AECU5543

ATOMIC ENERGY W j B & LTNERGIE ATOMIQUEOF CANADA LIMITED Y j f i j f DU CANADA LIMITEE

FORCED CONVECTIVE TRANSITION BOILING

REVIEW OF LITERATURE AND COMPARISON

OF PREDICTION METHODS

by

D.C. GROENEVELD and K.K. FUNG

Cha'k River Nuclear Laboratories

Chalk River, Ontario

June 1976

FORCED CONVECTIVE TRANSITION BOILING

REVIEW OF LITERATURE AND

COMPARISON OF PREDICTION METHODS

by

D.C. Groeneveld and K.K. Fung*

*Graduate s tudent , University of Toronto

Advance Engineering Branch

Chalk River Nuclear Laboratories

Chalk River, Ontario

June 1976

AECL-5543

Ebull i t ion de transit ion dans des conditions convectives

forcées: revue de la l i t té ra tu re et comparaison

des méthodes da prédiction

par

D.C. Groeneveld et K.K. Fung*

•'Etudiant gradué, Université de Toronto

Résumé

Ce rapport passe en revue les informations publiées concernant

le transfert de la chaleur en ebul l i t ion de transit ion dans des conditions

convectives forcées. On a constaté que les données relatives à 1 'ebul l i t ion

de transit ion n'ont été obtenues que dans une gamme limitée du conditions

et nombreuses sont celles considérées comme peu sûres. Ces données ne

permettent pas d'effectuer de corrélat ion; cependant, des tendances

paramétriques peuvent en être extrai tes.

Plusieurs auteurs ont proposé des corrélations valables dans la

région de 1'ebul l i t ion de t ransi t ion. Cependant, la plupart de ces

corrélations ne sont valables que dans une gamme étroi te de conditions.

Une comparaison avec ces données a montré, en générais un mauvais accord.

La corrélation de Hsu est provisoirement recommandée pour les faibles débits

et pressions.

L'Energie Atomique du Canada, LimitéeLaboratoires Nucléaires de Chalk River

Chalk River, Ontario

J'.iin 1976

AECL-5543

FORCED CONVECTIVE TRANSITION BOILING

REVIEW OF LITERATURE AND

COMPARISON OF PREDICTION METHODS

by

D.C. Groeneveld and K,K.. Fung*

ABSTRACT

This report reviews the published information on transition

boiling heat transfer under forced convective conditions. It was found

that transition boiling data have been obtained only within a limited

range of conditions and many data are considered unreliable. The data do

not permit the derivation of a correlation; however the parametric trends

can be isolated from the data.

Several authors have proposed correlations valid in the

transition boiling region. Most of the correlations are valid only

within a narrow range of conditions. A comparison with the data <shows

that in general agreement is poor. Hsu's correlation is tentatively

recommended for low flows and pressures.

^Graduate student, University of Toronto

Advance Engineering Branch

Chalk River Nuclear Laboratories

Chalk River, Ontario

June 1976 AECL-5543

CONTENTS

Page

ABSTRACT

INTRODUCTION 1

MECHANISM OF TRANSITION BOILING 4

Pool Boiling 4

Forced Convective Boiling 7

PARAMETRIC EFFECTS 8

Effect of Mass Flux 8

(a) Subcooled or Low Quality Region 8

(b) High Quality Region 10

Effect of Quality 12

Effect of Pressure 14

Effect of Subcooling 14

Effect of Surface Condition 16

Effect of Transient 17

T"'-;--ST.TION BOILING EXPERIMENTS 18

General 18

Electronic Feedback 18

Forced Convective Heating 20

Stabilizing Fluid Technique 22

Transient Technique 24

Transient Boiling Results 26

TRANSITION BOILING CORRELATIOUS 26

General 26

Correlations Containing Boiling and Convective Components 27

(a) Tong's Correlation 29

(b) Mattson's Correlation 29

(c) Ramu and Weisman's Correlation 34

(d) Hsu's Correlation 34

Phenomenological Correlations 38

(a) Tong and Young's Correlation 38

(b) Iloeje's Model 39

Page

Empirical Correlations 39

(a) Ellion's Correlation 39

(b) Berenson's Correlation for Poo.l Boiling 39

(c) McDonough, Milich and King's Correlation 40

Comparison with'Data 40

(a) Ellion's IV. f a * 42

(b) Plumper's Data 42

(c) Peterson's Data 45

(d) Ramu's Data 45

(e) FLECHT Data ' 45

Discussion 48

CONCLUSIONS AND FINAL REMARKS 50

REFERENCES 51

NOMENCLATURE 60

TABLES 63

INTRODUCTION

In heat transfer studies an increase in heated surface temperature

normally results in an increase in heat removal rate. There is however ane

exception: in transition boiling (the boiling mode occurring between

nucleate and film boiling) an increase in surface temperature usually results

in a decrease in surface heat flux. This is illustrated schematically in

figure 1 where the variation in surface heat flux is shown as a function of

heated surface temperature.

Nukiyama (1934) was the first one to postulate Lhe existence cf

the transition boiling mode. He gradually increased the heat flux of an

electrically heated platinum wire, submerged in a puol of stagnant water.

The. wire, after passing through the usual nucleate boiling region (BCD,

figure 1) experienced a sudden excursion in surface temperature, the so-

called boiling; crisis at the critical heat flux (D-F, figure 1). A subse-

quent reduction in surface heat flux showed the existence of a hysteresis

effect: the temperature reduced gradually to E where a subsequent reduction

in heat flux caused a jump back to the nucleate boiling region (EC, figure 1).

Since Nukiyama utilized a heat flux controlled system, he was unable to

observe the transition boiling curve*. Nevertheless he correctly postulated

the existence of such a curve.

As the name implies, transition boiling is an intermediate boiling

region. E .renson (1962) has provided a concise description of the transi-

tion boiling mechanism: Transition boiling is a combination of unstable

film boiling und unstable nucleate boiling alternately existing at

*Drew (1937) was the first one to observe the transition boiling curve.

CX.LxJ

:cLJJ

u_

CRITICAL HEAT FLUX

M I N SURFACE TEMPERATURE

FIGURE 1 BOILING CURVE

ami given location on a heating surface. The variation in beat transfer

rate with temperature is primarily a result of a change in the fraction of

time each boiling regime exists at a given location.

The transition boiling section of the. boiling curve is bounded by

the critical heat flux at D and the minimum heat flux at E. The critical

heat flux has been extensively studied and can be predicted by a variety of

correlations. The minimum heat flux has undergone less study; it is known

to be affected by flow, pressure, surface properties, fluid properties and

heated surface parameters.

