ML20073E188
| ML20073E188 | |
| Person / Time | |
|---|---|
| Site: | 05200002 |
| Issue date: | 07/31/1994 |
| From: | ENERGY RESEARCH GROUP, INC. |
| To: | NRC |
| Shared Package | |
| ML20073E067 | List: |
| References | |
| NUDOCS 9409280291 | |
| Download: ML20073E188 (64) | |
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{{#Wiki_filter:. . _ - . _.--. - .. ._ .--- . _. . . . _ _ . . . .- . -. ANALYSIS OF EX-VESSEL STEAM EXPLOSIONS FOR THE COMBUSTION ENGINEERING SYSTEM 80+ USING THE GT3F" COMPUTER CODE (Supplemental Report) i I i July 1994 l ! f f 9409280291 94o922 {DR ADOCK 05200002
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1 I. INTRODUCTION This document supplements Reference l1:. and includes calculated results for hy-pothetical ex-vessel steam explosions in the CE S0- reactors. using the computer code GT3F" [2.3]. This supplement has been prepared in response to the review and comments. addressing [1], by Energy Research Inc. [4). In Reference [1], fuel-water interactions resulting from the following three separate scenaries were simulated:
- 1. a central instrument tube rupture
- 2. an outer instrument t':be rupture
- 3. multipleinstrument tube rupture l l l The water pool in the above simulations was assumed to be at saturation initially.
l at 393 K [1]. The triggering, furthermore. was assumed to take place on the axis of symme:ry of the molten fuel jet. 4.1 m above the bottom of the water pool. l Calculations. to be discussed below, were repeated for scenarios (1) and (2) above. in which, as recommended in [4): a) The water pool was assumed to be initially at 353 K (40K subcooled). l b) Triggering was assumed to occur at 4.5 m above the bottom of the water pool. which correctly corresponds to the mid-plane elevation of the submerged portion of the corbel support. In addition. calculation results are also presented in this document which examine i i the effect of the assumed level of fuel fragmentation in the triggering spot, which sim-2 l
ulates the triggering in the numerical calculations. on the predicted pressure histories during the propagation phase of the steam explosions. II. CENTRAL INSTRUMENT TUBE FAILURE II.1 Premixing The system configuration, nodalization, time step, etc.. were all identical to those described in Section 2.1 of [1], with the exception of item (a) above. The water was 1 thus assumed to be at 353 K temperature initially. The calculated results are depicted in the figures listed below, where, in this section and elsewhere in this document. wherever applicable, the figure numbers for i the corresponding figures in [1] are also given in parentheses. l
. Figure 11.1 (corresponding to Figure 2.3 in [1)) .\!olten fuel volume fraction j contours j l
1 e Figure 11.2 (corresponding to Figure 2.4 in [1]) Void fraction (gas volume frac- l tion) contours
. Figure 11.3 (corresponding to Figure 2.5 in [1]) Pressure contours II.2 Propagation The system configuration, nodalization, time steps, etc., were identical to those described in Section 2.2 of [1]. However, as mentioned above, triggering was assumed to occur on the axis of symmetry of the molten fuel jet in the node (1.23), 4.5 m above the bottom of the water pool. The results are depicted in the figures listed below.
( . Figure 11.4 (corresponding to Figure 2.7 in [1)) Molten fuel volume fraction l 3 i
i l l
. Figure 11.5 (corresponding to Figure 2.5 in [1]) Void fraction (gas volume frac-tion) Contours
. Figure 11.6 (corresponding to Figure 2.9 in [1]) Pressure contours l
. Figure 11.7 (corresponding to Figure 2.10 in [1]) Pressure histories at various nodes e Figure 11.8 (corresponding to Figure 2.12 in [1]) Pressure impuia distrivations Pressure impulse distributions along the jet centerline (Figure II.Sa) and along the corbel support surface (Figure II.8b, corresponding to Figure 2.12 in [1]) are both depicted. (Pressure impulses representing 20% fragmentation at triggering are also included in Figure II.5a which will be discussed in the forthcoming subsection.)
