flow-induced vibration of nuclear power station components

7/23/2019 Flow-Induced Vibration of Nuclear Power Station Components

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AECL-5852

A T O M I C E N E R G Y m j L ' N E R G I E A T O M I Q U E

O F C A N A D A L IM IT E D

^ K j r

D U C A N A D A L IM IT E

F L O W - IN D U C E D V IB R A T IO N

OF

N U C L E A R P O W E R S T A T IO N C O M P O N E N T S

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


2/66

F L O W - I N D U C E D V I B R A T I O N OF N U C L E A R

P O W E R S T A T I O N C O M P O N E N T S *

by

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

^Presented

at the

90th Annual Congress

of the

Engineering InstituteofCanada, Halifax,

Nova Saotia, October 4-8,

1976

Atomic EnergyofCanada Limited

Chalk River Nuclear Laboratories

Chalk River, Ontario

KOJ

1J0

Se pterriber

1977

AECL-5852


3/66

VIBRATIONS ENGENDREES PAR L'ECOULEMEN T D E S F.LUIDES DA NS

LES COMPOSANTSD E S CENTRALES ELECTRONUCLEAIRE S *

par

M.J. Pettigrew

Plusieurs composants des centrales lectronuclaires CANDU** sont sujets

des vitesses d' coulement des fluides relativement g randes en rgime

liquide ou biphas (eau/vapeur). L e combustible nuclaire dans les canaux

de combustible et les faisceaux de tubes dans les gnrateurs de vapeur

sont des composants typiques. Souvent on augmente les vitesses d' coule-

ment pour amliorer le rendement des composants, par example, pour obtenir

un meilleur change calorifique dans les canaux de combustible. Pour des

raisons conomiques on prfrerait spcifier des composants plus petits ou

liminer des lments de structure, par example, on utilise des tubes de

petits diamtres pour rduire l' inventaire d'eau lourde. D e grandes vitesses

d'coulement et une rduction des lments de structure peuvent causer des

problmes de vibratio ns. C etL ? communication traite des problmes et analyses

de vibrations des composants des centrales lectronuclaire engendres par

les coulements.

L' usure par frottement, la fatigue, le bruit acoustique et les difficultes

oprationelles sont les problmes causs par les vibratio ns. On examine de

rcents problmes comme l'usure de tubes de gnrateur de vapeur.

L es coulements dans les composants nuclaires peuvent tre parallles ou trans-

v e r s a ux . D ans les canaux combustible l'coulement est surtout par-

allle. L' coulement est transversal et liquide au travers des faisceaux

de tubes d'changeurs de chaleur tandis qu'il est aussi transversal mais

biphas dans la rgion des gnrateurs de vapeur o les tubes sont couds

en U. On discute des mcanism es d'excitation dominants en coulement

parallle et transversal. Eh coulement parallle on considre deux

mchanismes principaux qui sont l'excitation alatoire due la turbulence

de l'coulement et l'instabilit fluidelastique. En coulement transversal

on considre en plus le dtachement priodique des tourbillons. N otre mthode

d' analyse des composants nuclaires est prsente. L ' analyse des vibrations

des gnrateurs de vapeur est donne en example.

Nos tudes courrantes sur les vibrations engendres par les coulements sont

dcrites. C eci inclus l'tude du comportement vibratoire des lments de

combustible nuclaire dans un racteur exprimental.

On conclu que, mme si le travail de recherches n'est pas encore termin,

la plupart des problmes de vibrations peuvent tre vits, pourvu que les

composants nuclaires sont analyses au stage de la conception et que ces

analyses sont appuyes par des tudes exprimentales au besoin. On n'a pas

encore rencon tr de situa tions o les vibrat ions ont srieusement limit

l'ingnieur au stage de la conception.

* Cormuniaation prsente au BOieme congrs annuel de l Institut canadien

des ingnieurs, Halifax, Nouvelle-Eaosse, octobre 4-8, 1976.

** CANDU - CANada Deuterium Uranium.

L'Energie Atomique du

Canada, Limite

Chalk River , Ontar io

Cana da, KOJ 1J0 AECL-5852

Septembre 1977


4/66

FLOW -INDU CED VI BRATI ON OF NUCLEAR POWER ST AT ION COMP ONEN TS *

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

Atomic Energy of Canada Limited

Chalk River Nuslear Laboratories

A B S T R A C T

Several components of CANDU** nuclear power stations are subjected to relatively

high flow velocities in either liquid or two-phase (steam/water) flow. Typical

of such components are the nuclear fuel in the fuel channels and tube bundles

in the steam generators. 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 constraints,

for example small diameter tubes are used in steam generators to minimize heavy

water inventory. High flow velocities and decreased structural rigidity could

lead to problems due to excessive flow-induced vibration. This paper generally

treats the problems and the analyses related to flow-induced vibration of nuclear

power station components.