In general, we can distinguish between three boiling processes:

i) pool boiling where boiling takes place on a submerged surface in a

stagnant pool of liquid; ii) flow boiling or forced convective boiling

where the flow can be either perpendicular to the heated surface (cross flow)

or parallel to the heated surface; and iii) transient boiling where a

transient in pressure, flow and/or heat flux takes place during pool boiling

or flow boiling. The system used in the boiling study can be either heat

flux controlled (electric or nuclear heating, no thermal inertia), tempera-

ture controlled (completely isothermal) or a combination of the above. In

practice, during a fast transient, the thermal inertia of the system becomes

important and the system's behaviour approaches that of a temperature

controlled system while during steady-state operation electrically or

nuclear heated systems behave like a heat flux controlled system (except for

operation at the critical heat tlux).

Although nuclear reactors normally operate at power levels well

below th£ critical power*, situations can be postulated where the critical

*The critical power is the power level corresponding to the firstindication of boiling crisis occurrence.

power is exceeded. In the thermal analysis of such postulated situations it

is usually assumed that, when the critical heat flux is exceeded, the heat

transfer mode will change from the very efficient nucleate boiling mode

directly to the inefficient film boiling mode. This assumption ignores the

contribution of the intermediate transition boiling mode. Also> in analyzing

the thermal behaviour of a hot surface which is being rewetted (such as may

occur during emergency core cooling of a nuclear reactor) it is often assumed

that film boiling is followed immediately by nucleate boiling, again ignoring

the transition boiling heat transfer mode. In both cases, the assumption that

film boiling rather than transition boiling occurs will result in an over-

prediction of the calculated temperature-time history. The purpose of this

report is to review the relevant transition boiling heat transfer literature "'

and present a comparison of available prediction methods with experimental data.

MECHANISM OF TRANSITION BOILING

In this section the physical mechanisms governing transition

boiling heat transfer are described. The mechanisms are illustrated in

figure 2a for pool boiling, in figure 2b for subcooled or low quality flow

boiling and in figure 2c for high quality flow boiling.

Pool Boiling (Figure 2a)

In a temperature controlled system the boiling crisis is reached

when the flow of vapour leaving the heated surface is so large that ii: pre-

vents a sufficient amount of liquid from reaching the surface to maintain the

heated surface in the wet condition. The phenomenon that limits the inflow

of liquid is the Helmholtz instability which occurs when a counterflow of

vapour and liquid becomes unstable. Zuber (1959) and Kutateladze (1966)

o

/V//7/////. /////.

( b ) FLOW BOILING (SUBCOOLED OR LOW <c) FLOW BOILING (HIGH QUALITY)(a) POOL BOILINGQUALITY)

FIG. 2 SCHEMATIC REPRESENTATION OF BOILING MODES

have derived equations for the CHF based on the Helmholtz instablity theory;

tlieir predictions agree with CHF values measured in pool boiling systems.

At surface temperatures in excess of the boiling crisis tempera-

ture, the heated surface will be partially covered with unstable vapour

patches (varying with space and time). The formation of such dry patches

will be accompanied by a drastic reduction in heat transfer coefficient; the

corresponding reduction in local vapour generation will permit t liquid to

momentarily rewet the heated surface. Liquid contact with the heated surfac2

will be frequent at low wall superheats but become less frequent at high wall

superheats (Ruckenstein (1964)). Bankoff (1962) and Stock (1960) have shown

that liquid-solid contact is of very short duration at high wall superheats:

an explosive formation of vapours occurred when the liquid contacted the

heated surface; the subsequent vapour thrust forced the liquid away trom the

surface*. There is no agreement in the literature regarding the question of

liquid-solid contact near the minimum of the boiling curve. Hesse (1973) and

Stock (1960) believed th^t the vapour film (that may be in violent motion)

will be maintained at wall superheats less than AT . while Berenson (1960)nun

and Ruckenstein (1964) believed that liquid-solid contact will occur up to

AT . .'<iin

Two mechanisms for liquid-solid separation at high wall superheat

ave postulated:

(a) thermodynamically contrclle.l separation (i.e., instantaneous

evaporation of the liquid at its maximum liquid superheat level) in which

case the pressure and the fluid properties govern the critical superheat level.

*Westwater (1955) did not believe that liquid-solid contact occurred intransition boiling; he did observe explosive formation of vapour whenthe liquid approached the heated surface.

(b) hydrodynarci.cally controlled separation (i.e. the vapour thrust is

greater than the forces directing the liquid towards the heated surface) in

which case the vapour superheat depends on properties or the fluid and the

heated surface.

During fast transients, where insufficient time is available to fully develop

the hydrodynamic forces, liquid-wall separation is expected to be thermo-

dynamically controlled while for low flows and low pressures, where suffi-

cient time is available and the volumetric expansion of the fluid near the

wall is large, liquid-wall separation is more likely to be hydrodynamically

controlled.

Forced Convective Boiling (Figures 2b and 2c)

In forced convective boiling the critical heat flux is no longer

controlled by Helmholtz instability; instead the. boiling crisis is due to an

agglomeration of bubble nucleation sites (Collier (1972), high subcooling),

bubble clouding (long (1965), slight subcooling or low quality) or film

depletion (Hewitt (1970), annular dispersed flow). Ellion (1954) studied

forced conve .tive transition boiling in subcooled water and observad

frequent raplacement of vapour patches by liquid. Although this may seem

similar to transition pool boiling as described previously, the introduction

of the cor.vective component v;ill improve the film boiling component by

reducing the vapour film thickness and changing the heat transfer mode from

free convection to forced convection. This will result in an increase in

<\> . and might also increase AT . (if AT . is hydrodynamicallym m -rim min

controlled).

8

In the high quality region (figure 2c) most of the heat transferred

during transition boiling will be d':e to droplet-wall interaction. Initially,

at surface temperatures just in excess of the boiling crisis temperature, a

significant fraction of the droplets will deposit on the heated surface but

at higher wall superheats the vapour repulsion forces vrould become signifi-

cant in repelling most of the droplets before they can contact the heated

surface. The repelled droplets will contribute to the heat transfer by

disturbing jhe boundary layer sufficiently to enhance the heat transfer to

the vapour. The heat transferred to the droplets was found to depend on

droplet size (Wachters (1965)), droplet impact velocity (Pedersen (1970)),

impact angle (McGinnis (1969)) and surface roughness (Wachters (1965)). These

variables also affect the minimum heat flux and corresponding surface temper-

ature.

PARAMETRIC EFFECTS

Effect of Mass Flux

(a) Subcooled or Low Quality Region

In the subcooled boiling region Ellion (1954) observed a shift in

the transition boiling curve upwards with an increase in flow (figure 3).

