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BIBLIOGRAPHICAL REVIEW OF DNB DATA IN NON­UNIFORMLY HEATED C H A N N E L | |

SfBND COMPARISON WITH THEORETICAL H M j PREDICTIONS BY WAPD­188, B u g

-, Α Ι W­2 AND W­3 CORRELATIONS I S Ä ;

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■Ml ft l i s t Wm M. GUYETTE and N. HOPPE

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lifl EURATOM/US Agreement for Cooperati©

EURAEC Report No. 1915 prepared by

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Contract Euratom/BelgoNucléaire/CEN No. 001­64­1 TRÜB

Paper presented at the European Two­Phase Flow Group Meeting,

Bournemouth, England ­ June 12­15, 1967

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EUR 3397 e BIBLIOGRAPHICAL REVIEW OF DNB DATA IN NON-UNIFORMLY HEATED CHANNELS AND COMPARISON WITH THEORETICAL PREDICTIONS BY WAPD-188, W-2 AND W-3 CORRELATIONS by M. GUYETTE and N. HOPPE (BelgoNucléaire)

European Atomic Energy Community — EURATOM EURATOM/US Agreement for Cooperation EURAEC Report No. 1915 prepared by BelgoNucléaire, Brussels (Belgium) Contract Euratom/BelgoNucléaire/CEN No. 001-64-1 TRUB Paper presented at the European Two-Phase Flow Group Meeting, Bournemouth, England — June 12-15, 1967 Brussels, November 1967 — 48 Pages — 15 Figures — FB 60

A bibliographical review of DNB data in non-uniformly heated chan­nels has been carried out.

The analysis of these data shows that the influence of the non-unifor­mities on the DNB decreases when the inlet quality increases, all the other parameters (geometry, pressure, mass velocity) being kept unchanged.

Various methods of predicting DNB in non-uniformly heated chan­nels are examined.

A comparison between experimental values and theoretical predictions shows that the use of the F factor developed by Westinghouse, always improves the validity of the predictions for all the considered corre­lations.

In the case of marked non-uniformities like hot patches and low qualities the discrepancies between experimental values and theoretical predictions are generally too large as to allow the use of the selected method of calculation for detailed design and performance studies.

EUR 3397e

EUROPEAN ATOMIC ENERGY COMMUNITY - EURATOM

BIBLIOGRAPHICAL REVIEW OF DNB DATA IN NON-UNIFORMLY HEATED CHANNELS AND COMPARISON WITH THEORETICAL

PREDICTIONS BY WAPD-188, W-2 AND W-3 CORRELATIONS

by

M. GUYETTE and N. HOPPE (BelgoNucléaire)

1967

EURATOM/US Agreement for Cooperation EURAEC Report No. 1915 prepared by

BelgoNucléaire, Brussels - Belgium Contract Euratom/BelgoNucléaire/CEN No. 001-64-1 TRUB

Paper presented at the European Two-Phase Flow Group Meeting, Bournemouth, England - June 12-15, 1967

SUMMARY

A bibliographical review of DNB data in non-uniformly heated chan­nels has been carried out.

The analysis of these data shows that the influence of the non-unifor­mities on the DNB decreases when the inlet quality increases, all the other parameters (geometry, pressure, mass velocity) being kept unchanged.

Various methods of predicting DNB in non-uniformly heated chan­nels are examined.

A comparison between experimental values and theoretical predictions shows that the use of the F factor developed by Westinghouse, always improves the validity of the predictions for all the considered corre­lations.

In the case of marked non-uniformities like hot patches and low qualities the discrepancies between experimental values and theoretical predictions are generally too large as to allow the use of the selected method of calculation for detailed design and performance studies.

KEYWORDS

NUCLEATE BOILING HEATING BIBLIOGRAPHY VARIATIONS TUBES NUMERICALS COOLANT LOOPS

Departure nucleate boiling

- 5 -

BIBLIOGRAPHICAL REVIEW OF DNB DATA IN NON-UNIFORMLY

HEATED CHANNELS AND COMPARISON WITH THEORETICAL PREDICTIONS

BY WAPD - 188, W - 2 AND W - 3 CORRELATIONS ( " )

INTRODUCTION

The heat flux distributions to be considered in core design and performance

studies are generally non-uniform ones.

In the cases where these distributions have large non-uniformities such as hot

patches most of the predictions by existing correlations differ appreciably from

the measured values. In order to achieve a higher core performance in these

cases it is desired to have an improved method of DNB calculations in non-uniform

channels.

A bibliographical review of DNB correlations and methods of calculation has

therefore been carried out with a view to select the most appropriate means of

calculation of DNB heat fluxes in the case of marked non-uniformities.

Γ71 Manuscript received on September 29» 1967,

1. EXPERIMENTAL DATA FOR AXIALLY NON-UNIFORM HEAT FLUX PROFILES. A s e a r c h for DNB e x p e r i m e n t a l d a t a for n o n - u n i f o r m l y h e a t e d c h a n n e l s hae

b e e n c a r r i e d out in the l i t e r a t u r e . Al l the d a t a c o l l e c t e d a r e s u m m a r i z e d in

the t a b l e s of A p p e n d i x I and Append ix II. Append ix I i s r e l a t i v e to ax i a l non -

u n i f o r m i t i e s , while Append ix II i s r e l a t i v e to r a d i a l n o n - u n i f o r m i t i e s . One

h a s d i s t r i b u t e d t h e s e d a t a in t h r e e m a i n g r o u p s a c c o r d i n g to the type of

ax i a l p r o f i l e s .:

(i) hot pa t ch p r o f i l e s

(ii) c o s i n e o r chopped c o s i n e p r o f i l e s

( i i i) and m i s c e l l a n e o u s p r o f i l e s inc lud ing s k e w e d c o s i n e .

The d a t a e x a m i n e d a r e g e n e r a l l y too s c a n t y and too l a c k i n g in p r e c i s i o n

to d r a w p r e c i s e c o n c l u s i o n s on the e f fec t s of hea t flux n o n - u n i f o r m i t y on

DNB. H o w e v e r s o m e g e n e r a l t r e n d s can be found :

1. 1. Hot p a t c h e s

T h e s e p r o f i l e s a r e g e n e r a l l y c h a r a c t e r i z e d by a hot spot f a c t o r £

which i s the r a t i o of the hea t flux at a poin t in the hot p a t c h to the

one t ha t would e x i s t at t ha t point if the s e c t i o n w a s not p a t c h e d .

The e x p e r i m e n t a l v a l u e s a r e often e x p r e s s e d in t e r m s of the p e a k

e f f e c t i v e n e s s E . T h i s p a r a m e t e r i s g iven by :

E = q D N B u n i f o r m " q D N B avg Ρ q" _ η "

^ D N B p e a k MDNB avg

w h e r e :

ali . , : DNB h e a t flux of a u n i f o r m h e a t e d s e c t i o n wi th the n D N B u n i f o r m

s a m e fluid cond i t i ons (at the in l e t o r at the DNB

l o c a t i o n d e p e n d i n g on the a u t h o r s ) and the s a m e

channe l g e o m e t r y . q^uTT, , : l o c a l v a l u e of t he hot p a t c h flux when DNB o c c u r s

DNB p e a k r

QÌ-L-TT , : average value of the heat flux in the patched section DNB avg ö r

when DNB occurs.

