ML20198N519
| ML20198N519 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 10/31/1997 |
| From: | Delose F, Ofstun R, Spencer D WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20198N516 | List: |
| References | |
| WCAP-14327, WCAP-14327-R01, WCAP-14327-R1, NUDOCS 9711050146 | |
| Download: ML20198N519 (121) | |
Text
.,,- s ' . s: :
~
lL . .; m u T 9 Q;m:h..; e z 6 (%$,. q, :. s m M G -
. :m,:yp,q;yy A if'
,.n;l'Q fty lle 3 ayy;;p':f.l fh[lQ %j Y. Jgdy n :,.
g: :q l
w%yp;. f , ! h,n,y,ly;,
" g ist y
- '. >;v x ;. y b in,n ;m. ^M u% .- %: + <> :
, , y6, , ~s* ~ . T;,3 r%, a>
- - . ~
- ,4* , :. . f: n;,;i,:Q,o,ce
,,. ;! 's
,,,,.;-;,<.j' '-
.?-,
Qvi:.. h A ,V.k .L.,k k{ehL ' L ? , ..N ?
( 'b ), ; 3.M-
%H:
.,w;s;.k;;< .., ~a t,:s. - >: . ; .. r.4- g p' . : 7.h : :;y M- ,
.< , . . .n s $su $ y h ;imu a'.,w8 . %r .Cfu,4. ps % 1. y A, jV .; ' ;o i.8:
j
.,1
, . , , - r9 v m?
i
&,.,@..f..f.
2x (Y b , ' ' , ' $;$
'Y'f,h>.%.fllf<,'
'.- 3 A'
m..
's,' ,l,(>
Nf ,fY
,7' .'
- t
. n% an' R
l ,'id .
g , y p 'i e i
- Y f
@ j k kk gi. . o;[ a. h'l , ..h~ M-b e t
- W h;
- .
-( t%g y: W.,!$ .x. , e ..p< ' ' b+. p. . . .s h 3+ r*.-
r 1n.q;w,.Ao.
gy @sxe~M Vy M;S,,v(;y ' Q? :q % ; ,
,a ; , w. p *p , n ,I m p ,"c
%q
, r ,
a t,', ya ;. A H*,Q c
N .W .;w/o(m\;ip a w icv y' ? aD} ;
\
'f a ik?i'
&.<a t
$ 5f.hh P.H v s; 9 w; c . v. , Wi. ,
4
- v. f
- j9 ,': a. .
f h.! ?.al' :h .
.,e , . , ~e q %, .
.y 9 l y n :::il';c'Y: q.yy s ,
gg Q.
g.% ,,. g; 5 < rg,$. $
m m my.:t ., , s.vmn
(:(hYY . %:N u lfr_
4 Tf f v p f, 7 h :mj)c' . -W;.
. $w. . r, m a ,'
, ~,3 w p; , ;s.of,s m n m . 3v J ,J4 w v m :h /
? .i
,e q,,,. , q , ,w@, m. o, Ae y. . sv.w, , tg 4 a,p. s, .y, , , -
e- -
.- ,5 ;,;, s t a q, g V
ywp:a; M., ' ; i.yp.,y n/
r' . r::m - r m W.n>< -
g u .U:: %
^ ~
- l {. , ;
i Y m c y rp q
) D 4
- v. py'. m pSc &c q.3 3 /Mp y,,'g%g $ mMan 4
ll.l; ' flI h, @ h N.% hk
{j 3 !
[Th a irma i
gdj .M>4 h(N"th Q e M s %:n l1 ;.
h l
k
- g')pk ., ..\;lk, M w >> , +s m[.WhW f :%e[> "yghm:w 0 - a Y
. w ij k,'h[~[, e
+a o .m s .- ,
- m. ,
{ 4 h, yA f:Q'l %
f:&,f Wqu .u&qu k Q'y sg a'LO.: +
$Q&.1 g .s >&
E e
o Q> m & l.&.(vp?
y.
3.
a% ;a's h ym kh;.g; ,q G p
$s[W;.y,~:yff+:LpQiq ,'d n ?,m
.7 ~
Ii hg)( hlA . iy Q &m' W.%y{n L} gO&q.,& ll,f c. '.i ;,$h &
I 5 a.: Q.x/.0!Y i ': l } wl; j '." j W t % wo l W~~ 'YQ H. y _.:y-j ,
t 4
- H.-r;:.
' y. s * , se9...n w.,.N .qo w %;iv%wy,g n
'5 -n .
W
, .e y [,-
i n . .
ci,i sn A+
Q" D
9 iM., hgj p. f 3.,..,. 'f/ , M.m A [' %..;!,hN.d;[.
s o /aa a :y . . , 1,; h ik , et <
. N. k 4 -N '
,7 -
h h
\
kh('h.w'Mw%%QM v * "
'uPiDO b .{e ' b*ty(M;f M 2W'.MT bdbWd ML ww i
be Md, }",W 5 4Q%
f MW JMQM '.N;l'Q
\
E "e 9NM
.SU@8V W;.O h y.w s;QQd &w$ bii @ $ b, '~ '. d m x$iq;i MTEYbdqf y
Li <
h h vy. k 9 L
, W h & us M L,.d]f 4. 4f k'Q;yik'li L.o j, g n& m 9711050146 971023 PDR ADCCK 05200003 h4:y
@b 6 wQfae iM9%' Y 4
f h h ,(i j; t
^
., a .s .. w,5- d N$/ hbk s h I
I WESTINGHOUSE NON PROPRIETARY CLASS 3 WCAP-14327 Revision 1 Experimental Basis for the AP600 Containment Vessel
. Heat and Mass Transfer Correlations
/
y October 1997 F. Delose R. P. Ofstun -
D. R. Spencer s
Westinghouse Electric Corporation Energy System Business Unit P.O. Box 355 l Pittsburgh, PA 15230-0355 C 1997 Westinghouse Electric Corporation i
All Rights Reserved I
l oA3542w.non:Ib-101397 Revision i OctoHr 1997 l
4 4
i-.
, TABLE OF CONTENTS (Continued) -
4
'I Section .Tidt P.nat 1
4
. 4.4 Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 13 -
4 4.4.1 ne Westinghouse Heated Flat Plate Test . . . . . . . . . . . . . . . . . . . . . . . . . . 4 13 +
- 4.4.2 The Westinghouse Large. Scale Test . . . . . . . . . . . ; . . . . . . . . . . . . . . . . . . '4 14
[
4.4.3 The University of Wisconsin Condensation Tests ....................415
- - 4.4.4 Open Literature Tests ....................................... 4 l 4.5 Mass Transfer Correlation Blases . . . . . . . . . . . . . . . . . . . . . . . . , , . . . . . . . . . , . 4 17 4
p .
i 5 Conclusions ....................................................... 5-1
!. 6 Nome nc latu re . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1 l 7 Re fere nc e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . 71 1
i-1 1
i 1
i i
i
?-
j.
d i
i-l l-l 1- .9' l
i-i .
I i
i ,-
4' 5
i E
i l= o:\3542w.non:Ib.101397 Revnion I
- jy Odober 1997 l
.'i. .
j
TABLE OF CONTENTS Section Title flage LIST OF TABLES . , .................... .................................v LI ST OF FI G URES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi S UM M A RY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l I Introduction ....................................................... 1-1 2 Analytical Bases for the Heat and Mass Transfer Correlations . . . . . . . . . . . . . . . . . . . . . 21 -
2.1 Heat Transfer in the Annulus Region . . . . . . . . . . . . , . . . . . . . . ........... 21 2.2 Entrance Effects ................................................ 2-6 2.2.1 Heat Transfer in the Well Region Below the Baffle . . ................. 2-8 2.2.2 Entrance Effects in the Riser Annulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 2.2.3 Conclusions .............................................211 2.3 Heat Transfer Inside Containment ................................... 2-11
. 2.4 Liquid Film ..................................................212 2.5 Mass Transfer Inside and Outside Containment . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12 2.6 Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 13 3 Experimental Basis for the Heat and Mass Transfer Correlations . . . . . . . . . . . . . . . . . . . 31 3.1 The Hugot Mixed Convection Heat Transfer Tests . . . . . . . . . . . . . . . . . . . . . . . . . 3-1 3.2 The Eckert and Diaguila Mixed Convection Heat Transfer Tests . . . . . . . . . . . . . . 3-10 3.3 he Siegel and Norris Mixed Convection Heat Transfer Tests . . . . . . . . . . . . . . . . 3 23 3.4 The Westinghouse Dry Flat Plate Tests .............. ................ 3-34 3.5 he Westinghouse Large Scale Dry External Heat Transfer T:sts . . . . . . . . . . . . . . 3-37 3.6 he Gilliland and Sherwood Evaporadon Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 3-41 3.7 The Westinghouse Flat Plate Evaporation Tests . ...,....................3-48 3.8 The University of Wisconsin Condensation Tests . . . . . . . . . . . . . . . . . . . . . . . . . 3-53
~
3.9 he Westinghouse Large-Scale Internal Condensation Tests ... . . . . . . . . . . . . . 3-63 3.10 Chun and Seban Liquid Film Conductance Model . . . . . . . . . . . . . . . . . . . . . . . 3-71 4 Assessment of Results and Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 41 4.1 Convection Heat Transfer . . . ...................................... 4-1 4.2 Evaporation ............................. ............. ....... 4-5 4.3 Condensation .............................. ................... 4-9 oA3542w.rmn.lb-101397 Revismn i iii october 1997
I LIST OF FIGURFS (Continued)
Figure Title hge 3.4-1 Heat Transkr Data for the Dry Flat Plate Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35 3.4-2 Comparison of Predicted-to-Measured Nusselt Numbers for the Westinghouse Dry Flat Plate Tests ... .........................3-36 3.5 1 Comparison of Predicted-to-Measured Nusselt Numbers for the Westinghouse Large Scale Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-40 3.6 1 Calculated Steam Partial Pressure Distribution for a Typical Gilliland and Sherwood Evaporation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-46 3.6-2 Comparison of Predicted-to-Measured Evaporation Rates for the Gilliland and Sherwood Evaporation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-47 3.7 1 Bulk to-Film Steam Partial Pressure Differences from Selected Westinghouse Flat Plate Evaporation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-50 3.7 2 Comparison of Predicted-to-Measured Sherwood Numbers for the Westinghouse Flat Plate Evaporation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . , . 3-51 3.7 3 Mass Transfer Data for the Westinghouse Wet Flat Plate Tests . . . . . . . . . . . . . . . 3-52 3.8 1 Balk-to-Film Steam Partial Pressure Difference Variation Over Channel-Length from Selected Wisconsin Condensation Tests . . . . . . . . . . . . . . . . 3-57 3.8 2 The Effect of Surface inclination on the Predicted to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests . . .... .. .... 3-58 3.8-3 The Effect of Reynolds Number on the Predicted-to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests ... . . . . . . . . . . 3-5 9 3.8-4 The Effect of Steam Concentration on the Predicted-to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests . . . . . . . . . . . . . 3-60 3.8-5 The Effect of Heat Flux on the Predicted-to-Measured Sherwood Number Ratio for theWisconsin Condensation Tests . . . . . . . . ... .... .... 3-61 3.8-6 Mass Transf~ Data for the Wisconsin Condensation Tests . . ... . ..,... .. 3-62 3.9-1 Predicted to-Measured Condensation Sherwood Number Ratio for the Westinghouse Large-Scale Tests ... ... .. .. ........ 3-66 3.9-2 The Effect of Hen Flux on the Predicted-to-Measured Condensation
. Sherwood Number Ratio for the Westinghouse Large-Scale Tests ...... ... 3-67 3.9-3 Comparison of Predicted-to-Measured Sherwood Numbers for the Westinghouse Large-Scale Tests ............... .............. ,. 3-68 3.9-4 Condensation Mass Transfer Data for the Westinghouse Large-Scale Tests ... . ... ............ ...................... 3-69 3.9-5 Predicted-to-Measured Sherwood Number Ratios for the MSLB Large-Scale Tests ...... ..... .. ....... . .............. . . . 3-70 3.10-1 Data from the Wisconsin and Chun and Seban Tests Compared to the Chun and Seban Wavy Laminar and Turbulent Correlations , ...... .. .. 3-72 oV542w.non:lts101397 Revnion i vii October 1997
LIST OF FIGilRES (Continued)
Figure Title Eage 4.1-1 The Effect of Reynolds Number on the Predicted-to-Measured Nusselt Number Ratio for Convection lleat Transfer in a Channel . . . . . . . . . . . . . . . . . . . . 43 4.1 2 The Effect of Grashof Number on the Predicted to-Measured Nusselt Number Ratio for Convection lleat Transfer in a Channel . . ................. 4-4 4.2 1 The Effect of Reynolds Number on the Predicted to-Measured Sherwood Number Ratio for Evaporation ...................................... 4-6 4.2-2 The Effect of Grashof Number on the Predicted-to-Measured Sherwood Number .
Ratio for Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 4.2-3 The Effect of Steam Concentration on the Predicted to-Measured Sherwood Number Ratio for Evaporation . . . . . . . . . . . . . . . . . . . . . ....................... 4-8 4." l The Effect of Reynolds Number on the Predicted.to-Measured Sherwood Number Ratio for Condensation Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 4 10 4.3-2 Re Effect of Dimensionless Density Difference on Predicted to-Measured Shenvood Number Ratio for Condensation ....................,. .........,,.411 4.3-3 The Effect of Steam Concentration on the Predicted to-Measured Sherwood Number Ratio for Condensation . . . . .....................................412 4
oA3s4hhen:lb-101397 nevision i viii October 1997
. , _ _ _ _ . - . _ . _ . . . . _ _ . _ . . _ _ . _ . ~ . . . _ _ _ _ _ . . _ . . _ . _ _ _ _ _ . . _ _ . _ . _ _ _ -
e LIST OF TABLES I
i T.altit .TMs East I 11- Operating Range for AP600 Heat and Mass Transfer Parameters . . . . . . . . . . . . . . . . 12 L 3.11- Entrance-Effect Multipliers for the Hugot Heat Transfer Test . , , , . . . . . , . . . . . . . 32 3.1 2 - Hugot Mixed Convection Heat Transfer Test Data . . . . . . . . . . . . . . . . . , . . . . . . 38 i i-F ,
3.2 1 Entrance-Effect Multipliers for the Eckelt and Diaguila Heat Transfer Tests . . . . . . 310 4
3.2-2 Eckert and Diaguila Mixed Convection Heat Transfer Test Data . . . . . . . . . . . . . . 3-11 3.3 1 _
Entrance-Effect Multipliers for the Siegel and Norris Heat Transfer Tests . . . . . . . . 3 23 l + 3.3-2 Siegel and Norris Mixed Convection Heat Transfer Test Data . . . . . . . . . . . . . . . . 3-24
[
I 3.4 1 -Westinghouse Dry Flat Plate Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 34 l 3.5-1 Entrance Effect Multipliers for the Westinghouse Large-Scale Dry Heat Transfer Data .............................................338 i: 3.5 2 Westinghouse Large-Scale Dry External Heat Transfer Test Data . . . . . . . . . . . . . 3-39 ,
3.61 Gilliland and Sherwood Evaporation Test Data . . . . . . . . . . . . . . . . , . . . . . . . . . 3-42.
- 3.6-2 Entrance-Effect Multipliers for the Gilliland and Sherwood Mass Transfer i Te st s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 -4 5
- 3.7 1 Westinghouse Flat Plate Evaporation Test Data . . . . ._. . . . . . . . . . . . . . . . . . . . . 3 49
- 3.8 1 Wisconsin Condensation Test Data ................. ,, ............. 3-54
{ 3.9 1 Westinghouse Large Scale Internal Condensation Test Data ................. 3-64 i
o:\3542w.non-lb-101397 Revtsion i V October 1997
LIST OF FIGURES 2.1 1 .Metais and Eckert Plot Showing the Downcomer, Riser, and Chimney Heat Transfer Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.12- Opposed Convection Nu-d as a Function of Gr-d for Various Re-d . . . . . . . . . . . . . 2 2.1 3 Assisted Mixed Convection Nu-d as a Function of Gr-d for Various Re-d . . . . . . . . . 5
-2.1-4 PCS Air Flow Path Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Comparison of Eckert and Drake Correlation to Measured Air-Steam Diffusion Coefficients at 14.7 psia ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 15 -
3.11 Nusselt Number Comparison for Hugot Test 1 .. . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1 2 Nusselt Number Comparison for Hugot Test 2 . . . . . . . . . . . . . . . . .' . . . . . . . . . 3-4 3.1-3 Nusselt Number Comparison for Hugot Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1 -4 . Nusselt Number Comparison for Hugot Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 3.15 _ Nusselt Number Comparison for Hugot Test 5 . . . . . , . . . . . . . . . . . . . . . . . . . . . 37 3.1 Comparison of Predicted-to-Measured Nusselt Numbers for Hugot Tests 1 -5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' 3 -9 3.2 1 Nusselt Number Comparison for Eckert and Diaguila Test 1. . . , , . . . . . . . . . . . 312 3.2 2 Nusselt Number Comparison for Eckert and Diaguila Test 2 . . . . . . . . . . . . . . . . . .- 313 3.2 3 Nusselt Number Comparison for Eckert and Diaguila Test 3 . . . . . . . . . . . . . . . . . , 314.