Fretting-wear, fatigue, acoustic noise and operational difficulties are the problems

caused by flow-induced vibration. Some recent problems such as fretting of Jteam

generator tubes are reviewed.

Flow in nuclear components may be parallel or transverse. In fuel channels the

flow is mainly parallel to the fuel elements. Liquid cross-flow exists in heat

exchanger tube bundles and U-bend tube regions of steam generators are sub-

jected to two-phase cross-flow. The vibration excitation mechanisms predominant

in parallel and transverse flow are discussed and formulated. In parallel flow

two basic vibration excitation mechanisms are considered, namely random excitation

due to flow turbulence and fluidelastic instability. The above and periodic wake

shedding are considered in cross-flow.

Our approach to the vibration analysis of nuclear components is presented. This

is illustrated by the vibration analysis of steam generator designs.

Current investigations related

to

flow-induced vibration are outlined. This

includes the experimental study of the in-reactor vibration behaviour of fuel

elements.

It is concluded that, although there are still areas of uncertainty, most flow-

induced vibration problems can be avoided provided that nuclear components are

properly analysed at the design stage and that the analyses are supported by

adequate testing and development work when required. There has been no case

yet where vibration considerations have seriously constrained the designer.

* Pr esente d at the 90th Annual Congre ss of the Engi neer ing Instit ute of

Canada , Halifa x, Nova Saoti a, Ootobev 408, 1976.

CANDU - CANada Deute ri um Ura nium.

Chalk River, Ontario KOJ 1J0

September 1977 A E C L -5 85 2


5/66

C O N T E N T S

P a g e

1. I N T R O D U C T I O N 2

2.

FL O W-I N D U C E D V I B R A T I O N PR O B L E M S 3

3. FL OW C O N S I D E R A T I ON S I N N U C L E A R S T A T I O N

C O M P O N E N T S 5

4 . V I B R A T I O N E X C I T A T I O N M E C H A N I S M S I N A X I A L FL OW . .. 8

Fluidelastic I nstability 8

Forced V ibration . 10

5. V I B R A T I O N E X C I T A T I O N M E C H A N I S M S I N C R O S S -FL O W . .. 17

1) Forced V ibration 17

2) Fluidelastic I nstability 18

Periodic Wake S hedding R esonance 20

6. V I B R A T I O N A N A L Y S I S OF N U C L E A R C O M PON E N T S 21

7. C U R R E N T V I B R A T I O N S T U D I E S

V ibration Behaviour of N uclear Fuel in R eactor .. 25

Vibration Damping and Support Dynamics of Heat

E xchanger T ubes 26

Other Vibration and Related Studies Currently

Underway 27

8. C O N C L U D I N G R E M A R KS 28

R E F E R E N C E S 3 0

FIG U R E S , 35


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-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

developed

1

'

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)


7/66

-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 station

3

. 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


8/66

-4 -

hlgher than expected flow velocities in the region of

the damage . A voidance 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

C A N D U -BL W* type. T he fuel bundles (Fig. 5) are assembled

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

porting tube. T he 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. T hey 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 1

The mass flux is typically 4400 kg.m .s . The fretting

problem was attributed to transverse flow-induced vibra-

tion of the fuel strings. U nexpectedly some of the flux

suppressors were assembled eccentrically. T his 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)


9/66

- 5-

shown on Figure 7. They extend past the horizontal

booster fuelrods. 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)


10/66

-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

crossflow 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 - 2 0%

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 3 00 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)


11/66

-7-

condensed after going through

the

turbine.

The

condenser

is

an

enormous heat exchanger whose tubes

are

exposed

to

high velocity steam flow. Theimmersion heaters located

atthebottomof thepressurizerareanother categoryof

interesting components.

The

heater elements

are

exposed

to

incoming liquidortwo-phase flow during station start-up

andoutgoing 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

tosubmerged

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 bundlesofcylinders subjectedtoaxialortransverse

flow.

The

flow

may be

internal

or

external

to the

cylinders

and

it may be

liquid, vapour

or

two-phase. This

is

outlined

on Table1. Thefirst taskin anyflow-induced vibration

analysisis todefinetheflow conditions prevailingin the

nuclear component under study.