Data of Weiss (1_0)(1JJ, Styrikowitch (14), Tong (17), Todreas (18)

and Stevens (19) (2 1) were examined. Qualitatively all these data

show that the peak effectiveness E decreases when the quality at the

DNB point increases. In other words at a given pressure the influence

of a hot patch in DNB will be stronger for smaller values of the local

enthalpy. A decrease of the length of the hot spot decreases the peak

effectiveness while an increase of the hot spot factor increases the

peak effectiveness.

Consistent trends in the effects of the other parameters as pressure, mass

velocity, channel geometry, on the peak effectiveness could not be

deduced from the analysis of the considered results.

1.2. Cosine or chopped cosine profiles.

More confusing is the examination of the data obtained with cosine or

chopped cosine profiles. (1), (7j, (9), (l_3j, (22)> (ID· (lâ)> (§J- (25),

(26), (27), (28), (29), (30), Q8J, (31), Q6) , (20), (43), (44).

Indeed the difference between the data for uniform and corresponding

cosine profile having the same inlet conditions is often smaller than

the experimental error.

One can only conclude that the DNB power of a cosine or chopped cosine

profile is generally comprised between + 20 % of the power for a

uniformly heated section having the same geometry and the same inlet

conditions.

1.3. Miscellaneous distributions.

These distributions comprise primarily dissymmetrical cosine as

upskewed or downskewed chopped cosines or ramps (44), (18), (30),

(26), (22), (15), (42), (3), (4), (5), (12), (37), (38). The downskewed

cosine profile (peak near the outlet) shows generally a smaller DNB

power than the uniform one having the same geometry and the same

inlet conditions. The upskewed cosine profile (peak near the inlet) is from the DNB point of view very near the same as the symmet r i c cosine profile. A consistent t rend for all these dis t r ibut ions is that a profile having a peak near the outlet is l e s s favourable than a uniform profi le. The influence of the peak is general ly more pronounced when the local quality at the level of the peak is sma l l e r .

2. METHODS OF APPLICATION OF EXISTING CORRELATIONS FOR

AXIALLY NON-UNIFORM DISTRIBUTIONS.

One has examined in the literature the main methods used for predicting

the DNB heat fluxes in non-uniformly heated channels. These methods are

summarized hereunder.

2. 1. System parameter and local parameter correlations (2), (39), (6).

DNB correlations are generally expressed in terms of either system

parameters or local parameters. In the first type correlations the

independent variables are generally the inlet enthalpy, the mass

velocity, the equivalent diameter, the length of the channel and

the system pressure. The dependent parameter is in this case

either the DNB heat flux or the DNB enthalpy.

The second type correlations involve as independent variables :

local enthalpy or quality, mass velocity, equivalent diameter, length

of the channel and the pressure, the dependent variable being gene­

rally the DNB heat flux.

For uniformly heated channels, these two types of correlations can

be deduced from one another with the help of the heat balance

equation :

, /G H

In this equation :

DNB H, in P h L 'DNB'

H DNB

H.

enthalpy at the DNB point

inlet enthalpy

heated perimeter of the channel

L : total heated length

G : mass velocity

q'!^TT, : DNB heat flux HDNB This is no more true when the axial heat flux distribution is non-uniform.

10

H o w e v e r s o m e a u t h o r s s t a t e tha t the a v e r a g e DNB hea t flux of a n o n -

u n i f o r m l y h e a t e d channe l i s a p p r o x i m a t e l y equa l to tha t of a u n i f o r m l y

h e a t e d one hav ing the s a m e in le t e n t h a l p y , m a s s v e l o c i t y and g e o m e t r y .

H o w e v e r e x p e r i m e n t a l e v i d e n c e shows tha t t h i s i s not a l w a y s t r u e .

F o r i n s t a n c e a channe l with s u b - c o o l e d ex i t cond i t i ons hav ing a d i s t r i ­

bu t ion wi th a p e a k n e a r the ex i t wil l have an a v e r a g e DNB hea t flux

s m a l l e r t han in the c a s e of an u n i f o r m d i s t r i b u t i o n . The s i m p l e

a p p l i c a t i o n of a s y s t e m p a r a m e t e r s c o r r e l a t i o n for a n o n - u n i f o r m l y

h e a t e d p ro f i l e i s t h u s only va l id for l i m i t e d a p p l i c a t i o n s .

2 . 2 . R e f e r e n c e c h a n n e l .

G e n e r a l l y the c a l c u l a t i o n of the DNB h e a t flux for a non u n i f o r m l y

h e a t e d channe l i s c a r r i e d out for a n u m b e r of po in t s a long the c h a n n e l .

F o r e a c h point of c a l c u l a t i o n it i s c u s t o m a r y to def ine a " r e f e r e n c e "

u n i f o r m l y h e a t e d c h a n n e l . The p a r a m e t e r s s e l e c t e d for d e s c r i b i n g

t h i s " r e f e r e n c e " c h a n n e l d i f fer f r o m one a u t h o r to the o t h e r . The

m o s t c o m m o n o n e s a r e g iven h e r e u n d e r .

2 . 2 . 1. Le_ng_th_p_f_the__re_fe r e n ç e _çhaJ^ne_L_

(i) L o c a l l e n g t h .

The l e n g t h of the r e f e r e n c e c h a n n e l i s equa l to the length

of the n o n - u n i f o r m l y h e a t e d channe l f r o m i t s in le t up to

the point of c a l c u l a t i o n .

(ii) T o t a l l e n g t h .

The l eng th of the r e f e r e n c e channe l i s equa l to the to t a l

l eng th of the n o n - u n i f o r m l y h e a t e d s e c t i o n .

( i i i) E q u i v a l e n t l e n g t h .

The l eng th of the r e f e r e n c e c h a n n e l i s equa l to the l eng th

of an h y p o t e t i c a l u n i f o r m l y h e a t e d channe l hav ing :

- a t o t a l p o w e r output e q u a l to t ha t of t he n o n - u n i f o r m l y

h e a t e d channe l b e t w e e n the in l e t and the c o n s i d e r e d po in t .

- an u n i f o r m hea t flux e q u a l to the l o c a l flux at the c o n s i ­

d e r e d point of the n o n - u n i f o r m l y h e a t e d c h a n n e l .

11

2 . 2 . 2 . p iam^e j^of^h^^e j ' ^ r^ j i^^channe^^

(i) Wetted equivalent d i ame te r . The reference channel is assumed to be a round tube having a d iameter equal to the wetted equivalent d i amete r of the non-uniformly heated channel D e defined by :

D = I A P w

where : D equivalent wetted d iamete r

e A c ro s s section of the channel Ρ wetted p e r i m e t e r of the channel

w (ii) Heated equivalent d i ame te r .

The reference channel is considered as a round tube of the same d iamete r as the heated d iameter of the non-uniformly heated channel defined by :

D - 4 A h " ^

where : P, heated p e r i m e t e r of the channel.