These pressure impulses all represent 20 ms integration times. The calculated impulse j values for the jet centerline (Figure II.Sa) are realistic since, as noted in Figure II.7a. l the pressures on the center line all decay to the base pressure within 20 ms. The pressure impulses for the corbel support surface depicted in Figure II.Sb, however, l co not represent the full impulses since, as noted in Figure ll.7b, the pressures on the corbel support surface do not decrease to the base pressure within 20 ms after j triggering. The calculated maximum impulse on the centerline, as noted, is about 15 kPa.s, and takes place 4.S m above the pool bottom. On the corbel support surface, the cal-culated pressure impulse decreases with height, from a maximum of about 6.8 kPa.s at the bottom elevation of the corbel support, to a minimum of about 5 kPa.s at the axial node (1,27) representing the water level height before the initiation of premix-
- 4
- I ing. The calculated pressure impulses for the corbel support surface, as mentioned above, do not represent the full impulse due to the short simulation time. They are.
nevertheless, significantly lower than the 5th percentile impulse capacity for corbel support which is approximately 35 kPa.s (5). Thus, it appears that the fullimpulse on the corbel support surface would also be considerably lower than the 5th percentile impulse capacity for the corbel support. In Figure ll.8a the calculated pressure impulses for an initially saturated water l pool [1] are also depicted. The r.ssumption of initially saturated water pool thus l l resulted in the underprediction of pressure impulses in the explosion zone. j II.3 Effect of Triggering Strength j i l All the simulation of the propagation phase in Reference [1], as well as everywhere , 1 I l ! in this document except for the case to be discussed in this subsection, were obtained by simulating the triggering assuming that, at the triggering time,10% of the molten ) l fuel in the node where triggering takes place (node (1.21) in [1] and node (1,23) everywhere in this document) underwent complete fragmentation in one time step. I Figure 11.9 depicts pressure histories at various nodes during the propagation phase. These calculations were performed using all the parameters which were utilized I in obtaining Figure 11.7, except that triggering was simulated here by assuming 20% l l of the fuelin node (1,23) underwent complete fragmentation during one time step. i Comparing Figures 11.7 and 11.9, it can be noted that the pressure peaks in the triggered node (1,23) and the depicted adjacent nodes (1,21) and (1,25) are sensitive to triggering strength, as expected. The pressure peaks at nodes located further away from the triggering location, however, are only slightly affected. It thus appears i that the important simulation results, and in particular the pressure histories on the 1 i 5 4 r
l l structural surfaces away from the triggering location. are relatively insensitive to the triggering strength. Calculated pressure impulses resulting from 10% and 20% fragmentation at trig-gering are compared in Figure II.Sa. As noted, the pressure impulses obtained with 20% fragmentation are slightly higher than those obtained with 10% fragmentation. The maximum impulse is increased from 15 kPA.s to about 16kPa.s in the explosion zone. III. OUTER INSTRUMENT TUBE RUPTURE III.1 Premixing The system configuration nodalization, time step, etc., were all identical to those described