écoulements diphasiques

8/9/2019 coulements Diphasiques

1/34

22.06

Engineering

of

Nuclear

Systems

MIT

Department

of

Nuclear

Science

and

Engineering

NOTES

ON

TWOPHASEFLOW,BOILINGHEATTRANSFER,ANDBOILINGCRISES

IN

PWRs

AND

BWRs

Jacopo

Buongiorno

AssociateProfessorofNuclearScienceandEngineering


2/34

Definitionofthebasictwophaseflowparameters

In

this

document

the

subscripts

v

and

indicate

the

vapor

and

liquid

phase,

respectively.

Thesubscriptsgandfindicatethevaporandliquidphaseatsaturation,respectively.

AvVoidfraction: Av A

M Av v vStatic

quality: xst

Mv M Avv A

m

v A

v v v vFlow

quality:

x

mv m vvAvv vAvSlip

ratio: S

v

v

Mixture

density: m v (1)

Flowquality,voidfractionandslipratioaregenerallyrelatedasfollows:

1

1xv1 S

x

Figures1and2showthevoidfractionvsflowqualityforvariousvaluesoftheslipratioandpressure,

respectively,

for

steam/water

mixtures.


3/34

In22.06weassumehomogeneousflow,i.e.vv=vorS=1. Thisassumptionmakesitrelativelysimpleto

treattwophasemixtureseffectivelyassinglephasefluidswithvariableproperties. IfS=1,itfollows

1

x

1

ximmediatelythatxst=xand,aftersometrivialalgebra, .

m v

Notethattheassumptionofhomogeneousflowisveryrestrictive,andinfactaccurateonlyunder

limited

conditions

(e.g.

dispersed

bubbly

flow,

mist

flow).

In

general,

a

significant

slip

between

the

two

phases

is

present,

which

requires

the

use

of

more

realistic

models

in

which

vvv. Suchmodelswillbediscussedin22.312and22.313.

Twophaseflowregimes

With

reference

to

upflow

in

vertical

channel,

one

can

(loosely)

identify

several

flow

regimes,

or

patterns,

whoseoccurrence,foragivenfluid,pressureandchannelgeometry,dependsontheflowqualityand

flowrate. ThemainflowregimesarereportedinTable1andshowninFigure3. Notethatwhatvalues

offlowqualityandflowratearelow,intermediateorhighdependonthefluidandpressure. In

horizontal

flow,

in

addition

to

the

above

flow

regimes,

there

can

also

be

stratified

flow,

typical

of

low

flowratesatwhichthetwophasesseparateundertheeffectofgravity.

Table1. Qualitativeclassificationoftwophaseflowregimes.

Flowquality Flowrate Flowregime

Low Lowandintermediate Bubbly

High

Dispersed

bubbly

Intermediate Lowandintermediate Plug/slug

High Churn

High High Annular

High

(postdryout)

Mist


4/34

Morequantitatively,onecandeterminewhichflowregimeispresentinaparticularsituationofinterest

resortingtoanempiricalflowmap(seeFigure4). Notethatsuchmapsdependonthefluid,pressure

andchannelgeometry,i.e.,thereisnouniversalmapfortwophaseflowregimes. However,there

existmethodstogenerateaflowmapforaparticularfluid,pressureandgeometry. Thesemethodswill

be covered in 22.312 and 22.313.

Typical configuration of (a) bubbly flow, (b) dispersed bubbly (i.e. fine bubbles

dispersed in the continuous liquid phase), (c) plug/slug flow, (d) churn flow,

(e) annular flow, (f) mist flow (i.e. fine droplets dispersed in the continuous vapor

phase) and (g) stratified flow. Note: mist flow is possible only in a heated channel;stratified flow is possible only in a horizontal channel.

a b c

g

d e f

Image by MIT OpenCourseWare.