3.2-4 _ Nusult Number Comparison for Eckert and Diaguila Test 4 . . . . . . . . . . . . . . . . . 3-15 l 3.2-5 Nusselt Number Comparison for Eckert and Diaguila Test 5 . . . . . . . . . . . . . . . . . 3-16 3.2-6 Nusselt Number Comparison for Eckert and Diaguila Test 6 . . . . . . . , . . . . . , , , . 3-17 3.2 7 Nusselt Number Comparison for Eckert and Diaguila Test 7 . , . . . . . . . . . . . . . . . 318 3.2 8 ~ Nusselt Number Comparison for Eckert and Diaguila Test 8 . . . . . . . . . . . . . . . . . 3-19 3.2 9 _ Nusselt Number Comparison for Eckert and Diaguila Test 9 . . . . . . . . . . . . . . . . . 3 20 3.2-10 Nusselt Number Comparison for Eckert and Diaguila Test 10 . . . . . . . . . . .:. . . . . 3-21 3.2-11 Comparison of Predicted-to-Measured Nusselt Numbers for the Eckert and Diaguila Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22 3.3 1 Nusselt Number Comparison for Siegel and Norris Test 1. . . . . . . . . . .-_. . . . . . . . 3-25 3.3 2 - Nusselt Number Comparison for Siegel and Norris Test 2 . . . . . . . . . . . . . . . . . . . 3 26
- 3.3-3 Nusselt Number Comparison for Siegel and Norris Test 3 . . . . . . . . . . . . . . . . . . . 3-27 3.3-4 Nusselt Number Comparison for Siegel and Norris Test 4 . . . . . . . . . . . . . . . . . . . 3-28 3.3.5 -
- Nusselt Number Comparison for Siegel and Norris Test 5 . . . . . . . . . . , . . , . . . . . 3 29 i3.3 Nusselt Number Comparison for Siegel and Norris Test 6. . . . . . . . . . . . . . . . . . . 3 30 3.3-7 Nusselt Number Comparison for Siegel atal Norris Test 7 . . . . . . . . . . . . . . . . . . . . 3-31 1 3.3-8 Nusselt Number Comparison for Siegel and Norris Test 8 . . . . . . . . . . . . . . . . . . . 3-32 3.3-9 Comparison of Predicted-to-Measured Nusselt Numbers for the Siegel and Norris Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33 i< oA3542w.non.it>l01397 Rewuon I vi _. October 1997
1
SUMMARY
i ne AP600 PIR@ and scaling analysism how s that condensation inside containment and evaporation outside containment are the dominant high importance transport phenomena for calculating
- containment pressure during design basis accidents (DBA). Heat transfer inside and outside 5
containment and conduction through the liquid film were identified to be low to-moderate importance, but require modeling correlations since they are included in the evaluation model.
Section 2 of this report describes the heat and mass transfer correlations selected for modeling heat transfer to and from the AP600 steel containment shell. De McAdamsm free convection and ColburnW forced convection heat transfer correlations were selected for use. An approximate method
- l. . recommended by Churchillm was implemented to combine the free and forced convection correlations
- in the mixed convection regime. A lower limit on the mixed convection correlation for assisting free
- and forced flows was selected based on work by Eckert and DiaguilaW. The result is a single heat transfer correlation that reduces to free convection values at low Reynolds numbers, forced convection values at low Grashof numbers, and a combination of the two in mixed convection. The mass transfer i
correlation is derived from the Nusselt number by the heat and mass transfer analogy The Chun and SebanW correlations for wavy laminar and turbulent conduction heat transfer were selected for both condensing and evaporating liquid films.
Heat and mass transfer data from individual data sets were compared to the analytical correlations in
- Section 3. The mean and standard deviation for each comparison was calculated and presented.
The individual data sets were combined and compared to the respective correlations for heat transfer in i Section 4.1, for evaporation mass transfer in Section 4.2, and for condensation mass transfer in Section 4.3. Factors are determined in Section 4.5 that make the analytical mass transfer correlations i
from Section 2 into bounding correlations for evaporation and condensation. The range of
- dimensionless groups that characterize AP600 operation are shown to be within the range of the measured test parameters.
Test measurement errors were estimated and presented and the multipliers that make the heat and mass transfer correlations bcund the test data are defined.
r t
J i
oA3542w.non:lb.101397 Reymon i I October 1997 f
m.- _ _ __ _ _ _._ _ _ _ _ . . . _ _ _ . . _
~1L INTRODUCTION -
- De AP600 plant design utilizes a passive containment cooling system (PCS) to transfer heat from the-
- containment shell to the environment following an ' accident. The AP600 PCS is designed to remove -
sufficient heat from containment during the limiting DBA to maintain containment pressure below the
~ design limit. Reference 1 provides an overview of PCS design and operation (Section 1.3) and shows 4 the containment systems and structures (Section 3.2).
- Heat is removed from the containment atmosphere by condensation, radiation, and convective heat transfer to the free surface of the liquid film. De heat is conducted through the liquid film and shel:
and rejected to the atmosphere on the outside of containment. Air from the environment flows via natural draft cocling through the annulus region between the shield building and containment shell. ~ A .
baffle divides the annulus into separate downcomer and riser legions. Water is applied to the exterior surface of the containment shell for evaporative cooling. Heat rejection from the shell to the -
atmosphere is by convection to the buoyant cooling air, radiation to the baffle, and evaporation of the extemal cooling film to the cooling air, De PIRMand scaling analysis (2) show condensation and evaporation are the dominant heat transfer
= mechanisms for the AP600. Constitutive relationships are needed to calculate heat and mass transfer to the condensing film inside containment, heat transfer through the condensed and evaporating film _s, evaporation and heat transfer from the external film, and heat transfer from the baffle to the riser and downcomer.
An upper range of operating parameters was calculated for the AP600 heat and mass transfer correlations in the scaling analysis (2) De parameters, listed in Table 1 1, are those that should be
- covered by the range of the test parameters. De correlations that include these operating parameters are presented and discussed in Section 2 and the range of test parameters is summarized in Section 4.
De parameters are defined in Section 6, Nomenclature,
, - . ' This report describes the correlations selected to model heat and mass trrnsfer from the AP600
. containmerrt and provides comparisons with test data to validate the use of these correlations.
e e
i
?
- oA3542w.non:lt>101397 R on
. _.. . _ _ _ . _ . ______.m _ _ _ _ _ . . _ _ . . . _ _ _ . . . . _ _ . _ . _ _ _ . _ _ . _ _ . - _ . _ ._ . _ . . . _ . _ . _ .
TABLE 1 1 OPERATING RANGE FOR AP600 HEAT AND MASS TRANSFER PARAMETERS Correlation Parameter AP600 Range Internal Free Convection: Ap/p < 0.401 Heat Transfer and Condensation Mass Transfer Sc - 0.52 -
External Mixed Convection: Red
< 189,000 (Riser)
< 151,000 (Downcomer) .
Heat Transfer and Evaporation Mass < 282,000 (Chimney)
Transfer Grd < l.2 x 10'(Riser)
< 6.2 x 10'(Downcomer)
< 2.1 x 1012 (Chimney)
Pr - 0.72 Sc - 0.52 Liquid Film Heat Transfer Re < 4000 Pr 1.5 to 3.0 e
I 1
.ns a - nwnos m
,, gg,y 1
l
,, - m-
i 2 ANALYTICAL BASES FOR THE HEAT AND MASS TRANSFER CORRELATIONS 2.1 Heat Transfer in the Annulus Region he flow regime for turbulent convective heat transfer is typically qualified as either free, forced, or mixed. The combination of free and forced convection in the mixed regime is either assisting (i.e., they work in the same direction, as in upward now in a hot pipe) or opposed (i.e., they work against each other, as in downward How in a hot pipe). Operating points for the Grashof and
, Reynolds numbws are calcula:ed in the scaling analysis (2) for the PCS air How path (downecmer, riser, and chimney) and plotted on a Metais and Eckert(s) plot to determine the heat transfer regime, ne results are t.hown in Figure 2.1-1. De riser and downcomer operate in forced convection and the chimney operates in mixed convection. The convective heat transfer in the AP600 annulurs shown in Figure 2.1-1, is turbulent rather than laminar, since the Reynolds numbers are all greater than 3000(8) .
3 Based on a review of the literature, the turbulent free convection heat transfer correlation for gas mixtures has the form Nu = C (Gi?r)N, with the value of C varying between 0.09 and 0.15, and the value of N varying between 0.3 and 0.4. The McAdamsO ) correlation with C = 0.13 and N = 1/3, was selected for calculating turbulent free convection heat transfer in the annulus:
Nug = 0.13(Gr4Pr)lO (1)
This correlation is widely used to calculate turbulent free convection heat transfer from both vertical and inclined surfaces with either constant temperature or constant heat aux boundary conditions, he hydraulic diameter is the characteristic length in the Grashof and Nusselt numbers. The experimental work of Vlie8) shows the full gravitational acceleration should be used to evaluate the Grashof number, not just the vector component parallel to the plate.
9 oM542w.non:Ib.101397 R uogi
k 1.0E + 06-WelW.. ...oor
- : Forced Convection ._5cajteg.__.~l5 T Turbulent Flow / '
m-O
/
nn 1,0E + 05.
Downcomei f ScalN N'~
N ,a J j
/
$ 1,0E +04- e e Chimney
=_7 _
56slinc f
Mixed Convection _
Turbulent Flow 1.0E + 03 -
f Free convection e' Turbulent Flow - -
/
/
1.0E +02 i . . . u. . ...u- . . . uim ....u.. ...u- .. iiiu . . "" i o ui 1,0E + 03 1.0E+05 1.0E + 07 .1,0
. "E + 09 - 1,0E + 11 -
1,0E +04 1.0E + 06 1,0E +08 1.0E +10 1.0E+12 Ra D/L .
l l
l 1
I i
[ Figure 2.1 1 Metais and Eckert Plot Showing the Downcomer, Riser, and Chimney Heat Transfer j Regimes l-o:\3542w.non:Ib.IOl397 Revnion I I 2-2 October 1997 I- - _ _
_ ._. _ ._ _ . _ _ _ _ _ _ _ _ - - . _ . _ . _ . _ _ . _ m._ _
De ColbumW correlation was selected for calculating turbulent forced convection heat transfer in the i annuhis:
Nug, = 0.023Re[Pr U3 (2)
De ColburnW correlation is applicable to both constant temperature and constant heat flux boundary l
conditions for fully developed flow in channels. The correlation is widely used to calculate turbulent forced convection heat transfer in long tubes and ducts. The hydraulic diameter is the characteristic
, length in the Reynolds and Nusselt numbers.
4 l A length or distance dependent multiplier can be used to account for the increase in forced convection j heat transfer as the boundary layer develops at the entrance of a heated channel. His is an important consideration wrien modeling heat transfer in short channels. he entrance-effect multiplier is j described in more detail in Section 2.2.
A method for combining separate free and forced convection heat transfer correlations into a single
- correlation that covers free, mixed, and forced convection was recommended by ChurchillW. For i opposed free and forced convection
3 Nu = (Nu ,, ?Nurm)"
g (3) and for assisting free and forced convection, Nu, is the larger of the following three expressions:
1/3 3 3 j abs (Nug,,- Nu f ). ;
Nufree ; 0.75Nu r , (4) t The lower limit in the latter equation, which prevents the value of Nu, from going to zero when Nuf,,
and Nur , are equal, comes from Eckert and DiaguilaW .
.i The opposed mbed convection correlation, Equation (3), is used for the downcomer and chimney.
Under opposed convection (downflow along a heated surface or upflow along a cooled surface), the mixed convection correlation increases the value of the predicted Nu number over the value predicted using either the free or fated convection correlations alone. The opposed mixed convection correlation is shown in Figure 2.1-2.
[ ne outside surface of the containment shell is expected to operate in assisted convection (upflow along a heated surface or downflow along a cooled surface) during a DBA event. The assisted mixed convection correlation. Equation (4;, shown in Figure 2.1-3 is asymptotic to both the individual free
~
oA3542w.non:ib.ioi397 R s on
, g
, .. . . . . - . - - , ~ = . - - . - .. . --, . . - - . . ~ . . ~ . . - .~,-.--.n. ..n. . _ . . . . . . ~ . - . . ,
.s l
1000 4
a : ; a-a__e.-a-e-ed
, m. [
m : : : : : -e-t-*#* e'e * ,
/
e**' ~ .
j 100-
~
i 10 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+0S 1.00E+07 1.00E+06 - 1.00E+09 1.00E+10 1.00E+11 1.00E+12 Gr<1 I-e--RE=50000 -e-RE=100000 + RE=150000i Figure 2.1-2 Opposed Convection Nu-d as a Function of Gr-d for Various Re d c:U542w.non Ib-101397 Revuion 1 2-4 october i997
i .-
i' e
i 1000 B
e ; & 6 a 0 % --e - s q 4
- # O e - e--- q j e
- 0 0 0 0- s p
i 10 -
' t.00E+02 1.00E+03 1.00E+04 1.00E+06 - 1.00E+06 1.00E+07 1.00E+08 1.00E+00 . 100E+10 100E+11 1.00E+12 Gr-d v
l-e-RE=50000 -e-RE=100000 + RE.150000l Figure 2.13 Assisted Mixed Convection Nu-d as a Function of Gr-d for Various Re-d oA3542w.non:Ib-101397 Reviuon i 2-5 october 1997 e
I and forced convection correlations, and penalizes heat transfer when free and forced convection are of l about the same magnitude.
Equations 3 and 4 are asymptotic to both the inoividual fn e and forced convection correlations.
Consequently, it is unnecessary to a priori choose whether the heat transfer regime is fr e, forced, or mixed when Equation 3 or 4 is used.
As the angles of inclination approach horizontal, the assisting and opposed convection heat transfer ,
coefficients should become equal. Although the correlations used for AP600 do not provide this, it is )
addressed for AP600 as follows:
- Only free convection is assumed inside containment, so the definition of mixed convection is not relevant inside containment.
- The downcomer and chimney have too little horizontal surface area and too little heat and mass transfer to be a concern.
Below the first water distribution weir on the containment dome, the slope is greater than 30" so opposed / assisting are well defined. Above the first weir, the liquid film is subcooled. With little or no evaporation, and the surface area is less than 4 percent of the total siiell area, so shallow slopes are not a significant concern for the external containment shell.
2.2 Entrance Effects he heat transfer coefficient at the entrance to a heated channel is significantly higher than the fully developed value predicted by the ColburnW forced convection heat transfer correlation. The increase it, heat transfer at the entrance is attributed to the thianess of the boundary layer that develops with distance from the entrance. He entrance effect is important for modeling heat transfer in short channels, so is used for all the test data comparisons in this report. Since the net entrance effect on the long AP600 riser channel is only a small increase in heat transfer, it is recommended that entrance- ,
effect multipliers may reasonably be neglected for AP600 licensing calculations.
The entrance-effect correlation and coefficients used in this report are those recommended by Boelter, '
Young, and IversonUO):
=1+FA i (5) h,, L l l l
o V542w.non:Ib-10t 397 Revision i 2-6 october 19'n
= - -
where:
I h., = the fully-developed heat transfer coefficient calculated from the ColbuiaW correlation h,- = the mean or length. average heat transfer coefficient over length L !
Fi = . a geometry-dependent constant from Reference 7 For step wise calculations up a channel, an equation is needed that gives a length average heat transfer .
, coefficient between step bounde. ries x3 and x2, Given an equation for h(x), the average value of h on the interval (xi,x2) IS:
=
hxj,x2 x2 - x3 fA:12h(x)dx (6)
Analytically, h,,,,, cannot be derived from the above definition over the interval (0, L), since the equation produces a singularity when this is attempted. However, a modest change to the exponent results in:
bxi,x2 3
= d(xf -xi ) (7) h,, 1 + F L.3(x,_ x,)
a form that has the same average over length L, but with slightly lower values for small values of x, and with f!ightly higher values for higher values of x.
A Nusselt number multiplier, M, is defined with Equation 7 as M = hat, x2/h .. 'Ihis multiplier sincreases the forced convection component of the mixed convection heat transfer ccefficient when entrance effects are included. Entrance effects are not appropriate for, and are not applied to, free -
convection or to the free conuction portion of the mixed convection heat transfer correlations.
o _ The heat and mass transfer correlations calculated with entrance effects are compared to eight data sets in Sections 3.1 to 3.8. De comparisons show the heat or mass transfer coefficients (as represented by
- the Nusselt and Sherwood number.) are underpredicted by 2 to 14 percent in six of the data sets, overpredicted by 3 percent in one (Eckett and DiaguilaW, Section 3.2), and overpredicted by 18 pe rcent in one (Hugot data (ID, Section 3.1). He Hugot overprediction reduces to 10 percent if heat transfer at'x/dh< l.0 is not included in the compari:;ons. The multipliers become large and l increasingly uncertain for x/dh< l.0. These comparisons show that overall, the entrance-effect l multipliers improve the agreement between the test data and the analytical heat or mass transfer predictions, I
o:\3542w.non:Ib-101397 R is av^ y're-f-w----i g gr - --
7-g q wv' 7 u-mty y ' rw- y e W-r--~-ew-v+4m- 9 y h-w Mt'Nw W 's-
The AP600 riser channel differs from the test geometries due to the 6-foot well, or turning region at -
1 the bottom of the bafne. For modeling simplicity it is desirable to use a fully-developed heat transfer coefficient over the full channel height. The following subsections show the use of a fully-developed heat transfer coefficient over the full riser height is conservative. i ne calculations show the heat transfer decrease (relative to fully-developed heat transfer) is more than offset by the heat transfer increase due to neglecting the entrance effect in the channel above the well. He geometric features of the well region and riser channel are shown in Figure 2.1-4.
2.2.1 Heat Transfer in the Well Region Below the Bame ne annular duct created by the baf0c for the AP600 starts G feet above the bottom of an annular l "well." His well is 3 feet wide and is heated on the inside surface in the AP600 evaluation model it is assumed, for simplicity, that the forced convection heat transfer correlations used in the annular
- . region can be applied within this region as well. It is more realistic to assume a free convection heat transfer relationship on the heated containment shell side of the well.
Although the upper half of the 6-foot height may undergo transition to turbulent free convection, the laminar free convection correlation predicts lower heat transfer coefficients and is used. He effect of i using forced convection in the 6-foot well is evaluated by comparing the total heat transfer calculated 4
with laminar-free convection in the well to the total heat transfer calculated with forced convection
! everywhere.
4 ne empirical formula of McAdamsW was chosen for the laminar free convection mean Nusselt number:
{
L T
- Nu = 0.555(Ra,)l'4 (8)
The Nusselt number for forced flow convection is given by the ColburnW relationship:
9 Nu = 0.023Re /5Pr l'3 4
(9)
Assuming the active length of the annulus above the baffle is 90 feet, then the active heat transfer length is 96 feet. The fractional decrease in total heat transfer over the 96-foot height due to free convection in the 6-foot well region is equal to the factor $ determined by length weighting.
Equations (8) and (9):
6 Ra,3/4 1 2( 555) .-
(10)
$ = 96-- 6(.023) Re 4/5 Pr t/12 ,
o:uS42w.non:lb-101397 R o
l I
i i
i i
4 I
4 i;
i
- l l
i i
j Chimney i
! l l Weir # h l
( HContainment Shell Riser -
-4 Downcomer - -g l
() Baffle 96' i) Shield Building l
Annular Channel Entrance y l
Well Region 6' y
---3' -
Figure 2.1-4 PCS Air Flow Path Features o.\3542w.non:Ib-l?'197 Revision i 2-9 October 1997
i Equation (10) was evaluated for both wet and dry containment surfaces at temperatures between 125* and 205'F for annular flow velocities of 1,7, and 20 ft/sec. The density difference in the Grashof number was taken between dry air at 115'F and saturated vapor / air mixtures at the assumed surface temperature for the wet surface, and between dry air and dry air at the surface temperature for the dry surface.