TABLE1: Possible Flow ConditionsinNuclear Power Stations

STATION COMPONENTS

F u e l C h a n n e l

F e e d e r P i p e

F u e l ( N o r m a l l y

I D u r i n g L o a d i n g

Ca l a n d r i a T u b e

C o n t r o lRod

Steam

G e n e r a -

tors

Entrance

U

tube

Ptehee r

Elseirhere

Heat Exchangers

Condenser

3

e

01 41

s

M w

/

/

g

H

i

r

/

,/

,'

/

/

/

J

1

l/

/

/

/

/

/

/

/

/

/

1

1

u

1

a a

j

z

/

/

/

ii

a

tu

Yes

/

/

Ho

/

/

/

/

/

J

/

/


12/66

-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 vibration

5

and parametric vibra tion

1

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 Paldoussis

8

.

Fluidelastio Instability

Fluidelastic instabilities result from the interaction

between hydrodynamic forces and the motion of structures.

For cylinders in axial flow, the pertinent hydrodynamic

forces

9

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

efforts

10

, 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 Paldoussis

8

'

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:


13/66

-9-

-

C

T ^

Hl-f6)L-x}

_I _

{6 To +

i

(1

_

)e

;

M

U

2

}

^

3x 3x*

i j

=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 C

D

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 problem

8

'

1 1

.

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


14/66

-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 considered

11

.

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


15/66

-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 1 4 , 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:


16/66

-12-

y2(x)

=

E E T ^ 7 7 V ^

)

/ | H

r

f ) | | H

s

f ) | c o s [ e

r

f ) - e

s

f ) ]

r s r s m

JJ 4>

r

x)

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 ( 2 i r f )

dT ..(4)

2) the frequency response function is

a

< f >

?

r

r

is the damping ratio at the r mode and 6 is the argument

ofH

r

(f).

r

3 ) (x) and < f > (x) represent the normal mode of

r 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.


17/66

- 1 3 -

lonsider now the fundamental mode only of a lightly

lamped simply supported cy

sin (TTX/A). If weassume:

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:

|H

g

(f)j cos U ( f ) -e

s

(f)|df = f

x

/4 ..(8)

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

(i.e.,

midspan):

2

7

(ft/2)

=

L

..(9)

16m f

ir

where ip

t

is a ratio of effective cylinder length over

actual length and is a measure of the spatial correlation

of the forcing function. \pis defined as:

*L l f f * 1

< X )

* 1

1/2

=

K e f /(2 p m

f

2

c|

2

(x)dx)

S

J

S

J

..(13)

J

X

l

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

determined experimentally, p is the fluid density and

x

1

, x. define the length over which the cylinder is

subjected to flow.

Equation (13) is a generalized expression derived from

Connor's formulation

2 3

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 = Airmf, Equation 13 reduces to Connors'

expression

V

r c

/fD =K(m6/pD

2

)

Js

..(14)

in which the logarithmic decrement


24/66

-20-

Peviodio Wake Shedding Rsonance

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 shed ding

2 5

; 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 t heo ry

2 6

; 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:

irf

r

/

/o

C

T

p D V

2

( x ) ( x ) d x . . . ( 1 5 )

L

r

where: C

T

is the dynamic lift coefficient attributed to

L i

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

tribution at any point along the cylinder.


25/66

-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 tubes

2 0

, 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.


26/66

- 2 2 -

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 be independent of frequency.

Typical values for c are

0.04-0.07

kg rad/cm.s and 0.25-

0.5 kg rad/cms in liquid and two-phase flow respectively.

These correspond roughly to = 0.02 and = 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 Darnley

2 7

. 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 = 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.


27/66

- 2 3-

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), (4 ); then the response is calculated

in the form ofy(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.


28/66

- 2 4 -

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 doubt

2 1

. 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 2 1 ) .

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 Paidoussis

18

. 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

Establishment

2 8

'

2 9

.


29/66

-25-

C U R R E N T V I B R A T I ON S T U D I E S

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 topossible 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 Laboratories

3 8

.

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

phase test loop simulating a CANDU-BLW fuel channel as

shown on Figure 2 2 . 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/cm

2

heat flux),

from 70 C of subcooling to 2 5% steam quality, at pressures

2 1

of 28 to 90

bars,

and at mass fluxes up to 4 600kg-m s .

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 2 4 . 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.


30/66

-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.