(iii) The reference channel has a d i amete r which is a function of the values D e and D, defined hereabove.

2 . 2 . 3 . Reference fluid conditions.

The m a s s velocity and the enthalpy of the fluid in the reference channel are taken the same as in the non-uniformly heated one e i ther at the inlet or at the considered point according as use is made of a sys tem p a r a m e t e r or a local p a r a m e t e r concept.

2 . 2 . 4 . Vahae_s_of_tJie_Jie_at^ha2C_c^mjpar^ The value of the DNB heat flux predicted by the cor re la t ion can be compared with e i ther the local heat flux or the average heat flux up to the point of calculation.

- 12

2 . 3 . C u r r e n t m e t h o d s of c a l c u l a t i o n .

It r e s u l t s f r o m the h e r e a b o v e p a r a g r a p h s tha t a v a r i e t y of v a l u e s can

be u s e d in p r i n c i p l e for e a c h of the p a r a m e t e r s i n t e r v e n i n g in the

DNB c o r r e l a t i o n , l e a d i n g to a n u m b e r of d i f f e ren t v a l u e s of the p r e ­

d i c t e d DNB f l u x e s . H o w e v e r , only t h r e e m e t h o d s of c a l c u l a t i o n a r e

c u r r e n t l y u s e d :

2 . 3 . 1. Oy e r_al l_gowe r _o r _§Υ_?_Γ_?Ε.?_ ίΐ-ϋϊ.·

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

a s s u m e s tha t for the s a m e in le t c o n d i t i o n s and the s a m e

g e o m e t r y , the n o n - u n i f o r m l y h e a t e d channe l and the r e f e r e n c e

c h a n n e l have the s a m e to t a l h e a t i n g p o w e r i . e . the s a m e

a v e r a g e h e a t flux o r the s a m e e n t h a l p y i n c r e a s e when DNB

o c c u r s . T h i s m e t h o d i s a l s o c a l l e d o v e r a l l l eng th concep t

b e c a u s e the c o m p a r i s o n i s m a d e on DNB p o w e r o v e r the

whole channe l length in e a c h c a s e r e g a r d l e s s of the p o s i t i o n

of D N B .

2. 3 . 2 . E q u i v a l e n t l e n g t h m e t h o d o r i n t e g r a t e d p o w e r m e t h o d .

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

At any point of c a l c u l a t i o n r e f e r e n c e i s m a d e to the equivalent

l eng th def ined a s h e r e a b o v e . C o m p a r i s o n of the DNB h e a t flux

is m a d e with the loca l hea t flux.

2 . 3 . 3 . Loc3l_JLej^^_method_.

C a l c u l a t i o n s a r e m a d e u s i n g the l oca l l eng th concep t def ined

h e r e a b o v e .

C o m p a r i s o n of the DNB hea t flux i s m a d e on the l o c a l h e a t

flux when u s i n g a l o c a l p a r a m e t e r c o r r e l a t i o n and on the

a v e r a g e h e a t flux for a s y s t e m p a r a m e t e r c o r r e l a t i o n .

13 -

3. SELECTION OF A PREFERRED METHOD OF CALCULATION OF THE DNB HEAT FLUXES FOR AXIALLY NON-UNIFORM DISTRIBUTIONS

F r o m the previous paragraph it appears that there exis ts three main possibi l i t ies of choosing the " r e f e r e n c e " channel for the calculation of DNB heat fluxes in non-uniformly heated channels. The f irst possibil i ty is based on the overal l power method. Predic t ions of the DNB power by this method do not depend upon the shape of the heat flux distr ibution and their successful application is therefore l imited. This method appears to give fair predict ions of the DNB power in some cases as cosine profiles but does not provide any indication on the location of DNB. Moreover , this method fails completely to predict DNB occurence for hot patched profiles. For this reason, this method has not been selected as the p re fe r red one. On another hand the equivalent length method and the local length method allow to predict the location of DNB occurence. The local length method can be easi ly applied and is cur ren t ly re fe r red to in the l i t e ra tu re . Fo r this reason this method has been selected he re . However the use of this method does not lead to a fair predict ion of the known exper imenta l data. An improved mean of calculation based on the local length method has therefore been worked out. This makes use of the F factor developed by Westinghouse (40). This method takes into account the memory effect on DNB. It is based on the fact that the DNB occurence depends as well upon the bulk fluid conditions as upon the conditions of the boundary l a y e r along the heating surface. A method of determinat ion of these boundary l a y e r conditions has been worked out based on the fact that a superheated liquid layer is insulated from the bulk coolant flow by a bubble layer .

Using a simplified model for the represen ta t ion of the liquid layer and making a heat balance of this l ayer , leads to an express ion giving the non-uniform DNB heat flux as a function of the heat flux in the equivalent uniformly heated channel.

14 -

In this express ion the value of a constant C is given by an empi r ica l cor re la t ion . This relat ion is genera l and can be used with any cor re la t ion predict ing the DNB heat flux in uniformly heated channels. Hereaf ter use will be made of this factor in conjunction with three co r r e l a t i ons , in o rde r to de te rmine the improvement brought by the use of the F factor. The express ion of the F factor is as follows :

,, , /, -C lDNB ν • q" loc ( 1 - e ) o

; :

DNB % Ν Β - Ζ ' q"(z)e

with q" DNB, Ν q" DNB,EU

F

where q" DNB, Ν q" DNB, EU C

DNB

non-uniform DNB heat flux equivalent uniform DNB heat flux empi r i ca l constant axial dis tance from inception of local boiling distance from inception of local boiling to point of DNB

The value of the constant C in the repor t of Tong (40) is given by :

C = 0. 44 Ρ " Χ PNB* ( G / 1 0 6 )

7. 9

1. 72 i n . -1

where

X DNB : quality at DNB point

G : m a s s velocity

Studies have a lso been performed by Fiat and Sorin QJ, (30) i n o rde r to improve the value of the constant C in the equation of F.

- 15 -

These studies have led to the following equations

for - 0. 25 < "X < 0. 15

v sat ;

with a = 6. 1 0 5 + 0 . 44 10" 3 ( p - 1 0 0 0 )

f(T J = 39. 74836 1 0 ~ 1 5 T t - 64.83156 Ι Ο - 1 2 Τ 3 sat sai sai

38.6336 ΙΟ" 9 Τ " + 47.189 10" Τ sat sat

1.9452 10" 3

for 0. 15 < X < 0. 65

-5 1 -1 C = 8. 09 10 — in.

X V (G/106) X · 5 De

Ιό

4. COMPARISON OF THE PREDICTIONS BY THREE SELECTED CORRELATIONS WITH EXPERIMENTAL VALUES

4. 1. Corre la t ions used

The three following cor re la t ions WAPD-188, Westinghouse W-l or W - 2 and Westinghouse W-3 have been used for comparing available exper i ­mental data on non-uniformly heated channels with theoret ical predict ions.

4. 1. 1. WAPD-188 corre la t ion

Use has been done of the best fit cor re la t ion for round tubes given

in the Appendix III.