Calculations show there is very little change in the value of $ with surface temperature or with the assumption of wet or dry surface conditions. At an annulus velocity of I ft/sec, $ is negative, ,
ir.dicating that the free convection heat transfer coefficient is greater than for forced convection. There is very little difference between $ values at 7 or 20 ft/see with the greatest value of 0.056 occuning for the 20 ft/sec velocity at a dry surface temperature of 125'F. Most of the $ values are in the 0.03 to 0.04 range. He maximum effect is a 5.6 percent reduction in the net heat transfer from the shell due to the assumed laminar heat transfer below the baffle. As shown in the next section, this heat transfer reduction is less than the heat transfer increase due to the entrance effect.
2.2.2 Entrance Effects in the Riser Annulus ne heat transfer enhancement due to developing therrnal profiles is based on eigenvalue solutions from Hatton and Quarmby02) for the developing thermal distribution within a hydrodynamically developed flo v in an annulus. While the analytical solutions are quite complex, charts have been presented for enhanced heat transfer for Reynolds numbers of 7,100,73,600, and 495,000 at Prandtl numbers of 0.1,1.0, and 10.0. The AP600 Prandtl number is very nearly unity, and the riser Reynolds number ramps to 189,000. For reference, a velocity of 7 ft/see yields a Reynolds number of about 70,000.
An empirical fit of Hatton and Quarmby's02) curves for a constant heat flux Nusselt number, the condition giving the least heat transfer enhancement at a Prandtl number of 1.0, and a Reynolds number of 73,600, gives a ratio of the Nusselt number to that for fully-developed flow:
Nu(x/dh)
= 1.4667 ( x ) .H26 (yj)
Nu o dh l
- The integration of Equation (11) between x = 0.0 and x/d h= 30, the position of intersection between Equation (11), and the fully developed Nusselt number yields:
l Nu = 1.147Nu o (12) l indicating that, on the average, the heat transfer over the first 60 feet of the annulus will exceed the l
fully-developed value by 14.7 percent. The average heat transfer coefficient increase over the 96-foot oM542w.non-Ib-101397 Revtuoa.I 2-10 october i m
~
l length is 7,9 percent. De same calculation for the Reynolds ntimber of 7,096 develops a heat transfer -
increase'of 8.7 percent, and at Re = 495,000 yields a 10.8 percent increase. De reason for the increase at the higher Reynolds number is that the thermal profile does not become fully developed in 90 feet.
2.2.3 ' Conclusions
_ , _ ne heat transfer enhancement of 8 to 11 percent due to the entrance effect, more than offsets the heat transfer degradation of approxiniately 6 percent due to free convection in the we'1. Both deficit and enhancement calculations are conservative for the following reasons:
- De presence of a turbulent eddy within the well region will disrupt the free convection boundary layer and increase the heat transfer
- _ Any deviation of the velocity profile, from that for fully-developed turbulent conditions at the entrance to the annulus will also increase the heat transfer.
De calculations show it is conservative to neglect the free convection below the bt'fle and the entrance effects in the AP600 riser channel, and simply use a heat transfer correlation for fully-
- developed turbulent flow over the full height frLm the bottom of the well to the first weir.
2.3 Heat Transfer Inside Containment Heat is transferred from the containment atmosphere to the containment inner shell surface by condensation, radiation, and convection. - De AP600 containment calculations assume condensation and convective heat transfer takes place at the outer surface of a thin liquid film that develops on the
' inside surface of the containment vessel _ De liquid film provides a relatively small, additional resistance to heat transfer from the containment atinosphere to the wall. Heat transfer through the liquid film is characterized by the film Reynolds and Prandtl numbers, and is discussed in Section 2.4.
De inside of the containment shell is expected to experience a high velocify flow of steam and air
- during the main steamline break (MSLB) event and the blowdown phase of a large loss-of coolant'
- 1 accident (LOCA) event as the break jet vigorously circulates the gas (Ref. 2, Section 6.5).~ This indicates
-that heat and mass transfer during this period are turbulent forced or mixed convection. After the LOCA
- blowdown is complete, the asnosphere is circulated less vigorously and the velocity of the steam and air flowing along the inside surface of the containment shell is lower. His indicates turbulent free convection heat and mass transfer after blowdown. However, the inside of containment is conservatively modeled using tart,ulent free convection throughout both transients. Section 3.9 presents dua that show a significant increase in the mass transfer for a high kinetic energy souice relative to free convection mass transfer.
oA3542w.nostib 101397 Revuion i 2-1I ociober 1997
De height-based Grashof number representing the lowr limit for turbulent free convection heat transfer is approximately 1010. After the first few seconds of the transient, the height based Grashof number is greater than 1030 over all but the lower 3 feet or less of the interior shell surface. Since the turbulent free convection heat transfer correlation underpredicts laminar free convection heat transfer, its use is conservative over the lower 3 feet.
The McAdamsW correlation, was selected for calculating turbulent free convection heat transfer inside containment. The correlation can be written as a 1.metion of local properties: ,
h tree = 0.13I L 2 k
$ l (Grt.Pr)3g= 0.13 (yPr j'3)t/3 [ p ]I'3 (13) he term (Ap/p) is the differente between the bulk density and the surface density, divided by the bulk 2
density. The term (v fg)1/3 has the units of length and is used as discussed in Reference 2, subsection 4.3.1. Note that "g" is not reduced by the sine of the slope from horizontal, consistent with VlietM.
2.4 Liquid Film The AP600 containment calculations assume the liquid film is a distinct control volume with mass transfer, convection heat transfer, and radiation heat transfer into the free surface, and conduction to the solid surface. Heat is transferred through th- 'hin films on both the inside and outside of the containment shell. The Chun and SebanW correlation is shown in Section 3.10 to model both wavy laminar and turbulent heat transfer across the film. For wavy laminar films:
Nu = 0.822 Re 4 22 (j4)
For turbulent films (Re > 5800 Pr'I") :
Nu = 0.0038 Re0A0 Pr08 (15)
Note that the gravitational acceleration is multiplied by the sine of the slope above horizontal for ,
liquid film calculations.
2.5 Mass Transfer Inside and Outside Containment Convective mass transfer is a result of a concentration gradient between a flowing steam-air gas mixt and a surface. The steam concentration gradient is approximated as the difference in steam partial pressure between the bulk gas and liquid surface. Condensation occurs when the bulk gas steam concentration is greater than the concentration at the surface of the liquid. Evaporation occurs when the bulk gas steam concentration is less than the concentration at the surface of the liquid.
Kreith03) defined the steam mass flux between the surface and the bulk gas to be:
o \3542w.non:16101397 Re s o
' H th sun = k,M,,(psun.ur- Psun. bulk) Ob)
De mass transfer coefficient, k g, can be predicted using empirical correlations similar to those for the convective heat transfer coefficient, he . He Sherwood number for mass transfer is analogous to the Nusselt number for laat transfer, and is derived from the Nusselt number using the heat and mass transfer analogy:
Sh =
(17)
(Pr/Sc)l0 he mass transfer coefficient for gas-phase mass transfer is defined:
k = SC (18) 8 RTP g k ('Pr')30 Pg is a term that accounts for the change in heat transfer at high mass transfer rates. The Nusselt number is based on the heat transfer correlation evaluated at the boundary layer temperature. The properties in the Prandtl and Schmidt numbers are evaluated at the boundary layer temperature.
Equation 16 is used to calculate both condensation and evaporation mass transfer. Boundary layer properties are evaluated at the mean of the bulk and surface conditions.
2.6 Thermal Properties All of the thermal properties used in the heat and mass transfer correlations are represented by -
correlations to an estimated accuracy of I percent, with the exception of the air-steam diffusion coefficient. The condensation and evaporation mass transfer rates calculated for AP600 are linearly proportional to the air-steam diffusien coefficient. The diffusion coefficient correlation that is used for
, all AP600 and test comparison mass transfer rates, overpredicts the measured diffusion data from the literature, and hence, overpredicts the mass transfer rates by approximately 10 percent over the AP600 containment temperature range of approximately 100 to 300*F. However, as noted in the following discussion, the mass transfer bias factors offset the diffusion correlation bias.
De diffusion coefficient correlation is trom Eckert and Drake", Table B-9, p. 787. When the units are converted to English units, the Eckert and Drake egaation is:
o \3542w.non. lb-101397 Revmon i 2-13 October 1997
' 14.2*' ' ' T "#)
D' = 0.892 ft 2/hr (19) c P , ,460.8, where P is the total pressure in psia, and T is the gas temperature in degrees Rankine.
1i
%c Eckert and Drakedd) correlation, Equation 19, is shown as the solid line in Figure 2.61, compared to three data sets: Kestinus) Rohsenowo6).and Eckert and Drakedd) ' ne dotted line in -
Figure 2.6-1, is 0.9 times Equation 19, and appears to be a best estim te fit to the data. Consequently.
_ Equation 19 overpredicts the air steam diffusion coefficient by approximately 10 percent. ,
l Equation 19 and the theoretical development presented in Bird, Stewart and Lightfoot07) show the diffus,- coefficient is proportional to 1/P. Although date were not included at higher pressures to support 1/P, the references agree on the expected 1/P pressure dependence he correlations all give the temperature dependence to be 1*, where n is greater than 1.5. The theoretical development of - -
Bird recommends temperature exponents of 2.334 for water vapor diffusing through a non-polar gas, and 1.823 for two non-polar gasses (water is a polar gas and air is non-polar). However, the Ecke t
- and DraireUd) value of n = 1.81 in Equation 19 appears to represent the measured temperature dependence very well. Consequently, Equation 19 properly represents the diffusion coefficient -
sensitivity to temperature change.
Equation 19 was used in all of the AP600 PCS analytical work, including evaluation of separate effects tests (SETS) (Sections 3.6 to 3.9). Consequently, the mass transfer coefficient bias factors
- (defined in Section 4.5) reduce the (over) predicted mass transfer coefficients to values that lower-bound the measured coefficient data.
}
aA3542w.non:lt>101397 Revision i 2-14 october 1997
l l
1 I
I l
.J ..
4*5- ~ ~
- - - ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ ~ - - - ~ ~ - - - - - - -
4-
--~~-~~~~~~~~-~~~~-~~~~~..v.'...e..R ~ ~ - -
3.5- ---------.Eckeft.A.Qm82.CwJ.9N ~~" - -- - <'-
iip - -- --- --- --
3- m #...-
.e 2.5- ~ ~-~ ~~ ~ ~~ - ~ ~-~~-
3.d - ~ - ~ ~ ~ ~ ~ ~ - ~ ~ ~ ~ - - ~ ~ ~ -
2- --,-':.....' - - - - - <
1.5-' -
- , .g# - - - - - - - - - -
- g. . . . . . . . . .. .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
m 0.5- -~~- AP600 Range " ~ ~ ~ ~ ~ ~ ~ - - - ~ ~ - - - - - ~ ~ -
C . . . . . . . a 0 100 200 300 400 500 600 700 800 Temperature, Degrees F e Kestin o Rhosenow a Eckert & Drake Figure 2.61 Comparison of Eckert and Drake Correlation to Measured Air. Steam Diffusion Coemcients at 14.7 psia o 0542w.non:lb-101397 Revision i 2 15 ocober 1997
% U _ .
3 EXPERIMENTAL BASIS FOR Tile IIEAT AND MASS TRANSFER CORRELATIONS De experimental data used to validate the AP600 containment heat and mass transfer correlations are presented in this section. The analytical conciations for mixed convection heat transfer in channels, from Section 2.1, are compared to the data in Sections 3.1 through 3.5 We analytical conciations for condensation and evaporation mass transfer from Section 2.5 are compared to data in Sections 3.6 through 3.9 De correlations for liquid film heat (*ansfer from Section 2.4 are compared to data in Section 3.10.
De validation ( % and mass transfer conelations for the PCS air flow path uses test data from channel-type geometries. .he Nusselt, Sh rwood, Reynolds, and Grashof numbers for channel conelations are basei on the channel hydraulic diameter. Data on heat and mess transfer inside the pressure vessel are conelated using (u2fg)w u the length parameter in the Nusselt and Sherw xxl numbeni.
De mean and standard deviation is presented for each data set in Sections 3.1 to 3.9. Data sets are combined and furtl.cr evaluated in Sect on 4.0. Error bars in the Westinghouse testes are specified in Section 4.4 and shown on the ugures in Sections 3.4, 3.7, 3.8, and 3.9.
3.1 The llugot Mixed Convection Heat Transfer Tesd3D llugot00 conducted heat transfer asts on a set of symmetrically heated, parallel, vertical, isothermal plates w;th closed sides, ne channel width was 1.0 meter, the channel height was 3.3 m, and the plate separation distance was variable at 10 and 60 cm. De plate temperatures were varied between 40 and 160*C, Assisting mixed convection heat transfer for moderate Reynolds and Grashof numbers was validated by the test data.
The llugot reportOU presented the local heat transfer coef0cient, but did not report the air Ihw rate or velocity induced in the heated channel; therefore, it was necessary to use a computer model to calculate air flow rates as well as heat transfer. The tests were modeled using the WOOTHICUU code with nominal inte.ts. The test section was divided into 11 axial volumes. Because most of the rapid changes occue y the entrance, the first 10 volumes were cach 1/15th of the total volume; the last volume was 1/.i of the total volume. The code calculated the buoyancy induced air velocity, air temperature, and heat transfer coefficient in each of the 11 volumes. De calculations assumed a combined entrance and exit form loss of 1.5. Since the air flow rate a s calculated and the channel loss coef0cient was estimated to be 1.5, the heat transfer calculv includes the effect of uncertainties on the air flow rate.
De Nusselt number, Nu, is defined as Nu = hd h /k, wheread e a channel hydraulic diameter. De entrance-effect multipliers were calculated as described in c n 2.2 and are presented in Table 3.1 1.
De mixed convection Nusselt numbers were calculated a r wribed in Section 2.1. The calculated Nusseit numbers for each of the five tests are compared with the test data as a function of dimensionless height in Figures 3.1 1 through 3.15. De relevant test parameters are presented in Table 3.12.
ous4:w.i.non ib ionw7 agogn
_____o
TABLE 3.1 1 ENTRANCE.EFFECT MULTIPLIERS FOR Tile HUGOT llEAT TRANSFER TESTS Distance from bottom, ft 0.72 1.44 2.17 2.89 3.61 4.33 5.05 5.77 6.50 7.21 10.82 Muhiplier for 5.539 2.049 1.723 1.569 1.476 1.414 1.368 1.333 1.305 1.292 1.224 dh= 2.46 f t. .
Multiplier for 2.100 1.254 1.175 1.138 1.115 1.100 1.089 1.081 1.074 1.%8 1.0$$
dh= 0.162 ft. ,
O V.M.w l.m.lbl0130 sg
M
$00
\
400 I
j m.
1 2
200 e
, e e e e e e e - - -
100 0
0 1 2 3 4 5 D;rrenskmless Height (X/d) e Test Data ---W Prodction Figure 3.11 Nusselt Number Comparison for ilugot Test 1 (69 cm and 58'C) o\M42* twltel01397 gn,,,, g 3-3 ocioter i997
)
i 1
. I J
l
?
I E
i 800 '
400 I
j .. '
1 e- -
e e e . . . .
e 100 0
0 1 2 3 4 8 ,
Dmmonises Height (H) e Test Data -W Predcton
-1 1
1
)
I
. Figure 3.12 Nusselt Number Comparison for Hugot Test 2 (60 cm and 150.2*C) c:\3542w l.non.lbl01397 Rmsson i 3-4 Oci*r 1997
_ ;- , _ _ , . - _ . _ . , . _ . . . . . _ _ _ . . - . . _ _ _ _ _ _ _ . _ - - _ . _ . _ . , _ . , _ _ _ . . _ _ _ - - ,-c-_... . . _ - - _ _ . . _ .
F l
l 800 000 400 <
I 300 -
~
I
.00
-e e
100 * * , , , , , ,
, e
- 0 0= 6 10 15 BC Dm.h Heght (XM) l i
e Test Data -W Produkm l
I l-t i
}
4 i.
l Figure 3.13 Nusseh Number Comparison for Hugot Test 3 (10 cm and 154.9'C)
- oA3542w l.non:it>101397 Revison i 35 octot=r 1997
.o. m -- ... ng. , ..__..m.._._.___~.._..__-_____..-- . ~ , _ . . _ _ . -
l i
i r t
6 h
000 ,
900 -
400 I !
300 1
e
- * - a e , e 100 . -
+ . . . ,
-0 0 6 to 15 90 m H## 00d) e Test Dee -W Predew, a .
4 Figure 3.14 Nusselt Number Comparison for Hugo: Test 4 (10 cm and 89.I'C) s
-1 o:U542w-l .non.it>101397 Reymon i 36 october 1997 we y m> pmy yir-1 <-yr'T tpwp- 1wp-g-. my g -rw+,. .-r-,9%.9 -
mp.*yge % gu. - my g- e e - w ry-e+-up-b--y -p-yw-g9--wmmma ,.w.ww.-,e - - -__m- - . ' - ------------a--
l i
i 9
?. 800 000 <
400 I
l-1
- 100 0
0 6 to 15 20 m Heght 00d) e Test Date -W Predeten Figure 3.15 ~ Nusselt Number Comparison for Hugot Test 5 (10 cm,60.9'C) oV342w l.non:lb 101397 Revison 1 37 october 1997
l l
TABLE 3.12 IfUGOT MIXED CONVECTION HEAT TRANSFER TEST DATA ,
Surface to Ambient Test Number tid h AT ('C) Grd Range Reg _
l 4.4 58.0 2.40 x 10' . 2.61 x 10' 35400 2 4.4 150.2 3.31 x 10' . 3.65 x 10' 42400 .
l 3 18.15 154.9 3.30 x 10 7 4.70 x 107 12900 7
- 4 18.15 89.1 3.25 x 10 4.45 x 107 12200 7 7 5 18.15 60.9 2.71 x 10 3.65 x 10 11000 A compilation of the predicted to measured Nusselt numbers for all Ove tests is shown in Figure 3.16.
, The mean predicted to-measured value is 1.179, and the standard deviation is 0.429. Both the mean and standard deviations are strongly affected by the relatively large predicted-to measured Nusselt number ratios at the channel entrance, if only the first entrance value is removed from each data set, the mean falls to 1.095 and the standard deviation falls to 0.213.
