Atomic Energy of Canada Limited

AN INVESTIGATION OF

HEAT TRANSFER IN THE LIQUID DEFICIENT REGIME

by

DC. GROENEVELD

Revised by

E.O. MOECK

Chalk River, Ontario

December 1968

Revised August 1969

December 1969 AECL-3281

AN INVESTIGATION OF 11EAT TRANSFER IN

THE LIQUID DEFICIENT REGIME

by

D.C. G r o e n e v e l d

R e v i s e d by E.O. '-loeck

ABSTRACT

He.-il t r a n s f e r d a t a w e n 1 o b t a i n e d f o r f o r c e d C O U V Y I I î-'ii s t e a m

w a t e i f l o w in a 0 . 7 6 0 " O . D . , 0 . 6 0 0 " 1.1), a n n u l u s at p r e s s u r e s b e t w e e n6 2

6 0 0 a n d 1 2 0 0 p s i a a n d m a s s v e l o c i t i e s u p t o 3.0 x 10 I b m / h . f t .

A l i t e r a t u r e s u r v e y o f s t a b l e f i l m b o i l i n g h e a t t r a n s f e r

c o v e r e d s e v e r a l f l u i d s at a w i d e r a n g e of p r e s s u r e s a n d t h e e x i s t i n g

t h e o r i e s o n f i l m b o i l i n g w e r e r e p o r t e d . A v a r i e t y of c o r r e l a t i o n s

wa.-i c o m p a r e d w i t h t h e a v a i l a b l e w o r l d d a t a . T h r e e n e w c o r r e l a t i o n s

w e r e d e v e l o p e d - lor L u b e s , a n n u l i , a n d t u b e s a n d a n n u l i c o m b i n e d .

T h e R M S e r r o r w a s r e s p e c t i v e l y 11.57,., 6.97., a n d 12 . 4 Z .

A d v a n c e E n g i n e e r i n g B r a n c h

C h a l k R i v e r N u c l e a r L a b o r a t o r i e s

D e c e m b e r , 1 9 6 8

R e v i s i o n 1 A u g u s t , 1 9 6 9

R e v i s i o n 2 D e c e m b e i , 19ft°>

AECL-32 81

Etude du transfert thermique dans un régime déficient en liquide

par D.C. Groeneveld

révisé par E.O. Moeck

Résumé

Des données concernant le transfert thermique ont été

obtenues pour un écoulement de vapeur et d'eau en convection forcée

dans un anneau de 0.760 in. de diamètre extérieur et de 0.600 in. de.

diamètre intérieur entre 600 et 1 200 psia et a des vitesses massiquesfi ?

allant jusqu'à 3.0 x 10 lbm/h.ft .

Une enquête effectuée dans la littérature en ce qui concerne

le transfert thermique de films stables en ebullition pour plusieurs

fluides soumis à toute une gamme de pressions et les théories

actuelles sur l'ébullition des films font l'objet d'un commentaire.

Toute une série de mises en corrélation ont été comparées avec les

données actuellement disponibles dans le monde. Trois nouvelles mises

en corrélation ont été développées pour tubes, anneaux ainsi que tubes

et anneaux combinés. L'erreur RMS a été respectivement de 11.57°,

6.97» et 12.47...

L'Energie Atomique du Canada, Limitée

Centre de Chalk River

Décembre 1968

Premiere révision en août 19b9

Deuxième révision en décembre 1969

AECL-3281

- i -

TABLE OF CONTENTS

Pa e

ABSTRACT

TABLE OF CONTENTS i

LIST OF ILLUSTRATIONS H i

1.0 INTRODUCTION

1.1 Definitions I

1.2 Film Boiling 1

?.. 0 LITERATURE SURVEY

2.1 Theories of Film Boiling

2.1.1 ANL Studies 3

2 . 1 . 2 Q u i n n 1 s F i l m B o i l i n g M o d e l 4

2 . 1 . 3 MIT S t u d i e s 7

2.1.4 AERE Studies 8

2.2 Experimental Studies

2.2.1 Film Boiling Experiments with

Steam-Water Mixtures 9

2 . 2 . 1 . 1 Tubes 9

2 . 2 . 1 . 2 Annu l i 9

2 . 2 . 1 . 3 M u l t i - r o d B u n d l e s • 10

2 . 2 . 1 . 4 I n - r e a c t o r E x p e r i m e n t s 12

2 . 2 . 2 F i lm B o i l i n g E x p e r i m e n t s w i t h Other F l u i d s 12

3 .0 EXPERIMENTAL APPARATUS

3. 1. T e s t S e c t i o n 12

3 .2 H e a t e r s 1 *»

4 . 0 EXPERIMENTAL DATA i >

5 . 0 ANALYSIS OF AVAILABLE FILM BOILING DATA

5 . 1 O u t l i n e oE t h e Study !?

5.2 D e s c r i p t i o n of t h e Ana lys i s l 7

- i l -

Page

6.0 DISCUSSION

6.1 General 29

6.2 Range of Application of the Equations 29

6.3 Radiative Heat Transfer in Film Boiling 29

6.4 Film Boiling in Fluids Other Than Water 30

6.5 Effect of System Describing Parameters

6.5.1 Pressure 30

6 .5 .2 Mass Veloci ty 32

6 . 5 . 3 Qual i ty 32

6 .5 .4 Geometry , 35

6 . 5 . 4 . 1 Tubes and Annuli 35

6 . 5 . 4 . 2 Complex Geometries 35

6 .5 .5 Heat Flux 38

6.5.6 Orientation • 38

6.6 Augmentation of Film Boiling Heat Transfer 40

7.0 CONCLUSIONS AND RECOMMENDATIONS 41

ACKNOWLEDGMENTS 44

REFERENCES 45

NOMENCLATURE 50

APPENDIX I 5 2

APPENDIX II 55

- iii -

LIST OF ILLUSTRATIONS

Figure page

1 Regimes of Two-Phase Flow 2

2 Modes of Heat Transfer in Film Boiling 5

3 Film Boiling Regions According to Quinn 6

A Film Boiling Regions According to Hench 11

5 Test Section With Heaters 13

6 Typical Sheath Temperature Plot Obtained

from FLARE Dryout Test 16

7 Comparison between h e x p and h c a^ c for tubes

and annuli using Miropol1 skiy' s equation • 23

8 Comparison between h 1 and h , for tubes

using equation 5.5 26

9 Comparison between h,exp and n

c a [ c for annuliusing equation 5.7 27

10 Comparison between h e x p and h , for tubes

and annuli using equation 5.9 28

11 Effect of Pressure and Quality on h 31

12 Effect of Heat Flux and Mass Velocity on h_n

(P = 1000 psia X = 60Z) 33

13 Steam Quality vs h in an Annulus 34FB

14 Steam Quality vs hpB in a Three-rod Test

Section Thermocouples Located Opposite

Heated and Unheated Walls 36

15 . Comparison between hg and h c a^ c for muJti-rodbundles using equation 5.9 37

16 Effect of Test Section Orientation on the

Wall Temperature 39

- iv -

Figure Page

17 Variation of Specific Heat with Temperatureand Pressure 42

18 Variation of Steam Thermal Conductivitywith Temperature and Pressure 43

1 .0 INTRODUCTION

1.1 D e f i n i t i o n s

T o e n s u r e t h a t t h e r e a d e r is f a m i l i a r w i t h the t e r m s used in

t h i s r e p o r t t h e f o l l o w i n g d e f i n i t i o n s a r e o f f e r e d :

D r y o u t (or D N B ( D e p a r t u r e f r o m N u c l e a t e B o i l i n g ) ) o c c u r s w h e n the

l i q u i d f i l m c o v e r i n g t h e h e a t e r s u r f a c e in t w o - p h a s e a n n u l a r flow

b r e a k s d o w n . It c a u s e s s m a l l but r a p i d r i s e s in s u r f a c e t e m p e r a t u r e

c o r r e s p o n d i n g t o the a p p e a r a n c e a na d i s a p p e a r a n c e of the dry p a t c h e s

C r i t i c a l H e a t F l u x ( C H F ) is th a t h e a t f l u x at w h i c h d r y o u t o c c u r s .

B u r n o u t r e f e r s to the f a i l u r e of the h e a t i n g s u r f a c e d u e t o h i g h

s u r f a c e t e m p e r a t u r e s c a u s e d by the poor h e a t t r a n s f e r t h r o u g h the

v a p o u r f i l m w h i c h c o v e r s t h e h e a t e r b e y o n d d r y o u t .

L i q u i d D e f i c i e n t R e g i m e ( L D R ) is the r e g i m e w h e r e I n s u f f i c i e n t l i q u i d

is a v a i l a b l e at t h e h e a t e r s u r f a c e to c o m p l e t e l y wet it.

T r a n s i t i o n B o i l i n g * is t h e p h e n o m e n o n of i n t e r m i t t e n t w e t t i n g of the

h e a t e r s u r f a c e w h i c h o c c u r s at the onset of the li q u i d d e f i c i e n t

r e g i m e .

S c a b l e F i l m B o i l i n g is a h e a t t r a n s f e r m o d e in u h i c n the l i q u i d 's

c a r r i e d in a d i s p e r s e d f l o w of e n t r a i n e d d r o p l e t s I n a c e n t r a l c o r e .

Heat t r a n s f e r c o e f f i c i e n t s are low but s t e a d y . T h i s t y p e of heal

t r a n s f e r w i l l be r e f e r r e d t o as film b o i l i n g .