4. 1. 2. W-l and_W^2^orj^l_a_tions_(29j

The W-2 cor re la t ions differ from the W-l ones by a factor taking into account the influence of non heated walls in the channel. For channels without unheated walls the express ions of the W-l and W-2 cor re la t ions a re identical. As in this paper one has only considered exper imenta l resu l t s for channels without unheated walls no dist inction is made between these two cor re la t ions . The equations a re also given in Appendix III. The first equation has been used for quali t ies smal le r than zero. The second one is used for quality values l a rge r than zero. The DNB margin predicted by the two cor re la t ions hereabove is not necessa r i ly the same for a quality equal to zero . As it will be shown la ter thie is the reason for some observed d i sc repanc ies .

4. 1. 3. Wj:^^or_relation

The express ion of this cor re la t ion is given in the Appendix III. This equation is valid in the range of outlet quali t ies between - 0. 15 and + 0 . 15. When at tempt is made to use it for quali t ies l a r g e r than + 0. 15 the cor re la t ion gives very small values of DNB heat fluxes and even negative values. Care must thus be taken when using this cor re la t ion out of i ts validity range.

17

4. 2. Comparison of theore t ica l predict ions with exper imenta l data

The difference between the exper imenta l values and the predicted ones

when the F factor is not used a re general ly more important for d i s t r i ­

butions with hot patches. For this reason the available exper imenta l

data on hot patches were chosen preferent ia l ly to show the effect of

the use of the F factor with the three considered cor re la t ions . Almost

all the known exper imenta l data with hot patches a re relat ive to round

tubes. This allows to el iminate the uncer ta in t ies involved in the choice

of the equivalent d iamete r (either wetted or heated).

4. 2. 1. D a t a j r q m AEE_W_­R_4_26Jl_9)

These data were ex t rac ted from (19) and were adapted to a

water sys tem using the scaling factors determined, by Eastwood

and Stevens (45) (21). Comparison has been made for three

values of the channel length and one value of the m a s s velocity.

The exper imenta l values a re plotted v e r s u s the corresponding

predicted ones for the same inlet enthalpy in Hgures 1 , 2 and 3.

F igure 1 is relat ive to the WAPD­188 corre la t ion. Agreement

is much bet ter when the F factor is used although calculat ions

still largely underpredic t the DNB fluxes. The agreement

becomes however s imi la r to that obtained for the data on uniform

heated channels , repor ted in (19).

The W­2 cor re la t ion predic ts very well in this par t icu la r case

altough the F factor is not used for quali t ies l a rge r than zero.

For the points between b racke t s a DNB margin of 1 was calculated

in the subcooled region before this marg in reaches 1 in the

quality region. This is due to the overpredic t ion of the Λ H

equations for the very short lengths. The predict ion of the W­2

cor re la t ions for these points should therefore not be regarded as

valid.

All the points for L = 38. 80 in.and 73. 50 in.in these data have

outlet quali t ies far out of the validity range of the W­3 corre la t ion.

For this reason the W­3 cor re la t ion could not be used. When

applying the F factor it can be seen from F igu re s 1 to 3 that there

is li t t le difference between the resu l t s obtained with respect ively

thé Tong and the Fiat express ions .

4 . 2 . 2 . Data J r om JWAPJD-TH- 338J IO)

These data a re re la t ive to rec tangular channels . The exper imenta l values and the theoret ical predict ions a re given for each cor re la t ion on F igures 4, 5 and 6. These F igures show that the agreement between exper imenta l and predicted values is bet ter when using the F factor for all the cor re la t ions . The difference between predict ions using r e spec t i ­vely trie Tong and the Fiat express ions of F is ra ther small .

4. 2. 3. D a t a j r o j n D^kladY_vol^J7J^°_7_(l_4)

In this repor t data obtained in the absence or in the presence of a compress ib le volume between the inlet thrott le and the heating section a re given in form of curves for var ious total lengths, hot spot lengths and m a s s veloci t ies . Only those with no compress ib le volume have been examined. One has used the data in the - 0. 2, + 0. 2 outlet quality range for the short tubes (16 cm) and in the whole outlet quality range for the longer tubes (50 and 94. 5 cm). Comparing the exper imenta l and predicted values one must bear in mind that the p r e s s u r e (1422 psia) l ies out of the validity range (1850 - 2150 psia) of the WAPD-188 corre la t ion . Again the =r- rat io for the smal les t length (rat io of 20) l ies out of the β validity range of the WAPD-188 and W-2 cor re la t ions (between 21 and 365) and the smal les t section length (6. 3 in) l ies out of the validity range of the W-3 cor re la t ion (10-79 in). These cor re la t ions have never the less been applied to the considered data but such a compar ison is given only to examine the behaviour of these co r re la t ions out of their validity range.

For the smal les t length notable d i sc repanc ies a re obtained. However it can be seen f romFigures 7 to 1 2 that the F factor util ization reduces it and in this case e r r o r s a re general ly l ess than 20 % in the - 0. 2, + 0. outlet quality range.

- 19

In the average length case (50cm) the util ization of the F factor is most favourable for the WAPD-188 corre la t ion. Discrepancies dec rease from about 40 % below 20 % for the highest m a s s velocity except for an outlet quality higher than 0. 35 and from 50 % below 30 % for the lowest m a s s velocity. In the same way uti l ization of the F factor reduces d iscrepancy for the W-2 cor re la t ion but large e r r o r s a r i s e in cer ta in cases (in brackets) when along the tes t section the subcooled equation and the quality equation a re used success ively , leading to an e r roneous DNB predict ion ups t r eam the hot spot assoc ia ted with the q" DNB corre la t ion. The W-3 cor re la t ion predic ts general ly well except for outlet quali t ies far from its validity range (- 0. 15 to + 0. 15) in outlet quality. Utilization of the Fia t F factor general ly yields bet ter agreement than the util ization of the Tong F factor. In the l a rges t considered length, the agreement when F factors a re applied to WAPD-188 cor re la t ion is much bet te r ; the e r r o r s dec rease from 50 % to 25 % even at high outlet quality (0 . 6), the F Fiat uti l ization giving e r r o r s below 20 %. WAPD-188 predic ts r a the r well the uniform case . Except at outlet quali t ies l a r g e r than 0. 55, the Δ H DNB-W-2 cor re la t ion gives good resu l t s ( < 20 %) , the agreement being bet ter than that for the uniform case prediction (25 %). The W-3 cor re la t ion has not been examined for this length, the DNB quali t ies lying much out of i ts validity range. With the shortcomings mentioned hereabove, it appears that uti l ization of the F factor yields an improved agreement (- 20 %) within the cor re la t ion validity range, the Fia t F factor being general ly be t ter than the Tong F factor especial ly at low DNB quali t ies . The best ag reement is general ly obtained with the W-3 co r r e l a t i on .