in Section 3.1 of [1], with the exception of item (a) describe. in Section I above. The water was thus assumed to be at 353 K temperature initially. The i calculated results are depicted in the figures listed below. i e Figure 111.1 (corresponding to Figure 3.3 in [1]) Molten fuel volume fraction centours e Figure 111.2 (corresponding to Figure 3.4 in [1]) Void fraction (gas volume frac-I tion) contours l e Figure 111.3 (corresponding to Figure 3.5 in [1]) Pressure contours i III.2 Propagation The computation domain, depicted in Figure 111.4,is a cylinder 300 cm in diam-cter, centered on the centerline of the molten fuel jet, as recommended in [4]. The simulated cylindrical domain thus replaces part of the solid structure, including the 6 l
corbel support. with liquid coolant. This was necessary for the 2-D calculations. Twenty-seven axial nodes, with A: = 20 cm, and 50 radial nodes with Ar = 3 cm. were used. Other parameters were all similar to those described in Section 3.2 of [1], except for the location of triggering. As explained before, triggering was assumed to take place on the axis of symmetry of the molten fuel jet 4.5 m above the bottom of the water pool, in node (1,23). The results are depicted in the figures listed below. e Figure 111.5.\lolten fuel volume fraction contours -
. Figure III.6 Void fraction (gas volume fraction) contours l
. Figure III.7 Pressure contours j
. Figure III.S Pressure histories at various nodes
. Figure III.9 Pressure impulse distributions Calculated pressure impulses on the corbel support surface, as noted, are in the S.5 kPa.s to 13.0 kPa.s range, and are thus lower than those calculated in [1] by an order of magnitude. These pressure impulses represent 20 ms ofintegration time, and are realistic because, as can be seen in Figure 111.8, within 20 ms after triggering the l pressures decrease to the base value. Calculations using the nodalization scheme in
[1] were highly conservative and overpredicted the pressure impulses on the corbel support surface due to the imposition of a rigid boundary around the 30 cm-diameter cylindrical computational domain. The calculated results depicted in Figure 3.9, on the other hand, are believed to underpredict the pressure impulses. A 3-D analysis 7 l l
appears necessary for a more rigorous analysis. The aforementioned two 2-D solution results, nevertheless, can be assumed to bracket the 3-D calculation results. I REFERENCE
- 1. Analysis of Ex-vessel Steam Explosions for the Combustion Engineering System 50+ using the GT3F" Computer Code, Attachment to letter from S. I. Abdel-Khalik and S. M. Chiaasiaan to M. Khatib-Rahbar (June 3,1994).
- 2. W. M. Ren, S. M. Ghiaasiaan, and S. I. Abdel-Khalik, CTSF: An Implicit Finite-Diferbnce Computer Codefor Transient Three-Dimensional Three Phase Flow l
l Part I: Governing Equations and Solution Scheme, Numerical Heat Transfer, Part B: l Fundamental, Vol. 25, pp.1-20,1994. l
- 3. W. M. Ren, S. M. Ghiaasiaan, and S. I. Abdel Khalik, CTSF: An Implicit Finite-Diference Computer Codefor Transient Three-Dimensional Three-Phase Flow
! Part II: Applications, Numerical Heat Transfer, Part B: Fundamental, Vol. 25, pp. 1 21-33. 1994. i
- 4. CESystem SO+ Ez-vessel Calculations Using GT3F Computer Code. Memo, dated June 13,1994, from H. Esmaili to M. Khatib-Rahbar, Energy Rvecch, Inc.
- 5. H. Esmaili and M. Khatib-Rahbar, Analysis of Ez-vessel Steam Explos:ons for the Combustion Engineering System 80+, ERI/NRC 94-201, Energy Resear.;5. Inc.