1 . 2 F i l m B o i l i n g

C o n s i d e r a f1 ow of s u b c o o l e d l i q u i d i n t o the b o t t o m ot H long

uni f t>rnly h e a t e d v e r t i c a l t u b e ( F i g u r e 1 ) , T h e flow c h a n g e s from the

l i q u i d p h a s e at A ( F i g u r e !) to a t w o - p h a s e m i x t u r e w h e r e tho liquid

* S o m e a u t h o r s r e f e r to t h i s a s P a r t i a l F i l m B o i l i n g

- 2 -

ïiôô

WALLTEMP

VAPOURTEMP ~

Ol

STEAM

G

c

D

C

B

A

ELQWREGION'S

SINGLEPHASESTEAM

HEAT TRANSFERREGIONS

CONVECTIVE HEATTRANSFER TO

SUPERHEATED STEAM

LIQUID DEFICIENT REGION

SPRAY ORLIQUIDDISPERSEDREGION

FORCED CONVECTIVEHEAT TRANSFER

THROUGH LIQUID FILM

ANNULARFLOW

- j -SLUG, CHURNOf t ^RQIH FLOW

BUBBLE ORFROTH FLOW

NUCLEATEBOILING

4SINGt EPHAS£WATER

SUB-COOLED BOILING

CONVECTIVE HEATTRANSFER TO WATER

TEMP QUALITY

FIGURE 1: Regimes of Two-Phase Flow (7)

- 3 -

is distributed over the walls in the form of a thin relatively slow

moving liquid film at E. Further along the tube the vapour velocity

becomes so high that the friction forces at the vapour-liquid inter-

face cause the liquid droplets to entrain in the vapour stream

(Section F in Figure 1). Due to this entrainment and the evaporation

at the interface, the liquid film is disrupted and carried away by

the flow. Upstream of this transition region the heat transfer coef-

ficient is high and the wall temperature low; downstream the heat

transfer coefficient is low and the wall temperature high.

(1-8)*• Many correlations have been suggested for the heat

transfer coefficient in the liquid deficient region but they do not

agree well with each other (.see Section 5.2). In this study film

boiling correlations are derived, based on consistent experimental

data, some of which have been obtained at AECL.

2.0 LITERATURE SURVEY

2.1 Theories of Film Boiling

2.1.1 ANL** _§tud_ie^

Parker studied the film boiling heat transfer charac-

teristics of a dispersed flow of vapour and liquid droplets, flowing

vertically in a tube. He noticed 1) that at high qualities the

heat transfer coefficient decreased slowly once the CHF was exceeded,

and 2) that a considerable superheating of the vapour occurred, even

in the presence of liquid droplets. This resulted in a significant

difference ber.ween the actual vapour quality and the thermodynainic

(equilibrium) quality. In his model he assumed that if the wall

* Numbers in brackets refer to references listed at the end of this

report

**ANL - Argonne JMational laboratory

- 4 -

temperature was below the Leidenfrost point all the droplets striking

the wall were evaporated, but if the temperature was above the

Leidenfrost point no wetting of the wall occurred and all the heat

was transferred directly from the wall to the superheated vapour

film*.

This model predicted a heat transfer coefficient that was

three to six times higher than that for dry steam at the same con-

ditions, except when the wall temperature exceeded the Leidenfrosl

point; then the heat transfer coefficient was approximately the same

as for dry steam.

2.1.2

In references (2), (16), (26), (40) Quinn presented a theo-

retical analysis of film boiling in tubes and annuli. He considered

film boiling to be either space dependent film boiling (a function of

the distance from the dryout location) or fully developed film boiling

(Figure 3 ) . A method of determining a maximum and a minimum film

boiling heat transfer coefficient (h ) was described . The

minimum h fer annuli was found by assuming a non-homogeneousF B

mixture (all the liquid is present in the liquid film on the unhealed

wall, nc droplets appear in the superheated vapour annulus and

thermal equilibrium does not exist) while for the maximum h theF B

mixture was assumed to be homogeneous and in thermal equilibrium

(X = X T = T ) . The analysis recommends the Sieder-TateE A b sat J

equation for the evaluation of the heat transfer coefficient for the

superheated vapour layer at the wall ' . An expression for the

*It is the author's opinion that some of the heat is transferred

directly from the wali to the dispersed liquid droplets. This heat

transfer is sometimes referred to as Leidenfrost heat transfer

(Figure 2 ) .

ENTRAINEDo * LIQUID

3 • DROPLETS- IN HIGH

C VELOCITY1 VAPOUR

CORE HEAT TRANSFER FROM WALLTO SUPERHEATED VAPOUR

HEAT TRANSFER ^ROiviSUPERHEATED VAPOUR TOLIQUID

IEIDENFROST HEAT TRANSFER

FROM WALL TO LIQUID

FILM OFSUPERHEATED

VAPOUR

i w

SAT

DISTANCE FROM WALL

F I G U R E 2 : M o d e s o f H e n t T r r n s ÏL-V i n K 1 I n; ! ' > . ' : i n : j ;

- 6 -

EXTREME POSITIONS OF FLOWWALL LIQUID FILM _ ~ "" "

• • * • • *

DRY WALL '

ONSET OF STABLEFILM BOILING

MAXIMUM TEMPERATUREFLUCTUATION

SPACE DEPENDENT— FILM BOILING

TRANSITIONBOILING

FULLY-DEVELOPED

FILM BOlLiNG

FIGURE 3: Film Bo i l ing Regions According t o Quinn (2)

- 7 -

h e a t t r a n s f e r t o the d i s p e r s e d d r o p l e t s in t h e s u p e r h e a t e d b o u n d a r y

1 . . ( 8 ) ( 4 0 )l a y e r w a s p r e s e n t e d

Q u i n n ' s f i l m b o i l i n g m o d e l s e e m s v e r y p r o m i s i n g b u t f u r t h e r

s t u d y o f t h e d r o p l e t s i z e , v e l o c i t y a n d d i s t r i b u t i o n is n e e d e d .

2 1.3 M T T * _ S t u d i e s _

A t M I T an e x p e r i m e n t a l s t u d y i n t o t h e m e c h a n i s m s of f i l m

b o i l i n g h e a t t r a n s f e r h a s b e e n I P p r o g r e s s s i n c e 19^9 T h e y h a v e

a d o p t e d t h e t w o - s t e p he-?t t r a n s f e r m o d e l i . e . it w a s a s s u m e d tlntt ;i 1 1

of the h e a t w a s t r a n s f e r r e d f r o m t h e w a l l t o t h e s u p e r h e a t e d v a p o u r

l a y e r , t h e n f r o m t h e v a p o u r t o the l i q u i d in the c o r e

T h e f i r s t s t u d y w a s p e r f o r m e d by K r u g e r w h o i n v e s t i g a t e d

f i l m b o i l i n g f o r a s t r a t i f i e d f l o w of F r e o n - 1 1 3 i n s i d e h o r i z o n t a l

t u b e s at l o w q u a l i t i e s . A m e t h o d of c a l c u l a t i n g the t e m p e r a t u r e

d i s t r i b u t i o n a l o n g t h e c i r c u m f e r e n c e of t h e t u b e w a s p r e s e n t e d .

D o u g a l l s t u d i e d f i l m b o i l i n g h e a t t r a n s f e r of F r e o n - 1 1 3

f l o w i n g u p w a r d s in v e r t i c a l t u b e s He n o t i c e d that at q u a l i t i e s

g r e a t e r t h a n 1.0"X. t h e h e a t t r a n s f e r i m p r o v e d . T h e r e s u l t i n g d e c r e a s e

in w a l l t e m p e r a t u r e s for h i g h e r q u a l i t i e s w a s i n t e r p r e t e d a s a

t r a n s i t i o n f r o m a f l o w r e g i m e w i t h v a p o u r at the w a l l s a n d l i q u i d in

t h e c o r e t o w a r d s a f l o w r e g i m e of l i q u i d d r o p l e t s d i s p e r s e d in a

p r e d o m i n a n t l y v a p o u r f l o w at t h e h i g h e r q u a l i t i e s .

T h e d e p a r t u r e oi t h e r m a l e q u i l i b r i u m b e t w e e n a d i s p e r s e d

( 1 8 )l i q u i d a n d i t s v a p o u r w a s d e s c r i b e d by F o r s l u n d - J w h o u s e d l i q u i d

n i t r o g e n in h i s i n v e s t i g a t i o n . He f o u n d d i f f e r e n c e s of u p t o 5 0 %

b e t w e e n t h e a c t u a l q u a l i t y a n d the t h e r i n o d y n a m i c ( e q u i l i b r i u m )

q u a l i t y . T h e f l u i d p r o p e r t y , m a i n l y r e s p o n s i b l e for t h i s n o n -

* M T T - M a s s a c h u s e t t s I n s t i t u t e of T e c h n o l o g y

- 8 -

equilibrium is the vapour thermal conductivity, k . Fortunately the

non-equilibrium in steam is relatively small due to the high k of

steam (seven times that of nitrogen).

Laverty investigated film boiling over the entire range

of vapour qualities. He used the modified Dittus-Boelter equation*

to calculate the local heat transfer coefficient between the wall and

the superheated vapour. He also found expressions for the size,

acceleration and heat transfer characteristics o£ the dispersed

droplets. An overall heat transfer correlation for the liquid

deficient regime of nitrogen was presented in (10).

2 . 1 . 4

Kearsey developed a semi-theoretica4 method of calcu-

lating the surface temperature startin,'; from the known conditions

at the dryout point. He assumed that no wetting of the walls occurred

once the CHF was exceeded. The heat transfer coefficient for the

wall-vapour film was calculated from the known dry steam heat

transfer correlations.

To obtain the bulk steam temperature four differential

equations were solved. These equations calculated the gradient of

the quality, droplet velocity, droplet diameter and bulk steam temp-

erature along the tube length. The results of Rearsey's method

agree with experimental data.

* Nu = 0 . 0 2 3g

JL vv0 '8Pr

0 . 4

gg c

**AERE - A t o m i c E n e r g y R e s e a r c h E s t a b l i s h m e n t , H a r w e l l , U . K .

- 9 -

2.2 Experimental Studies

2.2.1 J?iJ;m_B^i

2.2.1.1 Tubes

Most film boiling experiments were done in directly heated

t'41)tubes. kearsey reports film boiling experiments at 1000 psia in

a 48 inch long stainless steel tube in which wall temperatures up to

o (54)1200 F were readied. Bennett obtained film boiling data from a

19 foot long tube. Bertoletti et al. ' reported experiments in

the Liquid deticient region at 1000 psia with several tube diameters

C o l l i e r ^

(Table 1 ) .

Collier derived a film boiling correlation from Bertoletti's data

Bishop et al. obtained h at high pressures (2420 toFB

31?0 psia). The coolant entered the test sections as subcooled

liquid and during certain runs left as superheated steam. Their

recommended heat transfer correlations ' are presented in Table 1

More film boiling experiments at high subcritical pressures

(4)were reported in (4), (1.3) and (20). Miropol1 skiy' s experimentb

covered pressures from 300 to 3200 psia. His heat transfer corre-

lation assumes a homogeneous model.