5/34


6/34

L 1 G 2

Pfric

0 f D 2

dz

(3)

e m

L

Pgrav

m gcosdz (4)0

Notethattheaboveequationsareformallyidenticaltothesinglephasecasewiththemixturedensity,

m=v+(1),usedinsteadofthesinglephasedensity. ThefrictionfactorinEq.3canbecalculated

fromasinglephasecorrelationandusingtheliquidonlyReynoldsnumber,Reo=GDe/.

For

each

abrupt

flow

area

change

in

the

channel

(again

including

the

inlet

and

outlet),

the

associated

pressurelossisthesumofanaccelerationtermandanirreversiblelossterm:

Pform Pform,acc Pform,irr 1

(G22 G1

2 )K G 2

(5)2 2m m

wherethesubscripts1and2refertothelocationimmediatelyupstreamanddownstreamofthe

abrupt

area

change,

respectively.

Boilingheattransfer

Boilingisthetransitionfromliquidtovaporviaformation(ornucleation)ofbubbles. Ittypically

requiresheataddition. Whentheboilingprocessoccursatconstantpressure(e.g.intheBWRfuel

assemblies,

PWR

steam

generators,

and

practically

all

other

heat

exchangers

in

industrial

applications),

theheatrequiredtovaporizeaunitmassofliquidishfghghf,whichcanbefoundinthesteamtables.

Writingthe(YoungLaplace)equationforthemechanicalequilibriumofabubblesurroundedbyliquid,it

canbeshownthatthevaporpressurewithinthebubblemustbesomewhathigherthanthepressureof

thesurroundingliquid. Itfollowsthatthevapor(andliquid)temperaturemustbesomewhathigher

thanthesaturationtemperature,Tsat,correspondingtotheliquid(orsystem)pressure. Usingthe

ClausiusClapeyron

equation

to

relate

saturation

temperatures

and

pressures,

it

can

then

be

shown

that

themagnitudeofthesuperheat(TnucleationTsat)requiredtosustainthebubbleisinverselyproportionalto

theradiusofthebubbles,rbubble:

1T

nucleation Tsat (6)r


7/34

etc.)isfullofmicrocavities,naturallypresentduetoroughness,corrosion,etc. Therefore,airorvapor

trappedinthosecavitiesserveasnucleationsitesforthebubblesandensureinitiationoftheboiling

process.

The

bottom

line

is

that

one

needs

to

raise

the

temperature

of

the

surface

a

little

bit

above

Tsatifboilingistobeinitiatedandsustained. ForarigorousderivationofEq.6andmoredetailsabout

bubblenucleation,refertoanyboilingheattransfertextbook(e.g.Boiling,CondensationandGasLiquid

FlowbyP.B.Whalley,OxfordSciencePublications,1987).

PoolBoiling

Considerasimpleexperimentinwhichwater(orotherfluid)boilsofftheuppersurfaceofaflatplate.

The

plate

is

connected

to

an

electric

power

supply,

and

thus

is

heated

via

Joule

effect.

This

situation

is

referredtoaspoolboiling(vsflowboiling)becausethepooloffluidabovetheheaterisstagnant. Inthis

experimentwecontroltheheatfluxq"(viathepowersupply)andwemeasurethewalltemperatureTw

(viaathermocouple). Thenaq"vsTwTsatcurvecanbeconstructedfromthedata. Thiscurveisknown

astheboilingcurveandisshowninFig5.

)/(

2mWq

505 1500

106C

O

A

B

Tw Tsat (C)

Figure5. Qualitativeboilingcurveforwateratatmosphericpressure(Tsat=100C)onaflatplate.

Asoneprogressivelyincreasestheheatflux,severalregions(orheattransferregimes)canbeidentified

from

this

curve.

A

depiction

of

the

physical

situation

associated

with

these

heat

transfer

regimes

is

shown

in

Fig

6.

OA

ThewalltemperatureisnotsufficientlybeyondTsattoinitiatebubblenucleation. Inthisregiontheheat

from the wall is transferred by single phase free convection


8/34

Manybubblesareformedandgrowatthewall,anddetachfromthewallundertheeffectofbuoyancy.

