchanger Tubes", Paper No. 611 ,I n t e r n a t i o n a l Symposium on Vibrat ion Problems in Indus try ,Keswick, U.K. 1973.

4 . R . I . Hodge, P.L. Ko, and A.O. Campagna,Personal Communication, Aug. 1976.

5 . E.P. Quinn, "Vibration o f Fuel Rods in P a r a l l e l Flow",U.S. Atomic Energy Commission Report GEAP-4059 ( 1 9 6 2 ) .

6. Y.N. Chen, "Flow-induced Vibrat ions i n Tube Bundle HeatExchangers wi th Cross and P a r a l l e l Flow. Part 1: P a r a l l e lFlow", Symposium on Flow-induced Vibrat ion in HeatExchangers, New York: ASME 5 7-66 (19 7 0 ) .

7. M.P. Pal'doussis, "Stabi l i ty of Flexible Slender Cylindersin Pulsat i le Axial Flow", J. of Sound and Vibration,42 (1 ) , 1-11 (1975).

8. M.P. Païdoussis , "The Dynamical Behaviour of CylindricalStructures in Axial Flow", Annals of Nuclear Science andEngineering, Vol. 1, No. 2, pp 83-106 (1974).

9. M.P. ?aïd?y»sif» , "Dynamics of Cylindrical StructuresSubjected to Axial Flow:, J. of Sound and Vibration,Vol. 29, No. 3, pp. 365-385 (1973).

10. M.J. Pettigrew, M.P. Païdoussis , "Dynamics and Stab i l i tyof Flexible Cylinders Subjected to Liquid and Two-PhaseAxial Flow in Confined Annul!", Paper D2/6, 3rd Interna-t ional Conference on Structural Mechanics in ReactorTechnology, London, U.K. Sept, 1-5, 1975, also AtomicEnergy of Canada Limited Report AECL-5502 (1975).

- S i -

11. M.P. Païdoussis , "Mathematical Model for the Dynamicsof an Articulated String of Fuel Bundles in Axial Flow",Paper D2/5 presented at the 3rd International Conferenceon Structural Mechanics in Reactor Technology in London,U.K., Sept. 1-5, 1975.

12. W.T. Thomson, "Vibration Theory and Applications",Prentice-Hall , Englewood Cl i f f e s , N.J. , 1965.

13. L. Meirovitch, "Analytical Methods in Vibration",Macraillan Company, N.Y., 1967.

14. S.H. Crandall, and W.D. Mark, "Random Vibration inMechanical Systems", Academic Press, N.Y., 1963.

15. D.J. Gorman, "The Role of Turbulence in the Vibrationof Reactor Fuel Elements in Liquid Flo"", AtomicEnergy of Canada Limited Report AiîCL-3371 (1969).

16. D.J. Gorman, "An Analytical and ExperimentalInvest igation of the Vibration of Cylindrical ReactorFuel Elements in Two-phase Paral le l Flow", J. NuclearScience Engineering 44. 277-290 (1971).

17. J.R. Reavis, "Vibration Correlation for Maximum Fuel-element Displacement in Paral le l Turbulent Flow",J. Nuclear Science Engineering 38, 63-69 (1969).

18. D.J. Gorman, "Experimental and Analytical Study ofLiquid and Two-Phase Flow-Induced Vibration in ReactorFuel Bundles", ASME Paper 75-PVP-52, 2nd National Congresson Pressure Vessels and Piping, San Francisco, June 23-27,19 75.

19. M.J. Pettigrew and D.J. Gorman, "Experimental Studieson Flow Induced Vibration to Support Steam GeneratorDesign, Part 1: Vibration of a Heated Cylinder in Two-Phase Axial Flow", Paper No. 424, InternationalSymposium on Vibration Problems in Industry, Keswick,U.K. 1973, also Atomic Energy of Canada Limited ReportAECL-4514 (1973).

20. S. Mirza and D.J. Gorman, "Experimental and AnalyticalCorrelation of Local Driving Forces and Tube Response inLiquid Flow Induced Vibration of Heat Exchangers",Paper F6/5, 2nd Conference on Structural Mechanics inReactor Technology, Berlin 1973.

-32-

21. M.J. Pettigrew, J.L. Platten, Y. Sylvestre,"Experimental Studies on Flow Induced Vibration toSupport Steam Generator Design, Part II: TubeVibration Induced by Liquid Cross-flow in the EntranceRegion of a Steam Generator". Paper No. 424, InternationalSymposium on Vibration Problems in Industry, Keswick, U.K.1973, also Atomic Energy of Canada Limited ReportAECL-4515 (1973).