2.2.1.2 Annuli

(1 451 ? oPolomikv ' measured h 's between 800-1600 Btu/h.ft- F

FB

at pressures of 800, 1100 and 1400 psia, Three empirical correla-

tions ' given in Table 1 were found to give satisfactory predictions

for nis data.

Quinn ' investigated the effect of small fins and ridges

on the heated surface temperature in an annular test section. He

found that a finned surface produced a large reduction in the rnagni-

- 10 -

tude of film boiling temperature fluctuations and improved the heat

transfer coefficient. However it also caused a reduction in the CHF

of up to 25%. Quinn also reported that a change in heat flux of only

67o was required to pass completely through the transition boiling at

constant quality.

( 25)Bennett et ai. reported h ' s at high qualities (90-100%)

FB

which were up to 40% higher than those to be expected from steam only.

This suggested that most of the heat transferred was used to superheat

the steam rather than to evaporate the liquid droplets.

2.2.1.3 Multi-rod bundles

(14 Ie» 34)Hench ' "' investigated transition and film boiling in

a two-rod test section at 600, 1000 and 1400 psia. He plotted the

heat flux against the wall temperature and noticed that the resulting

curve consisted basically of two straight lines, the nucleate boiling

line and the film boiling line (Figure 4 ) . The slope of the film

boiling line, d0/dl was called the effective heat transfer coefficient

and several correlations to evaluate d0/dT were suggested in (14).

Transition boiling was described as an oscillation between nucleate

boiling and film boiling as shown in Figure 4.

Film boiling experiments with a three-rod geometry were con-

(21 29)ducted by Kunsemiller ' at 600, 1000 and 1400 psia. As predict

by single rod tests, a finned surface was found to increase the hFB

by 15% or more.

Some heat transfer coefficients beyond dryout were measured

(22)at Columbia University in a 19-rod test section at 1000 psia.

These data however were obtained in the transition region. Recently

some fully developed

Columbia University.

some fully developed h 's in a 19-rod bundle were obtained atr a

- 11 -

NUCLEATE BOILING,

fut

- HEAT FLUX

FIGURE 4 : F i l m B o i l i n g R e g i o n s A c c o r d i n g t o Hench

- 12 -

2.2.1.4 In-reactor Experiments

Experiments in the liquid deficient region have been done at

Chalk River (ref. 33 and more recent unpublished experiments). Data

on single rod, 2-rod and 18-rod geometries were obtained. Due to the

thermocouple location, the measured wall temperatures may have been

in error.

2.2.2 £i!m_B£i:L.i,ng_Exper,im£nt_s_wi_th. Other. F_lu.ids_

Film boiling experiments on nitrogen and Freon-113, conducted

at M I T ( 1 0 > 1 2 j l 8 > 2 3 \ were referred to in Section 2.1. Bromley^

investigated film boiling of ethyl alcohol, n-hexane, carbon-tetra-(9)

chloride and benzene flowing across a heater tube. Chi reported

film boiling in hydrogen and presented a film boiling correlation

which is valid for most liquids.

3.0 EXPERIMENTAL APPARATUS

This experiment was reported internally in (53) but the data

were not analysed at that time.

3.1 Test Section

The experiments were performed in a recirculation loop called

FLARE, which is described in references 42 and 53. The schematic

design of the 'double-ended1 test section ia shown in Figure 5.

The flow tube is a l£" Schedule 80 pipe made of SS 304, with

a bore of 0.760" - 0.002. The tolerance is verified at the ends, but

probably increases to + 0.005 over the whole length. Stralghtness is

1 in 120C, the same tolerance as is required of the heaters (0.600"

- 0.005 O.D.). Each heater is located concentrically in the flow

tube with the aid of centralizers or 'warts', three spaced approxi-

- 13 -

REFERENCE ELEVATION (ZERO)IN DATA REDUCTION PROGRAM

DOWNSTREAMHEATEOLENGTH

LH = I 35"UNHEATEO BRIDGE LENGTH=15 WITH HEATERSFULLY EXPANDED

UPSTREAMHEATEO LENGTH

L H = 19.5"

FLOW TUBE

0.760" I D

WATER SPRAYEDINTO STEAMFLOW AT THIS

POINT

SAFETY WELDEDCOLLAR

HEAD BLOCK WITHCONAX FITTINGS

FIGURE 5: Test Section with Heaters

- 14 -

mately 120° apart every 9" axially. As a safety measure, a small

collar 0.350" 0. D. by 0.25" long is welded to each heater just below

the head block Conax fitting, to prevent the heater leaving the test

section in the event of a seal failure.

Water and steam enter the mixer from the bottom, the water

being sprayed through four small holes into the steam flow, and

directly impinging on the upstream unheated part of the heater. The

location of these holes define the upstream end of the test section,

which extends to the exit branch pipe 'see Figure 5).

Four pressure taps are provided, only three of which are

used. The absolute pressure is read at the downstream end of the

heated length, and two pressure drop readings are taken, (a) across

the heated length, ana (b) from the mixer to the upstream end of the

heated length. Thermocouple TE-17 (Figure 5) measures the water

temperature at the mixer inlet, and IE-18 measures the twj-phase

temperature in the exit line.

3.? Heaters

The ideal heater for this experiment is one with a long

heated length, high flux capability and a good internal electrical

insulator with a high coefficient of thermal conductivity to permit

high surface temperatures without destroying the heater. The heater

was designed and manufactured at AECL to meet these criteria. Heat

is generated electrically (A-C) in a helically wound Kanthal ribbon

(0.250" by 0.015") insulated from a 0.6" 0.D. Monel sheath by a

0.040" thick boron nitride sleeve.

Boron nitride was chosen as an insulator sii'ce it was found

to be the cnly suitable material having a relatively high thermal

conductivity (8 Btu/h.ft -°F). This enabled the heaters to operate

- 15 -

r 2

at high heat fluxes (to 1.0 x 10 Btu/h.ft ) and to reach sheath

surface temperatures up to 1200 F.

Each heater was instrumented with a number of 0.020" iron-

constantan, SS-sheathed, alumina-insulated, ungrounded thermocouples.

These thermocouples were embedded in the surface of the heater, leaving

a smooth sheath surface.

4.0 EXPERIMENTAL DATA

Data were obtained in the form of thermocoup Le tract's and data

sheets. The data were processed with a special computer program ,ind

the results are presented in Appendix I.

Thermocouples were considered to be in film boiling when the

wall temperatures were much greater than the saturation temperatures

but steady with time as displayed by the traces. A typical thermo-

couple trace obtained from earlier FLARE experiments is shown in

(33)Figure 6 . Note the surface temperature fluctuations in the

transition region, due to discontinuous rewetting of the heated

surface by the liquid film.

Since the thermocouples were embedded in the wall a correction

(24)must be applied. This correction was incorporated in the data

reduction program.

The following ranges were covered in the experiment:

Pressures 600, 1000, 1200 (psia)

f» 2Mass velocity 1.0 to 3.0 (10 lbm/h.ft )

ft 2Heat flux 0.0067 to 0.6 (10 Btu/h.ft )

Inlet quality 0% to 40%

Heater failures occurred at zero inlet quality and at a heat

2flux of approximately 600,000 Btu/h.ft .

CALCULATED SHEATH TEMPERATURE USING ClSE DATA

500

- -CALCULATED SHEATH TEMPERATURE USING G E "DATA

s?r - oo —r^ 06 tJ5

<x> *n t*-

E.,

È S-

UJ

a:

4OO

< •

o

IE M-

a

a.u

i

UJa.SUJ

•300

T IME

FIGURE 6: Typical Sheath Temperature Plot

Obtained from FLARE Dryout Tesr

- 17 -

5 . 0 A N A L Y S T S O F A V A I L A B L E F I L M B O I L I N G D A T A

5 • 1 O u t l i n e o f t h e S t u d y

E l e v e n h e a t t r a n s f e r c o r r e l a t i o n s f o r i h e l i q u i d d e i i c i i - n t

r e g i o n w e r e f o u n d i n a l i t e r a t u r e s u r v e y . T h e s e e q u a t i o n s ( s e e

T a b l e 1 ) a r e b a s i c a l l y t h e s i n g l e p h a s e h e a t t r a n s f e r e q u a t i o n

N u = a ( R e ) \ p r ) C ... S . 1

m o d i f i e d b y m u l t i p l i e r s t o a c c o u n t f.<r s p e c i f i c i i v p h a s e tl>'.-

e f f e c t s . A l t h o u g h m o s t o | t h e s i ' e q u a t i o n s w e r e d e r i v e d i > o m a

l i m i t e d r a n g e o i e x p e r i m e n t a l d a t a , t h e y h.-ivi h c o n e v t r ,ip • 1 .. t <. i! i

c o n d i t i o n s n u t s p e c i f i e d b y t h e e x p e r i m e n t s . T h e o b j e i i i v e i>L 1 ti i s

s t u d y w a s t o a p p l y d a t a f r o m t h e d i i i e r e n t s o u r c e s t o e a c h e q u a l i m

a n d d e t e r m i n e w h i c h p a r a m e t e r s s u c h a s R e , P r s h o u l d h e u s e d i n o u r

f i n a l a n a l y s i s . A c o m p u t e r p r o g r a m w a s u s e d t o e v a l u a t e t h o s e e o n -

s t a n t s ( a ) a n d e x p o n e n t s ( b , c ) w l i i c h r e n d e r e d a m i n i m u m R M S e t r . u ,

O b v i o u s l y , s u c h a n e q u a t i o n i s >n1 y a n e x p e d i e n t l n r t h e p r e d i c t i o n

o f t h e h a n d t h e u l t i m a t e g o a l m u s t s t i l l b •.• a l u n d a m e n t n l a n a l y s i s

t o p r o d u c e a s a t i s f a c t o r y m o d e 1 . T h e e q u a t i o n ; : p r e s e n t e d i a n h . - w c v i r

p r e d i c t h ' s w i t h m u c h g r c . i t o r r e l i a b i l i t y t h a n p r e v i o u s l y n s c r lF B

c o r r e l a t i o n s ( s i n c e t h e y w e r e d e r i v e d f r o m a n n u c v a r i e d s e l e c t i o r >'|

d a t a ) a n d s h o u l d p r o v e u s e f u l i n p r e d i c t i n g h e a t e r s u r f a c e t e m p é r a t u r e s

5 , 2 D e s c r i p t i o n o f t h e A n a l y s i s

T h e e x p e r i m e n t a l h e a l , t r a n s f e r d a t a , o b t a i n e d f r o m a n e x t e n -

s i v e l i t e r a t u r e s u r v e y ( T a b l e 2 ) , w e r e a r r a n g e d i n t o t h r e e g e o m e t r i c a l

c a t e g o r i e s ; r o u n d t u b e s , a n n u l i a n d m u l t i - r o d b u n d l e s .