Note that $ was increased but that cj) . and AT . remained unchanged,max m m inxn

An increase in hmT, was also reported by Pramuk (Jordan (1968)) whoID

studied transition boiling in an agitated pool of water.

Kutateladze (1966) observed an increase in <f> and <b . with flowmax nun

for water (figure 4) and alcohol (figure 5). The ratio <j> /cb . for bothmax min

fluids remains approximately constant with an increase in flow, hence it seems

reasonable to expect h,n_ to increase at the same rate as d) or 6 . .TB max min

0 x 1 O " 5 10

5BTU

1..0

0 .5

5 FT/SEC

10 100

F I G , . 3 E F F E C T OF V E L O C I T Y ON B O I L I N G CURVE ( E L L I O N , 1 9 5 4 )P = 16 P S I A , A T S U B = 5 0 ° F

<p x 10

BTU

H - F T 2

- 5 15

5 -.

8 10

U, FT/SEC

FIG. 4 EFFECT OF FLOW VELOCITY ON 0 M A X AND 0 H | N; WATER BOILINGON GRAPHITE SURFACES (KUTATELADZE, 1966)

0

H

x 10

BTU

-FT

-5

T

4

3

2

5 10 15 20

U» FT/SEC

FIG 5 EFFECT OF FLOW VELOCITY ON 0 H A X FOR ISOPROPYL(KUTATELAOZE, 1966)

10

The increase in <j> was expected since a higher vpTocity penuits

more efficient removal of bubbles thus delaying the DNB phenomenon. A higher

velocity also improves filn boiling heat transfer and, because of a corres-

ponding higher turbulence level of the flow, is expected to improve wall-

liquid interaction in the rransition boiling region. From the above argu-

ments one would expect an increase in AT . as well as an increase in (f> . .

min m mThe expected effect is illustrated in figure 6.

(b) High Quality Region

Ramu (1975) studied forced convective transition p oiling at two

different flows; unfortunately at the higher flow, the quality tended to be

lower than at the lower flow. His results may be interpreted two ways:

i) there is no effect of mass flux on transition boiling, or ii) if there

is an effect of mass flux, it is compensated for by the difference in

qualities. It may well be that the velocity of the mixture is the important

——I as is the case in film boiling.

Pv Pz J

Toda (1972) studied transition boiling of a disc cooked by a spray

of droplets. He observed h to increase with droplet velocity. In an

analytical study Iloeje (1974) showed that at wall superheats typical of the

transition boiling region, the dominant heat flux is due to direct wall-

droplet interaction. At higher mass flows the droplet deposition flux is

higher resulting in an increase in h_D and <j> . with mass flow. Plummerla iuin

(1973) analyzed transient post-dryout data obtained in high quality steam-

water flow. For the low flows studied (G <. 105lb/h.fc2), uT . increasedmin

slightly with flow. The accuracy of the AT . value however is questionable*.

'•'private communication, General Electric Company

1.1

CD

oen

ccCJ

CJz—>oCD

zoX=31

| |

COCO

u_

°t—CJUJU_

O

oroC3UJ

ooCJmCO

UJ

1—CJUJ

zoCJ

aLLJCJccC3

CO

CD

12

Groenevelri (1973) studied the boiling curve for Freon-12 using a

heeit flux controlled system; he noticed that at high flows the usual excursion

in surface temperature at the boiling crisis (DF in figure 1) was absent;

instead the surface temperature continued to increase with surface heat flux

but the slope of the boiling curve (d<f>/dT) above the C H F was reduced, This

effect, which was also observed in water by this author and others

(Bertoletti (1964)) is illustrated in figure 7. Note that the CHF is not greatly

affected by the flow: depending on mass flow, quality and pressure it may

increase or decrease with flow. However, (f> . is strongly affected (because

of the improved h,,- at higher flows); at very high flows, the minimum

disappears completely.

Effect of Quality

High pressure CHF studies with Freon-12 and steam-water mixtures

(Bertoletti (1964), Groeneveld (1974)) show that, at high flows and high

qualities, the temperature jump at dryout is usually absent: the boiling

curve only displays a change in slope which may be accompanied by s lrface

temperature fluctuations. This is not surprising as at higher qualities the

CHF drops while h-,, and presumably <J> . increase as illustrated in figure 8.rli min

The effect on AT . is pot clear; the only known study is by Plummer (1973)min

who analyzed questionable transient post--dryout data obtained at 1000 psia;

bis results suggest a slight reduction in AT . with an increase in quality.

13

T W T S A TFIG, 7 EFFECT OF MASS FLUX ON BOILING CURVE

(ANNULAR FLOW REGIME)

T W ( S » T

FIG. 8 EFFECT OF QUALITY ON FORCED CONVECTIVE BOILING CURVE

14

Effect of Pressure

Hesse (1973) measured Lhe complete boiling curve in pool boiling

for Freon-114 at pressures between 3 and 20 bar. His results are shown in

figure 9: at low pressures the pressure effect was small but at high pres-

sures a significant reduction in h_,,, 6 . , AT and AT . was observed.TB nun max m m

Ellion (1954) obtained forced convective boiling curves (subcooled

boiling) for 16 and 60 psia. No effect of pressure was observed.

In general, for the same flow and quality, hp_ increases slightly

with pressure because of improved heat transport properties while (f>IT13.X

increases until it reaches a maximum value ai.. P/P =0.25; it subse-

quently decreases with pressure. Near the critical pressure the boiling

curve changes to that characteristic of a single phase fluid as here the flow

becomes homogeneous and the difference between boiling modes disappears.

'•"ffect of Subcoolinf;

The effect of subcooling on transition boiling has been studied in

steady state pool boiling systems (Tachibana (1973), Nishikawa (1963)),

quenching experiments (Bradrield (1967), Tachibana (1973), Stevens (1971))

and forced convective boiling systems (Ellion (1954)). In general, increased

subcooling was found to increase <b , h , <j> . and AT . . The exception tomax TB m m min

this was a study by Stevens (1971): on quenching of a hot sphere he observed

a slight reduction in AT . with an increase in subcooling. Ellion (1954)min

did not observe an effect of subcooling on AT . .° mm

The effect of subcooling on <f> and § . in a pool-boiling systemmax m m

has been evaluated theoretically by both Zuber (1961) and Kutateladze (1966).