Except for the channel entrance, the predicted Nunelt numbers are close to the measured values for tests I and 2. Dese two tests had the highest Red numbers of the set and were performed with a gap wiath of 60 cm. The entrance-effect multiplier for the calculated forced convection heat transfer coef0cient is height dependent, and has both a lar;;e value and a large uncertainty near the entrance.
The predicted Nusselt numbers are slightly higher than raeasured for tests 3 and 4. The overprediction is believed to be the result of laminar now persisting to near mid height at the lower Reynolds -
numbers. Since the AP600 extemal annulus operates in turbulent How, tests 3 and 4 are not -
representative of AP600 conditions.
The predicted Nusselt numbers are lower than the measured values for test 5. Although the gap width is the same as tests 3 and 4, the trend in the Nusselt numbers was not the same. This test was performed at a relatively low temperature. .
omu..imn ib.ioov7 38 ONIN
_ _- . - - _ . _ _ _ _ _ _ . _ _ _ _ . _ _ . _ _ __. _ , . _ . - _.-- _ _ _ _ _ _ _ _ . . ~ . _ __
3.6 3<
1 .s
]a 2 1s . .
+__.. _ . : :
i< m ,,,,88ese
- ++.
- 0.5 l
0 0 $ to 15 to De==netenieu Height pus)
. one -u.en(t.in)
I Figure 3.16 Comparison of Predicted to Measured Nusselt Numbers for Hugot Tests 15 o \3542w l.non.lb-101397 Revuton 1 39 October 1997
3.2 The Eckert and Diaguila Mixed Convection llent Transfer Tests (6)
Eckert and Diaguila(6) conducted heat transfer tests on a vertical tube that was 13.5 feet high with a 23.25 inch inside diameter. Inlet and outlet air pipes and dense screens were located at each end. A 10 foot steam jacket supplied steam slightly superheated as the heat sour e. Sixteen condensation chambers collected and piped condensate to a station where the Dow rate was measured and the local heat aux was determined. An air now at approximately 80*F, at pressures from 1 atmosphere to 99 psia, was forced through the test section. Tests were conducted with forced now in both the ,
upward (assisting mixed convection) and downward (opposed mixed convection) direction.
Dermocouples at the tube center and in the tube wall provided a temperature difference from which the local heat transfer coefficient could be determined. The test data were used to validate the mixed convection heat transfer correladon at prototypic Reynolds and Grashof numbers.
The Nusselt number, Nu, is defined as Nu = hdh /k, where dh is the hydraulic diameter. Entrance-effect multipliers were calculated as described in Section 2.2 and are presented in Table 3.21. The mixed convection Nusselt numbers were calculated as described in Section 2.1. The calculated Nusselt number for each of the ten assisting convection tests are compared with the measured data, and are shown as a function of the dimensionless height in Figures 3.21 through 3.210. De relevant test parameters are presented in Table 3.2 2.
TABLE 3.21 ENTRANCE EFFECT MULTIPLIERS FOR THE ECKERT AND DIAGUILA HEAT TRANFFER TESTS Distance from bottom, ft 0.63 1.25 1.88 2.50 3.13 3.75 4.38 5.00 5.63 6.25 6.88 7.50 8.13 8.75 9.38 10.0 Multiplier 2.89 1.44 1.30 1.24 1.20 1.17 1.15 1 14 1.13 1.12 1.11 1.10 1.10 1.09 1.09 1.08 for d, =
1.94 ft.
e 1
o VM2*.I.non.itul01397 R u
1 1
1 TAllLE 3.2 2 ECKERT AND DIAGUILA MIXED CONVECTION llEAT TRANSFER TEST DATA Test Number Grol'r Range Red i 6.9 x 10' . l.1 x 1010 377000 2 6.9 x 10' 1.1 x 1010 180000 3 6.9 x 10' 1.4 x 1010 100000 4 7.5 x 10' . l.6 x 1010 36000 5 1.4 x 1010 1.8 x 1010 231000 6 1.3 x 1030 2.5 x 1030 134000 7 1.4 x 1010 3.7 x 1010 55000 8 3.5 x 10 10 5.1 x 1010 314000 9 3.5 x 10 10 5.5 x 10 10 246000 10 3.4 x 10 10 7.2 x 1010 77000 he predicted.to-measured Nusselt numbers for all ten tests are shown in Figure 3.211. De mean value is 1.028 with a standard deviation of 0.272. The Eckert and Diaguila(6) data showed large, unexplained variations in the original report; thus, the standard deviation reported here is not excessive. However, the good agreement with the mean indicates that the significent trends are represented by the correlation.
The calculated Nusselt numbers are about equal to or slightly higher than the measured values for cases with lower Reynolds numbers (tests 4,7, and 10). The calculated Nusselt numbers decrease in comparison with the measured values as the Reynolds number is increased. The apparent trend of the
, Eckert and Diaguila* data with the Reynolds number may be due to the fact that the measured centerline temperature is not the same as the bulk temperature, i.e., the difference between the bulk and centerline temperatures change as the flow develops away from the entrance. The data were scaled from figures in the referenced paper and this procesr. may also have introduced some of the scatter, o \M42w 1.non:1tul01397 R s
1000
.1400 tm f1000 * .
6 . . .
soo .
l ,
=
4o0 m
o
" ' ts
- u 3 33 , 4'6 8 h Hespe 000)
. Test Done ~w p%
Figure 3,21 Nusselt Number Comparison for Eckert and Diaguila Test I-o:U542w.g h lbl01397 nevan i 3-12 Octohet 1997
m_..__._..__.___m____.1_.____.___.___ .__ . . _ _ _ . _ _ _ _ _ _ _ . . _ _ . . . . . _ . . - . _ . _ _ _ _ - . _ _ _
I 1
i i
i r
l r
- l. i
- e. ,
f i
e 1000 -
i 900 <
000 <
700 J. .
800 e * *
- I'
[
i 1400 *
+
300 ' +
l m
100 <
0 0 0,6 1 1.8 3 2.8 3 3$ 4 4.6 6 Dwnerwonisse Heght 000)
. Test Date -W Prodcton Figure 3.2 2 Nusselt Number Comparison for Eckert and Diaguila 'fest 2 I- - o:\3542w-l.norrib 101397 Reusion I l 3 13 onober 1997
-iy--sy - -m- r y y m e y y 1 -. cy-Wuy'W'-*"TN-T'"" ' '9 "r**""'N'9 9#' ' ' " " ' ' "
" ~ **
@M --
-W9""TN#PD'N'8
i i
i h
i i
C k
i I t
4 I
e .
l 800 ,
800 ,
l 900 !
0 r
.400 I. . .
j,00 .
s j0 .
=
ISO 100 t
60 !
0 !
0 0.5 1 1.6 -2 35 3 3.6 4 4.8 8 D'maeconises % 00D) .
. Test Data -W Psodemon Figure 3.2 3 Nusselt Number Comparison for Eckert and Diaguila Test 3. l 1
oM542w l.non.it>101397 Rctuum I l
=
3 14 October 1997 1
_ . _ . . . - - . . . . _ - . ~ _ _ _ . . _ . _ _ . . _ - . . . _ _ . _ . _ . _ _ _ _ _ . _ _ .._ _.__._
e 4 -
Sno .
300 '
l
.feso .
soo . . .
' 1160 e
100 so 0 +"
0 0.5 1 ?.5 t 2.8 3 38 4 4.8 6
, Dann**se w A e Test Done -W Promoton i
Figure 3.2 4 Nusselt Number Comparison for Eckert and Diagulla Test 4 cA3542w-l.nmlb 101397 - Revision i 3 15 Oci*r 1997
=____---_l
..~..m____.-____....-_.._... - _ _ _ _ - _ . _ _ . _ -
.m~_m._____.-__m..---___..,.. - . . . _ - _ -
1 l
i 1000 goo . .
. l 800 '
. . 1
= . .
l la . .
900 .
. i 1# i r
300 ' i-300 ,
k 100 < i 1
0 0 06 1 1.5 2 2.8 3 3.8 4 4.8 8 Dynenestmises HugN (EO) .
. Test Done -W Preec.on j e
e i
Figure 3.2 5 Nusseh Number Comparison for Eckeri ani Diaguila Test 5 eM542w.l.nonsb 101397 Revtuon 1 -
=- 3. ] 6 . October 1997 u
.,+---...--~,n,--- ...< , - - , e,,-.,- -- w n ,---..,n -.,. -.--.,,~,--,..,,-a.,,nn.,---,:-m.I<-,,,w-rn. a- , ~~- -!
l l
I e
e 800 700 000 <
$00 l
y300< ~ . . .
, e ,.
200
- 100 0
0 0.8 1 1.5 2 2.5 ' 3 3.8 4 4.8 5-
, N @ W D) e Test Date -W Predcton e
c.
' Figure 3.2 6: Nusselt Number Comparison for Eckert and Diaguila Test 6 b$42w 2.malb 101397 Revuton 1 3 17- ociober 1997
). .. .. . . . . .
i, i
l
- l e
800 l
900 i
400 e
A w ,
300 e e ,
- e e a o , e ,
- 300 e *
- IJO 0
0 0.5 1 1.5 2 28 3 3.5 4 4.6 6 Dunerm Hoeght (xg) .
e Test Does -W Predeon
)
Figure 3.2 7 Nunsett Number Comparison for Eckert and Disguila Test 7 e.0542w 2.malb 101397 Revision 1 3*I8 - October 1997
_ - - , . _ . , - _ - - , - . . . . . . - . - _ , _ . ~ . ~ , . ~ _ . - - . _ _ _ . - , = , - - . - - - . - . . . . , , - _ - . ~ . - . . . - - _ . . _ . - - ,
i s
a 1400 1P00 I ,
1000 E- .
g .
400 200 0
- 0 0.5 1 1.5 3 8.5 3 35 s 4 45 5
, Dunenscrha HegN 00D)
. Test Data -W Predeten Figure 3.2 8 Nusselt Number Comparison for Eckert and Diaguila Test 8
< ov>42. 2 non iMoi3n 3 19 R ErY
l 1200 -
1000 <
800 I .
1-
- e R . .
LX 0
0 0.6 1 1.5 2 f.5 3 35 4 45 6 Danormordens H**DN (X On ,
- Tesi Data -W Prodden Figure 3.2 9 Nusselt Number Comparison for Eckert and Diaguila Test 9 l
l c 0542w 2. rum Ib 101397 Revenm 1 3 20 o m eet la97
t f
t P
-. i soo
-i
- m. ,
eco -
e Isoo soo *.
Doo ,
100 <
0 . . . -
o c.s 1. 1.s a s.s a s.s - 4 4s s ,
, DwnrWweste Hosphi(10D) l
. T osi -w m h
\
t Figure 3.210 Nunnett Number Comparison for Eckert and Diaguila Test le 3 OUS42w 2ason:lb-101397 Revtsson i I
'32I October 1997 i
.,_,.m_, , . , __ , _ . . . _ . - , , . _ , . . . - , . . _ . - , ,~~____..-._..,..-_...,_..,a....,._,.,_,_, , . . , . . _ , , , . . _ , . . _ . . . _ , , - .
1 2 ,
is Se . . .
t .
, , , . * +
1 * . . ! .
yn ' * *
- I j . . . __L _' +
i . . : : * - .=3._
I t
- 0s . .
- 8
. 8 . .
06 , .
04 07 4
^
0 16 2 26 3 36 4 46 6 0 06 1 Dunenso*se H.vt (W)
. Omta um(4 028) ,
E Figure 3.211 Comparison of Predicted to Measured Nusselt Numbers for the Eckert '
and Diaguila Tes'.<
~
011M2* 2am Ib-lul)97 Reymon i 3 22 Octoter 1997
3.3 The Siegel and Norris Mixed Convection Heat Transfer Tests 00 i
Siegel and Norris0 ') conducted heat transfer tests on a set of symmetrically heated, parallel, vertical flat plate channels. De channel width was 4.417 feet, the channel height was 5.833 feet, and the plate separation distance ranged from 0.125 to 1.25 feet. A constant unifonn heat flux of approximately 1100 Bru/hr ft.2 was applied.
h effects of reduced air flow were also investigated by adding extensions to the bottom of the test
, secticn channel and successively decreasing the lateral area for flow into the test section. Only those tests that had the test r,cction open at the bottom were examined far comparison. The tests generated data that validated the assisting mixed convection heat transfer model for low Reynolds numbers and i
moderate Grashof numbers.
Since the air flow rate was not given, the tests were modeled using the EGOTlilCU8) code. De test
. section was divided into 11 axial volumes. Because the most rapid changes occurred at the entrance, the first ten volumes were each 1/15th of the total volume; the last volume was one third of the total volume. The code calculated the velocity, air temperature, and heat transfer coefficient in each of the 11 volumes. The effects of reduced air flow were analyzed by relating the flow area reduction in the test to an increase in the inlet loss coefficient.
1 he Nusselt number, Nu, is defined as Nu = hd h/k, where d 3is the channel hydraulic diameter.
Entrance-effect multipliers were calculated as described in Section 2.2 and are presented in Table 3.31, i De Nusselt number was calculated using the assisting mixed convection conelation desenbed in Section 2.1 De calculated Nusselt numben for each of the eight tests are ? own in Figure 3.31 throt.gh 3.3 8 as a function of the dimensionless length. De test parameters are shown in Table 3.3 2.
TABLE 3.31 ENTRANCE EFFECT MULTIPLIERS FOR THE SIEGEL AND NORRIS HEAT TRANSFER *1'ESTS
) Distance from bottom, ft 0.39 0.78 1.17 1.56 1.94 2.33 2.72 3.11 3.50 3.89 5.83 Multiplier for 7.67 2.54 2.06 1.84 1.70 1.61 1.54 1,49 1.45 1.41 1.31
, ds = 1.949 ft, hiuttipl':r for 5.80 2.11 1.76 1.60 1.50 1,44 1.39 1.35 1.32 1.30 1.22 dn = 1.4 ft. '
hiultiplict for 3.61 1.60 1.42 1.33 1.27 1.24 1.21 1.19 1.18 1.16 1.12 d, = 0.761 ft hiultiplier for 2.62 1.37 1.26 1.20 1.17 1.15 1.13- 1.12 1.11 1.10 1.09 d3= 0.473 ft hiultiplier for 1.83 1.19 1.13 1.10 1.09 1.08 1.07 1.06 1.06 1.05 1.04 4
dn = 0.243 ft oM542w.2malb laim R s
TA11LE 3.3 2 SIEGEL AND NORRIS MIXED CONVECTION llEAT TRANSFER TEST DATA Test Number Ud n Air Temp. ('F) Grel'r Range Red Range 4 4 1 3.00 80.6 86.4 4.23 x 10 8 6.10 x 10 8 1.07 x 10 1.13 x 10 3
2 4.16 80.9 88.5 1.58 x 10 8
2.42 x 10 8 S.73 x 10 9.18 x 10 3 3 7.66 81.2 93.5 2.40 x 10 7 4.19 x 10 7 5.77 x 10' . 6.03 x 103
- 4 12.33 81.5 99.4 4.40 x 106 1.05 x 10 7
4.01 x 10' . 4.18 x 103 6
5 24.00 82.6 . I14.6 6.43 x 10 5 1.48 x 10 2.20 x 10 3 2.28 x 10' 6 7 6 12 33 81.5 100.3 5.42 x 10 1.17 x 10 3.82 x lo i 3.98 x 10 1 6.43 x 106 7 1 7 12.33 82.1 107.6 1.17 x 10 2.76 x 10 3 2.89 x 10 8 12.33 83.4 123.4 6.70 x 106 1,29 x 107 1.65 x 103 . l.73 x 10' The predicted to-mensured Nusselt numbers for all eight tests are shown in liigure 3.3 9. The mean predicted to measured value is 0.857 and the standard deviation is 0.0903.
As demonstrated m tests I through 5, the calculated Nusselt numbers match the measured data fairly well at lower values of Udh, but increasingly undertredict as the Udh value increases. Tests 4,6,7, and 8 demonstrate the effect of reduced air flow (at constant Ud h) by increasing the channel loss coefficient from 1.5 to 35.6. 'Ihe calculated Nusselt numbers increasingly underpredict the measured values as the air flow is reduced.
O. W* ma bl0lD7
l i l
t k
i 6
i s
3-i i-e w i t
300 ,
i
?
4 Y
I M i
I h
- soo <
4 j 160 s e i
- e o
i * - o 4
i h
t 0
0 0.5 1 1,8 2 2,5 3 3.5 M Heght (w)
- . e Test Deen -W Podemon I
i i
l'
- . e i ;
1 4
1 l Figure 3.31 ' Nusselt Number Comparison for Siegel and Norris Test 1 (15 in., K=1.5)
L I
4
, o \3542w 2 non.it>101397 Revanon 1
( 3 25 cenober 1997 l
._,a,_, . . - - . _ - - - _ . _ , . ~ . - _ . , , , _ _ , - . _ _ . . - _ . , - - . - . . . _ . . . , . _ , . . - . _ _ _ - _ - . - - - _ , - - . . - . . - - _ . _ , _ . . , . . . - _ . _ . ~ ~ - _ . _
.. ._._m____.______. _,_....____.._____.._______.....__..___.m._.._..._.m.,____... _.m.._,_________.._
300 100 100 140 120 j ,m .
j E
- i
.0 .
j
. l so _
40 20 <
0 0 0.6 - 1 1.5 2 2.6 3 3.5 4 4.5 - 8 h Hoght W@ .
- Test Date -W Predeten l-
[ r l=
Figure 3.3 2- Nusselt Number Comparison for Siegel and Norris Test 2 (10 in., K=1.5) oM542w 2.non.1b-101397 Revtsso7n 3 26 october 1997
e e
100 90 <
00 70 g.0 .
- i. .
l.0 .
30 30
'10 0
0 0.5 1 1.8 3 3.5 3 34 4 4.5 - 6.5 4 8.5 7 7.6 8
. Dwnenatonless Hught 00@
. Test Deen -W Predeton e
- Figure 3.3 3 Nusselt Number Comparison for Siegel and Norris Test 3 (5 in., K=1.5) o:us42. 2= m ioim .
3-27 Oc' 58
, , ,1, J
i l
1 oo 60 k +
b0 .
i .
2 .
20
~
10 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Dmensonless HegN (XM)
. Test Data -W Prodcton Figure 3.3-4 Nusselt Number Comparison for Siegel and Norris Test 4 (3 in., K=1.5) oA3542w 2.ruwIb-101397 Re sion
c o'
30 26 to I -
- 11. .
1 .