A l l d a t a p o i n t s w e r e c o n s i d e r e d i n d i v i d u a l l y . M a n y w e n -

d i s c a r d e d b e c a u s e :

( a ) t h e t e m p e r a t u r e m e a s u r e m e n t m e t h o d w a s i n c i - r r c i t ( t t i e t h e r m ^ -

( 3 3 )c o u p l e w a s p r o t r u d i n g f r o m t h e s u r f a c e o r it w a s l o c a t e d

TABLE 1

1 . Nu — ^ • 0 .001 36f \ a / R ' f

• P r f n

Poloolk ce a l . (1 )

X

P o l o a U cr a i . (1)

P o l o n i k e ? j l . ( 1 )

o.u4 , Nu • 0 . 0 2 31 ~—" i Fr i Re X1b [ U J b [ b 1 a

r 2/3l

a l « 1 0; f J

quinn (2)

.0.14

5. Hufc . 0.0231—j• 0 . 8

R t b X ) P r b / 3

r i 0 6

Qulnn (2 )

6. Nu - 0 . 0 2 3 Be 1 ~ B ~ 1 Pr°" 4

K 1 si A j K8 L B\ c / j K

D o a g s l l e t s i . ( 2 3 )

Range

V

psla

8 0 0

t o

1400

1000

1000

iioo

1000

1000-1400

1000

of Appl lcjib

G x !0

l b / h . f t 2

0.75

l c

I .8

0.5

0 .5 - 1.0

1.1 - L . i

1 .4

7.0

0.B5

11 i ty for EquttIon

X

l

40

* 0

70

(Geometry

Annul us

- 5 5

30 - 40

45 - 53

- 7 0

34 - 38

72-79

Dispersed f low

Annulus

2-rod

3-rod

Tuber

Tubes

Equation agrees

utth data from

reterence

il,

Qulnn (2)

Sorlle (2)

Polonlk (1)

Hench (14)

Kunsrmlller (21)

Bennett (12)

DougaU (23)

Comments

Equations 1 - 3 based

on Colburn equation.

Modified to account for

steam ve loc i ty .

Exponent obtained from

least error procedure

using data from (I)

Modified Sleder-Tate

equation. Computes

heat transfer from wall

to bulk steam.

Sane as equation 4

transfer coeff ic ient

betueen the wall and the

vapour.

oo

i

Equation a n i i Re ference

7. Mu - 0.0193 Ref'8 Prî" 1 j .

r -, -0.68

I a + — (l-a;L °B J

Biahop at a l . (3)

0 .80 1.25 K8 . Hu - 0 . 0 3 3 Re Pr ' -*•

f w w Oj

, p, i - 0 . 7 3 8a + — ( l-Q)

I ° g J

B l a h o p e t a l . ( 3 )

9 . Su - 0 . 0 2 3g

Pr°V

Y - 1 - 0 .1

Mlrcpo l 'ak i

j R « g

• 8Ï

1c

i B

) <4

X -

• 1

0.068

0.197

I 0 ' 8

y t (i-x)!

.0. « [ D . ° - 2 / C X ° - 8 ] - 0.0137AT0-'21 '

C o l l i e r ( 7 )

r -i0 . 2 i

n - I 2&U

C o l l l « r ( 7 )

- C

25 <300

- 0

AT1 . 8

;/io S

4 Î C / 1 0 6

Range

P

pu La

580-3120

580-3120

S8O-32OO

a 1000

t 1000

TABLE 1 (Cont'd.)

of Applicability for EquationG » 10"6

l b / h . f t 2

0.5-2.5

0.5-2.5

0.3-1.5

0.7'. < b

G < 3.0

X

7.

7-100

7-100

6-lon

40-100

40-70

Ge one try

Tube a

Tubea

Roundtubes

Roundtubea

Roundtubea

Equation agreea

with data from

Bishop (3)

Miropol 'akiy

Bishop (3 )

Hlropo l 'ak ly

Miropol '«kly(4)

Svenaon (13)

B e r t o l e t t l (6)

B e r t o l e c t l (*)

Comment a

emplr lea l 1 y

T -T > 360°r orw aat

G < 0 .74 x 10*

I

TABLE 2 Film Boiling Data Used in This Study

Data Source

Polotnik et al.réf. (1)1961

S.C. Abrahamréf. (53)1966

Bishop et al

r e t . i. "*)

1965

Swenscn et al.

réf. .13)

1961

Schmidtret (20)1959

Bertoletti et a\.

vet. (6, 19)1964

Bennet t et al. jref. (54)196?

Pressure(psia)

8001100UOO

60010001200

2'* 20

to

311 S

3000

3125

1000

1000

Range

e> x 10"5

Btu/h.ft2

1.9to7.0

1.6to4.4

2.0

t o

6 5

0.9to1.8

1 0

* to

2. 1

0. 35

to

5.0

0. 75

to

4.0

G x 10"6

lb/h.ft2

0. 75

to1.9

1 .0to3.0

0 "i

r o

2. 5

0.7to

1 0

0 55

0.74to3.0

0.21to1.4

Local X%

15to90

10to50

10to90

20

to

90

10to90

40to90

25to90

Geometry

Annulus

De = 0.011

0.005'

AnnuliDe = 0.0133'

Round tubes

De = 0.0833'

0.0167'

Round tubes

De = 0.0 34'

Round tubesDe = 0.0260'

Round tubes

De = 0.0164'

0.0301'

Round tubesDe = 0.0415

1

Remarks

two heated sections

vertical flow

vertical flow

near critical pressures

vertical flow

near critical pressures

vertical flow

vertical and hori-zontal flownear critical pressures

vert ic al flow

19 ft. long tube

vertical flow

T A B L E 2 : ( C o n t 1 d . )

Data Source

Henchréf. (14, 15)1964

Kunsemillerréf. (21)1965

ColumbiaUniversityréf. (22)1963

Private communi-

cation from CISE

within the AECL-

CISE agreement

on two-phase

heat transfer

Bennett

réf. U 5 )

1964

Pressure(psia)

60010001400

60010001400

1000

1000

500

Range

0 X 10~

Btu/h ft 2

1.0to

6.0

1. 7

t 0

3.1

2.5

to7.4

1 .0to

i* .0

0.2to1 .4

-6G x 10lb/h ft2

0.5to

1 .95

0.250.501.0

0.5to

2.0

vl .6

-0 6

Local XX

20to90

30to70

17to60

40to90

80t o

90

Geometry

2 rodDe = 0.0 34*

3 rodDe = 0.0368'

19 rodDe = 0.0316'

round LubesDe = 0 01963'Ann u 1 iDe = 0.006/'

0 O1621

Anna 1 us

De = 0 OJ08'

Remarks

vertical flowdata for thermo-couples oppositeheated & unheatedsections

data for thermo-couples oppositeheated & unheatedwal Isvertical flow

transition boiling

vertical flow

vert ica1 floweffect of spacerswas investigated

vertical flow

- 22 -

close to a flow disturbance)

(b) it was doubtful whether fully developed film boiling was

reached(1'19'25'53'54)

(c) data points were obtained at qualities below 10% or above 90%

(at these qualities/ the flow regime might be different or a

significant thermal non-equilibrium was present)

(d) data points were taken too close to the inlet (due to extra

turbulence h 's obtained close to the inlet were found to be(1)

higher than usual )

(e) the gap between shroud and rod was sometimes only 0.030"(2)

where probably the flow pattern is seriously affected (see

Section 6.5.4.1)

(53)(f) h 's obtained just downstream of a spacer were unreliable

FB(spacers disturbed the flow pattern and caused extra turbulence)

If two h 's were obtained in a particular geometry at identical con-FB

ditions, the lower h was always used. This method of selecting dataFB

points tended to reject those h_ 's which were higher than the bulk ofFB

the data.

The data of each geometry were applied to all equations of

Table 1. Miropol'skiy's equation (Figure 7)

0.8

Nu = 0.023 I Re X + -* (1-X)I1 gPr°-8Y ... 5.2w

where

Y - 1 - 0.1 [ ^ - l ] (1 X ) 0 " 4

gave the best overall correlation for tubes and annuli; its RMS error

was 36.9% on 704 points.

- 23 -

RMS ERROR.1B773.39174.33007.Z31Z4.S31ZZ.143BZ.21352.16073.2*021.11304

NO. OF POINTS7061

QErrerr REF. 540 I 9 C P REF. 3BERTOLETTI REF. 6, 19

REF. 133CW1IDT REF. 20PRIUOTE CatlMCDTlONQEMCTT REF. 25

REF. S3POLOrllK REF. 1PRIUPTC arttfSICRTICNOUEROLL

Hau

FIGURE 7: Comparison between h and h for tubesexp calc

and annuli, using Miropol'skiy's equation

Our next step was to find a new correlation for each geomet-

rical category which would reduce the RMS error. The following

equation probably includes al l those system describing parameters and

dimensionless groups which may be important in film boiling heat

transfer:

calc a.

kRe X + U-X)

[•

D

a + -=• (i-a)l 5.3

Optimum values of a, b ... j, minimizing Lhe RMS error, were

obtained from a computer analysis. An example of the method used is

given in Appendix II. Steam and water properties were evaluated from

equations published in the 1967 ASME Steam Tables

It is unlikely that all the factors in'equation 5.3 are needed

for the new correlation. Therefore the reduction in the RMS error due

to each factor was investigated by setting its exponent equal to zero

e.g. j = 0. New optimum values of a,b ... i were obtained and the

previous RMS error was compared with the new one. If the difference

was less than O.IZ, the contribution of the factor with the exponent

j was considered negligible and this factor did not' appear in the

final correlation. Similarly, the contribution of the factors with

the exponents b,c ... i were tested.