31/66

-27-

Typical vibration damping results are shown on Figure 27

for a simply supported 12.7 mm diameter heat exchanger

tube.

T he net viscous damping due to water decreases

with frequency.

We are now preparing tests to study the dynamics of the

tube-totube support interaction. T his 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 Vibra ti on and Relate d Studie s Curre ntly Under wa y

We have discussed above two typical vibration studies

related to nuclear components. Other experimental and

analytical investigations are underway, such as:

1) V ibration vs Fretting Relationship: T his is the

subject of an extensive program for both nuclear fuel

and heat exchanger materials

3 1

'

3 2

. T he effects of several

parameters such as frequency, clearance, amplitude and

impact forces are investigated in both laboratory and

realistic environments.

2) A nalytical M odelling of the D ynamics of T ube-to-

S upport I nteraction: A n analytical model is being deve-

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

impacting in heat ex chan gers

3 3

. It takes into considera-

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

rance.

3) V ibration of Heat E xchanger Tube in Liquid C ross-Flow :

This work

21

* is continuing. S everal different triangular

and square heat exchanger tube bundle geometries have


32/66

-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) V ibration of T ube B undles in T wo-Phase C ross-Flow:

We are preparing further experiments in support of steam

generator designs. A ir-water mixtures will be used to

simulate steam/water two-phase flow.

5) D ynamics of Flexible Cylinder in C onfined Flow:

Further experiments are underway particularly to explore

the dynamics and stability of flexible cylinders

subjected to two-phase axial flow.

6) N uclear Fuel D ynamic Parameters: T ests 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. C O N C L U D I N G R E M A R KS

It is concluded that, although there are still areas of

uncertainty, most flow-induced vibration problems can be

avoided. T his 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. A lthough some-

times difficult to analyse, vibration problems usually

require simple solutions.


33/66

-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.


34/66

- 3 0 -

REFERENCES

1. R.I.

Hodge,

J.E.

LeSurf,

J.W.

Hilborn,

"Steam Generator Reliability, The Canadian Approach",

Presented

at the XIX

Nuclear Congress

of

Rome, March

1974,

also Atomic Energy

of

Canada Limited Report

AECL-4471 (1974).

2. D.G.

Dalrymple, "Current Canadian

Use of

Explosive

Welding

for

Repair

and

Manufacture

of

Nuclear Steam

Generators", AECL Research and Development in

Engineering, Atomic Energy

of

Canada Limited Report

AECL-4427, Winter

1972.

3.

R.T.

Hartl en, "Recent Fi el d Experience with Flow-induced

Vibration

of

Heat Exchanger Tubes", Paper

No. 611 ,

International Symposium

on

Vibration Problems

in

Industry,

Keswick, U.K. 1973.

4.

R.I.

Hodge,

P.L. Ko, and A.O.

Campagna,

Personal Communication,

Aug. 1976.

5.

E.P.

Quinn, "Vibration

of

Fuel Rods

in

Para l le l Flow",

U.S. Atomic Energy Commission Report GEAP-4059 (1962 ).

6.

Y.N.

Chen, "Flow-induced Vibrations

in

Tube Bundle Heat

Exchangers with Cross

and

Pa ra l lel Flow. Part

1:

Parallel

Flow", Symposium

on

Flow-induced Vibration

in

Heat

Exchangers,

New

York: ASME

5 7-66 (19 70 ) .

7.

M.P. Pal'doussis, "St abil it y of Flexible Slender Cylinders

in Pulsatile Axial Flow", J. of Sound and Vibration,

42 (1 ) , 1-11 (1975) .

8. M.P. Padoussis, "The Dynamical Behaviour of Cylindrical

Structures in Axial Flow", Annals of Nuclear Science and

Engineering, Vol. 1, No. 2, pp 83-106 (1 974) .

9.

M.P. ?ad?ysif , "Dynamics of Cylindrical Structures

Subjected to Axial Flow:, J. of Sound and Vibration,

Vol. 29, No. 3, pp. 365-385 (1973).

10.

M.J. Pettigrew, M.P. Padouss is , "Dynamics and Stabil i ty

of Flexible Cylinders Subjected to Liquid and Two-Phase

Axial Flow in Confined Annul ", Paper D2/6, 3rd Interna-

tional Conference on Structural Mechanics in Reactor

Technology, London, U.K. Sept, 1-5, 1975, also Atomic

Energy of Canada Limited Report AECL-5502 (1975).