20

4. 2. 4. Ρ ^ ^ £ 9 2 Ώ ^ £ ^ 4 9 _ 0 _ β _ ( 3 0 )

These exper imenta l data, obtained with downskewed cosine profiles having a form factor of 1.4, have been compared with cor re la t ions (Fig. 1 3 to 1 5). Application of F „ and

v 6 ι vt- Tong F p . . factors has pract ical ly no influence on the predicted values. This is due to the fact that the values of the F factors a re close to unity in the DNB region. Corre la t ions give overpredic ted values , par t icu lar ly for the WAPD-188 and W-2 cor re la t ions at a m a s s velocity of 0. 142 k g / c m sec when the exit quality is positive (overpredict ion l a rge r than 20 % for χ > 3 % or χ. > - 30 %). Except for this case

out in predict ions by the three considered cor re la t ions show a good agreement with exper imenta l values , the W-3 corre la t ion appearing to be the best one.

21

CONCLUSIONS

F r o m the analys is of available exper imenta l data on DNB heat flux in non-uniformly heated channels one could deduce some genera l t r e n d s . The most significant one is that the influence of the non-uniformit ies on the DNB d e c r e a s e s when the inlet quality i n c r e a s e s , all the other p a r a m e t e r s (geometry, p r e s s u r e , m a s s velocity) being kept unchanged. A survey of var ious methods of application of DNB cor re la t ions has a lso been pe r fo rmed . Out of these the local length method appears to give bet ter predic t ions than the overa l l power method and is more easi ly ap ­plied than the equivalent length method. The local length method was ap­plied with the WAPD - 188, W-2 and W-3 c o r r e l a t i o n s . The use of the F factor developed by Westinghouse always improves the predict ions p a r ­t icular ly for profi les with hot pa t ches .

The values of the F factor calculated by the Tong cor re la t ion do not dif­fer appreciably from those calculated by the FIAT cor re la t ion . Of the th ree considered co r r e l a t i ons , the W-3 appears to be the best one when used in its range of validity for what concerns the quality (outlet quality between - 0.15 and + 0 .15) .

However in the case of marked non-uniformit ies like hot patches and low quali t ies the d i sc repanc ies between exper imenta l values and theore t ica l predic t ions a r e general ly too la rge as to allow the use of the selected method of calculat ions for detailed design and performance s tud ies . Fu r the r exper imenta l and theore t i ca l work in this field appears t h e r e ­fore to be d e s i r a b l e .

22

ACKNOWLEDGEMENTS

The authors wish to acknowledge the useful d iscuss ions they had with M. de Waegh in the course of the prepara t ion and the accom­pl ishment of this work.

23

BIBLIOGRAPHY

(1) P rev i t i et a l .

(2) P rev i t i et a l .

(3) Alessandr in i et a l .

(4) Styrikovitch et a l .

(5) Becker

(6) Barnet t

(7) Lee

(8) Lee and Oberte l l i

(9) Lee

(J_0) Weiss

(II) Weiss

An investigation on some p a r a m e t e r s influencing non­uniform heat flux DNB predict ion EUR 3114 e (1966)

Forced convection burnout and hydrodynamic instability exper iments for water at high p r e s s u r e . P a r t III -Comparison between exper imenta l burnout data and theore t ica l predict ion for uniform and non-uniform heat flux distr ibution EUR 3113 e (1966)

Cr i t ica l heat flux for fully developed flow s team -water mix tures in round ver t i ca l tubes with an in te r ­mediate non heated section CISE R-69 (1963)

Teploenerget ika n° 5 (I960) p . 81

A cor re la t ion for burnout predict ion in ve r t i ca l rod bundle S 349 (1966)

The predict ion of burnout in non-uniformly heated rod c lus t e r s from burnout data for uniformly heated round tubes AEEW-R 362 (1964)

Burnout data for high p r e s s u r e water in a tube with uniform and cosine axial heat flux dis t r ibut ions V D M C / P W P / P 134 (1964)

An exper imenta l investigation of forced convection burnout in high p r e s s u r e wa te r . P a r t II - P re l imina ry resu l t s for round tubes with non-uniform axial heat flux distr ibution AEEW - R 309 (1963)

An exper imenta l investigation of forced convection burnout in high p r e s s u r e wa te r . P a r t III - Long tubes with uniform and non-uniform axial heating AEEW - R 355 (1965)

Hot patch burnout tes t s in a 0. 097 in χ 1 in χ 27 in long rectangular channel at 2000 psia WAPD - TH - 338 .(1957)

1 . 3 : 1 hot patch burnout tes t s at 800, 1200 and 2000 psia in a 0.093 in χ 1 in χ 27 in long rec tangular chan­nel WAPD - TH - 412 (1958)

- 24

(IA)

OD

OD

(lì)

(16)

(17)

(il)

(11)

(20)

(21)

(22)

(23)

ludd et a l .

De Bortoll i et a l .

Styrikovitch et a l .

Styrikovitch at a l .

Cas ter l ine

Tong

Burnout in tubular flow with non-uniform heat flux BAW - 3238 - 9 (1965)

Forced convection heat t ransfer burnout studies for water in rec tangular channels and round tubes at p r e s s u r e s above 500 psia WAPD - 188 (1958)

The influence of local ra ised heat fluxes along the length of a channel on the boiling c r i s i s Sov. Phys . Doklady vol. 7 n° 7 pp. 597-599 (1963)

The effect of uneven heating along a tube on the c r i t i ­cal t he rma l s t r e a m s Sov. Phys . Doklady vol. 6 n° 8 pp. 691-693 (1962)

Second exper imenta l study of dryout in a long ver t ica l tube with a cosine heat flux Columbia Universi ty Topical Report n° 5 of Task XVI of Contract (AT/30-3)-187

DNB (burnout) studies in an open lattice core Vol. 1 - WCAP 3736 (1964)

Todreas and Roe he now The effect of axial heat flow distr ibution on burnout in annular two phases flow AIChE p . 78 (1966)

Stevens et a l .

Lee

Stevens et a l .

Ber to le t t i et a l .

De Bortoll i et a l .

An exper imenta l compar ison between forced convection burnout in F reon-12 flowing vert ical ly upwards through uniformly and non-uniformly heated round tubes AEEW - R 426 (1965)

An exper imenta l investigation of forced convection burnout in high p r e s s u r e wa te r . P a r t IV - Large dia­mete r tubes at about 1600 psia AEEW - R - 479 (1966)

An exper imenta l investigation into forced convection burnout in Freon , with re ference to burnout in water uniformly heated round tubes with ver t i ca l upflow AEEW - R 321 (1964)

Cr i t ica l heat flux data for fully developed of s team water mixture in round tubes with a non-uniform axial power distr ibution CISE R - 74 (1963)

Additional burnout data for a rec tangular channel ha­ving a cosine axial heat flux WAPD - TH - 227 (1956)

- 25 -

(24) Cook A boiling water r eac to r r e s e a r c h and development p rog ram - F i r s t quar te r ly repor t (I960) GEAP - 3558

(25) ludd et a l . Non-uniform heat generat ion exper imenta l p rog ram BAW - 3238 - 8 (1965)

(26) Janssen and Kervinen Burnout conditions for non-uniformly heated rod in annular geometry GEAP - 3755 (1963)

(27) Bell Corre la t ion of burnout heat flux data at 2000 psia Nucl . Sci . & Eng. 7, pp. 245 - 251 (I960)