22. M.J. Pettigrew, D.J. Gorman, "Experimental Studies onFlow Induced Vibration to Support Steam Generator Design,Part iii: Vibration of Small Tube Bundles in Liquidand Two-phase Cross-flow", Paper No. 424, InternationalSymposium on Vibration Problems in Industry, Keswick,U.K. 1973, also Atomic Energy of Canada LimitedReport AECL-5804 (1977).

23. H.J. Connors, Jr., "Fluidelastic Vibration of Tube ArraysExcited by Cross Flow", Proceedings of the Symposiumon Flow Induced Vibration in Heat Exchangers, ASMEWinter Annual Meeting, New York, Dec. 1, 1970, pp. 42-56.

24. D.J. Gorman, "Experimental Development of Design Criteriato Limit Liquid Cross-Flow Induced Vibration in NuclearReactor Heat Exchange Equipment", J. Nuclear Science andEngineering 61, 324-336 (1976).

25. Y.N. Chen, "Fluctuating Lift Forces of the Karman VortexStreets on Single Circular Cylinders and in Tube Bundles,Part 1: The Vortex Street Geometry of the Single CircularCylinder, Part 2: Lift Forces of Single Cylinders,Part 3: Lift Forces in Tube Bundles", ASME Transactions,Series B, J. of Engineering Industry, Vol. 94 (2),603-628 May 1972.

26. P.R. Owen, "Buffeting Excitation of Boiler Tube Vibration",J. Mech. Eng. Sci. 7 (4), 431-439, 1965.

27. E.R. Darnley, "The Transverse Vibration of Beams and theWhirling of Shafts Supported at Intermediate Points",Phil. Mag. Vol. 41 (241), 56 Jan. 1921.

28. I.E. Oldaker, A.D. Lane, M.P. Pal'doussis and C F . Forrest,"An Overview of the Canadian Program to InvestigateVibration and Fretting in Nuclear Fuel Assemblies",May 1974. 73-CSME-89, EIC-74-Th; Nuc. 2 EngineeringJournal, Fall, 19 74.

- 33 -

29. D.J. Jagannath, "A Model fer Vibration of Nuclear FuelBundles" (to be published).

30. M.J. Pettigrew and R.B. Turner, "The In-reactorVibration Behaviour of Nuclear Fuel", Paper D3/7, Inter-national Conference on Structural Mechanics in ReactorTechnology, Berlin, Sept. 1973.

31. P.L. Ko, "Impact Fretting of Heat Exchanger Tubes",Atomic Energy of Canada Limited Report AECL-4653 (1973).

32. P.L. Ko, "Fundamental Studies of Steam Generator andHeat Exchanger Tube Fretting", published in AECLResearch and Development in Engineering, Winter 1975,Atomic Energy of Canada Limited Report AECL-5310 (1975).

33. R.J. Rogers, R.J. Pick, "On the Dynamic Spatial Responseof a Heat Exchanger Tube with Intermittent Baffle Contacts",Nucl. Engrg. and Design, 36, 81-90 (1976).

-35-

FIGURE la: Fretting-Wear of Steam Generator Tubes:Fretting Damage at Midspan.

-36-

Figure lb: Frettlng-Wear of Steam Generator Tubes;Fretting Damage and Hole at SupportLocation.

-37-

FIGURE 2: Typical Example of Heat Exchanger Tube Fretting-Wear,

-38-

FIGURE 3: Fretting Damage on Gentilly-1 Fuel Bundle.

GENTILLYNuclear Power Station ORDINARY WATER I. • ••.••! STEAM

RIVER WATER liiiiii HELfUM GAS

HEAVY WATER MODERATOR

TURBINE-GENERATOR BUILDING

ELECTRICITY

RIVER WATER INTAKE BAYRIVER WATER OUTLET

i

VOI

FIGURE 4: Simplified Flow Diagram of CANDU-BLW Station.

G6NTILLY 1 SECTION THROUGH CENTRE OF FUEL BUNDLE

COUPE TRANSVERSALE PE LAGRAPPE COMBUSTIBLE

OI

CENTRALIZING PADSSPACERSBEARING PADSUO2 FUEL PELLETSZIR.CALOY 4 SHEATHDELINEATING DISCEND CAPEND PLATE

PATTES DE CENTRAGECALES D'ECARTEMENTPATTES D'APPUIPASTILLES DE UOjGAINE EN ZIRÇALOY 4DISQUES Of SEPARATIONBOUCHON D'EXTRÉMITÉPLAQUE D'EXTREMITE

FIGURE 5: Gentilly-1 Fuel Bundle.