10 ,
e 5 o - d 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Dmensonlose Heght 00c0 Test Date -W Predeten 9
Figure 3.3 5 Nesselt Number Comparison for Siegel and Norris Test 5 (1.5 in., K=1.5) o:\3542w-2.non:Ib 101397 Revison i 3-29 october 1997
" l 50 e
40 1
j= -
3 e e
10 0
0 1 2 3 4 5 6 7 8 9 to 11 12 13 14 Dimermoniess Height (XM) ,
e Test Data -W Prodction 1
Figure 3.3-6 Nusselt Number Comparison for Siegel and Norris Test 6 (3 in., K=1.9) l o:\3542w 2.non:lb-101397 Revtuon 1 3-30 october 1997
4 i
e i ..
s e
to l
$0 1
40 I .
30 f +
.0 I *
-~
, 10 h'.
ll
. 0 0 1 2 3 4 5 6' 7 8 9 10 11 12 13 14 M Height M e Test Data -W Pro 6chon t
4 Figure 3.3-7 Nusselt Nurnber Coraparisor. for Siegel and Norris Test 7 (3 in., K=7.0)
.:u542w.2.non;isioim R 3,g ggsi,oQ
.._ . _ . _ _ . . _ . . . . _ . . . _ . . _ . _ _ _ _ _ . - - . - . . . . . . . . . ~ . ._. . _ . . , _ . . . .___..__.m._.. . _ . . . , _ _ _ _ _ _
i j
i i
i
) .
i 80 f l 1
l t
k
- I e.
- j. .
e 1 .
r *
, 10 0
0 1 2 3 4 'S 8 7 8 9 10 11 12 13 14 h6M .
-* Test Data -W Predicton i
i i.
I l
Figure 3.3-8 Nusselt Number Comparison for Siegel and Norris Test 8 (3 in., K=35.6) 0:\3542w.2.non:It>l01397 Revision I 3-32 October 1997
4 J
2 4
is I
- j. .
. t e ! .
-tis f. . .
0,5 4
u 0
10 30 20 3 Length (m)
+
. om. -u n to es7) a Figure 3.3-9 Comparison of Predicted to-Measured Nusselt Numbers for the Sieael and Norris Tests i
oA3542w-2.non:Ib-101397 Revision i_
3-33 October 1997 2
3,4 The Westinghouse Dry Flat Plate Tests
- The Westinghouse flat plate tests, performed at the Westinghouse Science and Technology Center, provided heat transfer data for channels with heat flux and cooling air flow rate representative of the AP600 riser annulus during a DBA, he test 'ection was a vertical,6-foot long, heated flat steel plate that had been coated with a highly wettriste, inorganic zine coating. A clear acrylic cover provided a channel 23 inches wide and ,
' inches deep for the forced air flow. The plate temperature and air flow rates were varied for each test. The measured parameters for each test are shown in Table 3.41.
De Nusselt number, defined in terms of the channel hydraulic diameter, is used for the data comparison. A length-averaged, entrance-effect multiplier of 1,13 was calculated as described in Section 2.2. De mixed convection Nusselt number was calculated as described in Section 2.1. The data are compared with the mixed convection correlation and shown as a function of the Reynolds number in Figure 3.4-1. Since these tests were forced convection 4ominated, the results correlate well with the Reynolds number, he measured data are compared to the mixed convection Nusselt number correlation in Figure 3.4-2. De mean value is 0.983 with a standard deviation of 0.072.
a,1 TABLE 3.41 WESTINGilOUSE DRY FLAT PLATE TEST DATA oA3542w 2mit> 101397 Revision t 3-34 oa d a 1997
1 a,b l
i A
i 4
4 4
i-t 4
i t
i.
4 .
i 6
t 4 -
a
- a.
4 1
1 4
Figure 3.4 Heat Transfer Data for the Dry Flat Plate Tests t
oA3542w,2.non.lb-101397 - Revision 1 3 3-35 october 1997 p
I
-l l
l l
I 1
2.0 1.5 l .
l1.0 e
- 0.5 0.0 30000 40000 50000 00000 70000 00000 90000 100000 110000 REYNOLDS NUtWER e TEST DATA -MEAN (0.983)
Figure 3.4 2 Comparison of Predicted.to-Measured Nnsselt Number for the Westinghouse Dry Flat Plate Tests o:\3542w 2.non:Ib-101397 Revision 1 3 36 oaober 1997
c.
3.5 - ne Westinghouse Large-Scale Dry External Heat Transfer Tests W
. A series of heat transfer tests was performed at the LST facility at the Westinghouse Science and
' Technology CenterG9. De purpose was to compile data for developing and validating the analytical
' heat transfer models. Circumferentially averaged, extemal heat transfer date were determined from the dry LST data.
De dry heat transfer tests were performed over a range of intemal test vessel pressures that bounded the AP600 containment design pressure to obtain heat transfer data at prototypic conditions, and to -
characterize heat transfer over a range of air cooling velocities.
He LST facility is approximately a 1/8-scale of the AP600. l %e AP600 containment shell is modeled by a 20-foot tall,15 foot diameter pressure vessel. The vessel contains air at I atmosphere when cold, and is supplied with steam at pressures up to 100 psig. Steam is injected in various source
. configurations to demonstrate the effect of momentum, buoyancy, and direction on heat and mass transfer performance.
A plexiglass cylinder surrounds the vessel, simulating the baffle that forms the air cooling annulus.
Air flows upward through the annulus to cool the vessel, resulting in condensation of the steam inside the vessel. A faa is located at the top of the annular shell to achieve higher air velocities than can be achieved by natural convectionc Thermocouples are located on both the inner and outer surfaces of the vessel at various circumferential angles, at each of ten different elevations to measure the shell temperature and heat flux distribution.
Thermocouples are also located inside the vessel on a rake to measure the bulk gas temperature at-various radial and vertical locations. De extemal cooling air temperature and velocity are measured
- at several locations in the annulus. The steam inlet pressure, temperature, and flow rate, and the condensate temperature and flow rate are measured to characterize the total heat in and out of the vessel.
Data that varied with time, angular position, and elevation were collected for each test. Nusselt numbers were calculated from the data using measured surface-to-bulk gas temperature and heat fluxes that were averaged over time and circumferentially-averaged at each measunng elevation. Bulk gas temperatures in the annulus were not measured at each elevation, where surface temperature and heat flux were measured, so the gas temperature was interpolated from values at the next higher and lower elevations.
- De steady-state, circumferentially-averaged heat transfer data from 14 of the 16 dry LSTs were used
' to define hydraulic diameter-based Nusselt number values. The Nusselt number values were compared with predictions of the turbulent, mixed convection correlation as described in Sections 2.1. (Tests RC015 and RC016 were omitted from this comparison because the forced asymmetric annular air flow rate imposed for these tests affected the circumferential-averaging.) Entnmce-effect multipliers oA3542w-3.non:Ib.101397 R is o
calculated as described in Section 2.2 are presented in Table 3.5-1. De ratio of the predicted-to-measured Nusselt numbers is shown as a function of dimensionless length from the bottom of the riser. Test parameters are presented in Table 3.5-2.
A compilation of the predicted-to-measured Nusselt numbers for all 14 tests is shown in Figure 3.5-1.
The average, predicted-to-measured values at each location and mean values over all locations are also shown. De mean value is 0.895 with a standard deviation of 0.122.
TABLE 3.51 .
ENTRANCE EFFECT MULTIPLIERS FOR TIIE WESTINGilOUSE LARGE SCALE DRY llEAT TRANSFER TESTS Distance from bottom, ft 2.76 5.51 8.26 10.26 11.62 13.87 15.74 17.52 Multiplier for dh = 0.50 ft. 1.70 1.16 1.11 1.09 1.00 1.00 1.00 1.00 oV542w 3.non:lb-101397 Revision 1 3-38 october 1997
- _ a,b TABLE 3.5 2 WESTINGHOUSE LARGE SCALE DRY EXTERNAL HEAT TRANSFER TEST DATA -
I
(!
oA3542w-3.non:lb-101397 " #
3-39 %El'if9}
i 2.00 i
1.50 -
h .
)
8 8 . g 3 . .
]i.00 . ; ' -
j - : :
l ! l l l 0.50 ,
1 : :
e
{ VERTICAL WALL l DOME j LEVEL D C B A W X Y &
0 00 0.00 0.10 0.20 0.30 0.40 0.50 0.E0 0.70 0.80 0.90 1.00 1.10 Dmensonless Length x/L
. Test Data -Mean (0 605) .
9 Figure 3.51 Comparison of Predicted to-Measured Nusselt Numbers for the Westinghouse Large Scale Tests .
l oU542w 3.norritet0l397 Reymon I 3-40 october 1997
3.6 The Gililland and Sherwood Evaporation Tests A isothermal evaporation mass transfer rates were measured in a vertical pipe by Gilliland and Sherwood(22) A water film was applied to the inside wall of the pipe and the evaporation rate was measured for both countercurrent and concurrent flow.
De test section was a ll7-cm long, vertical pipe with a 2.67-cm inside diameter. Calming sections
,_. were added at both ends of the test section. A falling liquid film covered the inside surface of the test l section. De film flow rate was held constant in all tests at approximately 790 cc/ min while the air flow rate was varied. The inlet air and liquid film temperat':res were maintained within 3*C, De reported parameters for each test are shown in Table 3.61. Since the liquid and air temperatures are nearly the same (isothermal) in these tests, the evaporative mass transfer was almost entirely driven by the difference in partial pressure between the liquid film surface and bulk mixture.
Relatively low air flow rates, compared to the mass transfer rates, were used in these mass transfer -
tests. He lower air flow rates caused a large difference in the bulk steam partial pressure from inlet-to-outlet, as shown for a typical test in Figure 3.6-1. Because of the large change in the bulk air / steam mixture properties over the length of the test section, average properties could not be used to evaluate the test data.' A simple,10-cell FORTRAN model was developed to evaluate the test data.
The Nusselt and Sherwood numbers were defined in terms of the channel hydraulic diameter.
Entrance-effect multipliers presented in Table 3.6-2 were calculated and used as described in Section 2.2. He mixed convection Nusselt and Sherwood numbers were calculated as described in -
Sections 2.1 and 2.5. He predicted local evaporative mass flux was integra.ed and compared with the measured total evaporation rate. De predicted-to-measured total evaporation rate is shown as a function of the Reynolds number for all 71 tests in Figure 3.6-2. The mean value for all tests is 0.925 and the standard deviation is 0.072.
O o:\35425 3.non:1b-101397 R i
. - _ .. . ~ - -- - _ . . -- .--- - .- . . -
TABLE 3.61 GILLILAND AND SilERWOOD EVAPORATION TEST DATA Air Evap l' T,i, Top T,i, Bottom T ,,,,, Top T,,,,, Bottom Pressure Flow Rate Test 'C 'C 'C 'C m m lig g/ min cc/ min 1 1 30.8 27 31.1 26.1 770 250 3.8 1 .
3 29.6 27.9 29.8 27.8 772 243 3.6
{
5 32.1 25.8 32.5 24.9 777 125 1.6 ,
9 32.6 28.3 33.1 27.4 777 143 1.8 11 32.1 28.I 33 27.4 770 54 0.73 4
13 32.2 26.8 32.9 26.2 770 214 2.5 1
15 28.7 27.3 29.4 26.7 772 324 4.7 17 30 27.8 30.6 27.I 770 218 3.2 19 32.6 28.9 33.1 28.3 770 158 2.7
~
21 32.3 28.6 32.9 28.2 770 103 1.8 23 32.4 29.2 32.9 28.5 770 74 1.4 25 41.1 38.4 41.7 37.8 785 220 6.2 4
. 27 40.4 41.3 41.4 40.8 800 80 2,4 29 38.9 35.8 39.5 35.2 782 48 1.5 31 40.5 28 30.1 26.5 775 502 7.4 33 42.4 37.2 42.6 36.6 777 11I 3.7 35 42.4 38.8 43.5 38.I 775 141 4.4 37 42 36.9 43.1 36.7 777 174 5.4 39 41.7 37.4 42.2 36.9 760 215 7.4 41 41.1 38.5 41.9 38 760 197 5.7 43 40.7 38.9 41.3 38.3 770 143 4.1 45 40.7 39.9 41.3 39.5 770 96 3.2 47 45.2 39.7 44.3 39.5 765 51 2 49 44.1 39.7 44.7 38.6 765 457 12.9 51 43.8 40 44 38.4 765 625 17 L
o V542w.3.non:Ib-101397 Re isso
I l
l l
TABLE 3.61 (Cont.)
GILLILAND AND SHERWOOD EVAPORATION TEST DATA Air Evap T,i, Top T,g Bottom T,,,,, Top T,,,,,, Bottom Pressure Flow Rate Test 'C 'C 'C 'C mm Hg g/ min ec/ min 53 56.1 50.9 55.2 50 760 46 3.3 55 52.8 46.1 53.5 45.4 802 96 5.9
, 57 51.6 49.2 50.I 48.4 767 88 5.3 59 52.6 43.2 53.2 42.7 767 119 6.5 61 53.9 48.2 53.5 47.8 785 248 13.2 63 54.6 49.1 54.3 48.5 785 168 9.6 65 53.1 48.3 53.3 47 787 475 22.8 67 52.1 49.6 54.7 49.1 782 126 8.1 2 34.9 33,4 35.6 33.2 772 63 1.6 4 33.8 32.1 34.5 32 114 60 12 6 36.2 34.9 36.4 34.6 2006 66 0.65 8 31.8 26.7 32.5 26.3 407 125 4.4 10 32.6 27.6 32.8 27.1 1480 127 1.1 12 31.9 28.1 32 27,9 269 122 6 14 33.1 28.6 31 28 941 123 1.6 16 31.4 28.8 32 28.5 1966 121 0.75 18 32.8 28.3 32.5 28 556 217 4.8 20 31 28.1 32 27.5 1419 216 1.75
-22 30.8 26 31.9 25.2 424 214 6.7 24 25.8 25.1 36 34.6 2325 65 0.44 27 31.9 27.6 33.6 27.I 1248 213 2.3 29 32.1 26.7 32.7 26.2 1958 218 1.5 31 32.9 29.I 34.I 28.7 919 374 4.8 33 43.8 38.9 44.3 39.5 765 51 1.9 35 40.8 37 41.9 36.5 112 47 15 ov542. 3.non.15 oi397 Pegig
.i d
i TABLE 3.61 (Cont.)
GILLIL/.ND AND SHERWOOD EVAPORATION TEST DATA Air Evap Tg, Top Tg, Bottom T,,,,, Top T,,,,, B ottom Pressure Flow Rate Test 'C 'C 'C 'C mm Hg g/ min ec/ min 37 42.8 40.4 43.6 40.2 1695 51 0.8 39 40.6 37.1 41 35.9 249 48 6.3 41 42.1 37.7 42.8 37.2 992 49 1.5 ,
43 42.7 39.4 43.3 38.9 1922 50 0.9 45 42.6 38.4 43.2 37.9 505 138 7.0 47 42.8 39.7 43.2 39.2 1385 137 2.4 49 41.8 35.8 42.3 35.3 396 134 9.1 51 41.8 37.8 42.5 37.2 1183 147 3.0 53 41.8 38.I 42.6 37.7 607 187 7.2 55 41.2 37.1 41.7 36.6 411 187 11.3 57 40.3 36.3 40.9 36 1235 195 3.6 59 42.7 38.6 43.1 37.9 1045 339 7.1 61 51.8 49.6 52.3 49 762 88 5.2 63 51.9 47.9 53.1 48.8 1321 88 3.2 65 53.4 49.4 56 49 320 121 20.8 67 55.I 49.9 55.6 49.6 1418 123 4.0 69 53.9 47.6 55.2 48.5 518 120 13.1 71 53.6 46.8 54.2 46 757 201 11.8 73 54.6 47.7 55.2 47.1 951 20I . 8.7 -
75 55.9 47.1 56.2 46.9 574 354 24.8 0:UM2w.3. sum:lb.101397 R so
t i
4 TABLE 3.6 2 ENTRANCE EFFECT MULTIPLIERS FOR THE GILLILAND AND i SHERWOOD MASS TRANSFER TESTS r
Distance from bottom, ft 0.38 0.77 1.15 1.54 1.92 2.30 2.69 3.07 3.45 3.84 1
. Multiplier for 1,16 1.037 1.026 1.020 1.017 1.015 1.013 1.012 1.011 1.010
, dh= 0.088 ft.
a 4
i 4
3 a
1 h
i l
I i
1 c:0512w-3.non:tb tot 397 R ion
I 40 n.
3a .
-^
as .
3 20 j
is j j'
- s#
10
/ l 5-0 0 11.7 23.4 36.1 46.8 68 6 70.2 81.0 93 6 105.3 117 ChannelLength (cm)
- -som + surtace .
Figure 3.6-1 Calculated Steam Partial Pressure Distribution for a Typical Gilliland and Sherwood Evaporation Test o:us42w.3 non:itrioi397 agisi,ong
. , . .. - . . . ~ . .. .. - - _ _ _ - - - .
e a
2 -
1.5 <
' f %.. *.; . .s t . .. .
~' s .; :* \ g .*
0.5 -
, 0 0 5000 100GO 15000 20000 M M
. Test Data -Mean (0.925)
Figure 3.6 2 Cornparison of Predicted-to-Measured Evaporation Rates for the Gilliland and Sherwood Evaporation Tests o:uS42.-3.non:id ioi397 R on g
= --
3,7 The Wc:/dnghouse Flat Plate Evaporation Tests (2"'
A series of liquid film evaporation tests was performed at the Westinghouse Science and Technolagy Center (2m. The purpose was to obsent the behavior of the liquid fiim and to provide data on evaporative mass transfer. The tent condi: ions were selected to simulate the outside of the AP600 steel containment vessel with the PCS in operation.
He test section was a vertical,6-loot long, heated flat steel plate that was coated with the AP600 ,
inorganic zine coating. A clear acrylic cover provided a 23-inch wide, by 4-inch deep channel for the forced air flow and allowed observation of the applied liquid film. He plate temperature, applied liquid film tempeature, and both the liquid and air flow rates were varied for each test. Measured -
parameters for each test are presented in Table 3.71 Tests 27 32 wem conducted with the plate sleped 15* from horizontal, while all other tests were conducted on a vertical surface.
Relatively high air flow rates, in comparison to the evaporation mass transfer rate, were used in these tests. Thus, as shown in Figure 3.7-1, the change in the bulk-to-film steam partial pressure difference from inlet-to-outlet was small, and decn:ased as the air flow rate increased. Herefore, inlet and outlet average properties were used to calculate the Sherwood number for comparison with the test data.