35/66

-S i -

11. M.P. Padoussis, "Mathematical Model for the Dynamics

of an Articulated String of Fuel Bundles in Axial Flow",

Paper D2/5 presented at the 3rd International Conference

on 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 if fes , 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 in

Mechanical Systems", Academic Press, N.Y., 1963.

15. D.J. Gorman, "The Role of Turbulence in the Vibration

of Reactor Fuel Elements in Liquid Flo"", Atomic

Energy of Canada Limited Report AiCL-3371 (1969).

16.

D.J. Gorman, "An Analytical and Experimental

Investigation of the Vibration of Cylindrical Reactor

Fuel Elements in Two-phase Parallel Flow", J. Nuclear

Science Engineering 44. 277-290 (1971).

17. J.R. Reavis, "Vibration Correlation for Maximum Fuel-

element Displacement in Parallel Turbulent Flow",

J. Nuclear Science Engineering 38, 63-69 (1969) .

18. D.J. Gorman, "Experimental and Analytical Study of

Liquid and Two-Phase Flow-Induced Vibration in Reactor

Fuel Bundles", ASME Paper 75-PVP-52, 2nd National Congress

on Pressure Vessels and Piping, San Francisco, June 23-27,

19 75.

19. M.J. Pettigrew and D.J. Gorman, "Experimental Studies

on Flow Induced Vibration to Support Steam Generator

Design, Part 1: Vibration of a Heated Cylinder in Two-

Phase Axial Flow", Paper No. 42 4, International

Symposium on Vibration Problems in Industry, Keswick,

U.K. 1973, also Atomic Energy of Canada Limited Report

AECL-4514 (1973).

20.

S. Mirza and D.J. Gorman, "Experimental and Analytical

Correlation of Local Driving Forces and Tube Response in

Liquid Flow Induced Vibration of Heat Exchangers",

Paper F6/5, 2nd Conference on Structural Mechanics in

Reactor Technology, Berlin 1973.


36/66

- 3 2 -

2 1.

M.J. Pettigrew, J.L. Platten, Y. Sylvestre,

Experimental Studies on Flow Induced Vibration to

Support Steam Generator Design, Part II: Tube

Vibration Induced by Liquid Cross-flow in the Entrance

Region of a Steam Generator . Paper No. 4 2 4 , International

Symposium on Vibration Problems in Industry, Keswick, U.K.

1973,

also Atomic Energy of Canada Limited Report

AECL-4515

(1973).

2 2 . M.J. Pettigrew, D.J. Gorman, Experimental Studies on

Flow Induced Vibration to Support Steam Generator Design,

Part iii: Vibration of Small Tube Bundles in Liquid

and Two-phase Cross-flow , Paper No. 4 2 4 , International

Symposium on Vibration Problems in Industry, Keswick,

U.K. 1973 , also Atomic Energy of Canada Limited

Report AECL-5804

(1977).

2 3 . H.J. Connors, Jr., Fluidelastic Vibration of Tube Arrays

Excited by Cross Flow , Proceedings of the Symposium

on Flow Induced Vibration in Heat Exchangers, ASME

Winter Annual Meeting, New York, Dec. 1, 1970, pp.4 2-56.

2 4 . D.J. Gorman, Experimental Development of Design Criteria

to Limit Liquid Cross-Flow Induced Vibration in Nuclear

Reactor Heat Exchange Equipment , J. Nuclear Science and

Engineering 6 1, 324 -336 (1976).

2 5. Y.N. Chen, Fluctuating Lift Forces of the Karman Vortex

Streets on Single Circular Cylinders and in Tube Bundles,

Part 1: The Vortex Street Geometry of the Single Circular

Cylinder, 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 ) ,

603-62 8 May 1972.

2 6 .

P.R. Owen, Buffeting Excitation of Boiler Tube Vibration ,

J. Mech. Eng. Sci. 7 (4 ), 4 3 1-4 3 9, 196 5.

2 7. E.R. Darnley, The Transverse Vibration of Beams and the

Whirling of Shafts Supported at Intermediate Points ,

Phil.Mag. Vol. 41 (241),56 Jan. 1921.

2 8. I.E. Oldaker, A.D. Lane, M.P. Pal'doussis and C F . Forrest,

An Overview of the Canadian Program to Investigate

Vibration and Fretting in Nuclear Fuel Assemblies ,

May 1974 . 73 -CSME-89, EIC-74-Th; Nuc. 2 Engineering

Journal, Fall,19 74 .


37/66

- 3 3 -

29. D.J. Jagannath, "A Model fer Vibration of Nuclear Fuel

Bundles" (to be published).