March 1994. 8
Figure 11.1 (Corresponding to Figure 2.3 in [1]) Central Instrunient. 'ITibe Failure-Preinixing , 1'nel Volinne Fraction ( Ar =- 3.0 cin, Az = 20.0 cin) ,. 37 . _ 27 27 27 e i 4 is . is ne ) is .I 3 f. U U d d a d e O O O O I I I i , N N N N e 9 . 9 - 9- 9. D 0 O^ h k b b ^10 og 3 g d'8DO O h^k 6 b io 0 ^ h k's b ^10 R-CELLS R-CE LLS R- C ELLS R-CELLS 0.25 sec U.50 sec 0.75 sec 1.00 sec 11=0.2402 11=0.2464 11=0.2471 11=0.2442 1,=0.0000 ' I,=0.0000 1,=0.0000 L=0.0000
I 1 i r Figure 11.2 (Correspoiuling to Figure 2.4 in [1]) Central Instrinnent Tulie Failure-Preinixing l' Void Fraction (Ar = 3.0 cin,6: = 20.0 cin) , 27 27 27 27- +m e
- es. te is se ,
M A M M
- 0 0 0 0 C3 g g g g N N N N 9 . 9- 9 - 9-1 l
I . k ^ h ~ k k ^ d^t'O UY4 10 0 5 k k k 1O 00 h k ~ d d'10 ! - n-cctts n-cctos n-cctts n-ccets 0.25 sec 0.50 sec 0.75 sec 1.00 sec . 11=0.7062 11=0.5177 11=0.7382 11=0.7212 i L=0.0001 1,=0.000 l L=0.000i L=0.0001 i i i
Figure 11.3 (Corresponiling to Figure 2.5 in [1]) Central Instrunient Tube Failure-l' remixing l'ressure (lear) (or = 3.0 cin, A: = 20.0 cin) _ 27 2 7 wme 27 27 7 LA.A11111 au u
~
V D ge. 1M- 15 - te. 9 J J d -- - - d d d
- y _
Y 1 y N N N -~ N s" / 9- 9 - 9 ggg- 9 }%
~
00 IlAAA AAA1. ski 1211 La- r , e a AAAA112. ,
%Aia.
Y$$O Og3ggg0 - O^2'4 6 k~lO d 00h ~ k ' d ~ b ^t o R - C E L LS R-CE LLS H -C E LLS R -C ELLS 0.25 sec 0.50 sec 0.75 sec 1.00 sec II=2A93 II =2.165 Ii =2.679 Il=3.053 1,=1.981 1,=2.019 L=2.016 L= 1.976
Figure II.4 (Corresponding to Figure 2.7 in [1]) Central Instrument Tube Failure-Propagation Fuel Volume Fraction (_\r = 3.0 cm.1: = 20.0 cm) l 27 27 27 f 1 l l l l 15 18 15 d M O I d d . d t W W l W I l 0 0 0 I I I N N N
. 1 9N' 9 '
9 - l l
- i ,
i 't l C 10 20 30 40 SO O to 20 30 40 50 0 10 20 30 40 50 R - C E LLS R - C E LLS R-CELLS 2.5 ms 5.0 ms 7.5 ms H=0.2332 H =0.1322 H=0.1148 L=0.0000 L=0.0000 L=0.0000 l l 12 I l i I
Figure II.4 (contd) Central Instrument Tube Failure-Propagation Fuel Volume Fraction (_\r = 3.0 cm, A: = 20.0 cm) 27 27 27
) L l
18 iSj , 18 d d d V V V i ' l l l N N N f l k O 10 20 20 40 SO O iO 20 30 40 SO O 10 20 30 40 SO R-CELLS R-CELLS R - C E LLS 10.0 ms 12.5 ms 15.0 ms H=0.0950 H=0.0515 H=0.0575 L=0.0000 L=0.0000 L=0.0000 l l l 13 l I l
Figure II.5 (Corresponding to Figure 2.8 in [1]) Central Instrument Tube Failure-Propagation Void Fraction (_\r = 3.0 cm, Ar = 20.0 cm) 27, 27 27
!( ' f)
H i , (
! i
- /
l /
\
l \ I I I { 18 15 18'- ' i d d d O U U l l I N N N gi . 9 g . . I' l { O 10 20 30 40 SO O 10 20 30 40 SO O 10 20 30 40 50 R - C ELLS R - C E LLS R - C E LLS 2.5 ms 5.0 ms 7.5 ms H=0.8791 H =0.9812 H=0.9944 L=0.0000 L=0.0000 L=0.0000 14 i d
Figure II.5 (contd) l Central Instrument Tube Failure-Propagation ; Void Fraction (Ar = 3.0 cm,3: = 20.0 cm) 27 27 27 l' , i
' l{ l ih l I l I
ji I i i } pi l . h l.. r n 1 l 15 16-is - f f l l i
- ,\ l M M ',
. M J i J ') f J l J J ' I J w w r W ;
O O ,' O .j i ! I I ,' ! I ,f N i N ., N .j s, , k
, t 9' 9 -
) 9 '; j .