The higher subcooling increases the CHF since for the same vapour flux leaving

L5

I i : i i i I I | I I I I I I I I I I I

10'

A T S A T ( ° C )

FIG 9 EFFECT OF PRESSURE ON POOL BOILING CURVESOF FREON 114 (HESSE, 1973)

TW~TSAT

FIG 10 EFFECT OF SUBCOOLING ON BOiLING CURVE

16

the surface the heat flux must be higher. Also <J> . and h are higherm m i B

because of reqvired higher surface heat flux to maintain the same vapour film

thickness. The above reasoning suggests that h will increase as illustrated

in figure 10. Piggott (1974) studied the effect of subcooling on rewetting

of a hot surface exposed to a jet of subcooled water. He found that a slighl

increase in subcooling C18°F) would reduce the rewetting delay significantly

(from 100 seconds to 1 second). Also the spreading of the drypatch occurred

much more rapidly with a slight increase in subcooling. This agrees with

previously mentioned observations that an increase in subcooling results in

an increase in <j) , <j) . , h,,.. and/or AT . .max min FB min

Effect of Surface Condition

Berenson (1960) studied the effect of surface roughness on transi-

tion boiling in a pool boiling system using a variety of organics. In

general, commercial surface finish did not affect <j> , tj> . or AT . but itmax m m m m

reduced AT (as compared to a mirror finish). Berenson'3 observationsmax

agree with those of Nishikawa (1963), although Nishikawa observed an increase

in <j) . with increased surface roughness.

In a forced convective system the roughness effect is not clear.

Groeneveld (1973) has reviewed the literature on surface roughness effects

and concluded that the surface roughness will increase h if the roughnessCD

height is larger than the laminar sublayer thickness. The effect on d> ismax

less clear: in the subcooled region the roughness effect is probably positive

but at high qualities the effect nay be positive or negative, depending on

the roughness profile. Surface roughness is also expected to increase AT .m m

and <j) . because of increased liquid-wall interaction near the minimum

17

(possible mechanism: the peak of the roughness may protrude through the

vapour film and initiate rewetting). Evidence for this was reported by

Iloeje (1973): At 1000 psia increases in AT . from 350°F to 900°F weremxn

attributed to an oxidized or crudded heated surface although improper

experimental techniques are also expected to have played a role*,

Piggott (1974) studied the rewetting of hot rods by bottom flooding

and falling films. No effect of surface finish on rewetting delay was

observed for the bottom flooding case but for the falling film case, rewetting

delay was decreased by surface roughness. No explanation for this has yet

been offered.

Effect of Transient

In this section the effect of a temperature transient, as encountered

in quenching, on transition boiling will be discussed. The most complete

study was carried out by Tachibana (1973) who measured boiling curves for a

variety of fluids during steady state pool boiling and quenching. The

quenching boiling curves were derived from the temperature-time history which

makes the results less accurate. Nevertheless, Tachibana's results show that,

as a first approximation, the quenching curves agree with the steady-state

boiling curves. Also AT , and d) . both seem to be somewhat lower duringb mxn mxn

quenching conditions than during steady-state conditions. Bergles and

Thompson (1970) also studied the pool boiling curves during quenching and

ateady-state conditions in several fluids. They observed ua. increased t)>

and hT_ for the transient runs. Unfortunately, the heated surface had become

cruc'.ded during the quenching runs thus making their comparison questionable.

^private communication, General Electric Company

18

TRANSITION BOILING EXPERIMENTS

General

The most widely used system in forced convective boiling studies

is a heat flux controlled system where the heat output of an electrically

heated clement is increased gradually. On reaching a power level corres-

ponding to the critical heat flux, the heated surface temperature will

usually fluctuate between the nucleate and film boiling curve. Eventually

with a small further increase in heat flux, the temperature will steady out

along the film boiling curve. This might result in physical failure of the

heated surface.

As shown in figure 11, a heat flux controlled system will not

permit measurement of transition boiling data; to do this i temperature

controlled system (in which case certain stability criteria must be satis-

fied) or a transient experimental set-up, using a high thermal inertia

heater, is required. Table I lists the previous transition boiling inves-

tigations, and gives the ranges covered. In this section derails of exper-

imental methods will be discussed. Since this review deals with forced

convective studies, pool boiling details will only be quoted if relevant to

the forced convective case.

Electronic Feedback

Peterson et al. (1973) used a forced convective boiling system

(0.487" OD, 0.005" ID annulus heated by a 0.005" platinum wire) where the

heater resistance became one arm of a comparator bridge circuit. The

bridge became unbalanced for heater temperatures different from the required

heater temperature, and the bridge signal was used to control power.

ABCD

- HEAT FLUX CONTROLLED SYSTEM- TEMPERATURE CONTROLLED SYSTEM- HEAT FLUX- TRANSIENT

^ /<v /

$/

/A,B,C,Ds

CONTROLLEDTESTING US

B,

SYSTEM ING HIGH

%

\ \

D

•01 TH AUXTHERMAL

ILIIN

E

ARYERT

i,C,

HEAT FLUXIA HEATER

/

D

SPI

/

A,B

KE

,C,D

FIG, 11 FORCED CONNECTIVE BOILING CURVE:SYSTEM REQUIREMENTS

= T W " T S A T

SUBDIVISION BASED ON EXTERNAL

20

A similar system has been used by Peterson (1971) and Sakurai (1974) in a

pool boiling study. Although this setup seems very promising, the data by

Peterson have a limited value since his heater geometry (0.005" OD, 2" b^-ted

length) differs greatly from heater geometries of interest. The boiling curve

derived from Peterson's data is based on the assumption that the heated

surface temperau-re is uniform in the axial direction. For long heaters this

is unlikely to be true because u: variations in quality along the length.

An improvement on Peterson's method could be a system whers the

test section power was controlled by the deviation from a preset temperature

as measured by a surface thermocouple.

Forced Convective Heating

Both McDonough (1961) and Ramu (1975) used a system where heat was

supplied by circulating liquid metals. McDonough obtained transition boiling

data inside a 0.152" ID tube externally heated by circulating NaK while

Ramu (1975) used an ann.ilar geometry (1" OD, 0.54" ID) for the boiling fluid

which was internally heated by mercury. Assuming a flat wall between the

liquid metal and the coolant the following relationship applies

(j) = UCV-T ) = 11,(1 -T .) = ~-(T ,-T .) = h_(T _-T JT 1 sat 1 1 wl o wl w2 2 w2 sat

where subscript 1 refers to the heating fluid and subscript 2 to ,_he boiling

!;ast fluid. The ij) vs, AT relationship for both fluids and the wall is shown

schematically in figure 11. Note that h.. is assumed to be constant (no

change in phase on heating fluid side) while h? varies depending on the

boiling mode.