(28) Longo A s ta t i s t i ca l study of subcooled burnout including the effect of local hot spots KAPL - 1744 (1957)

(29) Tong et a l . New cor re la t ions predic t DNB conditions Nucleonics (May 1963)

(30) Biancone et a l . Forced convection burnout and hydrodynamic ins tabi ­lity exper iments for water at high p r e s s u r e . P a r t I : P resen ta t ion of data for round tubes with uniform and non-uniform power dis t r ibut ion EUR. 2490 e (1965)

(31) Smith Non-uniform heat flux burnout with upward water flow WCAP - 2795 (1965)

(32) Styrikovitch et a l . Influence of non-uniform heating of the p e r i m e t e r of a tube on the c r i t i ca l heat flux Soviet Phys ics - Doklady vo l .4 , n° 4 p . 794 (I960)

(33) Miropolski i et a l . Cr i t ica l heat flux in uniform and non-uniform heating of the c i rcumference of s t eam generat ing tubes Teploenerget ika vol. 11, p . 64 (1958)

(34) Alekseev et a l . Burnout heat flux under forced water flow 3rd United Nation Internat ional Conference on the Peaceful Uses of Atomic Energy Paper A / C O N F . 2 8 / P / 3 2 7 a (May 1964)

(35) Lee Burnout in a channel with non-uniform c i rcumferen t ia l heat flux AEEW - R 477 (1966)

(36) De Bortoli Depar ture from nucleate boiling tes t s at 2000 psia on rec tangular channels with a flux peak in the co r ­n e r s WAPD - AD - TH 519 (1959)

- 26 -

(37) ludd et a l . Non-uniform heat generat ion exper imen ta l p r o g r a m s BAW - 3238 - 7 (1965)

(38) Wilson Burnout data co r re l a t ion from uniformly and non-uni ­formly heated channels CONF - 64507 p . 45 - 65 2nd E u r . AEC two phases flow meet ing Germantown (1964) and CONF - 651110 -5 (1965)

(39) Tong DNB predict ion for an axially non-uniform heat flux dis t r ibut ion WCAP 2815 Rev. 1 (1965)

(40) Tong et a l . Influence of axially non-uniform heat flux on DNB AIChE - P r e p r i n t 17, 8th Nat . heat t r ans fe r Los Angeles (1965) and WCAP - 2767

(41) Bennet et a l . Studies of burnout in boiling heat t r ans fe r to water in round tubes with non-uniform heating AERE - R 5076 (1966)

(42) Galson and Polomik Burnout data avai lable to boiling water r e a c t o r s ANS P i t t s . Meeting - June 6 (1957)

(43) ludd et a l . Effects of non-uniform heat generat ion r a t e s on burnout in annular and tubular flow BAW - 3238 - 12 (1966)

(44) Swenson et a l . The influence of axial heat flux dis t r ibut ion on the depa r tu r e from nucleate boiling in a water cooled tube ASME paper n° 62 - WA - 297 (1962)

(45) Eastwood The scal ing of two phase flow using F r e o n A p r o g r e s s r e p o r t . Pape r p resen ted at the 2nd E u r o ­pean meet ing on two phase flow lepra (1966)

­ A P P E N D I X 1

Kef.

*3

10

28

*2

13

11

it­

15

u

ltk

3

22

β

26

7

17

25

37

38

ι<0

30

9

31

19

Iti

5

•3

18

12

20

3ource

WAPD­TB­227

VAPD­TB­338

KAPH7**

OeLson­Polomik

UAPD­Ιθβ

WAPD­TH­l»12

OEAP­355Ö

Dokl.Vol.6 H*3

Dokl.Vol.7 H'7

ASME 62­WA­297

CÎSE R­69

CISE Η­7*

AER' R­309

OEAP­3755

vac­pwp/p 131»

WCAP­3736

BAW­3238­8

BAW­3Ï38­6

BAW­3238­7

Conr.651110­5

WCAP­2767

Eur. ?t»90 e

Bur. 2U90 e

Bur. 2l»90 e

AEÏW­R­355

WCAP­2795

AEEW­R­426 *

ABRE­R­5076

AERE­R­5076

AERB­R­5076

3­3*9

BAW­3238­12

u n 96*3­37

Columbia Uhi versi tj

AEtV­R­i»79

Date

56

57

57

57

58

58

60

6Γ

62

62

63

63

03

63

6*

6«

6»

65

65

65

65

65

65

b5

¿6

66

66

66

66

66

Axial pover

dl*tributlon

C

Η 1, ­ 1.375 in.

Η 1, ­ 0.065 to 0.675in.

non­uniform

C

B l , · 1.5 in.

C

UR­DS

B 1. » 0 to O.25 In.

C­UC­DC­HUC

CP

•JC­DR­C

C­UC

C­DC

C

HUC

C

UC

DC

non­uni form

CP­B­UR­Dft­C

C

UC

DC

C

H­CP 1 , / L , , 0.5

B 1, ­ 3 in.

CP 1. = 6 to 2* In.

CP 1 ­ 2* in.

'JS

UR­DR

C

C­UC­DC­UR­DR­HUC­B

C

C

M

I.98

1 to *

1.3

2.92

fc.9

1 ; 1.35 ; 2

2.36

2 . * and 9.70

5

5

2.05

2.5

NAIN SOURCES

B

1.3e

1.30

2,3

1.2 to 1.9

1.31

I.27 and 1.*2

1.27 and 1.Ί7 3-1* 1.1 1.4 1.*

1.« 1.* 1.1* 1.37

2 ; 3 ; 3-7 1.25 1.*

1.5* 1.16 to I.63

OF EXPERIMENTAL RESULTS WITH NOW UNIFORM AXIAL HEAT FUU DISTRIBUTIONS.

ft* Channel

«nape

R R T A R R A T T T τ τ τ Α Τ

bundle Τ Τ Τ

τ τ τ τ τ Α

Τ (Freon) Τ Τ Τ Τ Α Τ

τ τ

L

(inch)

27 27 δ

¡03

27

27

108

6.3

6­3 to 37

72

15 and 29

25·*

72

39·*

108

72

72

72

25 to 72

5Ι.5

*6.5

*6.5

1**

9·5 to 7* in

72 to 96

168

156

39·*

72

30 to ι*θ

192

39.*oad*7

De

(Inch )

0.12

0.170

0.25

O.298

0.11

0.176

O.336

O.238

0.31

0.*22

O.I9

O.3I*

O.383

O.625

0.*57

0.*17

0.1*17

0.*17

0.177 to 0.**6

0 6 7

0 *55

0.*55

O.373

0.2*

0.366

0 *97

0 *95

0 39*

(0 *17)

0 21*

0 «

0.625 ; 1.11

JL.