The Sherwood numbers were defined using the channel hydraulic diameter. The data from the 23 Westinghouse flat plate evaporation tests (2m were compared with predictions using the turbulent mixed convection correlation, with an entrance-effect multiplier of 1.13, as described in Sections 2.1,2.2, and 2.5. The predicted-to-measured Sherwood numbers for each of tFe 23 tests are shown as a function of the Re'ynolds number in Figure 3.7 2. The mean value is 0.936 with a standard deviation of 0.139.
Since the results of this test were forced convection-dominated, the results correlate well with the Reynolds number, as shown in Figure 3.7-3.
9
)
3-48 ocUoEUM
^
- a,b l
TABLE 3,71 WESTINGHOUSE FLAT PLATE EVAPORATION TEST DATA A
I 0:V542w-3 non:lb-101397 Revision 1 3-49 october 1997
a,b Figure 3.71 Bulk to-Film Steam Partial Pressure Differences from Selected Westinghouse Flat Plate Evaporation Tests 1 0:\3542w-3.non:Ib-101397 Reymon i 3 50 ociober 1997
+
d d
s t.0 t.s
] .
. e e * .
~ 05 0.0 0 20000 40000 00000 00000 100000 120000 140000 Reynolds Numb.t
. . T.st Date -- Mean (0.938)
Figure 3.7 2 Comparison of Predicted to-Measured Sherwood Numbers for the Westinghouse Flat Plate Evaporation Tests o:usuw.3.non:ib.ioi397 3-M $*lN
a,b .
4 I
I h
E Figure 3.7-3 Mass Transfer Data for the Westinghouse Wet Flat Plate Tests o:\3542w.3.non:Ib-801397 Revision i 3-52 ociober 1997
- - - . -- .- - -.. ~ - - - -. .-. - - . - . . - . - . _ -
3.8 The University of Wisconsin Condensation Tests (23)
- A series of condensation tests was conducted at the University of Wisconsin (23)- 3, purpose was to provide data on condensation mass transfer in the presence of a noncondensible gas at .various .
] inclination angles, velocities, and steam / air concentrations.
De test section was 6.25 feet long, with a 2.75 foot entrance length, and a 3.5-foot condensing surface
_ , length. De~ channel cross section was square with an area of 0.25 2ft , De top of the test section
_ was a thick aluminum plate coated with the AP600 inoiganic zinc coating. Seven 0.5 foot long i: cooling plates were attached to the back of the aluminun test plate to remove heat. Each cooling plate had both flux meters and cooling coils with thermocouples to provide redundant, diverse energy measurenents, The test section could be inclined from 0 to 90 degrees from horizontal. - Plate number i 1 was loca'ed at the end nearest the air / steam source and was always at the highest level when the test section _was inclined. Test parameters are shown in Table 3.81.
- . Relatively high air flow rates, in comparison to the mass transfer rates, were used in these tests. As a j- result, the change in the bulk-to-film steam partial pressure difference from inlet to outlet was small, as shown in Figure 3.8-1. Derefore, inlet to-outlet average properties were used to calculate the
- predicted Sherwood number for comparison with the test data.
[ De data from the 59 University of Wisconsin condensation tests (23) were converted to hydraulic
!- diameter based Sherwood numbers and compared to Sherwood numbers calcula'ed from the assisting j mixed convection mass transfer correlation described in Section 2.1 and 2.5. An a>erage entrance-
] effect multiplier of 1.20 was calculated as described in Section 2.2. The predicted-to-measured
[ Sherwood numbers for each of the 59 tests are shown as a function of the inclination angle in i Figure 3.8 2, as a function of the steam / air Reynolds number in Figure 3.8-3, as a function of the bulk
} air / steam concentration in Figure 3.8-4, and as a function of heat flux in Figure 3.8-5. . He measured -
j -- . data are compared with the mixed convection mass transfer correlation in Figure 3.8-6. The mean 4 value is 0.932 with a standard deviation of 0.179.
Five of the Wisconsin tests were conducted without noncondensables. These tests,95-99, were use:1 for the liquid film heat transfer correlation comparisons presented in Section 3.10.
f
+
i d- _
oA3542w.3.non:ltsl01397 Revision I 3 october 1997
TABLE 3.8.I WISCONSIN CONDENSATION TEST DATA Avg. Heat Flux Temp In Temp Out T wall Velocity Test W/m2 .C 'C 'C m/s Angle 83 27342 95.6 95.7 45.9 1 90 82 27493 95.4 95.7 49.5 1 45 .
80 26395 95.2 94.9 45.2 1 12 81 27117 95.1 94.8 45.6 1 12 76 27257 94.9 95.1 44.5 1 0 79 27189 94.6 94.6 47 1 6 86 27260 94.5 94.2 44.3 1 a 74 16913 90.I 89.9 29.2 1 12 73 16675 90.1 89.8 29.3 1 45 75 17681 90.3 89.7 30.7 1 6 76 16615 90.2 89.7 28.9 1 0 72 17178 89.7 89.7 31.3 1 45 71 1465I 90 89 29.9 1 90 77 16645 89.3 89.7 29,5 1 0 94 25223 90.5 89.3 39.5 2 0 55 11692 80.6 80.4 29.9 2 0 70 14171 80.5 79.7 29.9 3 90 l .
57 8592 80.1 80 99.8 1 12 48 8166 80.4 79.6 29.9 l 90 ,
43 10140 80.4 79.6 29.5 1 6 50 10168 80.1 79.6 29.6 2 90 69 14069 80.6 79.9 29.7 3 0 68 14537 79.9 79.9 29.7 3 6 OA3512w.3.non:Ib-101397
- Revtsson 1 3-54 (.w oixri997 1
TABLE 3.81 (Cont.)
WISCONSIN CONDENSATION TEST DATA r
Avg. Heat Flux Tempin Temp Out T wall Velocity Test W/m2 .C 'C 'C m/s Angle 64 14553 79.8 79.8 30.2 a 90
.. 44 10589 80 79.6 30.1 1 12 5I I0515 79.9 79.5 29.7 2 45 52 10807 80.1 79.3 29.6 2 12 55 7983 80 79 29.3 1 12 47 7973 80.2 78.8 30.1 1 45 54 10939 79.7 79.4 30 2 6 34 9931 80.6 78.8 30.1 1 0 53 10023 79.9 79 29.6 2 6 67 13100 79.5 79.3 29.8 3 12 66 14523 79.4 79.2 30.2 3 45 85 15974 79.4 79.3 30.4 3 0 31 9881 78.7 78.7 30 1 0
-32 9924 77.4 77.4 30.1 1 0 36 8194 72.2 72.1 30.1 2 0 62 8733 71.7. 71.8 29.9 3 45 42 8170 72.5 70.9 29.6 2 6
~
61 9286 71.5 71.3 30.3 3 12 4
. 59 8888 71 7 s .6 29.3 3 6 39 7960 71.8 71.4 30.2 2 0 46 6743 71 71.4 30.6 2 45 49 6561 70.8 70.8 29.3 2 90 41 8677 71.7 70.6 29.6 2 0 87 5572 71 70.2 30.2 1 0
-l 91 4736 70.6 69.9 29.7 1 45
}
- p. o:us42w-3.non: b-ioi397 ggisg
_ ~ -
TABLE 3.81 (Cont.)
WISCONSIN CONDENSATION TEST DATA Avg. Heat Flux Temp In Temp Out T. wall Velocity Test W/m 2 .C 'C 'C m/s Angle 63 8100 70.7 69.7 29.7 3 90 90 $173 69.7 70.5 29.7 1 12 .
92 4457 69.9 70.1 29.4 1 88 88 5364 70 70.2 29,8 1 6 40 9353 70 70 30.1 2 0 45 7868 69.4 69.4 29.5 2 12 60 9624 69.6 69.6 30 3 0 89 5411 69.2 69 29.9 1 12 l 58 4869 61.1 61.9 29.9 2 6 93 2769 60.4 60.4 29.7 1 0 65 6449 59.2 60.4 29.9 3 45 s
o-\3542w-3.non:Ib-101397 Revision 1 3-56 o:rober i997
l
- 4:
S ,, -
e 8
{ .
U 3
e b i m
E .
g
=
c- s -
L t.
g <
- . =
!e 3 -
' C o
O 1 g 3 4 Channel Length (f t)
- Test 83 Test 74 w Test 55 + Test 36 Test 58 i
Figure 3.81 Bulk to Film Steam Partial Pressure Differences Variation Over Channel Length from Selected Wisconsin Condensation Tests
.. oW42w 3.non:lt>101397 - Reviuon 1 3 57 a:ioter 1997
t.0 =
1.6 3, i i .
" , .0
. I' .
! J '.S 9 . .
, I e h g i ll !
0.6 1
0.0 0 10 20 30 40 60 60 70 60 90 100 Plat.Inclinston from Horirantal(D gr s)
. Test Data - Mean (0.932)
Figure 3.8 2 The Effect of Surface Inclination on the Predicted to Measured Sherwood Number Ratio for the Wisconsin Condensation lests i o \3s42w.3 non. it> 101397 Rensam i 3 58 octoter 1997
to i 1.8 g.
E I
'# d I. *- -
.t 00 D 10000 ' ** teo00 m
- Tem om. -- u ,,,
Figure 3.8 3 The Effect of Reynolds Nr.mber on the Predicted to Measured Sherwood Number Ratio for the Wisconsin Condensation Tests OW42w 3.non.lb-lol397 Oct [997
I e I e
8.0 .
, 1.6
- r I
.* g
& 4 1..
1.0 g. ,
- ts ', h. e
,. 3 0.84 00 0% 10% 30 % 30% 40% 60 % 40% 70% 40%
9 team Mole Frechan (%)
. Test Date - Mean (0 932) e
- Figure 3.8 4 The Effect of Steam Concentration on the Predicted to Measured Sherwood Number Ratio for the Wisconsin Condensation Tests o \)S42w.3.non.It>101397 Reymon I 3@ b*' 3 7
l A
s.0 1.6 1
g ' . . *. . .e 1.0 . #, '. .
'r
- g. -
0.0 0 1000 2000 3000 4000 5000 0000 7000 m 9000 10000 Heat Flus (STU4wM)
. t o.m - m :0.un Figure 3.8 5 The Effect of Heat Flux on the Predicted to Measured Sherwood Number Ratio for the Wisconsin Condensation Tests o.usu.-3 non 15:o:397 3-61
- 1
w._...-.__._
4 e
1000 l
I1. . .
W=0.083 Re*0.8 Set /3 b
10 1.00E+03 1.00E+04 1.00E+06 Wh
. Temoma - c e k
Figure 3.8 6 Mass Transfer Data for the Wisconsin Condensation Tests -
o:U542w 3.rmiklol397 Revision I i 3 62 October 1997
's-ww gy- 9 ,.h.-r.-gy-* g gpy- +wp----- w- g-p.-r-yyvy-y p py---- -q c y w ,,-w%- vvr'*-w- twwwey1. vg g y-yr y-ry yrv- ww w w vr www*<--eyuw.-'wwr-r -
7W4mr " wee-meWmrw,_g-.wme,,,.,,,,,,..w,4 ,,m-we reer,,.. --wuo.e-##
3.9 The Westinghouse Large Scale Internal Condensation Testst2o The Phase ? (confirmatmy) heat and mass transfec tests were perform d at the large scale test (LST)
, facility at th Westinghouse Science and Technology Center (24, 3, y .ase 2 tests provided data on the trant. lent heat transfer and distribution of noncondensible gas in a geometry similar to the AP640 containment vessel. The purpose was to provide data to develop and validate heat and mass transfer models.
De LST test facility is approximately a 1/8 scale of the AP600. He AP600 cc stainment shellis modeled by a 20 foot tall,15 foot ctiameter pressure vessel. The vessel contain. air at I atmosphere when cold, and is supplied with steam at pressures up to 100 psig. Stean, is injected in various source configurations to demonstrate the effect of momentum, buoyancy, and direction on heat and mass transfer perfonnance.
A plexiglass cylinder surrounds the vessel, simulating the baffle that forms the air cooling annulus.
Air flows upward through the armulus to cool the vessel, resulting in condensation of the steam inside the vessel. A fan is located at the top of the annular shell to achieve higher air velocities than can be achieved by natural convection. A liquid film is applied to the outside of the test vessel to provide additional, evaporative cooling.
Dermocouples are located on both the inner and outer surfaces of the vessel, at various circumferential angles, at each of ten different elevations to measure the shell temperature and heat flux distribution. Thermocouples are also located inside the vessel on a rake to measure the bulk gas temperature at various radial and vertical locations. He external cooling air temperature and velocity are measured at several locations in the annulus. He steam inlet pressure, temperature, and flow rate, and the condensate temperature and flow rate are measured to characterize the total energy in and out of the vessel.
The Sherwood numbers inside the LST are defined in terms of (v 2fg)t/3, for the length parameter, as described in Section 2.3. De measured Sherwood numbers were based on surface to bulk gas density differences and shell heat flutes that were averaged over time and averaged circumferentially at each measuring elevation. Steam partial pressures were not measured at each elevation, so the steam partial
. pressures were interpolated from the next higher and lower measurement elevations.
ne steady state, circumferentially averaged mass transfer data from 7 of the 25 Phase 2 tests were converted to Sherwood numbers and compared with predictions of the free convection mass transfer correlations described in Section 2.3. The Phase 2 tests all had a diffuser located below the simulated steam generator. Only tests with film coverage greater than 90 percent were included in the comparison because lower film coverage biases the circumferentially averaged test measurement. This eliminated 17 of the tests. Test RC062 (blind test fot ,WGOTHIC validation) was also omitted from the comparison because the data was not available when the evaluation was done. Relevant test parameters are presented in Table 3.91.
o umw-4 :uotwioim gpg
f i
, _ a,b TAHLE 3.91 WESTINGHOUSE LARGE. SCALE INTERNAL CONDENSATION TEST DATA l
l A compilation of the predicted-to-measured Sherwood numbers for all seven tests is shown in Figure 3.91, ne mean value is 1.045 with a standard deviation of 0.167. Figures 3.9 2,3.9 3, and 3.9 4 provide a comparison of the measured data with the mass transfer correlation as a function of heat flux, steam concentration, and Ap/p. De correlation matches the trend in the data.
The argument has been used that free convection heat and mass transfer on the inside of the shell is conservative during blowdown, when a significant increase in the transfer coefficient is expected due to the blowdown induced forced convection. LST RC064 (222.3) and RC066 (222.4) predicted to- -
measured mass transfer coefficients presented in Figure 3.9 5 show the effect of high internal break source kinetic energy. These two tests were conducted in a configuration that simulated an MSLB at the top of the steam generator. The steam source was a 3 inch inside diameter pipe elevnted to a level that simulated the top of the steam generator, rather than the LOCA configuration with a steam diffuser under the simulated steam generator model. Both tests consisted of two steady. state segments with approximately a factor of two on steam flow rate. Test RC064 had the steam source pointed horizontally at the far wall, and test RC066 had the steam source pointed vertically. The tests are described in Reference 24, Sections 4.15 and 4.16.
f
. W .U. Ol3M
l l
The data in Figure 3.9 5 show the predicted to measured mass transfer coefGeients are 5 to 10 times greater than the free convection mean value presented in Figure 3.91 for LSTs with the diffuser below the steam generator. The location of the maximum corresponds to the elevation where the jet impinges: at x/L = 0.4 for the horizontal jet, and x/L = 1.0 for the vertical jet. At all elevations the measured mass transfer coefficients are as high or higher than the mean of the measurements for free convection, with an average value approximately twice that of the free convection mass transfer coef0cient.
e f
4 OM142w4non:Ib 101397 ,
3 65 octobertw7
30-ts< l 1 2.0 <
ib l 9 1.s <
i t .
a l . !- . . a .
l 1.0 <
w g e . ;
a 1 . .
. 8 0.9 <
LEVEL 0 C B A W X Y Z l l l- l l l vem m w e i ooue 00 OJ 04 00 00 1.0 12 o===== w a
. v.m ou. -u oms, Figure 3,9-1 Predicted to Measured Condensation Sherwood Number Ratio for the Westinghouse Large Scale Tests o11542w-4.non:Ib-101397 Revision 1 3-66 oci*r 1997
4 1
1 4
3.o j
ss z.o .
i.. .
e .
<a-h,.,1 .
os.
o.0 o m 200o sooo 4o00 sooo sooo rooo oooo onno Med Mus (STukea2)
. Test Date Figure 3.9 2 The Effect of Heat Flux on the Predicted to Measured Condensation Sherwood Number Ratio for the Westinghouse Large Scale Tests 011542w4non.itsf ol397 Reymon i 3-67 ociober 1997
3.0 l
1 2.$ -
i !
2,0 -
t.s - *
, .0 . ,. .- . . :, . .
l0.6-
.o.. .
0.0 0% 10% 20% 30% 40% 60 %
Steam M Procton (%)
. Test Data e
Figure 3.9 3 Comparison of Predicted to Measured Sherwood Numbers for the Westinghouse Large Scale Tests o u.uz.4non. ibioin7 3-68 a1Er"IN
l a,b Figure 3.9 4 Condensation Mass Transfer Data for the Westinghouse Large Scale Tests oM542w-4.non:Ib 101397 ggygium g 3-69 octoter 1997
~
te ,
u w. O C B A tt X Y Z YERTICAL WALL DOME -I 10] l f
t 3 j _ a e
e 1 100
! $ g 6
l e o e s
06 e
o e e e e
4
- e 00 -
00 02 04 06 08 1.0 12 .
Demonalentees Length mA e acoes wat to wsu e noons pet m -wtan(61 mtspeu cONDENGAfth QF A D Dell W
Figure 3.9 5 Predicted to4teasured Sherwood Number Ratios for the MSLB Large-Scale Tests o V542w-4 non:lt*l01397 Revisam I 3 70 oct*r 1997
3.10 Chun and Seban Liquid Film Conductance htodel(7)
De Chun and Seban correlation is used to predict heat transfer through the condensing and evaporating liquid films. De conelation applies to both turbulent and wavy laminar films and was compared to data in the original paper. Data from tests at the University of Wisconsin (23) extend the validity of the Chun and Seban correlation to condensing wavy latninar flow and to surfaces that are inclined, as in the dome region of the AP600.