-41-

OUTLET

FUEL BUNDLE(̂ Z7 kg x 1OJ

10 .4 cm

CENTRALSUPPORTINGTUBE

PRESSURETUBE

SPRINGISSEMBLV

SHIELDy—PLUG

INLET

FIGURE 6: Ske tch of CANDU-BLW F u e l Channe l ,

- 4 2 -

GENTILLY-ÏCALANDRIA

ABSORBERSUIDE TUBE

D20

D20

BOOSTER ROD

NOZZLE

TOP VIEW

BOOSTER RODOUTLET NOZZLE

CALANDRIA TUBE

PROTECTIVE SHROUD

GUIDE TUBE

FIGURE 7a: Modification with Protective Shroud.

FIGURE 7: Control Absorber Guide Tube in Gentilly-1 Reactor Core.

REACTOR BUILDING I I MODERATOR J

| | ORDINARY WATER

HEAVY WATER

HELIUM GAS

LAKE WATER

TURBINE.GENERATOR BUILDING

FIGURE 8: Simplified Flow Diagram of CANDU-PHW Station.

- 4 4 -

MANWAY(ALSO IN WATER BOX|

TUBE BUNDLE

PRIMARY (IN TUBES)

SECONDARY (IN SHELL)

DOWNCOMER ORFEED WATER NOZZLE

PRIMARY CHANNEL COVER

DIVIDE* PLATE

BEND RADIUS OF TUBES

BAFFLE OR LATTICE BARTUBE SUPPORTS

PREHEAT SECTION(OR IEG IN U SHELL UNITSI

TUBE SHEET CLADDING

WATER BOX

FIGURE 9: Typical Nuclear Steam Generator.

-45-

FIGURE 10:

Clamped-Free Cylinder withBullet-Shaped Downstream EndExperiencing 4th Mode BucklingIn Liquid Flow.

E

oCI

tooaoIEI

30 H

25

20

15

10

10

LEGEND

PREDICTED rms DISP

MEASURED rms OISP

TOTAL MASS FLOW

RATE = 0.8fc kg/s

I4020 30

SIMULATED QUALITY {%)FIGURE 11 MEASURED AND PREDICTED VIBRATION AMPLITUDE vs SIMULATED STEAM QUALITY IN

TWO-PHASE AXIAL FLOW'•

O N

I

- 4 7 -

0 0

0.5

3.Û

0.3

Û.2

0. Î

MASS FLUX; 47 g/(s-cm2)PRESSURE; D 2.86 MN/m2

A 3.55 MN/m2

O 4.23 MN/m2

O 5 . 6 1 MN/m2

STEAM QUALITY; TO 65% MAX.

1b 9 12FLOW VELOCITY (m/s )

15

FIGURE 12: Effect of Steam Quality and Pressure.

- 43 -

Vr

10- 1

i o - 2

l u " 3

4

1 1

W 5ca

i

AièBURGREEN et al

QUINN

SOGREAH

ROSTRÔM & ANDERSON

PAIDOUSSIS

1

10-4 ID"3 10"2

Ui.85 L 3-V(EI)-8

5x10-4 K a"*

10-1

+ M L 2 U 2 / ( E I ) ) J | D 2 - 2 1 + 4M/m

FIGURE 13 AGREEMENT BETWEEN MEASURED AND PREDICTED VIBRATIONRESPONSE IN AXIAL FLOW USING PAIOOUSSIS SEMI -EMPIRICAL EXPRESSION

- 4 9 -

a.

ent—

C£. "=CCO 2 :

= 3 LLJSO

x o

1 .5

1 .0

0.5PRESSURE: Q 4.23 MN/m2

O 5.61 MN/m2

I I I

50 100 150

MASS FLUX (g/(s-cm2))

200

FIGURE 14: Effect of Mass Flux and Pressure.

moo

P/d

C CONNORS 1.41G GORMAN 8 MIRZA 1.33PI PETTIGREW 1.5P2 PETTIGREW 1.6

f(Hz)11.8 - 40

383017

S0.008 - 0.16

0.1120.1560.168

100

10

A • • • L I Q U I D FLOW^ ^ 3 ^ TWO PHASE:

OAt>pOA I RX ^ S INSTABILITY NOT

O S I N G L E ROWANORMAL TRIANGULAR>PARALLEL TRIANGULARDNORMAL SQUAREO ROTATED SQUARE

V „: Approach velocity normal-ized for uniform flowvelocity-

OI

0.1

FIGURE 1 5 :

1.0 10 100

Non-Dimensional Presentation of Experimental Thresholdsfor Fluidelastic Instabilities.