De

225

159

32

322

2*5

153

322

27

20 to 118

171

80 and 150

81

188

63

236

173

173

173

77

102

102

286

31.5 to 268

197 to 266

338

315

100

(173)

1*0 to 22*

*50

*2 ; 63

P (pela)

0 IO3 2X1CT

1

I II

it 1

—β

Il

ι—)

ι II

1 1

t 1

0 (106 lb/nrft*)

0 2 * 6

1 i

□

1—\

— 1 =

—π 1

= d

X1B

­1 0 1

■ 3 ,

3

3

— 3 ­

C­^

—ι

—ε

□

out ­1 0 1

0

"»Β .1 0 1

— ] t

NuMber of

point

26

2*

20

16

*2

2*

" 1 0 0

curves

825

135

238

176

3

65

55

66

i n

25

98

*0

> 9

2*3

97

139

*8

ks

98

1*0

>100

0 0-"> 1

—*===

ε

1—f I

4 1

4 1

G 4 1

I

1 4 > — ­— ι

1 I ι

ι Ο

1 Γ Ι

patch. Λ

• * = 5

1 t =

ι ι

* Range values have been translated in vater sys tea.

C : syaetrlcal chopped cosine UC : up&keved chopped cosine DC : downekeved chopped cosine Β : botpetch at tne eoa 01 the section

Τ : round tube

g : rectangular channel

A : annular channel.

UR DR CP BUC

inlet peaked ramp outlet peaked ramp cold patch

not patch on upskeved cosine

A P P E N D I X 2 ­

MAIN SOURCES OF EXPERIMENTAL RESULTS FOR NON UNIFORM RADIAL HEAT FLUX DISTRIBUTIONS.

Ref. Source Date

Circumferential

power distribution

M

«SM

A

channel

shape inch

De

inch

L

De

ρ psia

O 103 2.10

3

G (106 ib/hrft

2)

O 2 k 6

ι ι

in

■ 1 0 1

out

-1 0 1

Number

of

points

33 Teploenerg t1

36 WAPD-AD-TH-519

32 Dokl-Vol.4 n°4

34 Ρ/327 a Geneva

35 AEE W-R.Vn

AEE W-R.477

58

59

60

64

66

Flux tilt

peak in corners

Flux tilt

Flux tilt

Flux tilt

Flux tilt

3.6

3 to 18

1.8

1.38 ; I.83

1.5 to 3-7

1.12 to 1.5

1.21

I.29 A

5.9

12

5.9 ; 18.4

39·^

68

31.5

0

O.05

0.24 ; O.7Í+

O.39H

0.376

0.216

26.5

240

-fc>-

- ^

25

100

180

145

^3-

-Θ-

O-

■ ^

32

> 200

>100

30

12

fT :

1 R :

v. A :

A r Τ : rounâ tube

rectangular channel

annular channel.

31

A P P E N D I X I I I

E X P R E S S I O N S O F T H E C O R R E L A T I O N S USED

W A P D ­ 1 8 8 C o r r e l a t i o n (13)

a" q DNB

0 .28X10 6 ( J 1 D N B _ ) ­ 2 . 5 ( J +

10

G _ , 2 ­ 0 . 0 0 1 2 L / D e

~ ' e

10

w h e r e

q M D N B

H D N B

G

L

De

DNB h e a t f lux

l o c a l e n t h a l p y a t DNB

m a s s velocity­

l eng th

e q u i v a l e n t d i a m e t e r

B t u / h r f t '

B t u / l b

l b / h r f t 2

ft

ft

W ­ l and W ­ 2 C o r r e l a t i o n s (29)

for χ < 0 out

q"™vTD = ( 0 . 2 3 x 1 0 + 0. 094 G) ( 3 . 0 0 + 0 . 0 1 Δ Τ ) DIN Γ) SC

/Λ Aie j . ι o? ­ 0 . 0 0 9 3 L/De> , . , . . ­ a , (0. 4 3 5 + 1 . 2 3 e ) ( 1 . 7 ­ 1 . 4 e )

w h e r e

= 0. 532

Hr ­ Η. f in

Η fg

3 / 4 ­ 1 / 3

( e / e f )

for χ > 0 out

Δ Η ­ . ­ = 0 . 5 2 9 (Η ­ Η . ) + (0. 825 + 2. 36 e " 2 0 4 D e ) Η , β " 1 ' 5 G / 1 ° n w n χ f in χ ' fg DNB

0. 41 Η , e " 0 ' ° 0 4 8 L / ° e . 1. 12 H Ç / * f + 0. 548 Η f 8 fg g f ig

32

Appendix III - ρ 2

In these equations :

& Τ : local subcooling = Τ - Τ, sc sat loc

L

C g

« f

: dis tance from inlet to point of DNB : sa tura ted liquid enthalpy

: latent heat of evaporat ion

: density of sa tura ted s t r e a m

: density of sa tura ted liquid

ft

Btu/ lb

Btu/ lb

lb/ f t 3

lb / f t 3

W-3 Corre la t ion (39)

P N B , E U I O 6

where

Ρ

Χ G

De

H sat

[(2. 022 - 0. 0004302 ρ)

+ ( 0 . 1 7 2 2 . 0 . 0 0 0 0 9 8 4 p) e (18. 177 - 0. 004129 p )X]

χ Γ(0. 1484 - 1. 596 X + 0. 1729 X. | X | ) G / l 0 6 + 1. O37]

χ Γ 1. 157 - 0.869 X | x [ " 0. 2664 + 0. 8357 e " 3 · * 5 1 D e ]

χ Γ 0. 8258 + 0. 000794 (Η - Η. ) [ sat in'

Η in

: p r e s s u r e

: local quality

: m a s s velocity

: equivalent d iamete r

: saturation enthalpy

: inlet enthalpy

psia

lb/hr ft'

in.

Btu / lb

Btu/ lb

- 33

COMRARfSON OF RESULTS FROM AEEW-R426 WITH Τ HE WAPD-Τάβ CORRELATION

2Û-

q"exp( l06BTU/hr f t

2)

Water scaled values

Circular tube

ρ = 1,000 psia

De=0.24in

G = 1.435 IO6 I b / h r f t

2

o<x

L = 9.48in

L/De=39.5

X

«·—

a­

9 I—

> a σ c

24.1.0 χ

OJ

q"pr-q"exp _-20% q"exp

L=12.96in

L/De=54

L=38.80in

L/De=l62l

0.5-

L=73.50in

L/De=306'

6 = 2.05 Il =2.88 ¡n

l!/De=l2

uniform heating

no F utilisation F Tong utilisation F Rat utilisation

FTong or F Fiat utilisation

0.5 1

Predicted average heat flux

- κ 1

-5

qM

pr( l06BTl>/hrf t

2)

Fig.1

- 34

COMPARISON OF RESULTS FROM AEEW-426 WITH THE W-2 CORRELATIONS^ DHB )

2.0

X

3

σ Οι

-C

Οι σι o Οι > Ο

1.5

c α* Ε k -

Φ Q. Χ

LU

1.0

0.5

q"exp( l06BTU/hrf t

2)

Water scaled values

Circular tube

ρ =1,000 psia

De=0.24 in

G = 1.435 IO6 lb/hr f t

2

o<x o u t <0.5

L =9.48 in L/De = 39.5

xq"DNB

L =12.96 in L/De=54 ■<

L = 38.80in

L/De=162 i

L = 73.50 in

L/Der306 <

0.5 1.0

Predicted average heat flux q"pr ( l0

6BTU/hr f t

2)