30. M.J. Pettigrew and R.B. Turner, "The In-reactor

Vibration Behaviour of Nuclear Fuel", Paper D3/7, Inter-

national Conference on Structural Mechanics in Reactor

Technology, 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 and

Heat Exchanger Tube Fretting", published in AECL

Research 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 Response

of a Heat Exchanger Tube with Intermittent Baff le Contacts",

Nucl. Engrg. and Design, 36, 81-90 (1976).


38/66

-35-

FI G U R E la: Fretting-Wear of Steam G enerator Tubes:

Fretting Damage at Midspan.


39/66

-36-

Figure lb: Frettlng-Wear of Steam Generator Tubes;

Fretting Damage and Hole at Support

Location.


40/66

-37-

FI G U R E 2: T ypical Example of Heat E xchanger Tube Fretting-

Wear,


41/66

-38-

FIG U RE 3: Fretting Damage on Gentilly-1 Fuel Bundle.


42/66

NTILLY

Nuclear Power Station

O R D I N A R Y W A T E R I

.

S T E A M

R I V E R W A T E R l i i ii ii H E L f U M G A S

H E A V Y W A T E R M O D E R A T O R

T U R B I N E - G E N E R A T O R B U I L D IN G

E L E C T R I C I T Y

R IV E R W A T E R IN T A K E B A Y

R IV E R W A T E R O U T L E T

i

VO

I

FIGURE 4: Sim plifie d Flow Diagramof CANDU-BLW St at io n.


43/66

G6NTILLY 1

SECTION THROUGH CENTRE OF FUEL BUNDLE

COUPE TRANSVERSALE PE LA

GRAPPE COMBUSTIBLE

O

I

CENTRALIZING PADS

SPACERS

BEARING PADS

UO2 FUEL PELLETS

ZIR.CALOY 4 SHEATH

DELINEATING DISC

END CAP

END PLATE

PATTES DE CENTRAGE

CALES D'ECARTEMENT

PATTES D'APPUI

PASTILLES DE U O j

GAINE EN ZIRALOY 4

DISQUES Of SEPARATION

BOUCHON D'EXTRMIT

PLAQUE D'EXTREMITE

FIGURE 5: Gentilly-1 Fuel Bundle.


44/66

-41-

O U T L E T

F U E L B U N D L E

(^ Z7kg x 1OJ

10 .4 cm

CENTRAL

SUPPORTING

TUBE

PRESSURE

TUBE

S P R I N G

I S S E M B L V

SHIELD

PLUG

INLET

FIGURE 6 : S k e tc h of CANDU-BLW F u e l C h a n n e l


45/66

- 4 2 -

GENTILLY-

CALANDRIA

ABSORBER

SUIDE TUBE

D

2

0

D

2

0

B O O S T E R R OD

N O Z Z L E

T O P V I E W

B O O S T E R R OD

O U T L E T N O Z Z L E

C A L A N D R I A T U B E

P R O T E C T I V E S H R O U D

G U I D E T U B E

FIG U R E 7a: M odification with Protective Shroud.

FIGURE 7: Control Absorber Guide Tube in G en ti l ly - 1 Reactor Core.


46/66

REACTOR BUILDING

I

I

MODERATOR

J

| | ORDINARY WATER

HEAVY WATER

HELIUM GAS

LAKE WATER

TURBINE.GENERATOR BUILDING

FIGURE8: Simplified Flow DiagramofCANDU-PHW Station.


47/66

- 4 4 -

M A N W A Y

(ALSO IN WATER BOX|

TUBE BUNDLE

PRIMARY (IN TUBES)

SECONDARY (IN SHELL)

D O W N C O M E R O R

F E E D W A T E R N O Z Z L E

PRIMARY CHANNEL COVER

DIVIDE* PLATE

BEND RADIUS OF TUBES

BAFFLE OR LATTICE BAR

TUBE SUPPORTS

PREHEAT SECTION

(OR IEG IN U SHELL UNITSI

TUBE SHEET CLADDING

WATER BOX

FIGURE 9 : Ty pical Nuclear Steam G ene rato r.


48/66

-45-

FIGURE 10:

Clamped-Free Cylinder with

Bullet-Shaped Downstream End

Experiencing 4th Mode Buckling

In Liquid Flow.