Thisheattransferregimeiscallednucleateboiling. Thebubblescreatealotofagitationandmixingnear

the

wall,

which

enhances

heat

transfer.

As

a

result,

nucleate

boiling

is

a

much

more

effectivemechanismthanfreeconvection,assuggestedbythehigherslopeoftheboilingcurveinthisregion.

BC

Atacritical (high)valueoftheheat flux,therearesomanybubblescrowdingthewallthattheycan

mergeandformacontinuousstablevaporfilm. Thus,thereisasuddentransitionfromnucleateboiling

to

film

boiling.

This

sudden

transition

is

called

Departure

from

Nucleate

Boiling

(DNB),

or

Critical

Heat

Flux

(CHF),

or

burnout,

or

boiling

crisis,

and

is

associated

with

a

drastic

reduction

of

the

heat

transfer

coefficient

because

vapor

is

a

poor

conductor

of

heat.

Consequently,

the

wall

temperature

increasesabruptlyanddramatically(to>1000C),whichmayresultinphysicaldestructionoftheheater.

Candbeyond. Thisisthefilmboilingregion. Heattransferfromthewalloccursmostlybyconvection

withinthevaporfilmandradiationacrossthevaporfilm.

Intheabsenceofanexperiment,thevarioussegmentsof theboilingcurvecanalsobepredictedby

Newtonslawofcooling, q"h(Tw

Tsat

),withtheheattransfercoefficient,h,givenbythefollowing

empiricalcorrelations:

OA Si l h f ti f fl t l t b di t d b th Fi h d d S d

Film boiling (C and beyond)

The heat transfer regimes in pool boiling.

Onset of nucleate boiling (A)

Nucleate boiling (A B)

Free convection (O A)

Image by MIT OpenCourseWare.


9/34

In this correlation (valid for 107


10/34

Flowboiling

The

situation

of

interest

in

nuclear

reactors

is

flow

boiling.

Consider

a

vertical

channel

of

arbitrary

cross

sectional

shape

(i.e.

not

necessarily

round),

flow

area

A,

equivalent

diameter

De,uniformlyheated

(axiallyaswellascircumferentially)byaheatfluxq". LetTinbetheinlettemperature(Tin


11/34


12/34

transfermostlyoccursthroughnucleationanddetachmentofbubblesatthewall,while intheforced

evaporationsubregiontherearetypicallynobubbles,andheattransferoccursmainlythruconvection

within

the

liquid

film

and

evaporation

at

the

liquid

film/vapor

core

interface.

The

heat

transfer

coefficientishighinbothsubregions. ThephysicalsituationisshowninFig8.

q"

q"

(a) (b)

Figure

8.

(a)

Nucleate

boiling

(typical

of

bubbly

and

plug

flow),

(b)

Forced

evaporation

(typical

of

annularflow).

Klimenkoscorrelationcomprisesthefollowingequations:

Nucleateboilingdominatedsubregion:

hLc

4.9103

Pem0.6

Prf0.33

PLc

0.54

(8)kf

Forced

evaporation

subregion:

0.2

hLc 0.6 1/ 6

g

k

0.087Rem Prf (9)

f f

Where

in

Eq.

8,

P

is

the

operating

pressure,

PrfistheliquidPrandtlnumberandthefollowingdefinitions

areusedforPem,RemandLc:

q"Lcfcp,fPe m

h fgg k f


13/34

Klimenko recommends use of the following criterion to determine if nucleate boiling or forced

evaporation

dominates

at

any

given

location

in

the

channel:

IfNCB1.6104,heattransferisforcedevaporationdominateduseEq.9

h

1/ 3

whereN

G

q

fg

"

1x

g

f 1

g

f

CB

Note thatKlimenkoscorrelation isvalidup to thepointofdryout,butnotbeyond it. Dryout isan

undesirable

condition

(asocalledboilingcrisis)becausetheheattransfercoefficientdropsdrastically

andthusthewalltemperaturerisesabruptly,whichcanresultindamageofthewall. SincePWRsand

BWRsaredesignednottoreachthepointofdryout,Klimenkoscorrelationisagoodpredictivetoolto

estimatetheheattransfercoefficientinourapplications.