. 1 .
1 i l l i\ \ 'i j, a i; ;'
. r!
l I
) r l l
f'E l O 10 20 30 40 SO O 10 20 .30 40 50 0 10 20 30 40 50 R-CELLS R-CELLS R-CELLS 10.0 ms 12.5 ms 15.0 ms H=0.9976 H =0.9991 H=0.9996 L=0.0000 L=0.0000 L=0.0000 l 15 l
Figure II.6 (Corresponding to Figure 2.9 in [1]) , Central Instrument Tube Failure-Propagation Pressure (bar) (or = 3.0 cm, A: = 20.0 cm) 27 27 - 27 l
, B :
' l 4 )
is - 15 iB I s d e d e d
)o O O O I I I N N N 9 - 9- 9 Id/ J I O 10 20 30 40 50 O 10 20 30 40 SO O 10 20 30 40 SC l R-CELLS R- C ELLS R-CELLS l l 2.5 ms 5.0 ms 7.5 ms )
l H =66.S6 H =26.53 H=44.88 L=1.895 L=1.859 L=1.897 l l l 16
l Figure II.6 (contd) l Central Instrument Tube Failure-Propagation l Pressure (bar) (3r = 3.0 cm. 3: = 20.0 cm) 27 27 27 e. b 18 iS - 15 - f d U i d U m d U l i I N N N g#
. 9 M 9 (
l M l I O 10 20 30 40 SO O 10 20 30 40 SO O 10 20 30 40 SO j j R-CELLS R-CELLS R- C ELLS I l 10.0 ms 12.5 ms 15.0 ms H=44.23 H=33.14 H=7.161 L=2.162 L=2.092 L=1.853 I i 1 17 l l I 1
. . . , ._ - -~ l
l Figure II.7 (Corresponding to Figure 2.10 in [1]) Central Instrument Tube Failure-Propagation Pressure (bar) (3r = 3.0 cm, a = 20.0 cm,10% Triggering) 100.0
?
(1,19) , 80.0 3 (1,21)-
-- q (1,23) ,
e j --- (1,25) d 60.0 r-- - - - - - (1,27)- 1
'2 5 l s
$ 40.0 .' !, It - -----
t c- - h ,l l' i ( ,\ ' , I l 20.0 -jl--a s[g -- - - -t 9g_
!l A ~ ? 2 % - i _ _ _ _ .
0.0 5.0 10.0 15.0 20.0 25.0 Time (ms) (a) Pressures along melt jet center line 20.0 ; - ;
~
[ ! 16.0 [--- h((50,19) 50,21)'
~~ ~
----l (50,23)
T --- (50.25) a 12.0 -
"(50',27) } ,
e 3 i 8 8.0 - t i i < l
,__....p... _s l
40 $ ,-; E5::.7 ~~ -_____, t,i r ,_. _._. ..,__,, I I I < 0.0 0.0 5.0 10.0 15.0 20.0 25.0 Time (ms) (b) Pressures along corbel support i 18
Figure II.8 Central Instrument Tube Failure Impulse (KPa s) (Ar = 3.0 cm, A: = 20.0 cm) 20.0 16.0 ; ,e q-
\
*1 i , .- -u w,/
i s ss g
$ 12.0 b---"=-
-% , , , _ - - - 7. . . .... g
- ..-m t 3 1 8.0 10 %, sufic36 fed E 2d%, subcooled 4.0 ; --- __1pidaturated i
0.0 18.0 21.0 24.0 27.0 Axial Location (node) Bottom of initial cortal support water level (a) Impulse Distribution Along Center Line 20.0 16.0 r--- -L --- 10%, subcooled K 20%, subcooled E 12.0 -- -- - - -L - 6 3 1E 8.0 - - -- ---- - - - - - - - -
~E i
4.0 ' ' i ! 0.0 18.0 21.0 24.0 27.0 Axial Location (node) I Bottom of Initial corbel support water level 1 (b) Impulse Distribution Along Corbel Support l 19 ; ! l \ l
i I l I Figure II.9 Central Instrument Tube Failure-Propagation , Pressure (bar) l (Ar = 3.0 cm,3: = 20.0 cm,20(7e Triggering) i 100.0 fg i(1,19) 80.0 - l l- ---- -r - -----l- (1,21)-- II - - - -i (1,23) , l c lI . - J (1,25) l .$ 60.0 -f'-j -?