We Wisconsin test facility is described in Section 3.8. Five of the Wisconsin (23) tests (95 through 99) were conducted without a noncondensible gas present. Without a noncondensible gas, the gas to-liquid heat transfer coefficient is so high that the gas to liquid temperature drop is negligible compared to the temperature drop across the liquid film. Consequently, the temperature of the liquid film surface may be assumed equal to the gas temperature and the liquid film heat transfer coefficient can be calculated from the heat flux divided by the liquid film temperature drop. Since the heat flux, solid surface temperature, and liquid film surface temperature are known, the heat transfer coefficient may be derived directly from the measurements. %e Wisconsin tests thus provida! a direct indication of the liquid film heat transfer coefficient for a range of surface inclinations from vertical to hormntal, covering a range of film Reynolds number in the wavy laminar regime.
%e Wisconsin (23) and Chun and Seban(7) data are compared to the Chun and Seban laminar and turbulent correlations in Figure 3.101, ne correlation predicts nearly best estimate values over the full Reynolds number range of data. De range of film Reynolds numbers on the outside of AP600 is also shown in the figure and falls well within the range of the test data. Reynolds numbers on the inside of containment are less than outside due to film removal at the crane rail and stiffener ring, and the fact that the inside film flow rate starts at zero at the top of the dome and increases as the film flows down. De AP600 liquid film Prandtl number range is approximately 1.5 < Pr < 3.0, whereas the range of the Chun and Seban data Prandtl numbert is 1,77 < Pr < 5.9, which adequately covers the AP600 range. Comparison of the correlation to the test data show that the Chun and Sebar$ correlation is a good, best estimate representation of the data.
The large scatter in the Wisconsin (23) I quid film heat tranafer data is believed to result from operating the tests at (or beyond) the range or operation for which the test facility was designed. He presence of even small amnunts of noncondensible gases would bias the results, s
OV.Ww 4 m lh 101WI si ni
1 1 Own and Seban Turbulent Larelation Chun and Seban Wavy ~
Nu = 0.0038 (Re ^ 0A) (Pr ^ 0.65)
~
Laminar Curelation -
Nu = 0 822 (Ho" 0 22) Pr = 6.1 2 -
Pr = 5.7 / Pr =2 91
. ~
d M M
M xg .
M A Pr =1.77 W
$ U x 8
- Bold X'o are Wioconoin Data. All othero are Chun g a and Beban data.
AP000 Range (from second wek) 0.1 0.1
, , , , , , , , , ,.T, -- , , , , , , , , , , , , , , , , , , , , , ,
10 100 1000 1 0000 100000 LigJd Farn Reynous Number, Re .
t Figure 3.101 Data from the Wisconsin and Chun and Seban Tests Compared to the Chun und Seban Wavy Lamir,nr and Turbulent Correlations oM542w-4 non Ib 101397 Reymon1 3 72 ocuda 1997
4 ASSESSMENT OF RESULTS AND STATISTICS De ratio of the predicted to-measured Nusselt number (for convection) or Sherwood number (for condensation and evaporation) was calculated, and comparisons for each of the individual tests were presented in Section 3. He predicted to-measured ratios are combined by mode of heat transfer opposed mixed (convection heat transfer, opposed mixed convection evaporation mass transfer, and free convection condensation mass transfer) for an assessment of the combined statistics. The results
=
show that the heat and mass transfer correlations represent the phenomena inside the AP600 containment vessel and m the PCS air now path over the expected ranges of the dimensionless groups during a DBA event.
4.1 Convection llent Transfer ne combined convection data consists of the llugotdU, Eckert and Diaguitat6 ), Siegel and NorrisO M, Westinghouse flat plate (20) and dry Westinghouse large scale tests (20. De predicted to-measured Nusselt number ratio was calculated from these data and Equation 4 for opposed mixed convection.
De ratios are shown as a function of the Reynolds number in Figure 4.1 1 and as a function of the Grashof number in Figure 4.12. De mean predicted-to measured Nusselt number ratio is 0.976 with a standard deviation of 0.278. The mean predicted to-measured Nusselt number value near 1.0 l indicates that the heat transfer correlation fits the measured data very well De large standard deviation is believed to result from poor fidelity in the data for the following reasons:
- The convective heat transfer correlation serves as the basis for the prediction of condensation and evaporation mass transfer. As shown in Sections 4.2 and 4.3, the standard deviation lor the predicted to measured evaporation and condensation mass transfer is much lower than the 0.278 value for heat transfer. Since the mass transfer data do not show large scatter, the varistion in the heat transfer data may be attnbuted to more uncertain data measur ments.
+
ne deviation between predicted and measured Nusselt numbers was large in four of the
, ilugot tests UU discussed in Subsection 2.2.1. The entrance-effect multiplier overpredicted the Nusselt number at small distances from the channel entrance (Ud h < 1.0) due to the asymptotic singularity at x = 0 in the entrance-effect relation.
De LST dry heat transfer test data have an uncertainty on the measured wall heat Oux (AT) that is as large or larger than the value of AT.
- The Eckert and Diaguila t6) data have a large variation that changes with distance due to the use of the tube centerline temperature to represent the bulk temperature.
+ The Hugot OU and Siegel and Norris0W tests may exhibit higher deviations due to the use or a predicted, rather than measured, test air flow rate.
o 0542w 4 non Ib 101397 wuo
During a DBA event, the riser Reynolds number can be as high as 1.9 x 105 and the riser Grashof 9
number can be as high as 1.2x10.1he convection test data covered a Reynolds number range up to 5 5
x 10, and a Grashof number range up to 10 ll. Therefore, the test data cover the expected range of both dimensionless groups within the annulus, it is concluded that Equation 4 provides an adequate mean prediction of the dry, assisting, mixed convection heat transfer for the AP600 vertical wall and dome. The test data encompass the expteted range of AP600 Reynolds and Grashof numbers. Since the phenomenon is not ranked high in the ,
PIR1*, it is unnecessary to bound the test results in the evaluation model. ilowever, the same multiplier developed for mass transfer in Section 4.5 is applied to convective heat transfer ia the evaluation model.
- a c AB42w-4 non. It* l01397 Revmon 1 42 October 1997
} .t! i 2 i . ,
>3'* ' '
] . .i j . '. - :-
4 * ,! .+ !.l it .
+ ,!
- u .
- :;J). i.. .
- , i .,
.:S ,1:-
i i' Il s a
- . f .- .
I
- o. . . ,. ,
- s. *
. AH00 hanga g o
ioos.ca t.oot.o4 t m .os 5 m .co 3
Figure 4.1 1 The Effect of Reynolds Number on the Predicted to Measured Nusselt Number Ratio for Convect 8an IIcat Transfer in a Channel nA3542w 4.non Ib-101397 Revmon i 43 octoter 1997
e 3 ~
98
- u. .
. . . t s
- . f . . . .' . .g .
. t
- V *.
+4 '4 . ,* 4 1 :'. J.
';. ~
' .y't' t..
g '.
~l ' Y g, .* t
.. . 4 :;f. .. t. s. l:. g. t. 1
- . .s+
y<
0.5 -
AH 00 kang.
0 1.0E+06 1.0E+07 1.DE+08 1.0E +09 1.0E+10 1,0E+11 1.0E e t#
Oreshal Number Figure 4.12 The Effect of Grashof Number on the Predicted to4feasured Nusselt Number Ratio for Convection IIcat Transfer in a Channel I
i
~
o 0542w-4 non It> 101397 Revmon i 44 Octater 1997
4.2 Evaporation he combined evaporation test data consists of the Westinghouse flat plate evaporation tests (203 and the Gilliland and Sherwood evaporation tests (22). De predicted to measured Sherwood number ratio for the Westinghouse flat plate evaporation tests is shown as a function of the Reynolds number, Grashof nmr.ber, and dimensionless steam concentration in Figures 4.21 through 4.2 3 De mean pred;cted to measured Sherwood number ratio is 0.936 with a standard deviation of 0.139.
De evaporation test data covered a Reynolds number range up to 1.2 x 105 and a Grashof number range up to 7.0 x 1010, based on hydraulic diameter. He evaporation test data adequately covers the 5
expected AP600 range of both the Reynolds number (1.8x10 ) and Grashof number (1.2x10')in the riser annulus during a D11A event.
'lVe Gilliland and Sherwood evaporation testg22) provided a companson of the measured and predicted total eve,wration rates at relatively low Reynolds and Grashof numbers. As shown in Section 3.6, the heu and mass transfer correlations predicted the measuwd total evaporation rates with a predicted to-measured mean value of 0.925 and a standard deviation of 0.072. Ilowever, local evaporation me. surements were not made and intemal variations in partial pressure vary too much to represent the data by an average Sherwood number. Ccaisequently, comparisons between the measurea and predicted Sherwood numbers are not meaningful for the Gil'iland and Sherwood tests, liowever, the range of Gilliland and Sherwood data are shown in Figure 4.21.
In conclusion, Equations 4 and 16 are considered to adequately model evapo ation mass transfer on the AP600 sidewall and dome When niultiplied by tne factor developed in Section 4.5, the evaporation correlation becomes a bounding correlation appropriate for use in the evaluation model he predicted to-measured Sherwood number using the bounding co Telation is shown in Figure 4.2 3. He range of Reynolds and Grashof numbers in the texts is sufficient to support the urs of :Se correlation over the expected operating range in APoo0.
0 4
oO w4 m:lk101M R isi si
e 2.0 -
=
3 ,..
l ,0 0 8 .
=06
- AP400 kange p
- 011111and a sherwood pat.
0.0 - .a
, - . . .. .. , 0, WW
. T.st Data -~ Mean (O 936)
Figure 4.21 The Effect of Reynolds Number on the Predicted to Measured Sherwood Number Ratio for Evaporation o V542w-4 non.It>101,797 Reymon 1 4-6 ocioteri997
l e
20 12 e
e 6e 14 e , , e ,
- e* ,
e # e 1
05 00 2.00C+10 4 00C+10 6.00E+10 800C+10 Orestof breer
, e T.m p.= u (0sw Figure 4.2 2 The Effect of Grashof Number on the Predicted to Measured Shtrwood Number Ratio for Evaporation oV542w-4 non.its101397 Reymon 1 47 n:tober 1997
20 1.6 s
e e
e
- 'e 1.0 , , ,, ,
e e
' e *
- 06 00 0% 10% 20 % 30% ang Steam MWe Fracts (%)
e Test Data -Mean (0 936) ,
Figure 4.2 3 The Effect of Steam Concentration on the Predicted to Measured Sherwood Number Ratio for Evaporation i
OMS 42w-4 non Ib-101397 Revmon i 48 October 1997
1 4.3 Condensation he combined condensation data consists of the Wisconsin (23) condensation tests and intemal condensation data from the Westinghouse LSTs(21). De predicted to measured Sherwood ratio is shown as a function of the Reynolds number, Ap/p, and dimensionless steam concentration in Figures 4.31 through 4.3 3. De mean predicted to-measured Sherwood number ratio is 0.988 with a standard deviation of 0.182. Since Reynolds numbers could not be determined inside the LSTs, only the
, Wisconsin condensation test data are shown in Figure 4.31.
4 The combined test data covered a Reynolds number range up to 2.6 x 10 and a density ratio, Ap/p of 0.08 to 0.55. %e Reynolds number will vary with time and position inside the AP600 containment vessel during a D11A event. D'. iring the relativ:ly short blowdown ph se, the velocity and corresponding Reynolds number will be largest on the wall nearest the break location and decrease as the flow moves away from the break. A natural circulation flow pattem is expected to develop during the depressurization phase when the PCS is in operation. %e Reynolds number along the wall will be small durir.g natural circulation. He value of Ap/p in AP600 ranges up to 0.40, so it is bounded by the test data.
In conclusion, Equations 13 and 16 are considered to a6quately model condensation mass transfer inside AP600. When multiplied by the factor developed in Section 4.5, the condensation correlatioit becomes a bounding correlation. De predicted to-measured Shc wood number ratio using the bounding correlation is thown in Figure 4.3 3. %c range of Ap/p measured in the tests encompass the range expected in AP600.
e o VS42m-4 non.it> 101397 Revtsson i 4-9 octobertw?
L I
20 1.5 1 l 1.0 h %N
- g 05 I
i 00 5000 10000 15000 20000 25000 30000 R.ynolds Numb.r Figure 4.31 The Effects of Reynolds Number on the Predicted to Measured Sherwood Number Ratio for Condensation Mass Transfer own.4 non:ib-ioim kgisig
__ ___ _ _ _ _ _ _ _ _ _ _ __._ _.--mm________.__-_.m _ . _ _
t -
1 1 .s . ...
- / **
.'.
- t. .
[ % .## ,'* *
. . . +.', g.+ +' # * ,'.
0.6 -
AP600 Range - >
0 0.00 020 0 40 0.60 WP Figure 4.3 2 The Effect of Dirnensionkss Density Difference on the Predicted to Measured Sherwood Number Ratio for Condensation 5
oA3542w-4 non.Ib.101397 Revnion i 41] Octoter 1997 E
s 4 2
15 E ,
(# .
- .* V * .
' ...g+' * *.
1- * *
/ .
. . . . 4
.*e, .$ .
. . e l 0.5 0
0% 20% 40% 60% 80% 100 %
Steam Mole fraction (%)
A Figure 4.3 3 The Effect of Steam Concentration on the Predicted to Measured Sherwood Number Ratio for Condensation o V542w-4 mw it> 101397 Revnion i 4 12 october 1997
. . . . . . . . . . . . . ~. .- -- - - - - - - - - - -
h
$ 4.4 Measurement Uncertainty b
The test measurements used to detennine the " measured" results presented in this report (Nusselt numbers, Sherwood numbers, acynolds numbers, and steam concentration) all have some uncertainty associated with them. Error estimates presented with the test results were deter.nined by applying test
[
instrument uncertainties to the individual measured parameters used to calculate the measured results.
For example, the Nusselt number is determined from measurements of the bulk fluid temperature, the
, wall surface temperature, and the wall heat fiux. The uncertainties associated with the individual measured parameters were applied to determine an estimate of the maximum error associated with the reported results. Therefore, the error estimates are considered to be conservative, in that it is not likely that the individual instmment errors would be simultaneously acting to maximize ucertainty.
Error estimates were determined for the Westinghouse Heated Flat Plate Test (20)(mixed convection and evaporation data), the Westinghouse Large-Scale Test (20 (mixed convection and intemal condensation data) and the University of Wisconsin Condensation Test (2n (condensation data).
Individual instmment uncertainties assn.iated with these tests are discussed in the following section.
~\
Error bars for these tests are shown on the corresponding figures iri Sections 3.4, 3.7, 3.8, and 3.9.
t The error bars are limited to the nuter envelope of data points to avoid excessive clutter on the figures.
Errors were not estimated for tw opa literature tests.
4.4.1 The Wesayhouse Heated Flat Plate Test (20)
L m
Test measurement unat+ int!~ for the Westinghouse Heated Flat Plate Tests are discussed in e
Reference 20. As reported. ;ieat fiux to the plate was determined by deducting experimentally determined heat losses from the total iritegrated electrical power supplied to the plate heaters. The power to the plate heaters was measured using a watt transducer. 'Ihe accuracy of this type of transducer is t"pically within 0.5 percent of full scale which corresponds to approximately 683 Btu /hr.
for a 40 KW range transducer. Based on reported heat flux measurements, total heat flux to the plate measured electrically was shin 4.5 percent (218 Btu /hr.) of that determined based on heat transfer to the air, and within 9.9 perr at (480 Btu /hr.) of measured heat transfer to the plate heating fluid. Since the experimentally determined results are within typical accuracy limits of a watt transducer, the typical watt transducer accuracy of 683 Btu /hr. (59.4 Btu /hr. ft2 ) s assumed for the heat flux measurement uncertainty.
Copper-constantan (Type T) thermocouples were used to measure plate wall temperatures, annulus air temperatures, ambient temperature, and the temperature of the water film flow onto the plate.
Assuming a typical thennocouple accuracy of e 0.9*F and a data logger error 0.8*F results in a total uncertainty of 1.2"F. The temperature of the excess film flow was measured using chromel-alumel (Type K) thermocouples. Assuming a typical Type K thermocouple accuracy of 2*F and a data logger error of 2 0.8'F results in a total uncertainty of
- 2.15'F.
oA3542w 5.non.lb-101397 Revmon 1 4 13 october 1997
._a
i p
I 1 .
j Duct air velocity measurements were obtained using a standard we $ge probe and pressure transducer.
l Assume a flow coefficient of 0.825 for a typical commercial pitot tube and a typical differential l pressure transducer accuracy of 0.5 percent of full scale. Base.] on the observed range of air I
velocities recorded in the tests, a differential pressure transducer having a full-scale range of 400 i inches of water would be required resulting in a differential pressure measittement error of 2 inches j~ of water. Considering the range of measured test air velocities and applying the relationship:
l-i
! V =K *[2' *g *h (20)
}
- where
I
{ K = flow coefficient. 0.825 for commercial pitot tube I i
V = the velocity in ft/sec.
j g = acceleration of gravity,32.17 ft/sec.2 l
j h = differential pressure in feet of flowing Duid i
l the air velocity measurement uncertainty is 0.32 ft/sec.
i l A variable area flow meter was used to measure film flow onto the plate. Assuming a typical l commercial accuracy of 2 2 percent of reading with a repeatability within I percent results in a to:al j- . uncertainty of 2.236 percent of reading. Applying a temperature measurement uncenainty of 1.2*F
{ and calculating the flow mecsurement error over the range of test Howrates (approximately 0.2 to i 4.2 GPM) and film now tempere*ures (70 to 150*F) results in an overall uncenainty of 2 2.3 percent t
for mass How onto the platei Excess film flow or mass now out was measured with a weigh tank using a scale accurate to " fractions" of a gram and a stop watch. Assuming that the mass of water
!- was determined to within 2 2 grams and elapsed time was measured 0.5 seconds over a period of
- 1. minute results in an uncertainty of approximately 21.2 percent for mass How out.
The measurement uncertainties discussed above resulted in measured Nusselt number uncertainty .
within 20 percent for the reported Westinghouse Dry Flat Plate tests (20) w th higher uncertainty i
corresponding to lower heat flux tests. The uncertainty reduced to 9 percent for tests in which the -
. measured wall heat fiux was greater than 1000 Btu /hr.-ft.2. The measured Sherwood number ' '
, uncertainty was within 2 5 percent for the Westinghouse Flat Plate evaporation tests that were typically conducted with a higher wall heat aux than the dry flat plate tests.
4.4.2 The Westinghouse Large-Scale Test (21)
Test measurement uncertainties for the Westinghouse Large-Scale TestCI) are presented in Reference 21.
os3c. 5mn:ib-ioi397
,Rgi,ogn
1 ,
~
T __
Chromel alumel (Type K) thermocouples were used for all test temperature measurements. Assuming a typical Type K thermocouple accuracy of 2'F and a data logger error of 2 0.8'F results in a total j' - uncenainty of 2.15'F for the Wesdnghouse Large Scale Test (21) temperature measurements.