Our final correlations had the form of equation 5.3 with the

exponents f,g,i,j equal to zero. Six sets of best-fit constants

a,b,c,d,e were obtained - for tubes, annuli, tubes and annuli combined -

with and without heat flux dependence (that is, e 4 0 and e set delib-

erately equal to zero). Tables 3 and 4 summarize the results.

- 25 -

TABLE 3

Best-i

Geometry

Tubes

Annuli

Tubes and

Annuli

.it

1.1.

1.5.

7.3.

Constants

8509

3020

7527

a

X

X

X

X

X

X

1010

1010

1010

-4-3

— i.

- £.

-4-3

to Equat

b

1.00

0.989

0.664

0.688

0,902

0.901

11

11

11

ion

c

.57

.41

.68

.26

.47 *

.32

3.3

-1-1

-1-1

-1-1

witl-

d

.12

.15

.12

.06

.54

.50

i C

0.

0.

0.

e

10

10

10

= 8

31

33

12

_ *

No. of

points

438438

266266

704704

j = o

PMSerror

10.1%

11 . 57.

6. IX

6 .9%

11 . 67=

12 .47.

Equat ion

Ne

55

55

55

> .

45

67

89

TABLE 4

Geometry

Flow direct

De

P,

e,x,

Nu

R(

Pr,

Y

inche s

psia

mill ion

Range

ion

lb/h.ft

% by weight

thousand

]Jx +

Btu/h.

L /I Y \ 1^ A — A J j

of

r

2

ft

Application of Best-Fit Constants

2

Tube

vert ical

0.20

1000

0.21

10

35

95

6.6 x 104

0.88

0.706

and

to

to

to

to

to

to

to

to

to

hor izontal

1.00

3125

3.0

90

650

1770

1.3 x 106

2.21

0.976

1

0

0 x

0

0.

Annulus

vert ical

.06

500

0.6

10

140

160

io5

.91

610

to

to

to

to

to

to

to

to

to

0.25

1400

3.0

90

700

640

3.9 x 105

1.22

0.963

Figures 8, 9 and 10 compare h and h calculated from

equations 5.5, 5.7 and 5.9.

Lack of consistent experimental data prevented us from finding

a reliable correlation for complex geometries. Section 6.5.4 discusses

the multi-rod bundle data.

- 26 -

i—i—i i i i i M MI—i—i—i—rBEf*CIT BET. 51PlShOP RET. 3OEBTOLCTTI BET. 6 ,StCPSOn RET. 13SCHMDT RET. TOPRIUOTC

OUCRPLL

WE ERROR.11139.11106. 11631.05133.1106).00013IISJ3

ro. or POINTSTO6165BO7%B?

438

« 1

\ -

1° ««D

a

• o

ISO?

HcetcTWot

FIGURE 8: Comparison between h and h for tubesexp calc

using equation 5.5

- 27 -

§ -

Ig -

i I

o BDCCTT RET. 2Sr£F\ 33hCT. 1

OJERflL-

rS ERROR NO..0G9T a.O7CP3 143..PSSS? bG.ŒX'3 4B

.06860 266

POINTS

"3500

FIGURE 9: Comparison between h and h for annuli* exp cak

u s i n g e q u a t i o n 5 .7

- 28 -

a OCTCTT RET. S4A O1SHCP REF. 3

aMrxtrri KEF. 6, ia. .Mjki-14 REF. 13

— D SCM11DT REF. 20

RMS ERROR no. OF.'5140.11334

§U- RET 2 5RDRfW-Tt RTF S3POLOnjK RE> . JPRju-irE coTUij ;(JJERFLL

3DB

Haxc

FIGURE 10: Comparison between h and h , for tubesexp calc

and annul! using equation 5.9

- 29 -

6 .0 DISCUSSION

6 .1 General

The proposed empirical correlations are based on exper itnent a i

data from many laboratories. In our analysis only those data points

obtained in the fully developed film boiling region were used. I

suspect that some investigators have derived empirical correlations

partially based on unreliable data (Section 5.2).

6 . 2 Range of Application of the Equations

The constants in Table 3 are based on data obtained in fully

developed film boiling of high-pressure steam and water. The range

of the data is limited, as shown in Tables 2 and 4. The behaviour

of equations 5.4 to 5.9 was not investigated outside of this range.

Note, for example, that at 71 psia and X = 107», Y = 0 and equations

5.4 to 5.9 would predict Nu = °° while Miropol'skiy's equation 5.2g

would predict Nu = 0.g

Direct extrapolation to different geometries (e.g. multi-rod

bundles) should be avoided although it is expected that the equations

will be useful in those areas as discussed in Section 6.5.4.2.

6.3 Radiative Heat Transfer in Film Boiling

The amount of heat radiated directly from the heated surface

to the liquid in the core may be estimated from

0 = £ 1.71 x 10" 9 (T 4 - T^ ) ... 6. !r w w sat

r -<} "Î 2 2 3h = = e 1 - 7 1 x 10 * (T + T T + T T + T )r T -T w w s a t w s a t sal

w sat

... 6.2

- 30 -

where ï = temperature in degrees Rankine

1 = emissivity of the wallw

oEvaluating equation 6.2 for e = 0.20, I = 1500 R and

w , wI = 1000°R results in h = 2.78 Btu/h.ft -°F. h varies betweensat 2 o r

500 and ?000 Btu/h.ft -°F hence the effect ot radiation on h mayr D

be neglected.

6.4 Film Boiling in Fluids Other Than Water

The bulk of the film boiling investigators use water as the

experimental fluid, This has the disadvantage of a high latent heat

of vaporization, requiring high heat fluxes i.up to 10 Btu/h.ft'") to

obtain stable film boiling. These high heat fluxes are often accom-

panied by heater failures. Therefore some investigators

have turned to low heat flux film boiling experiments in which

hydrogen, nitrogen or Freon was used as the .experimental fluid. Due

to the lower operating temperature and pressure, it was relatively

simple for them to observe the film boiling phenomena. However, the

low values of C , A. and k of these fluids may cause a significantp v

non-equilibrium and high superheats at the walls have been observed.

Hence caution must be exercised in using results obtained from these

fluids to predict the film boiling heat transfer, coefficient for water.

6.5 Effect of System Describing Parameters

6.5.1 _Pre s_s ure_

In the range 600-1500 psia (the operating range for power

reactors) h 's are essentially pressure independent other variables

held constant. However, as pressure increases from 2500 psia to the

critical pressure (3204 psia) the h_ is greatly increased and muchr B

lower wall temperatures occur (Figure 11). This is due to an increase

Btuhr ft2oF

5000

4000

3000

2000

1000

X 3100• 24000 1100

-

• *****' x

i i

psia

psia

psia

•

— * ^

G = l .5x|06

0 =3.9xlO5

^ ^

0

1 1 1

Ib/hr

Btu/hr

f t 2

f t 2

20 30 40 50 60 70 80

FIGURE 11: Effect of Pressure and Quality on

- 32 -

in steam thermal conductivity and specific heat and a decrease in the

liquid-vapour surface tension.

6.5.2

The effect of mass velocity is shown in Figure 12. The

increase in heat transfer (at given quality and pressure) is due to

the Increased velocity of the vapour film adjacent to the wall,

causing a more effective cooling. The effect of mass velocity is

identical for single phase and film boiling heat transfer correla-

tions (the exponent of the Reynold's number is approximately 0.8 in

both cases).

6.5.3 JÎHaUty^

Flow regimes are quality dependent and have important effects

on the heat transfer. At high qualities,> 90%, the flow is charac-

terized by a surface layer of superheated steam enclosing a core of

liquid droplets in saturated vapour. The heat transfer coefficient

is very close to that predicted by a single phase equation for super-

heated steam. At lower qualities the net steam velocity and h are

lower, the latter decreasing to a minimum between 35% and 55%

(Figure 13). Also the droplets tend to coalesce .and evaporation

decreases. However this effect is not important at low qualities

(10-30%) and h increases due to the availability of water, i.e.FB

appreciable heat goes into evaporation. The flow pattern has changed

from a dispersed liquid core to a more continuous liquid core with a

vapour film in contact with the heater surface. Below 10% steam

quality, the flow pattern alters and is not accounted for in these

correlations. It is important to realize that due to the superheated

vapour at the wall, the actual quality is lower than that calculated

by the heat balance. This causes the net steam velocity to be lower

resulting in lower heat transfer coefficients.

- 33 -

m

uo0)

intn

JE

•a s-sc o

î: «

- i ><;

4J COCfl - - I01 t/1

0 oo

4-1 r - lU01 II

U3

oi

oMbu

QQ H-

BT'FB

-T4R-FT2-'

1600

1400

1200

1000

8 0 0

6 0 0

G(IO"*) LB/FT2 HR

1.12 —I .50I 88

30 40

STEAM wt. FRACTION

50 60 70 80 90 100

FIGURE 13: Steam Quality vs h in an Annulus

- 35 -

6.5.4 Ge ome_t r_y

6.5.4.1 Tubes*and Annuli

There are two basic geometries, the round tube and the anr.ulus,

the principal difference b«ing the presence of an unheated wall in the

annulus where the liquid can accumulate. Since the abundance of liquid

against an unheated wall leads to greater superheating of the vapour at

the heated surface and causes the actual quality for annuli to be lower

than for round tubes at the same conditions, different correlations were

expected for the two geometries. The correlation for round tubes was

found to predict heat transfer coefficients slightly higher than experi-

mental values when applied to data from an annulus.

It was found that some of the data obtained by Polomik from

an annulus (D = 0.0051) do not correlate well. It was felt that thee

small gap between shroud and heater, 0.030", affected the flow regime.

For instance the thickness of the vapour film may not be small when

compared to the gap size and the superheating effects may be more

pronounced. His quality, calculated from the heat balance, may there-

fore be too high.