Fig.2

- 35

COMPARISON OF RESULTS FROM AEEW-R426 WITH THE W-3 CORRELATION

2D

χ 2

~ 1.5 Ο (b

­C

i l ·

en

e s σ c

α 1.0 χ

LU

0.5

q "exp ( l 06BTU/h r f t

2)

Water scaled values

Circular tube

ρ = 1,000 psia

De =0.24 in

G = 1.435 IO6 lb/hr ft

2

0 < x out < 0.20

Predicted average heat flux q"pr( lO"BTU/hrf t

¿)

Rg.3

36 ­

COMPARISON OF RESULTS FROM WAPD^TH-338 WfTH THE WAPD-188 CORRELATION

Rectangular channel

X

g 1.5 .c O· en o χ ­α» > σ

ρ= 2,000 psia

De= 0.193 ¡η

f q " e x p L=27 in

(lObBTU/hrft

2)L/De = 140

G=0.5;1.0;1.5,2.0 06l b / h r f t

2

c

E

S-1.0 χ

LU

0.5

Lt \·\ =1.375 in l,/De=7.1 6=1.98

-02<xo u t<+0.5

{:

Patched section (Ό no F utilisation [ · F Tong utilisation

•uniform heating χ

,q"pr

0.5 1.0

Predicted average heat flux

1.5· (l06BTU/hr"ft2)

F,g.¿

37

COMPARISON OF RESULTS FROM WAPD-TH-338 WITH THE W-2 CORRELATIONS

Rectangular channel

X

3

15 σ Οι

J C

a> en σ

c Οι

E ¿1.0 χ

LU

0.5

ρ =2,000 psia

De = 0.193 in

L=27 in

ι L/De = 140

q " exp G

= 0·5;1.0;15,20 106 Ib/hr f t

2

(l06BTU/hr ft

2)

Il =1.375 in

l1 /De =7.1

6 = 1.98

-0 .2<x o u t <0 .5

.0<>X+20·/. (x) / ·Λ·ν

-Patched section

õ no F utilisation

F Tong utilisation

- uniform heating

χ

q "pr

0.5 1.0

Predicted average heat flux

fi 1 5

o

(ΚΓΒΤυ/hrft2)

Fig. 5

- 38

COMPARISON OF RESULTS FROM WAPD-TH-338 WITH THE W-3 CORRELATION

Rectangular channel

1.5

<x>

c? χ ­α»

δ a

£ 1.0

' C <l· Q. χ

LU

0.5

q <?χρ (WÊBTU/hrft

2)

■ Lt=5 l, =1.375 in

l-,/De=7.1 ε = 1.98

ρ =2,000 psia

De= 0.193 in

L = 27 in

L/De=140 G=0.5;1.0;1.5;2.0;10

6!b/hrft

2

­0.2<x o u t< + 0.5 f207.

0.5 1.0

Predicted average heat flux OO^TU/hr f t

2)

F.g.6

- 39

COMPARISON OF RESULTS FROM DOKLADY VOL? M>7 WITH THE WAPD 188

CORRELATION

l l =04cm χ ®

l l = 1.6cm o ·

Il =6.4cm VT à »

χ ο ν no F utilisation

® · Α F Tong utilisation

A F Fiat utilisation

t FTong or F Rat utilisation

200 400

Predicted average heat flux

600

q"pr(W/cm2)

Rg.7.

- 40

COMPARISON OF RESULTS FROM DOKLADY VOL,7 NP7 WITH THE WAPD-188

CORRELATION

0)0 q"exp(W/crr/)

Circular, tube

ρ =100 kg/c m2

De = 0.8 cm

-0 .2<x o u t <0.6

G= 0.085 kg/cm2sec

X

_300

I > o O c C l ·

200

UJ

TOO

1 = o +

I·) = 1.6cm o ·

Il = 6,4cm V T A ▼ *

no F utilisation F Tong utilisation F Fiat utilisation no For F Tong utilisation FTong or F Fiat utilisation

100 200

Predicted average heat flux

300

q"p r (W/cm2)

Rg.8.

- 41

COMPARISON OF RESULTS FROM DOKLADY V0L.7 M>7 WITH THE W-2 CORRELATIONS

200 400

Predicted average heat flux q"pr(W/cm£)

Fig. g.

42

COMPARISON OF RESULTS FROM DOKLADY VOL.7 N°7 WITH THE W-2 CORRELATIONS

100 200

Predicted average heat flux q"pr(W/cmz)

F.g.ifj.

- 43 -

COMPARISON OF RESULTS FROM DOKLADY VOL.7 NP 7 WITH THE W-3 CORRELATION

600

X

Ό lb .C

Οι σι ρ §400

σ c α> Ε c <L· Q. Χ

LU

200

q"exp(W/cm2)

Circular

p=l00 kg /cm 2

De=0.8cm ■0.2<xout<0.4

G=0.200 kg/cm2sec

L = 50cm

L/De=64.

Il = 0.4 cm x®

λ l i= 1.6cm o · o

Il = 6.4cm 7 ▼

xov F Tòng utilisation ®·τ F Fiat utilisation

β F Tong or F Fiat utilisation

( )= | -0 .20<x D N B <-0 .15

| + 0 . 1 5 < x D N B < + 0 . 2 0

ï »= x D N B > 0 . 20

200 400

Predicted average heat flux

600 q "pr (W/cm2)

Fig.11

44

COMPARISON OF RESULTS FROM DOKLADY VOL7 N°7 WITH THE W-3 CORRELATION

G= 0.085 kg/cm2 sec

100 200

Predicted average heat flux

300 q"pr(W/cm2)

Fig. 12

COMPARISON OF RESULTS FROM EUR 2490e WITH THE WAPD-188 CORRELATION

tq"exp(w/cm2)

Circular tube

P=/132 kg / cm 2

'Ό.142 kg/cm2

TOO 200 300

Ptedicted average heat flux

400 0 (W/cnr/)

Fig. 13.

COMPARISON OF RESULTS FROM EUR 2490e WITH THE W-2 CORRELATIONS

4q"exp(w/cm2) ν

Circular tube

ρ =132 kg/cm

300

X 3

2 -C

σ, p ai 200

■3

c

¡E a χ

LU

100

G= Γθ.142 kg/cm2 sec χ

0.185

" 0.230

200 300

Predicted average heat flux

* > o

400 -(W/cm

z)

Rg.H.

COMPARISON OF RESULTS FROM EUR 2490e WITH THE W-3 CORRELATION

q"exp(Wcm2)

Circular tube

p i 132 kg/cm2

X

3

2 -C

a> en

| 2 0 0

ï|0.142 kg /cm2sec χ

0.185 o 0.230 Δ 0.315 ν

L = 118.3 cm De=l.l6cm L/De=l02

: J ^ 0 . 2 < X D N B < - 0 . 1 5

200 300

Predicted average heat flux

400 j (W/cm

z)

q-pr

4^

Rg.15.

mmm

s»

■iwj.3fflr5:s­4i:ui ffli&Wiße. i

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