Forthesakeofsimplicity,theabovediscussionhasignoredthermalnonequilibriumeffects. Inreality,

boiling

starts

at

the

wall

for

zTsat)whiletheliquiddropletsareatsaturation. ThisregionisimportantinBWRfuel

assemblies ifthepointofdryout isexceeded(e.g.duringanaccident). Postdryoutwillbecoveredin

22.312and22.313.


14/34

Boiling crises in LWRs

Jacopo BuongiornoAssociate Professor of Nuclear Science and Engineering

22.06: Engineering of Nuclear Systems


15/34

the thermal limits associated with the

Ex lain how the thermal limits are verifiedin core design:

- DNBR for PWR

- CPR (for BWR)

2


16/34

remove before it experiences a thermal crisis,i.e., a sudden and drastic deterioration of itsability to remove heat from the fuel.

,overheats and fails, thus releasing fission

.

To understand the thermal crisis we need tounderstand boiling.

3


17/34


18/34

Thermal-hydraulics of PWR Core (2)

q

Hot channel

Temperature

Subcooled boiling in

Tsat

Tco

Tb

z

5


19/34


20/34

Thermal-h draulics of PWR Core 4q (T ,G, P)Heat flux to cause DNB depends on Tb, G and P DNB b

Heat flux Heat flux

DNB

z

q

qDNB . .

q the US

7


21/34

Thermal-h draulics of PWR Core 5Correlation (Tong 68) to calculate qDNB

qDNB

KTon

G0.4

0f

.

.6hfg

e

Where:

KTong

[1.767.433xe

12.222xe

2 ]

p,

sat

bx

< 0 in a PWRe

hfg


22/34

Thermal-h draulics of BWR CoreFuel pin

CoolantChannel

16.2 mm

12.3 mm

geometryq

Average or hot

channel

Temperature

Saturated boiling inTco

Tsat

Tb

z 9


23/34

Thermal-h draulics of BWR Core 2q

Dryout (thermal crisis)in hot channel

Dryout of the

liquid film in

annular flow

Clad tem erature

increases sharplywhen dryout occurs

z

10

Temperature

Tb

co

Tsat


24/34


25/34

Thermal-h draulics of BWR Core 4

Correlation (CISE-4) to calculatexcr

Ph z

x

acrP zbw

Where:

cr

1/ 3

b0.199(Pcr

/ P1)0.4GDe

1.4

Note:

P is the thermodynamic critical pressure of water (22.1 MPa)

The units for G and De must be kg/m2-s and m, respectively


26/34


27/34

Boiling demos

Jacopo BuongiornoAssociate Professor of Nuclear Science and Engineering

22.06: Engineering of Nuclear Systems


28/34

Boilin a sim le ex erimentPool boiling of water at 1 atm. The current delivered to

.

Power su l

Electric resistance of the

wire

RIq 2

Water q

L

Wire LrwHeat flux at the

Wire radiuswire surface

15


29/34

crisis N or

Boiling a simple experiment (2)Plot of wire temperature vs. heat flux (the boiling curve)

/ 2mWq Boilin crisis or DNB or CHF

Film Boiling106

Burnout

typically

occurs

Nucleate Boiling

ONB

)( CTT satw

Main message: Nucleate boiling = good, DNB = bad 16


30/34

Lets run the demo!

18


31/34


32/34


33/34

-Injection of air into column of water.

Air compressor

Injection valve

Watch how the flow pattern changes as air flow is increased21


34/34

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22.06 Engineering of Nuclear Systems

Fall2010

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