- he reported total pressure measurement uncertainty for the LST is 20.26 psi. De measurement
- uncenainty is 20.9 psi for the air patial pressure measurement and 25 percent of reading for the j helium partial pressure. De resulting steam pressure measurement uncenainty, based on the combined
- , total pressure and air panial pressure measurement uncertainties is 0.94 psi.
i i Annulus outlet air velocity was measured t sing a fixed anemometer haviv. a reported measurement-l' uncertainty of 0.5 ft/sec.
LST wal! heat flux measurements were made using calibrated thermocouple pairs. De wall AT
, measurement uncenainty for a typical thermocouple pair is estimated to be within 2 0.25'F. LST wall
' heat flux measurement uncertainty is estimated r.s a function of the wall AT measurement uncenainty ,
, with respect to the overall measured wall temperature difference _(i.e., Heat Flux Uncertainty =
. 2 0.25/AT x Measured Heat Flux)._ De resulting wall heat aux uncenainty for the reponed large-scale
- intemal condensation tests was I to 15 percent with the great
- r uncenainty being associated with the lower AT or heat flux measurements, as expected.
. The above measurement uncertainties resulted in measured Sherwood number uncenainty within i 26 percent for large-scale intemal condensation tests with measured heat aux greater than l 2500 Btu /hr.-ft.2. De uncenainty for tests with measured wall heat flux between 1000 and -
{ 2500 Btu /hr.-ft.2 is approximately 40 percent. Tests conducted at low wall heat Dux (500 to 800 Btu /hr,-ft.2) re0ccted measured Sherwood number uncertainty from 50 to 75 percent as the l: - measured wall AT associated with these low heat aux measurements approached the estimated' wall AT
'- measurement uncertainty, i
Because wall heat Dux associated with the dry LSTs was typically very low, the resulting measured l,' . wdl ATs were of the same magnitude as the estimated wall AT measurement uncertainty ( 0.25'F).
This resulted in wall heat flux measurement uncertainties between 6 and 70 percent which resulted in high (greater than 100 percent) estimates of the maximum Nusselt number error for tests associated with the Svest wall heat flux measurements (approximately 100 Btu /hr.-ft.2),
= -
i i 4.4I The University of Wisconsin Condensation Tests (23) 4
- Test measurement uncenainties for the University of Wisconsin Condensation Test are discussed in i Reference 23.
{
T i
i:
i- oA3542w 5.non:Ib-101397 Revision 1 4 ocu*er 1997
, , . . , ..v- a ~_ ,- , , - - n- - - , - , - - - -
As discussed in the reference repon, heat flux to the plate was determined experimentally using heat flux meters and by performing coolant energy balances, resulting in an uncertainty within 3 percent associated with the reported heat flux measurements.
Chromel-constantan (Type E) thermocouples were used for all test temperature measurements.
Assuming a typical Type E thermocouple accuracy of 2 0.5'C and an instrumentation error of 0.02*C results in a total uncertainty of 2 0.5 C or 0.9'F.
Duct air velocity measurements in the Wisconsin Condensation Tests (23) were obtained using a pitot tube and pressure transducer as in the Westinghouse Flat Plate Tests (20). Assuming instrumentation similar to that considered in Subsection 4.5.1 was used in the Wisconsin Condensation Tests and that the resulting air velocity measurement uncenainty of 0.32 ft/sec is typical for the range of recorded test velocities results in an air velocity measuremen' uncenainty of 0.32 ftisec or 0.098 m/sec.
These test measurement uncertainties result in measured Sherwood number uncertainty within 212 percent for the reported University of Wisconsin condensation tests (23) ,
4.4.4 Open Literature Tests Uncenainties in the Hugot(3 3), Eckert and Diaguila(6), S egel and Norris(3M, Gilliland and Sherwood(22), and Chun and Seban(7) tests are discussed in the open literature references.
i e
oT3542w 5.non.lb 101397 Reymen i 4-16 ocwber 1997
'I L
L
- 43 Mass Transfer Correlation Blases h he mass transfer correlations selected for use on AP600 were compared to data from both SETS and l- -integral effects tests (IETs). De data comparisons were presented in the form of predicted-to-t
. measured Sherwood numbers. The comparisons show the correlations underpredict the data with mean
- predicted-to-measured values of 0.936 for evaporation and 0.988 for condensation. Dus, the selected correlations exhit'it an underprediction of the mean data.
As a conservative approach the correlations can be biased, such that the data points that are most l overpredicted with the nominal coiTelation are bounded, and the remainder of the data set is
[*
.underpredicted. That is, the biased _ correlation bounds all the data. His can be expressed as:
L i .Cp 51 (21)
- M t
i i.
where:
l C is the bias factor
- j. P is the predicted mass transfer coefficient value j; M is the measured mass transfer value L
l Rus, the value for C can be determined from the most overpredicted data point as:
Cs '(22)
De evaporation test data are plotted in Figure 4.2-3 and have a peak value of PM = 1.191. Thus, the
. value of the bias factor for the evaporating data is C = 0.840. By multiplying the evaporation mass
. transfer correlation by this factor, the correlation conservatively bounds the test data. De predicted. -
to-measured Sherwood number cale ilated with the bounding correlation is shown in Figure 4.2-3.
-- ,c De condensation test data are pbtted in Figure 4.3-3 and have a peak value of PM = 1.541. His particular value lies somewhat above the bulk of the data and corresponds to a single elevation on the LST, while five other simultaneous measurements at different elevations in the same test produced lower PM values. His peak value is considered a local anomaly that does not represent integral condensation rates.-
' Consequently, the next highest value, PM = 1.369 was selected for evaluating the bias factor. Thus, the value of the bias factor for the evaporating data is C = 0.730. ' By multiplying the condensation mass transfer co Telation by this factor, the correlation conservatively bounds the test data. De predicted-to-measured Sherwood number celculated with the bounding correlations is shown in Figure 4.3-3.
ousuw-5.non:ib.ioim
,R si
5 CONCLUSIONS Objectives This document presents and validates correlations that can be used to calculate energy transfer, by heat and mass transfer, between the containment gas and the extemal PCS air flow path, and between the i
PCS air flow path and the baffle, shield, and chimney. 'Ihe correlations represent the common phenomena of convective heat transfer, condensation mass transfer, and evaporation mass transfer.
. Specific objectives of this report are:
1, Identify appropriate correlations for the various heat and mass transfer regimes for the PCS surfaces.
- 2. Compare the correlations to SETS that cover the range of dimensionless parameters for AP600 -
operation.
)
- 3. Evaluate correlation uncertainties. !
- 4. Develop biases that can be applied to the correlations to bound the test data.
Energy Transfer Model The correlations developed in this document are used in the AP600 evaluation model, so are defined consistently with the way energy transfer is modeled across the containment shell and in the PCS air flow path. The evaluation model energy transfer is calculated as follows:
)
- With condensation or evapot . tion a liquid film is pr'sent. Energy is transported between the bulk gas and a solid through the liquid film by the following processes:
Between the bulk gas and the liquid film free surface by radiation heat transfer, convection heat transfer, and mass transfer By conduction through the liquid film to the solid surface
- Dry surfaces do not have liquid films or mass transfer. Energy is transported between the bulk gas and the solid surface by radiation heat transfer and convection heat transfer.
- The correlations assume the local bulk gas thermodynamic states are known both inside and outside containment. Phenomena that influence the distribution of bulk gas properties are separately evaluated to develop an overall bounding approach (PIRTW, Subsection 4.4.2.4).
o usuw-5mtib.ioim ,1<goyn 1 -
lleat and Mass Transfer Correlation Validation Analytical correlations selected from the literature are presented in Section 2 to represent heat and mass transfer to and from the AP600 containment shell and PCS air flow path surfaces. The correlations embody the correct physics to model energy transpon consistent with the energy transfer model described above. The correlations are compared to SET data and uncertainties are evaluated in Sections 3 and 4. Biases are evaluated in Section 4.5. Tha correlations selected for calculating heat and mass transfer and how the four goals are achieved for each follows. .
Opposed mixed convection heat and mass transfer occur in the PCS air flow path on the downcomer side of the shield and baffle, and on the chimney. Equation 3, from Churchill (5) , 3 used to model opposed mixed convection heat transfer in the PCS air flow path. Since heat and mass transfer on the baffle and chimney are both low ranked phenomena in the PIRY3), it is sufficient to model these without additional uncertainty, consistent with the conch'sion from the PIRT that only h.igh ranked phenomena require uncertainties (or bounding). However, the bias factor 0.73, determined for evaporation mass transfer (Section 4.5) is applied in the evaluation model.
Assisting mixed convection heat transfer occurs in the riser and chimney ponions of the PCS air flow path on the shell and baffle. Equation 4, from Churchilp5) and Eckert and Diaguila(6), ;3 used for assisting mixed convection heat transfer in the PCS air flow path. Since heat transfer on the shell and dome are ranked medium or low in the PIRT, it is sufficient to model those without additional uncertainty, consistent with the conclusions from the PIRY3) that only high ranked phenomena require uncenainties (or bounding). However, the bias factor 0.73, determined for evaporation mass transfer (Section 4.5)is applied in the evaluation model.
Comparisons of the assisting mixed convection heat transfer correlation to test data are presented in Section 4.1. The comparisons show the correlation underpredicts the mean Nusselt number by 2.4 percent, and the test Grashof and Reynolds numbers cover the range expected for AP600 operaton.
Assisting mixed convection evaporation mass transfer occurs in the riser and chimney ponions of the PCS air flow path on the shell and baffle. Equations 1 and 2, McAdamsO) and ColburnW , define the free and forced convection components of the mixed convection heat -
transfer correlation in the PCS air flow path. Comparison of the assisting mixed convection evaporation predictions and the data are presented in Section 4.2. The comparisons show the nominal cottelation underpredicts the mean data by 7.5 percent. Since this transpon phenomena is ranked high in the PIRY1) the data are bounded. The correlation is further biased with a multiplier of 0.84, in Section 4.5, to produce a bounding evaporation mass transfer correlation.
The comparisons show the test data encompass the expected range of AP600 operating conditions.
oM542w-5 non:Ib 101397 Revision i 5-2 october 1997
e - Free convection heat transfer is assumed on the inside of the shell throughout all transients.
Equation 13, the modified McAdams(3) correlation presented in Section 2.3 is used to calculate heat transfer to the shell inside containment. - Only free convection is assumed inside containment. Since free convection heat transfer inside the shell is ranked medium or low in the PIRW), it is sufficient to model this without additional uncertainty, consistent with the conclusions from the PIRT, The McAdams modification consists of replacing the characteristic geometric dimension, "L", with the local fluid property (v2 fg)tn n the Nusselt tnd Grashof
,- numbers.
- Free convection condensation mass transfer is assumed on the inside of the shell throughout all transients. Equations 16 and 18, from Kreith03) and the mass transfer analogy, Equation 17 are used to calculate mass transfer in the PCS air flow path and inside containment to the shell.
Free convection mass transfer, similar to free convection heat transfer inside containment, replaces the characteristic geometric dimension, "L", with the local fluid property (v2 fg)U3 n the Sherwood and Grashof numbers. Comparison of the free convec; ion condensation predictions and the data are presented in Section 4.3. De nominal correlation underpredicts the mean data by 1.2 percent. Since this transport phenomena is ranked high in the PIRT(I) the data are bounded. The correlation is further biased with a multiplier of 0.73, in Section 4.5, to produce a bounding condensation mass transfer correlation. De comparisons also show the range of the -
test data encompasses the expected range of AP600 operating conditions, e Conduction heat transfer through the liquid film occurs on the inside and outside of the containment shell and may_ occur on the inside of the baffle and chimney if condensation takes place. Equations 14 and 15, from Chun and Seban U ), are used to calculate the heat transfer through the intemal and external liquid films. Comparisons of predicted and measured film Nusselt numbers are presented in Section 3.10. De comparisons show the correlation is a good nominal p Aiction of the film Nusselt number for both condensing and evaporating films. -The comparisons also show the test data encompass the expected range of AP600 operating conditions. Since film conduction is ranked medium or low in the PIRW), it is sufficient to
,_ -model this without additional uncertainty, consistent with the conclusions from the PIRT.
- Radiation heat transfer occurs on all surfaces, but is ranked low in the PIRW) on all surfaces.
- Consequently, it is acceptable to use a traditional T' model with an emissivity and beam length
_ (for opaque gases). The radiation heat transfer model is not validated in this document.
ousu -5.nonab ioim 5-3 ONIN
1 6- NOMENCLATURE d_ h . . = - hydraulic diameter D, = air steam diffusion coefficient g = gravitational acceleration
-h = heat transfer coefficient k = : thermal conductivity.
s- kg = gas phase mass transfer coefficient L = length a sh,( = condensing or evaporating mass flux M,,, = molecular weight of steam P = total pressure
= partial pressure of steam at the interface Psim.srf
" Partial pressure of steam in the bulk gas mixture Pstm bulk p% = - log mean partial pressure of air
-(Pair. bulk - Pair srf)/in (Pair, bulk /Perad)
R - = universal gas constant T = absolute boundary layer temperature (T,,,f + TbulkW
.v.
channel average velocity x = distance l' = film flow rate v = kinematic viscosity 0 = angle ofinclination from horizontal p = dynamic viscosity
Dhnensionleis Groups: -
3 Grd *' AP. # A channel Grashof number P p/
bulk - Psud
-*: Ap/p - = density ratio Pbulk Nu- = I(v /g2 sin 0)l0 liquid film Nasselt number k
hd Nu = h channel Nusselt number -
k E
.- Pr = P Prandtl number k-o:us42*-5. rum :5 o u97 .
Rgi,m
Ra = GrPr Rayleigh number Re =
4r
_ liquid film Reynolds number P
Vd h Red
= channel Reynolds number u
Sc = v/DySchmidt number
- k8RT Pghd Sh d = channel Sherwood number s DP y
e a
o:V542w 5.non:lt>101397 Revision 1 6-2 October 1997
(-
-7 REFERENCES
- 1. Loftus, M., Spencer, D.' R., Woodcock, J., " Accident Specification and Phenomena Evaluation for AP600 Passive Containment Cooling System," WCAP-14811, December 1996, Westinghouse Electric Corporation.
- 2. Spencer, D. R., " Scaling Analysis for AP600 Containment Pressure During Design Basis Accidents," WCAP-14845, February 1997, Westinghouse Electric Corporation.
- 3. McAdams, W. H., # car Transmission, hird Edition, McGraw Hill,1954,
- 4. Colbum, A. P. ' "A Method of Correlating Forced Convection Heat Transfer Data and a Comparison With Fluid Friction," Transactions of the AlChE, Vol. 291933, p.174.
- 5. Churchill, S. W., " Combined Free and Forced Convection Around Immersed Bodies" (Section 2.5.9) and " Combined Free and Forced Convection in Channels" (Section 2.5.10), # cat Erchanger Design Handbook, Hemisphere Publishing Corp.,1983.
- 6. Eckert, E. R. G., Diaguila, A. J., " Convective Heat Transfer for Mixed Free, and Forced Flow Through Tubes," Transactions of the ASME, May,1954, pp. 497 504.
- 7. Chun, K. R., Seban R. A., " Heat Transfer to Evaporating Liquid Films," Journal of Heat Transfer, November 1971,
- 8. Metais, B., Eckert, E. R. G., Journal of # cat Transfer, Vol. 86, pp 295 2%,1964.
-9. Vliet, G. C., " Natural Convection Local Heat Transfer on Constant Heat Flux Inclined Surfaces," Journal of #ca Transfer, November 1%9, pp. 511'-516.
.- 10. . Boelter, L. M. K., Young, G., Iverson, H. W., NACA TN 1451,1948,
- 11. Hugot, G., " Study of the Natural Convection Between Two Plan . Vertical, Parallel, and Isothermal Plates," derived from doctoral dissertation University of Paris,1972, translated by D. R. de Boisblanc, Ebasco Services Incorporated, Jtme 1991.
12.
Hatton, A. P., Quarmby, Alan, "He Effect of Axially Varying and Unsymmetrical Boundary l
Conditions on Heat Transfer with Turbulent Flow Between Parallel Plates," Inter. Journal of
- Heat Transfer Vol. 6, pp 903-914,1%3. ~
- 13. Kreith, F., Principles of Heat Transfer, Second Edition, pp 549-561, International Text Book Company,1%5.
o:\3542w-5.non: b-ioi397 agg
- 14. Eckert, E. R. G., Drake Jr., R. R., Analysis of Heat and Mass Transfer,1972, hicGraw-Hill.
- 15. Kestin, J., et al., J. Phys. Chem. Ref. Data. 13,229,1984.
- 16. Rohsenow, W, bl., Hartnett, J. P., Handbook of Heat Transfer,1973, hicGraw-Hill.
- 17. Bird, R. B., Stewart, W. E., Lightfoot, E. N., Transport Phenomena,1960, John Wiley & Sons.
b
- 18. "WGOTHIC Application to AP600," WCAP-14407, Section 3, September 1996, Westinghouse Electric Corporation.
s
- 19. Siegel, R., Norris, R. H., " Test of Free Convection in a Partially Enclosed Space Between Two Heated Vertical Plates," Journal of Heat Transfer, April 1957.
- 20. Stewater, W. A., Pieczynski, A. T., Conway, L. E., " Tests of Heat Transfer and Water Film Evaporation on a Heated Plate Simulating Cooling of the AP600 Reactor Containment,"
WCAP 12665, April 1992, Westinghouse Electric Corporation.
- 21. " Heavy Water Reactor Facility (HWRF) Large-Scale Passive Containment Cooling System Confirmatory Test Data Report," HWRF-RPT-93-001, July 1993.
- 22. Gillitar.d, E. R., Sherwood, T. K., " Diffusion of Vapors into Air Streams," Industrial and Engineering Chemistry, Vol. 26, No. 5, pp. 516-523.
- 23. Huhtiniemi, I., Pernsteiner, A., Corradini, hl L , (University of Wisconsin), " Condensation in the Presence of a Noncondensable Gas: Experimer.tal Investigation," WCAP-13307, April 1991, Westinghouse Electric Corporation.
- 24. Peters, F. E., " Final Data Report for PCS Large-Scale Tests, Phase 2 and Phase 3,"
WCAP-14135, July 1994, Westinghouse Electric Corporation. ,
7'3542w.5mn;itelot397 Revision 1 7-2 octoter 1997
_ _ - _ _ _ - _ _ _ _ - _ _ _ _ ---