1000

- 5 1 -

v fry5frVORTEX SHEDDING

S = fD/V

2) V 0BUFFETING

OO

ooTURBULENT EDDIES

CONTROLLED BY GEOMETRYFIGURE 16: Postulated Mechanisms for Periodic Excitation.

T 1.00 —

UJ«a

i

az:

1.00

0.75

0.50

0.25

0

1

• • • •

—

1

1

cT«L

fi/ ^/ rtO

//O

1

1

6

\ j O

1

1 '

——

oi

10 . 2 0 . 4 0 . 6

MEAN WATER VELOCITY ( m / s )

0.8

toI

FIGURE 17: Vibration Response of First Upstream Tube In Liquid Cross-Flow20.

-53-

1.0m

11

12

r:oCO

-I-CO

1

OUTLETCROSS FLOW(20% QUALITY)333 kg/5n*s>

\ CLEARANCEHOLES(PINNED ,SUPPORTS)

FIXED SUPPORTS

I»1PARALLEL

FLOU

•* 210

kg/m2s

(SATURATED

TO 20»

QUALITY)

INLETCROSS FLOU

(SATURATED)359kg/4nz.s>

P

FIGURE 18: Typical Steam Generator Tube and Flow Conditions.

- 5 4 -

M M m CROSS F U I EICI m i CM

SUPPORT * 0

«MS .009

«EWTION .»0FOilCES .114

(H) •

.mo

.119

.095

.174 _

•

0

.209

.352

.«05

15

I0KL«MS 10

(HPLITUDE

.200

.352

.090

.113

.095

LENGTH (m)

FIGURE 19: Example of Tube Response Calculation.

-55-

S T A R T

11DESIGN: GEOMETRY, FLOW CONDITIONS

Calculation of Flow Distribution and Velocities

EXCITATION MECHANISMSExcitation Forcing Function

SYSTEM: TUBE DYNAMICSDamping £, Modes

I

FIGURE 21: Biaxir?. Accelerometer Probe for Heat Exchanger Tube Vibration Measurements.

- 5 7 -

147.40m

146.79m

140 .51 Q-

139.27m —

138.81m —

136.89m —

136.78m —

136.40m-=*

— DECK PLATE

TOP CLOSURE

' — ? » OUTLET

HANGER ROD

STRAIN GAUGELEADS

TOP INSTRUMENTED• BUNDLEX1

FUEL STRING

PRESSURE TUBE(104 mm I.D. )

'SPACER FOR LEADS•BOTTOM INSTRUMENTED

BUNDLE

STRAIN GAUGESPRINGCENTRAL SUPPORT

MIXER

STEAM INLET

WATER INLET

SG151SG153

SG152

SGI 5

-SG3SG2

U - 1 1 8 - I K X - X ' )

SG191SGI 93

G192

SGI I ISGI 13SGI12

U - 1 1 8 - H X - X ' )

U - 1 1 8 - I K Y - Y ' )STRAIN GAUGE LOCATION

FIGURE 22: Strain Gauge InstrumentedFuel String Installed inU-l LOOD of Reactor NRU.

00

FIGURE 23: Details of Weldable Strain Gauge Installation on a Fuel Bundle.

- 5 9 -

70 r -

50 75 100POWER (3!)

60

55

~Z 50u

§

£ 45

40

35

SG 1&3 U-118-II

SG 5

OM SG 12&14

SG 15S17

SG 18S20

* S3 151 U-118-I

X SG 191 U-118-I

- V O A D O * X : START-UP: SHUT-DOWN

50 75 100POWER(«)

FIGURE 2 4 : Fuel Element Natural Frequency vs Reactor Power

7u

ieno

rttcucNcr

FIGURE 25: Effect of Fuel History on Fuel Element ViDration Behaviour[SG No. 15, Liquid Flow, U-118-Il]

- 61 -

FIGURE 26: Heat Exchanger Tube Immersed in Trough toStudy Vibration Damping.

-62-

o.ior

1/1

LU_ lzotozLLJ

o

o

o

a.

0.01

0.001

y = 0.756.X-

TUBE

12.7 mm O.D.

304 S.S.

TEMP.

19.4-C

O AIR MEDIUM• WATER MEDIUM

NET VISCOUS DAMPING

10 100fn(FREQUENCY) Hz

FIGURE 2 7 : Typical Tube Vibration Damping Resu l t s Showingthe Effect of Frequency.

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ISSN 0067-0367

has been assigned to this series of reports.

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