49/66

E

o

CI

to

o

a

o

I E

I

30 H

25

20

15

10

10

LEGEND

PREDICTED rms DISP

MEASURED rms OISP

TOTAL MASS FLOW

RATE = 0.8fc k g / s

I

40

0 30

S I M U L A T E D Q U A L I T Y { )

F I G U R E

11

M E A S U R E D A N D P R E D I C T E D V I B R A T I O N A M P L I T U D E v s S I M U LA T E D S T E AM Q U A L I T Y

N

T W O - P H A S E A X I A L F L O W '


50/66

- 4 7 -

0 0

0 . 5

3 .

0 .3

.2

0 .

MASS FLUX;

47

g / ( s - c m

2

)

PRESSURE;

D

2.86 MN/m

2

A 3.55 MN/m

2

O 4.23 MN/m

2

O 5 . 6 1 M N / m

2

STEAM QUALITY;

TO

65 MAX.

1

b

9

12

FLOW VELOCITY

(m/s )

15

FIGURE 12: Effect of Steam Quality and Pressure.


51/66

- 43 -

V r

1 0 -

1

i o -

2

l u

3

4

1

1

W

5

c a

i

Ai

BURGREEN

e t a l

QUINN

SOGREAH

ROSTRM

&

ANDERSON

PAIDOUSSIS

1

1 0 -

4

I D

3

1 0

2

U i . 8 5 L

3

- V ( E I ) - 8

5 x 1 0 -

4

K a *

1 0 -

1

+ M L

2

U

2

/ E I J |

D

2

-

2

1 + 4M/m

F I G U R E13 A G R E E M E N T B E T W E E N M E A S U R E D A N D P R E D I C T E D V I B R A T I O N

R E S P O N S E IN X I A L F L O W U S I N G P A I O O U S S I S S E M I -

E M P I R I C A L E X P R E S S I O N


52/66

- 4 9 -

a.

en

t

C "=C

CO 2 :

= 3

LL J

SO

x o

1 .5

1 .0

0 .5

PRESSURE: Q 4 . 2 3 MN /m

2

O 5 .61 MN/m

2

I

I

I

50 100 150

MASS FLUX (g/(s-cm

2

))

200

FIGURE 14 : Effec t of M ass F lux and P ressure.


53/66

moo

P/d

C CONNORS

1.41

G GORMAN 8 M I R Z A 1.33

PI PETTIGREW 1. 5

P2 PETTIGREW 1. 6

f(Hz)

11.8- 40

38

30

17

S

0.008- 0.16

0.112

0.156

0.168

100

10

A L I Q U I D FLOW

^ ^ 3 ^ TWO PHASE:

O A t > p O

A I R

X ^ S IN STAB ILIT Y NOT

O S I N G L E R O W

A N O R M A L T R I A N G U L A R

> P A R A L L E L T R I A N G U L A R

D N OR MA L SQU A R E

O ROTATED SQUARE

V : Approach velo cit y normal-

ized for uniform flow

v e l o c i t y -

O

I

0 .1

F I G U R E 1 5 :

1. 0

10

100

Non-Dimensional Presentation of Experimental Thresholds

for Fluidelastic Instabilities.

1000


54/66

- 5 1 -

v fry

5

fr

VORTEX SHEDDING

S = f D / V

2) V 0

BUFFETING

OO

oo

TURBULENT EDDIES

CONTROLLED BY GEOMETRY

FIG U R E 16: Postulated Mechanisms for Periodic E xcitation.


55/66

T 1.00

UJ

a

i

a

z:

1.00

0.75

0.50

0.25

0

1

1

1

cTL

fi

/

^

rtO

/

/

O

1

1

\ j O

1

1

'

o

i

1

0 . 2 0 . 4 0 . 6

MEAN WATER VELOCITY ( m /s )

0 .8

to

I

FIGURE 17: V ibration Response of Fi rs t Upstream Tube In Liquid Cross-F low

20

.


56/66

-53-

1.0m

11

12

r

:

o

CO

I

CO

1

OUTLET

CROSS FLOW

( 2 0 %

QUALITY)

333 kg/5n*s>

\ CLEARANCE

HOLES

(PINNED ,

SUPPORTS)

FIXED SUPPORTS

I

PARALLEL

FLOU

* 210

kg/m

2

s

(SATURATED

TO20

QUALITY)

INLET

CROSS FLOU

(SATURATED)

359

kg/4n

z

.s>

P

FI G U R E 18 : T ypical Steam Generator Tube and Flow Conditions.