Figure 12b illustrates that, for cer*.u±n conditions (low values of

h^ and k, large 6), r>o transition boiling data can be obtained: If the

21

a S T A B L E O P E R f l T l O W D U R I N G T R A N S I T I O N B O i L i N G

'SAT

H E A T I N GF L U I D

TEST F L U I D

'HI

'SAT

b. U N S T A B L E OPERflTION D U R I N G T R A N S I T I O N B O I L I N G

FIG 12 0 vs AT R E L A T I O N S H I P FOR B O I L I N G S Y S T E M S H E A T E D BY H E A T I N G F L U I D S

22

overall temperature difference T,-T at the maximum exceeds T,-T atv 1 sat 1 sat

the minimum, the heat flux will suddenly drop from <j> to a value close toin 3.x

d> . (A-B in figure 12b) without permitting any measurements in the transi-mxn

tion boiling region (A-C).

Stabilizing Fluid Technique

Ellion (1954) studied transition boiling in a 2.5': 00 annulus

centrally heated by a 0.25" electric tubular heater, cooled internally by i

stabilizing fluid to avoid a dryout temperature excursion. Total heated

length was only 3 inches. His setup is shown schematically in figure 13.

Ignoring the temperature variation across the tube wall, the total heat

removal rate from the tubular heater (per unit of surface area) is:

• - • i + ^ 2 - V V T l ) + h 2 ( V T s a t }

where subscript 1 refers to the stabilizing fluid and subscript 2 to the

boiling test fluid.

As can be seen from figure 13, the system permits stable operation

in the transition boiling mode provided the slope of the <j> vs. T curve

is between 0° and 90°.

Although Ellion's technique looks potentially very promising, the

choice of stabilizing fluids which have sufficiently high heat transport

properties is very limited. Ellion used high pressure water as a stabilizing

fluid which limited his maximum operating temperature to the corresponding

saturation temperature.

'SAT

TESTFLUID

STABILIZING FLUID

F I G . 13 vs T w R E L A T I O N S H I P F O R B O I L I N G S Y S T E M U S I N G S T A B I L I Z I N G F L U I D ( E L L I O N , 1 9 5 4 )

24

Transient Technique

Forced convective transition boiling data for water have been

measured during transient conditions by General Electric (Iloeje (1973),

Plummer (1973)) and Westinghouse as a part of the FLECHT tests. In the G.E.

tests power was applied to a 4" long, 0.492" ID test section (wall thickness

0.254") until film boiling was established. The power was subsequently cut

off and the temperature at several locations along the test section was

recorded. Assuming axial conduction to be unimportant, the boiling curve

can be derived from the thermocouple trace by differentiating the temperature

time recording (e.g., see figure 14). In most experimental set-ups the

inverse heat conduction problem must also be solved. A similar method was

used by Iloeje (3.974) who studied boiling in nitrogen.

Transient methods of measuring transition boiling data in water are

by far the simplest methods for forced convective systems. However, they

suffer from several serious drawbacks:

(1) Axial gradients in temperature are present. These axial gradients may

be very large (rewetting is often due to a propagating rewetting front)

resulting in large variations in surface heat flux. Due to the limited

number of thermocouples, proper evaluation of the axial surface heat

flux distribution in the presence of a rewetting front is often

impossible.

(2) The temperature of the transient test section is usually measured by

thermocouples attached to the outside of the test section (for tubular

test section with internal flow) or embedded in the heated surface (for

heater rods). In both cases the true heated surface temperature is

different fiom the measured temperature or is affected by the thermo-

couples used for measuring. The use of outside surface temperatures xn

- I T .

0 - C

MIN

CHF

;AT

FILMBOiLING

TRANSITIONBOILING

V _LNUCLEATEBOILING

TIME, t

FIG. 14 DERIVATION OF BOILING CURVE FROM TEMP-TIME TRANSIENT LUMPED PARAMETER MODEL

26

deducing the inside heated surface heat flux and temperature can result

in large errors.

(3) Flow parameters are not steady because of variation in heated surface

temperature and vapour production at the heated surface.

Transition. Boiling Results

An extensive search of the literature produced six sets of transi-

tion boiling data, tabulated in Table I. None of these data sets can be con-

sidered reliable. Their shortcomings range from inadequate heated length or

diameter to unknown local conditions such as subcooling or surface heat flux.

The "comments" column of Table I lists the sources of uncertainty for each

data set.

The shortage of data on forced convective transition boiling is

directly reflected in uncertainties in the prediction of temperature time

histories of nuclear fuel elements during a LOCA. To reduce this uncertainty

transition boiling studies have recently been initiated in Canada and the

U.S.A.

TRANSITION BOILING CORRELATIONS

General

A review of relevant literature resulted in eleven transition

boiling correlations. These correlations and their range of validity are

presented in Table II. In this section the correlation trends will be

examint.d, over a wide range of conditions, on a if vs. AT plot (figures 15-23).

Most correlations gradually change into a film boiling correlation at higher

wall superheats. For the correlations which do not have this feature an

27

appropriate film boiling correlation (Groeneveld (1975)) will also be shown

on the same plot. Comparisons of correlations with transition boiling data

are shown in figures 24-27. A discussion of these comparisons is given at the

end of this section.

The transition boiling correlations can be subdivided into three

groups: i) correlations containing boiling and convective components,

ii) phenomenological correlations, and iii) empirical correlations. They

will be discussed in this order.

Correlations Containing Boiling and Convective Components

It was shown previously that during transition boiling the heated

surface is wetted intermittently. Rohsenow (1952) was the first one to

suggest that the transition boiling heat transfer component contains a

convective (h ) component and a boiling (h, ) component.

The boiling component represents the heat transfer during liquid

contact with the heated surface. Mathematically, this may be expressed a?

h = A exp(-BAT )D S

where A and E are constants.

Physically, this represents the probability of the liquid contacting

the heated surface on a time average basis (or the average wetted area at any-

instant) which disappears at high wall superheats.

The convectiv'P component represents heat transfer during vapour

contact and is usually correlated by the forced convective heat transfer

correlation:

h = i a Reb PrCc De

28

In the transition region just beyond CHF, and at low quality flow,

the dominant term is the boiling component. Therefore, we expect

h T B ~ A exp(-BATs)

or cf>TB " A exp(-BATs).ATs

By differentiation we find that 4> occurs at AT = —. Since!

ID, max S 15the maximum heat flux in the transition boiling region is the CHF, we can say

1B ~ AT

max

and also

= -.ATq)max e max

. max ,or A ~ e.— = e.h

AT maxmax

The boiling component, h, , of the heat transfer coefficient is

therefore

{ AT ) f Tmax-T ]hb = C-hmax exp " A T ~ = hmax^ max''

T max T Tmax'' \ max satj

In all of the correlations, the constants are derived empirically.

At the minimum heat flux, the boiling heat transfer coefficient approximately

equals the convective heat transfer coefficient:

(T -T ,, , max minh . « h exp •-c,mm max T -

h . « h exp r,c,mm max T -T _' max sat

29

(a) Tong's Correlation

Tong (1970, 1972) has presented two correlations: one for high

pressures and one for low pressures. The correlations are plotted in

figures 15 and 16, where the mixture velocity is evaluated as

1 J

It is seen that the correlations show f'he familiar boiling curve shape.