6.5.4.2 Complex Geometries

Little experimental information on film boiling in complex

geometries is available. It can be said in general that, due to

entrainment, the proximity of an unheated surface has a positive

effect on the heat transfer coefficient in multi-rod bundles. This

is illustrated in Figure 14 where thermocouples facing the unheated

shroud showed much lower temperatures than the thermocouples facing

(29)a heated surface

The experimental h for 2-, 3- and 19-rod bundles has been

plotted in Figure 15 against the h calculated from equation 5.9FB

Btuhrft2°F

900

800

700

600

500

400

300

• OPPOSITE WALL HEATED¥ UNHEATED

G= I.Ox I0 6 Ib/hr f t2

A OPPOSITE WALL HEATEDM « •• UNHFATED

G=0.5xl06 Ib/hr ft2

P = 1000 psia

30

FIGURE 1 4 :

40QUALITY , %

50

Steam Quality vs h in a Three Rod Test SectionFB

Thermocouples Located Opposite Heated and Unheated Walls(21)

- 37 -

D« M X GEBP-47-T1«HCH GCRP-4431:KUTSETIILLER GECT. 1KLNSQIILLER GEOM 2C0LLTD1Q fFB-Xl 11-2-B3COLUtS Ifl 1967 OPTR

RT6 ERROR

.19B40

.06390

.31350

.371 IB

.77479

.43BZ7

NO. OF KJINTS

701SZ581^3713

Hca.c

FIGURE 15: Comparison between h and h , forexp calc

multi-rod bundles, using equation 5.9

- 38 -

(G, X and D substituted in equation 5.9 were evaluated for a multi-

rod bundle cross section; no individual subchannels were considered).

The only conclusion which can be drawn from this plot is that the h

for ICunsemiller ' s 3-rod bundles and Columbia's 19-rod bundle* is much

higher than the one for tubes and annuli. This was to be expected

since each subchannel going irto film hoiling will experience a much

smaller dP/dC in that channel (due to the viscosity at a dry wall, p. ,

being much .smaller than M_£ of a wet wall). This will increase the

mass flow and h2nce increase the h for that subchannel. Figure 15I D

also shows that Hench' s data agree with equation 5.9. This was

expected since his 2-rod geometry has two symmetric subchannels and

hence no subchannel crossflow will occur.

6.5.5 _Heat_Mux

The effect of heat flux manifests itself indirectly through

the relationship AT = fl/h; a change in AT causes C , k anO u toPw w w

change accordingly. Our analysis showed that an extra heat flux term

in the correlation was necessary. The effect of the heat flux on the

h was demonstrated in Figure 12.Fa

6.5.6 _Or_i eji ta t J. on

Schmidt ' has compared film boiling in horizontal tubes

with film boiling in vertical tubes. He investigated film boiling at

approximately 3100 psia LT\ an 8 mm tube. Figure 16 shows his com-

parison in horizontal and vertical tubes at a mass flux of 0 52 x 102

lb/h.ft , Due to the high experimental pressures, the latent heat

of vaporization is very small and film boiling is more likely to occur

in the subcocled region. The maximum wall temperature for a horizontal

*It is doubtful whether all Columbia's h 'a were obtained in fullydeveloped film boiling. F

- 39 -

600-

500-

400

3 0 0 -

De s 8 mmP = 220 a?m

G = 70gr/cmz-sec

= 5>H05 Keel/m2 s

= 4 X I 0 5 Kcol/m2s

= 2.5x|05 Kcal/m2s

TUBE HORIZONTAL- TUBE VERTICAL

TWO-PHASE

400 500 600ENTHALPY KCAL/KG

700

FIGURE 16: Effect of Test Section Orientation on the Wall Temperature( 2 0 )

- 40 -

tube is approximately 30°C (54°F) higher than the corresponding

maximum temperature of a vertical tube. This is probably due to flow

stratification and the difference should disappear for mass flows

about. 10 lb/h.ft . It should be mentioned that caution is needed

using film boiling data at 2500-3200 psia for calculations at 1000

psia, since thermal propi

near the critical point.

psia, since thermal properties such as C , ii, k, etc. change rapidly

6.6 Augmentation of Film Boiling Heat Transfer

Several CHF and film boiling experiments have been conducted

on smooth and finned single rod and three-rod geometries • ' '

Small fins with heights varying from 0.002 to 0.004 inch were

attached ~o the heated rods, causing a 9% decrease in CHF. This

undesirable decrease was compensated for by a 307, increase in the

film boiling heat transfer coefficient and a 40% decrease in tempera-(21)

ture fluctuations as compared with smooth rods . Increases in

h up to 44% were reported in (26).

FB

The purpose of the fins was 'to break up the laminar vapour

layer, to introduce turbulence and to increase the heated surface

area.

The effect of film tripper» attached to the unheated wall was

investigated by Hench^ ' . Besides increasing the critical heat

flux, the trippers improved heat transfer in the liquid deficient region

by generating turbulence and removing the liquid from the unheated

wall.

Several other methods such as (a) adding a wetting agent,

(b) introducing subcooled liquid beyond dryout, or (c) special

turbulence promoter8 may also increase the heat transfer in the liquid

deficient region.

- 41 -

7.0 CONCLUSIONS AND RECOMMENDATIONS

(. 1 ) It i s a n t i c i p a t e d t h a t t h e p e r m i s s i b l e s h e a t h t e m p e r a t u r e , i ,-t

f u e l r o d w i l l b e r a i s e d t o p e r m i t f i l m b o i l i n g . A s i 1 1 u s t r a t i d

i n F i g u r e 1 1 , h a t p r e s s u r e s u p t c 1 1 0 0 p s i is r e l a t i v e l y l o wr D

R a i s i n g t h e p r e s s u r e t o a b o v e 2 5 0 0 p s i a c a u s e s a n i n c r e a s e in h .

r e s u l t i n g i n a m u c h l o w e r d r y s h e a t h t e m p e r a t u r e t o r t h e s a m e

m a s s f l o w a n d q u a l i t y

('2) M a n y a d v a n t a g e s m a y b e g a i n e d b y i n c r e a s i n g t h e r e a c t o r <. l a m

p r e s s u r e f r o m s u b c r i t i c a l t o s u p e r c r i t i c a l ( a b o v e 3 2 0 4 p s i a )

( a ) a n i n c r e a s e i n C _ a n d k ( f i g u r e s 1 7 a n d 1 8 ) r e s u l t s in mP v v

i m p o r t a n t i n c r e a s e i n t h e h ; ( h ) s i n c e a s u p e r c r i t i c a l m i x t u r e

i s h o m o g e n e o u s , n o c r i t i c a l h e a t f l u x e x i s t s a n d d r y o u i u r ( l o w

i n s t a b i l i t i e s d o n o t o c c u r ; (c) d u e t o t h e h i g h e r o u t l e i t e m p e r . t -

t u r e s a f t e r t h e b o i l e r , t h e t h e r m a l e f f i c i e n c y 77 = ( î - T V'l\ +• m a x n u n I I M X

o f t h e t u r b i n e i s m u c h h i g h e r ; ( d ) s i n c e s u p e r c r i t i c a l s L e a m lias

a m u c h h i g h e r d e n s i t y t h n n s u b c r i t i c a l l o w p r e s s u r e s t e a m t h e s i z e

of a s u p e r c r i t i c a l p o w e r p l a n t w i l l b e a f r a c t i o n o f t h e s i z e of .•>

p o w e r p l a n t o p e r a t i n g a t 1 0 0 0 p s i a w h i l e d e l i v e r i n g t h e s.imo ani.uint

o f e n e r g y . S e v e r a l c o n v e n t i o n a l s u p e r c r i t i c a l p o w e r p l a n t s h.ive

a l r e a d y b e e n b u i l t in E n g l a n d , G e r m a n y a n d R u s s i a

( 3 ) T h e e m p i r i c a l e q u a t i o n s w h i c h a r e n o w u s e d in f i l m b o i l i n g l a c k

a s o u n d t h e o r e t i c a l b a s i s . it is f e l t t h a t t h e f u n d a m e n t a l

a p p r o a c h a s d e s c r i b e d i n r e l e r e n t e s ( H i , 1 8 , 2 3 , 5 4 ) m a y r e n d e r

b e t t e r c o r r e l a t i o n s .

( 4 ) T h e p r o p o s e d c o r r e l a t i o n s a r e d e s i g n e d f o r t u b u l a r a n d n n n u l n r

t e s t s e c t i o n g e o m e t r i e s . W h e n a p p l i e d t o m u l l i - r o d b u n d l e s i l i r M 1

c o r r e l a t i o n s p r e d i c t h e a t e r t e m p e r a t u r e s w h i i h a r e h i g h e r t h a n

t h e e x p e r i m e n t a l o b s e r v e d t e m p é r a t u r e s . A p p l i c a t i o n ot t h e e q u a -

t i o n s r e c o m m e n d e d in t h i s r e p o r t t e.-ich s u b c h . m n e l m a y r e s u l t

in m o r e a c c u r a t e s u r f a c e t e m p e r a t u r e p r e d i c t i o n s .

- 42 -

40

30

r 20

CD

a.u

4UiX

utata

10

OS0.4

WATERI •11

-WA TER

11

1sI 1

—•—!

ATM

A

{1250

[-44I HAiy I \

ITM

Vo\

! %

===== !—a*a£2

32 200 400 600 CRITICAL 900TtMP

TEMPERATURE , °F

FIGURE 17: Variation of Specific Heat with Temperature(32)

and Pressure

- 43 -

3

m

ou-I4

acUJx

200 400 600 800TEMPERATURE,°F

1000 1200

FIGURE 18: Variation of Steam Thermal Conductivity(32)

with Temperature and Pressure

- 44 -

ACKNOWLEDGMENTS

The author wishes to thank S.C. Abraham for providing and

compiling experimental data for use in this study. Gratitude

should also be expressed to Mrs. A. Serdula for writing the

computer program and to Miss E. Gehlert for typing this report.