57/66

- 5 4 -

M M m CROSS F U I E IC I m i

M

SUPPORT

* 0

MS . 0 0 9

E W T I O N

.0

FOilCES .114

(H )

<

1

.016

.019

.25

012

OSS

164

195

. 0 0 7

. 1 1 1

. 2 1 5

. 1 0 6

TOTAL

. 1 9 0

4

. 0 2 2

.0

. 0 6 0

. 0 2 6

. 0 6 8

M O D E

1

3

I

4

M O D E S 1

F R E Q U E N C Y

Hi

3 4 . 7

t . S

5 9 . 7

7 3 . 0

T O

4

TOTAL

RMS

AMPLITUDE

HINDOU PARALLEL

FLO

EXCITATION

ODE

1

2

J

M O O E S 1

F R E Q U E N C Y

I

3 7 . 2

4 7 . 7

4 9 . 6

T O 3

S U P P O R T 1

RMS

R E A C T I O N

F O R C E S

H

T O T A L

>

.mo

. 1 1 9

. 0 9 5

. 1 7 4 _

0

. 2 0 9

. 3 5 2

. 0 5

15

I0KL

MS 10

(HPLITUDE

. 2 0 0

. 3 5 2

. 0 9 0

.113

. 0 9 5

LENGTH( m )

FIGURE 1 9 : Example of Tube Response C al cu la ti o n.


58/66

-55-

S T A R T

11

DESIGN: GEOMETRY, FLOW CONDITIONS

CalculationofFlow DistributionandVelocities

EXCITATION MECHANISMS

Excitation Forcing Function

SYSTEM: TUBE DYNAMICS

Damping

,

Modes


59/66

I

FIGURE 2 1: Biaxir?. Accelerometer Probe for Heat Exchanger Tube Vibration Measurements.


60/66

- 5 7 -

147 .40m

1 4 6 . 7 9 m

1 4 0 . 5 1

Q-

1 3 9 . 2 7 m

13 8 .81m

1 3 6 . 8 9 m

13 6 .78m

1 3 6 . 4 0 m - = *

DECK PLATE

TOP CLOSURE

' ? OUTLET

HANGER

ROD

STRAIN GAUGE

LEADS

TOP INSTRUMENTED

BUNDLE

X

1

FUEL STRING

PRESSURE TUBE

(104mm I.D. )

'SPACER FOR LEADS

BOTTOM INSTRUMENTED

BUNDLE

STRAIN GAUGE

SPRING

CENTRAL SUPPORT

MIXER

STEAM INLET

WATER INLET

SG151

SG153

SG152

SGI

5

-SG3

SG2

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

SG191

SGI

9 3

G192

SGI

I I

SGI

13

SGI12

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

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

STRAIN GAUGE LOCATION

FIGU RE 2 2 : Stra in Gauge Instrumented

Fu e l S t r i n g I n s t a l l e d i n

U - l LOOD of

Reactor

NRU.


61/66

00

FIGURE 23: Details of Weldable Strain Gauge Instal lation on a Fuel Bundle


62/66

- 5 9 -

7 0

r -

5

7 5 100

P OW E R ( 3 )

60

55

~ 50

u

45

40

35

SG

1 3 U-118-II

SG

5

SG 12 14

SG15S17

SG

18S20

S3 151 U-118-I

X

SG 191 U-118-I

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

:

SHUT-DOWN

5

75

100

POWER()

FIGURE 24: Fuel Element Natural Frequency vs Reactor Power


63/66

7

u

e

o

r t t c u c N c r

FIGURE 2 5: Effect of Fuel History on Fuel Element ViDration Behaviour

[SG No . 15, Liquid Flow, U- 118-Il]


64/66

- 61 -

FI G U R E 26: Heat Exchanger Tube Immersed in Trough to

Study Vibration Damping.


65/66

-62-

o . i o r

1/1

LU

_ l

z

o

to

z

L L J

o

o

o

a.

0.01

0.001

y= 0.756.X-

TUBE

12.7mm O.D .

304 S . S .

TEMP.

19.4-C

O AIRMEDIUM

WATER MEDIUM

NET VISCOUS DAMPING

10

100

fn(FREQUENCY) Hz

F I G U R E 2 7 : T y p i c a l T u be V i b r a t i o n D a m p in g R e s u l t s S ho w in g

t h e E f f e c t o f F r e q u e n c y .


66/66

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has been assigned to this series of reports.

T o identify individual docum ents in the series

we have assigned an AECL-number.

Please refer to the AECL-number when

requesting additional copies of this docum ent

from

Scientific Document Distribution Office

Atomic Energy

of

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flow-induced vibration of nuclear power station components

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