They also extend to the film boiling region with the correct trend in mass

flux and quality. As can be seen <£ and the corresponding temperaturenicLX

AT ar>i almost constant, independent of any system parameters. There is

no cross-over in the transition boiling region as postulated in figure 8.

Tong's high pressure correlation was found to be insensitive to pressure

for the range 500-2000 psia. The same was found to be true for Tong's low

pressure correlation in the range 15-100 psia.

(b) Mattson's Correlation (1974)

Mattson developed two correlations: one for tubes and one for

bundles. They both have a very small boiling component compared with the

convective component (figures 17 and 18). The correlations are based on

data obtained in heat-flux controlled systems, which usually do not show a

pronounced dip in the transition boiling region. Furthermore, these correla-

tions show a negative quality effect on the heat transfer coefficient in the

film boiling region. This does not agree with our physical understanding of

the film boiling process and with experimental observations (Bennett (1967),

Groeneveld (1973)). An increase in quality always leads to an increase in

vapour velocity thus increasing the convective heat transfer coefficient.

(a) (b)

107

104

P = 1000 PSIftXE= 0.3De= 0.4 IN.

G= 2.5x1O6 Ib/h .ft2

P = 1000 PSIAG = 105 Ib/h .ft2

Do = 0.4 IN.

0 400 800 1200 1600 0 400 80U 1200 160U

VTSAT- °F V T S A T - °F

FIG. 15 EFFECT OF MASS FLUX AND QUALITY ON TONG'S (1970) CORRELATION

o

31

M/nia)

j o

—

—

e l

CO

a-oLA

II

o

II

CO

X

o

II

CO

O

AA\ \-Q \— \

\CO \

o \

LA

fNJ

. II

/kX

\\\\CO IO \

//hIf

\\

C D

O

XLAfNI

'IA

/A

\X\COO

T —

XT—

•

/

\

q d O7 O

0 7

iCM

CD

0 0

C3

3

X

ooD

O

o

OO00

oo

o

CD

CD

(a) (b)

10'

CO

-e-

I I I I I ! I i !P = 1000 PS!AX = 0.1

G=2.5 x10 6 Ib /h . f t 2 _

1 0 s .

De = 0 . 4

107

105

104

P = 1000 PSIAG = 10 5 I b / h . f t 2

D B = 0 . 4 I N .

X = .90

400 800 1200 ifeOO0 400 800 1200 1600 0

V T S A T « ° F V T S » T . ° F

FIG, 17 EFFECT OF MASS FLUX AND QUALITY ON MATTSON'S (1974) TUBE CORRELATION

33

o>-

oo

oofNI*"~

oo00

oo

1—

CO

•

a<cX

1

u.COCO"=£

11

o1—CJLULL.LL.LU

CO

CD

o o

34

(c) Ramu and Weisman's Correlation (1974)

Ramu and Weisman correlated the boiling component using the

suppression factor proposed by Chen (1963). In figure 19b we see that, at

high flow, the CHF is much reduced, which is contrary to usual observations.

Also, at high flow (above 106lb/h.ft2) the correlation predicts a very low

boiling component, with the result that the entire boiling curve resembles

that of film boiling (figure 19b).

In a later paper (Ramu and Weisman (1975)), the authors found that

this correlation did not agree with their experimental data, which were

obtained at low flow and high quality conditions. They corrected their

correlation by replacing Sh with <t>.,T,_/AT wherein unr max

f(a) as shown in figure 20 (Ramu and Weisman "975)*CHF pool

and AT = 3.86v<frr,mf0.074 (McAdam's correlation for nucleate boiling)max \J Mr

(d) Hsu's Correlation (1975)

Instead of a forced convective component, Hsu used a rree con-

vection film boiling heat transfer coefficient, together with a boiling and a

radiation component to correlate the FLECHT data. Hence, Hsu's correlation

does not depend on flow or quality, but is pressure dependent. At low flows

such an approach is justified. At higher Elows nowever the flow effect

becomes important and a forced convective film boiling correlation should

be used beyond dryout. The effect of pressure on Hsu's correlation is

illustrated in figure 21.

10'

10B

CD

•e-

104

(a)

: G = IO5

xe =0.1DB =0.4

1 1 1 1 1Ib/h -ft 2

IN.

= 2000 PSIA

500

- 100-15

i-—

|

0 400 800 1200 1600T - T ° F'W ' S A T , h

10'

106

CD

10"

(b)

P = 1 0 0 P S I A

I N .Xe -D e =

G = 2 . 5 x 1 0 B I b / h . f t 2

0 400 BOO 1200 1600

T -T °F'w ' S A T ,

h

F I G . 19 EFFECT OF PRESSURE AND MASS FLUX ON RAMU'S ( 1 9 7 4 ) CORRELATION

1 .0

.2 -

.2 . 4 .b

VOID FRACTION

1 ,0

F I G 2 0 LOW FLOW C R I T I C A L H E A T F L U X AS A F U N C T I O N O F V O I D F R A C T I O N

10]F 1 I I I 1

G = 105 i b / h . f t 2

Xe = 0.1De = 0.4 IN.

i i—r

P = 15 P S I AP = 5 0 P S I A

P = 1 0 0 PS I ft

en

FIG 21

1200 1600

°F

EFFECT OF PRESSURE ON HSU'S ( 1 9 7 5 )

CORRELATION

S A T ,

F I G . 22 E L L I O N ' S LOW PRESSURE TRANSITION

BOILING CORRELATION ( 1 9 5 4 )

38

Phenomenological Correlations

(a) Tong and Young's Correlation (1974)

Tong and Young expressed the hoiling heat flux component as a

fraction of the overall heat flux. Thus

The film boiling heat transfer coefficient is evaluated from a Dittus-Boelter

type correlation where the effect of slip between liquid and vapour phase is

taken into account. The non-equilibrium in vapour superheat is also accounted

for. The equation however is based on data from Bennett (1967) which were

obtained in a steady-state heat flux controlled system. Caution should be

exercised when applying thij correlation in the transition boiling region.

The above relationship may be rearranged as

(j>FB = <M1-*)

For a given system at a fixed exit quality and wall superheat, we may write

where C is a constant.

By L'Hopitai's rule we find the limit of <J) to be C. Thus, ifr o

the calculated <]>„„ is greater than the value of C, no solution will ber B

obtained. This is a mathematical rather than physical limitation.