- 45 -

R E F E R E N C E S

1 . E . E . P o l o m i k e t a l . , " H e a t T r a n s f e r C o e f f i c i e n t s w i t h A n n u l a r

F l o w D u r i n g O n c e - t h r o u g h B o i l i n g o f W a t e r t o 1 0 0 p e r c e n t

. Q u a l i t y a t 8 0 0 , 1 1 0 0 a n d 1 4 0 0 p s i , " G E A P - 3 7 O 3 , 1 9 6 1 .

2 . E . P _ Q u i n n e t a l . , " T r a n s i t i o n B o i l i n g H e a t T r a n s f e r P r o g r a m , "

T w e l f t h Q u a r t e r l y P r o g r e s s R e p o r t , O c t o b e r - D e c e m b e r 1 9 6 5 , "

G E A P - 5 0 8 1

3 . A . A * B i s h o p e t a l , " F o r c e d C o n v e c t i o n H e a t T r a n s f e r a t H i g h

P r e s s u r e A f t e r t h e C r i t i c a l H e a t F l u x , " ASME 6 5 - H T - 3 1 , 1 9 6 5 .

4, . Z . L M i r o p c l ' s k i y , " H e a t T r a n s f e r i n F i l m B o i l i n g o f a S t e a m -

W a t e r M i x t u r e i n S t e a m G e n e r a t i n g T u b e s , " T e p l o e n e r g e t i k a ,

V o l . 1 0 , N o . 5 , p p 4 9 - 5 3 , 1 9 6 3 .

5 . L _ S . T o n g , " B o i l i n g H e a t T r a n s f e r a n d T w o - P h a s e F l o w , "

J o h n W i l o y i> S o n s , 1 9 6 5 .

6 . S . B e r t o l e t t i e t a l . , " H e a t T r a n s f e r a n d P r e s s u r e D r o p w i t h

S t e a m - W a t e r S p r a y , " C I S E R - 3 6 , 1 9 6 1 .

7 . J . G , C o l l i e r , " H e a t T r a n s f e r a n d F l u i d D y n a m i c R e s e a r c h a s

A p p l i e d t o F o g C o . l e d P o w e r R e a c t o r s , " AECL 1 6 3 1 , 1 9 6 2 .

8 . " T r a n s i t i o n B o i l i n g H e a t T r a n s f e r P r o g r a m , " F o u r t e e n t h

Q u a r t e r l y P r o g r e s s R e p o r t , A p r i l - J u n e 1 9 6 6 , G E A P - 5 1 9 1 .

9 . J , W . H . C h i , " S l u g a n d » " i i m B o i l i n g o f H y d r o g e n , " ASME 6 5 - W A / H T - 3 2

1 0 . W . F , L a v e r t y a n d W . M , R o h s r n o w , " F i l m B o i l i n g of S a t u r a t e d

N i t r o g e n F l o w i n g i n a V e r t i c a l T u b e , " J o u r n a l o f H e a t T r a n s f e r ,

ASME, V o l . 8 9 C , N o . 1 , p p 9 0 - 9 8 , 1 9 6 7 .

1 1 . J . D . P a r k e r a n d R „ J . G r o s h , " H e a t T r a n s f e r t o a M i s t F l o w , "

A N L - 6 2 9 1 1 9 6 2 .

- 46 -

12. R.A. Kruger aad W.M. Rohsenow, "Film Boiling Inside Horizontal

Tubes," Proceedings International Heat Transfer Conference,

Chicago, 1966.

13. H.S. Swenscn et al., "The Effects of Nucleate Boiling Versus

Film Boiling on Heat Transfer in Power Boiler Tubes,"

ASME 61-WA-201, 1961.

14. J.E. Hench, "Transition and Film Boiling Data at 600, 1100 and

1400 psi in Forced Convection Heat Transfer to Water," GEAP-4492,

1964.

15. JCE. Hench, Multi-Rod (Two Rod) Transition and Film Boiling in

Forced Convection to Water at 1000 psia," GEAP-4721, 1964.

J16. E.P. Quinn, "Physical Model of Heat Transfer Beyond the

Critical Heat Flux," GEAP-5093, 1966.

17. G.B. Wallis and J.G. Collier, "Two-Phase Flow and Heat Transfer,"

Summer Course Notes, Vol. Ill, Dartmouth College, 1966.

18. R.P. Forslund and W.M. Rohsenow, "Thermal Non-Equilibrium in

Dispersed Flow Film Boiling in a Vertical Tube," MIT Report

75312-44, 1966.

19. S. Bertoletti et al., "Heat Transfer to Steam-Water Mixtures,"

CISE R-78, 1964.

20. K.R. Schmidt, "Thertnodynamic Investigations of Highly Loaded

Boiler Heating Surfaces," AEC-tr-4033, 1960.

21. D.F. Kunserailler, "Multi-rod, Forced Flow Transition and Film

Boiling Measurements," GEAP-5073, 1965.

22. B. Matzner, "Basic Experimental Studies of Boiling Fluid Flow

and Heat Transfer at Elevated Pressures," Columbia University

Monthly Progress Report, MPR-XIII-2-63, February 1963.

- 47 -

23. R.S. Dougall and W.M« Rohsenow, "Film Boiling on the Inside of

Vertical Tubes with Upward Flow of the Fluid at Low Qualities,"

MIT Report 9079-26, 1963.

24. J.G. Collier et al., "The Effect of Certain Geometrical Factors

on Dryout for High Quality Steam/Water Mixtures Flowing in a

Vertical Internally Heated Annulus at 1000 psia," AECL-1788,

1963.

25. A.W. Bennett et al., "Heat Transfer to Mixtures of High

Pressure Steam and Water in an Annulus," AERE-R4352, 1964.

26. E.P. Quinn, "Forced Flow Transition Boiling Heat Transfer from

Smooth and Finned Surfaces," GEAP-4786, 1965.

27. "Transition Boiling Heat Transfer Program," Quarterly Report

No. 16, October - December 1966, GEAP-5426.

28. E.P. Quinn, "Transition Boiling Heat Transfer Program,"

Eighth Quarterly Progress Report, October - December 1964,

GEAP-4769.

29. "Transition Boiling Heat Transfer Program," Eleventh Quarterly

Progress Report, July - September 1965, GEAP-4963.

30. J. Hilsenrath et al., "Tables of Thermal Properties of Gases,"

National Bureau of Standards, Circ. 564, 1955.

31. Anonymous, "Supercritical Boiler for Drakelow-C Power Station,"

The Engineer, Vol. 28 ; pp 697-700, 1.964.

32. E.R. Eckert and R.M. Drake, "Heat snd Mass Transfer," 2nd Ed.,

McGraw-Hill, 1959.

33. A.D. Lane and J.G. Collier, "Thermal and Irradiation Performance

of Experimental Fuels Operating in Steam-Water Mixtures,"

AECL-2016, 1964.

- 48 -

34. J.E. Hench, "Forced-Flow Transition Boiling Experiments in a

Two Rod Test Section at High Pressures," ASME 64-WA/HT-44.

35. J.G. Collier, "The Problem of Burnout in Liquid Cooled Nuclear

Reactors," AERE-R-3698, 1961.

36. National Engineering Laboratory, "Suppl. to Steam Tables," 1964.

37. L.A. Bromley et al., "Heat Transfer in Forced Convection Film

Boiling," Industiial & Engineering Chemistry, Vol. 45, No. 12,

pp '639-2646, 1952.

38. A.S. Kon'kov, "Experimental Study of the Conditions under which

Heat Exchange Deteriorates when a Steam-Water Mixture Flows in

Heated Tubes," Teploenergetika, Vol. 13, pp 53-57, 1966.

39. J.G. Collier et al., "First Experimental Irradiation of Fog

Cooled Fuel," AECL-1819, 1963.

40. E.P. Quirin, "Forced Flow Heat Transfer to High-Pressure Water

Beyond the Critical Heat Flux," ASME 66-WA/HT-36.

41. H.À. Kearsey, "Steam Water Heat Transfer - Post Burnout Con-

ditions," Chemical & Process Engineering, Vol. 46, pp 455-459,

1965.

42. E.R.C. Ayers, "FLARE Loop Revised Operating Manual," APPE-37,

1965 (AECL unpublished report).

43. M.L. Pomerantz, "Film Boiling on a Horizontal Tube in Increased

Gravity Fields," ASME 63-HT-17.

44. L.H. McEwen et, al., "Heat Transfer Beyond Burnout for Forced

Convection Bulk Boiling," ASME 57-SA-49.

45. E.E.,Polomik et al., "Film Boiling in Steam Water Mixtures in

Annular Flow at 800, 1100 and 1400 psia," ASME 62-WA-136.

- 49 -

46. S.W. Gouse and P. Griffith, "Two Phase Gas Liquid Flew and Heat

Transfer," Summer Course, M.I.T., July 1967.

47. G.F. Hewitt and D.C. Leslie, "Two Phase Flow and Heat Transfer,"

The Engineer, Vol. 31, pp 298-302, 1967.

48. Y.Y, Hsu and J.W. Westwater , "Film Boiling From Vertical Tubes,"

ASME 57-HT-24.

49. M. Uchida and S. Yamaguchi, "Hear. Transfer in Two Phase Flow of

Refrigerant 12 Through Horizontal Tubes," Proceedings Inter-

national Heat Transfer Conference, Chicago, 1966.

50. P.G. Barnett, "The Scaling of Forced Convection Boiling Heat

Transfer," AEEW-R134, 1963.

51. E.A. Okazaki and J.K. Fowler, "Library Programs for the AECL

G-20 Computer," AECL-1744 (Part A), 1963.

52. D.C. Groeneveld, "Review of Scaling Methods as Applied to Dryout

in High Pressure Water," CRNL-33, 1967 (AECL unpublished

report).

53. S.C. Abraham, "Preliminary Post-Dryout Da*~.a for Vertically Upward

Steam Water Annular Flow," APPE-43, 1967 (AECL unpublished

report).

54. A.W, Bennett et al., "Heat Transfer to Steam-Water Mixtures

Flowing in Uniformly Heated Tubes in Which the Critical Heat

Flux has been Exceeded," AERE-R5373, 1967.

55. C.A. Meyer, R.B. McClintock, G.J. Silvestri and R.C, Spencer,

"Thermodynamic and Transport Properties of Steam," ASME,

New York, 1967.