39

(b) Iloeje's Model (1974)

iloeje developed a sophisticated heat transfer model for a flow

of dispersed droplets beyond the point of dryout. He divided the surface

heat flux into three components:

0 - accounts for heat exchange between wall and droplets

hitting the wall

d) , - accounts for the increase in wall-vapour heat transfer duendc

to a disturbance of the thermal boundary layer by droplets

which are repelled from the wall by a vapour thrust force

before they can touch the wall

<t> - convective heat transfer between wall and vapour,conv

Iloeje's model takes into account virtually all important physical mechanisms;

it has the correct asymptotic trends but because of its complexity it is

difficult to use. Also, its range of application is limited to the dispersed

droplet flow regime. For these reasons it has been left out of the comparison.

Empirical Correlations

(a) Ellion's Correlation (1954)

Ellion's correlation only depends on the temperature excess above

saturation (figure 22). It is based on data obtained at only two pressures

(16, 60 psia), two flows (1.1, 5 ft/s) and two subcoolings (50°F, 100°F).

As such, its range of application is very limited,

Cb) Berenson's Correlation for Pool Boiling

Berenson (1960) proposed that the transition pool boiling region

be represented by a straight line on a log-log plot of heat flux vs. wall

superheat. The application of this correlation depends on the knowledge

40

of two of the following sets of unknowns:

(i) CHF and TC

(ii) <t . and T .m m m m

(iii) Slope of line on the log-log plot.

In general, knowledge of (i) and (iii) is assumed, i.e.

, (T -T _q> _ 1 w sat

CHF ~ I

Peterson and Zaalouk (1971) reported values of n between -3.0

and -4.1, while Groeneveld (1976) obtained a better agreement with the data

with n = -1. Figure 23 shows the Bsrenson type correlation for n = -1

and n = -3; for n = -3 the transition boiling region seems rather steep,

as compared to other correlations at low flows.

(c) McDonough, Milich and King's Correlation (1961)

McDonough et al's correlation (figure 24) is particularly

restricted to the pressure range shown in Table I. Outside this range the

calculated heat flux values become unreasonably large at low pressure due

to the exponential term.

Comparison with Data

In this section, experimentally measured transition boiling data

are compared with the applicable correlations. On some of the graphs some

correlations, fall well beyond the range of the graph. This is indicated

by an arrow followed by tl.2 name of the correlation. The correlations labelled

Peterson and Groeneveld are basically Berenson-type correlations with an

10'

10B

105

104

I

CHF =ATCHF :

Xe -P

1 ! i

= 520,000 BTU/h .ft2

= 59.fe°F

= -0001= 40 PSIA

(VJ= -I(GROENEVELD)

\ (PETERSON) ' "1 i 1 1 I

10'

sz

CD

•e-

0 400 800 1200 1600

T -T °F'w 'SAT, r

FIG 23 BERENSON TYPE CORRELATION FORLOW FLOW

10'

G =105 Ib/h -ft2

= 0.4 IN.

P =1000 PS I A

2000

0 400 800 1200 1600

T -T °F

'w 'SAT, r

FIG. 24 EFFECT OF PRESSURE ON McDONOUGH,MlLICH AND KING CORRELATION (1981)

exponent of wall superheat of -3 and -1 respectively.

(a) Ellion's Data (1954)

In Ellion's experiment the water was s t i l l subcooled at the exit

of the test section and therefore comparison of his data with correlations

which contain quality terms may be misleading. Where needed, an estimated

quality of 0.000075 and a void fraction of 0.1 were used. As shown in

figure 25, Hsu's correlation is the closest to Ellion's and also to the

data. Furthermore, Hsu's correlation connects smoothly to the nucleate

boiling region.

(b) Plummer's Data (1973)

Plummer's data are above the values predicted by most of the

correlation? in the applicable range (figure 26). Possible reasons for

this are:

(i) Plummer noted that there was an oxide film present on the

test section, which could increase the heat flux.

(ii) Plummer's surface heat flux and surface temperature were

calculated values obtained from transient data. These

calculations may have introduced errors.

( i i i ) Axial conduction affected both calculated surface heat flux

and inside surface temperature.

400 500

VTSAT

600 700 800 900

FIG.. 25 COMPARISON OF TRANSITION BOILING CORRELATIONS WITHELLION'S DATA

44

106

105

TUBE

G = 99,fe00 Ib.h " ' f f 2

P - 1000 PSIA

• EXP. DATA

I I I L0 100 200 300 400 500 600 700 800 900 1000 1100

VTS»T en

F I G . 2 6 C O M P A R I S O N O F T R A N S I T I O N B O I L I N G C O R R E L A T I O N S W I T H P L U M M E R ' SD A T A

45

(c) Peterson's Data (19.73)

Peterson's data are plotted in figure 27. The trend of the data is

not predicted by the correlations. Ramu's correlation is closest to the data.

Ellion's correlation overpredicts the heat flux but displays the same trend as

the data.

(d) Ramu's Data (1975)

Ramu's data lie below all the correlations (figure 28) except the

Berenson-type correlations which are based on experimental values of CHF and

AT,,,,-,. At the typical system parameters of the data (G = 130,000 lbm/ft^h and

X = 0.A5), the void fraction is close to one, thus giving a very low value of

$_„„ (figure 20). We therefore adopted Hsu's (1975) recommendation that <?>„„_

be not less than 90,000 Btu/ft^h. With this value Ramu's correlation is

replotted on figure 28. As can be seen, the revised correlation still lies

above the data and the trend is not in close agreement. No other data at high

quality, low flow and low pressure are available to compare with the revised

correlation.

(e) FLECHT Data

The FLECHT* experiment was carried out in a 49- and a 100-rod bundle,

initially heated to temperatures up to 2300°F and subsequantly cooled by

injecting subcooled water at the bottom of the channel. Local coolant param-

eters are not known but are calculated, the largest- uncertainty existing in

the coolant enthalpy and surface heat flux (due to severe axial conduction

near the rewetting front). Hsu's correlation gave the best fit to all FLECHT

*FLECHT: j[ull Length Emergency pooling Heat ^Transfer

46

10

105

I—CO

104

40

I E L L I I

TONG (LOW PRESSURE;

ANNULUSG = 1 ,420,000 Ib.hP = 14.7 PSIA

ATslJB = 0°F• EXP. TATA

ft-2

80 100

V T S A T

120 140 160

FIG,. 27 C O M P A R I S O N O F T R A N S I T I O N B O I L I N G C O R R E L A T I O N S W I T H P E T E R S O N ' SD A T A

CD

•e-

TONG (LOW PRESSURE)ELLIONHSU

104L

ANNULUSG = 13,000 Ib.hP = 27 PSIAX = 0.45• EXP. DATA

ft"-2

50 00 150 200 250

F I G . 2 8 C O M P A R I S O N O F T R A N S I T I O N B O I L I N G C O R R E L A T I O N S W I T H R A M U ' SD A T A

48

data although Tong's low pressure transition boiling correlation also seemed

to agree with most data. A sample of the FLECHT data is shown in figure 29.

Discussion

In general, agreement between transition boiling correlations and

data was poor. This was to be expected as the data used were unreliable and

each set of data covered only a very limited range of condition • (Table I).

Figures 25-29 showed that the slope of the data on a log <j> vs. log

AT plot was indeed -1 as suggested by Groeneveld. However, the agreement

between the correlation labelled Groeneveld and the data is artificial since

experimental data for the CHF and AT_,-F were used as an input in the

correlation:

-1

CHFexp

T -Tw sat

ATCHF,exp_

Prediction of the CHF value is not an unsurmountable problem hut A"" is

more difficult to predict.

No comparison could be made with McDonough (1961) data since, with

the exception of a single point, the data have been lost (Ramu (1*374)).

XL

\—CD

10B

ELLION

100 ROD BUNDLE

G = 112,000 (P = 15 PSIA

T | M -" 137°F

• EXP DATA

b . h •' ft - 2

1 1 1 1 i100 200 ^00 400 500 6U0 700 800 900

V T S A T

29 COMPARISON OF TRANSITION BOILING CORRELATIONS WITH FLECHT DATA

50

CONCLUSIONS AND FINAL REMARKS

1. Transition boiling is a combination of unstable film boiling and unstable

nucleate boiling alternately existing at any given location on a heating

surface. The variation of heat transfer rate with surface temperature

is primarily a result of a change in the fraction of time each boiling

regime exists at a given location (Berenson (1962)).

2. Very few experimental studies or. forced convective transition boiling

have been carried out. The available studies suffer from serious short-

comings and cover only narrow ranges of conditions. This situation is

expected to be improved soon, as a response to urgent demands by the nuclear

industry, for reliable sets of transition boiling data.

3. Present thermohydraulic reactor analysis usually ignores the transition

boiling beat transfer mode. Instead it is assumed that, during reflood

the film boiling mode will suddenly be rep]ac.ed by the nucleate boiling

mode (or vice versa during dryout occurrence). In both cases the assumption

that film boiling rather than transition boiling takes place will result

in an overprediction of the calculated surface temperature.

4. During transition boiling, roost of the heat is carried away during the

fraction of time that nucleate boiling takes place. Hence the observed

parametric trends for nucleate boiling are also valid for the transition

boiling region.

5. Present transition boiling correlations are valid only for the narrow range

of conditions of the data on which they are based. A transition boiling

correlation having a wider range of applications may be developed if

<J> and AT or i> . and AT . can be predicted with confidence. Themax max mxn mxn

present state of the art permits the approximate predict on of c|> ; the

prediction of A T ^ , <|>mln and A T ^ are stjll subject to a large degree of

uncertainty.

51

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Boiling, Int. J. Heat Mass Transfer, 1J5, 1237-1240 (1970).

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7_, No. 3, 485-487 (1961).

BANKOFF, S.G. and Mehra, V.S., A Quenching Theory for Transition Boiling,

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52

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53

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54

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60

A

B

C

CHF

Cp

De

f

G

h

h

k

L

P

Q

R

S

T

U

X

NOMENCLATURE

Constant

Constant

Constant

Critical heat flux

Specific heat

Hydraulic equivalent diameter, tube diameter

Friction factor

Acceleration due to gravity

Conversion factor

Mass flux

Enthalpy

Heat transfer coefficient

Thermal conductivity

Ltngth

Pressure

Surface heat flux

Gas constant

Slip ratio, suppression factor

Temperature

Velocity

Quality

Btu/h.ft2

Btu/lbm°F

ft

ft/s2

lbu.ft/lbf.s2

lbm/ft2h

Btu/lbm

Btu/ft2h°F

Btu/h.ft°F

ft

psia

Btu/ft2h

Btu/lbm°R

°F

ft/h

61

Greek

a

Y

*

&

£

p

a

AH

AT

Subscripts

Void fraction

Ratio of specific heats

Surface heat flux

Droplet diameter

Roughness height

Dynamic viscosity

Density

Surface tension

Local subcooling, hg-h

Local subcooling, Ts-T

Ibm/h.ft

ft

ft

lbm/h.ft

lbm/ft3

Ibf/ft

Btu/lb

°F

a Actual value

b Bubble, bulk, boiling

c Critical (thermohydrodynainic), convection

CHF Critical heat flux

e Equilibrium value

f Film temperature, (average of wall and bulk temperature)

fg Difference between satm'ated vapour and saturated liquid value

g Saturated vapour

i Inside, inlet

1. Liquid

m Maximum

max Maximum

min Minimum

o Outside, outlet

62

s

V

w

oaturation value

Vapour

Heated wall

Abbreviations

CKF Critical heat flux

DNB Departure from nucleate boiling

FB Film boiling

TB J ransition boiling

TABLE I

TRANSITION BOILING DATA OF WATER

IN A FORCED CONVECTIVE SYSTEM

GEOMETRY

Annulus0.25" ID2.5" OD

TubeDe =0.152"

Annulus| 0.005" ID0.477" OD

TubeDe =0.492"

Annulus0.54" ID1.0" CD

RodBundlesDe = 0.50"

REFERENCE

Ellion(1954)

McDonoughet al.(1961)

Peterson(1973)

Plummer(1973)

Ramu &Weisman(1975)

WestinghouseFLECHT

Hsu (1975)

RANGE OF DATA

Ppsia

16-60

800,1200,2000

atmos.

1000

25-30

15-90

G v 106

lbm/ft2h

0.24-1.1

0.2-1.5

0.47-1.42

0.05-0.25

0.012-0.034

0.035-0.184

* i 105

Btu/ft2h

4.67-6.22

1-12

1.3-6.3

0.2-0.87

0.10-0.81

0.045-0.87

Subcooiing(°F) orQuality

50-100°F

Subcooiingand lowquality

^saturated

X - 0.30-1.00"

X = 0-0.500

0-140°F

COMMENTS

6-controlled systemwith stabilizing fluidLH = 3"

Nak used as heatingfluid. T w inferredfrom heat transfercorr'a for Nak. Datano longer available.

Heat flux controlled byelectronic feedbackL R - 2"

Transient test

Hg used as heating fluid.X not reported. Limitedrange in T

Transient test.AT , or X unknown,

sub

64

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65

'1'ABLIi 1 1 U.ont '<!)

K Cp . V " " 1-X ~* lr .1

KANCIE OF AHI'LICAHIUTV FOR WATEK

Subcon l in> ; *(•'

t - s ! . - [ , mndtfl ofdlsjx-rii-J tfi'rtii:.

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