- 50 -

NOMENCLATURE

A Flow area

C Specific heat Btu/lb FP

D Hydraulic equivalent diameter fte

D Heated equivalent diameterH

G Mass velocity

h Heat transfer coefficient

H Enthalpy

k Thermal conductivity

Nu Nusselt number

P Pressure psia

Pr Prandtl number

Re Reynolds number

RMS Root mean square

T Temperature °F

3

V Specific volume ft /lb

X Vapour quality

Y Miropol1skiy1s two-phase flow factor (see Table 1)AT Difference in temperature between wall and

sat r

osaturation temperature F

lb/h.[

Btu/h

Btu/

•j

.ft"-

Btu/

ft-h-

hDe

f t

2

0

l b

°F

/ k

- 51 -

Greek

Q Mean steam void fraction

€ Emissivity

0 Heat flux Btu/h,ft"

|i Viscosity * lb/ft-h

p Density lb/ft

V Latent heat of vaporization Btu/lb

Subscript s

A Actual

b Vapour properties at bulk temperature

c Core

calc. Calculated value

E Eiuilibrium

exp Experimental value

FB Film boiling

f Vapour properties at film temperature -

mean o£ wall and saturation temperature

g Saturated steam

JL Saturated liquid

r Radiative

sat Saturation conditions

w Wall

- 52 -

APPENDIX I

F i lm B o i l i n g Data Obta ined at AECL on 0 . 1 6 0 i n c h Annulus

F = 600 psia

Run No. Mass Flow(lb/h.ft2)

JC 10-6

Quality Heat Flux(Btu/h.ft2)

x lu"5

W a l l Temp. Heat TransferCoefficientBtu/h.ft2-°F

27-03-4727.03-4627.04.4727.04.4627-05-4727-05*4627-05-3927-06-4727.06-4627.06*3927-07-4727.07.4627.07.4027.07-3827.08-4727.08.4627.08.4027.09-4727.09.4627.09.4027.09.3828.03.4720.03.4630.12-4730-12-4030.12-3930.13.4130.13.4(30.13.3930.14.4730.14.4030.14.3930.15.4730.15-4030.15.3930.16*4730.16.4030.16.3930.17-4730.17.4630.17.4030.17-3930.18.4730.18-4630.18.4030.18-3930.18.3830.19-4730.19.4630.19-4030-19-3930-19-38

1.0791.0791.0791.0791.0791.0791.0791.0791.0791,0791.0791.0791.0791.0791.0791.0791.0791.0791.0791.0791.0793.2983.2982.1022.1022.1022.1022.1022.1022.1022.1022,1022.1022.1022.1022.1022.1022.1022.1022.102?.1O22.1022*1022.1022.1022.1022.1022.1022.1022.1022.1022*102

.465

.464,472.471.482• 481.460• 486.485.463.499.498.477.469.512,511.487.528,526.500.4*9.194.193.358.347.345.365,354.351.371.358.355.376.362.359.379.365.361.387.396»370.367.400.399.381.377.374.406.404.385• 380• 377

1.6501.6501.8101.S102.0462.0462.0462.1232,1232.1232.4282.4282.42R2.4282.7242.7242,7243,0853,0853,0853.0853,0853.0851.9681.9681.9682.2762.2762.2762.5772.5772,5772.7972.7972.7972.9422,9422.9423.2963.2963.2963.2963.9753.9753.9753.9T53,9754.2374,2374.2374.2374.237

774.0753.9799.7781.0B37.8R37.182R.2859.4861.4860,2905,7911.9909.4907.3954.7961.4974.7

1002.51011.01024.51019.3

e

768,2704.9709,4706.2751,8753,9753.2790,3786,2790,1816.8818.6324,1842,0842,9851.3872.5865,6882.0890.4944 „ 3939.9954.9970.3964.8981.4977.2994.11012*2988.0

575.9619.4580,0617,0584,2585.5602,1571.1568,2571.0581.2572,9577,0580,3583.6575,4560.4599,2589,5575.5581.5

1180,01114.9920,4906,3920.9872.1869,5872,5862,0877.8867,1859,7«58.1844.6838.8839,8820,7865,1881,1846,a829.6877,9387.6861,4834.0844,1866,0873,6846.4817.4857,9

- 53 -

APPENDIX I ( C o n t ' d . )

P = 1000 psla

Run No. Mass Flow(lb/h.f t2)

x 10-6

Quality Heat Flux(Btu/h.ft2)

x 10" 5

Wall Temp. Heat TransferCoefficientBtu/h.ft2-°F

23-15-4720.15-4620.15.3920>15.3820.16.4720.16.4620.16.3920-16-3820-17-4720-17.3920-17-3620-18-4720-18-3920-13-3820-19-4720-19-3920-19-3821-04-4721-94-4621-05-4721-05-46?1-06-4721-06-4623-04-4723-04-4623-05-4723-05-4623-05-4023-05-3923-06-4723-06-4623-06-4023-06-3924-05-4724-05-4624-06-4724-06-4624-06-4024-06-39

2.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0142.0102.0102.0102.0102.0102.0101.040l « 0 4 01.0401.0401.0401.0401.0401.0401.0401*0403.1213*1213.1213*1213.1213.121

.477

.474

.458

.456

.4B6

.483

.465

.462,494.471.468.502.477.473.510.4R2.479• 240• 239

-241.247.245.453.452.4B5

• 458.452.499.497• 469• 463

• 190.200

160

2.7972.7972.7972.7973,1563.1563.1563.1563,5043.5043.5043.B423.8423.8424.1724.1724.1723.Z963.?963.3663.3663.5723.5721=9681.96B2.5772.5772.5772.5772.B702.8702.9702.8703.7083.7084.3664*1664*3664.366

785.2BIB.678-6.4B04.7B21.2059.8830.3038.5889,4666.7881.4926.9900*3919.7960.5939.B956. «976*6979.1983.5985.4

1024.91032.5

856.9986*6988.4967.5969.8

1035.31033*»1044*31050*4918*4896,7

1011*9989.3966*0987.7

1162.71021.S1160.01078,81141.61002,21108.01077,21017.41091.31043.91006.11083.61027.71004.41058.91015.5763.2758,8767.1763.9744.2732.5601.9632.4584.9582.5611.7608.4586.6588.5576,4569.4994.9

1056.6937.6985.6

1042.3991.4

- 54 -

APPENDIX I (Cont 'd . )

P = 1200 psia

Run No.

16-16-1016.17.1016-17- 916.17. 816.18.1016.18. 916.18- 816.19-1016.19. 916.20-1016.20. 914.04.4714.04-4614-05-4714-05-4614-06-4714-06-4614-07-4714-07-4614-06-4714-08-4614-08-3814-09-4714-09-4614-09-3914-09-3814.10-4714.10.4614.10.3914-10-3815.04-4715-04-4615-05-4715.05-4615.06-4715.06-4616.13.3916.13.3816.14.3916.14.3816-15-3916-15-3816-16-3916-16-3816-17-3916-17-3*16-18-3916-18-3016-19-3916-19-3816-20-3916-20-38

Mass Flow(lb/h.ft2)

x 10~6

1.9551.955i.9551.9551.9551.9551.9551.9551,9551,9551,9551,0101.0101*0101.0101.0101*0101*0101*0101*0101*0101*0101.0101*0101*0101*0101.0101.0101.0101.0101.9371.9371.9371.9371.9371.9371.9551.9551.9551.9551.9551.9551*9551.9551.9551*9551*9551.0551.9551.9551.9551*955

Quality

.415

.418

.418

.403

.421

.421

.405

.424

.424

.425

.425

.433• 431.443• 440• 457• 453• 474• 470.482.478• 444• 482.478• 448• 444.506.501.466.461.246.243.256.252.264.261.436.434.441.440.445• 443•451• 449• 459• 456• 467• 4*4• 474•471• 4«0• 476

Heat Flux(Btu/h.ft2)

x 10~5

3.0193.3913.3913.3913.7363.7363.7364,0574,0574.3594,3591.6501.6501.R10l.«102.(1462»0462.3522.3522.5032°«5O32.503-2.5032.5032.5032.5032.9422.0422.9422.0423.0853.0853.4353.4353,7753.7751.7301.7301.96A1,06»2.1232.1232«42«2.42R2.7972.7973.1563.1563*5041*5043*8423.84?

W a l l Temp.

°F

791,1849.4«30,9824.488J.9A68.3B84.O921. «919.7965.9969,375«,975?. 3814*4813*4847*9ft46«2905*0902.2927. B922.fi920.3925.9915.6918*6032.1

1007.3999.9

1021.71036.6937.S940.3997.1

• 994.01052.61055,0692.5699,172n,7726,2737,0743.1759.4766*0807*4806*6837*8839.8894*2885.O947.5924*3

Heat TransferCoefficientBtu/h.£t2-°F

1355.01207,21292.71326,41191.71245,81184,71147.81154.81097.71088.4«60,8891,3732.2735.4728.8733.3696.4702.2'94,0703.9709,3697.8718.4712.6686,3668,6680.1647.7627.1«33,2«27,8799,6«05,6778,7775,0

13B1.81313.11382.41239 01252.81209.21264.61223.0U66.71170.71167.5H 59.1107J.81103.31012.01078.0

- 55 -

APPENDIX II

This appendix describes an example of the method used Lu

evaluate the exponents of equation 5.3.

Problem: Find the best fits of the parameters a, b and c in the

correlatIon :

k b ch = a — Re Prexp D

e

k. b cSolution: The equation h = a Re Pr may be written as

cale De

H = A + log — + b log Re + c log Pr

e

where H = log h and A = log ac c a 1 c

)2 = t where H = log hi e exp

i

Hence

1=1 " 1=1

where n is total number of h !sexp

Minimizing E with respect to A, b and c results

Z 2 (H - H ) = 0 ... (II. 0

e c1=1

2 (H - H ) log Re = 0 ... (II.2)e c

1=1

- 56 -

2 (H - H ) log Pr = 0e c

... (II.3)

a, b and c can now be found directly from equations II.1 - II.3

Additional copies of this documentmay be obtained from

Scientific Document Distribution OfficeAtomic Energy of Canada Limited

Chalk River, Ontario, Canada

Price - $1.50 per copy .

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