-- b(1,27)-
I e s' i ! I i I i'i i
-jr,i ! .
@ 40.0 ,
Q- ,851 1!
~
,[yN 20.0
,iI k .. j O0 0.0 5.0 10.0 15.0 20.0 25.0 l Time (ms)
(a) Pressures along melt jet center line j i 20.0 , I T e ! i (50,19) 16.0 j-- '-(50,21) - j
- - - - (50,23) !
W f --- m;p -(50,25) I a 12.0 { (50.27f- ~~ : E t i 3 ! i y 8.0 [- ; O. f .
!,.[C.___7-_..
4.0 77{,7{[7, o ,.s-.s s _,
---~.,_
_ ;u l I l 0.0 O.0 5.0 10.0 15.0 20.0 25.0 Time (ms) (b) Pressures along corbel support 1 20
.i 1
1 Figure III.1 (Corresinnuling to Figure 3.3 in'[1]) Outer Instruinent Tiilie Failure-l'remixiing ; l'uci Voluine 1'raction (or = 3.0 cin, A: = 20.0 cin) _. 27 m 37 s e-w 37- m 27 m t
. t, 7
) .. ...
'l
$ 5 L 3 5-d d d d
'A ? ? ? ; ?
~ ~ ~ ~
g a l 1
-l 1 ott3:s "st13:s
( oints diists a-cctts n-cctts n-cctts n-ccets 0.25 sec 0.50 sec 0.75 sec 1.00 sec 11=0.2333 11=0.2422 11=0.2447 11=0.2425 L=0.0000 L=0.0000 L=0.0000 L=0.0000 i, - 1~ 1' ____m.__ _ _ . _ _ .___ _ _ . . _
. i Figure 111.2 (Corresg>oinling to Figure 3.4 in [1])
Outer Instruinent Tulie Failure-l'reinixing l Voi<l Fraction (Ar = 3.0 can, Az = 20.0 cin) . . 27 e 27- - 2F- 27 m c ... .. i. ,. 5 5 5 5 d d d d IS ? ? ? ? N N N N I 9- 9 - 9 - 9.
- j i i
dtists ottits oo t31:5 os itits j R-CELLS R- CE LLS R-CE LLS R-C ELLS ; 0.25 sec 0.50 sec 0.75 sec 1.00 sec e 11=0.6894 11=0.5993 11=0.7001 11=0.6549 i L=0.0001 L=0.0001 L=0.0001 1,=0.0001 7 s
Figure 111.3 (Correspomling to Figure 3.5 in [1]) Outer Instrument Tube Failure-l'reinixing I'icssiac (lear) ( Ar = 3.0 cin, A: = 20.0 cin) ,. 21 m 21 m 39 m 21 m 3 LALL k A s us.A. LA11. N 6 Ag h k (AAL O en._. en. tn- se. J " J J e -- J U U h 90 U U W l I i F i N \ N - N N sAAA-
---- 3-
'Au-an ~
Y uu. .ut m , di132s %ist;s 6tt33 %ti1 3 H-CELLS R - C E LLS R -CELLS R -C E LLS 0.25 sec 0.50 sec 0.75 sec 1.00 sec I!=2.38I Il=2.828 1i=2.290 II=4.601 1,=1.878 1,=1.92i L= 1.971 1,=2.014
\ I /
\ /
%j J :
l
;. ,3
- 15 cm 9- .
I l
.........=
i c
.. , u
. c
*^
l : X l : 300 cm i Figure III.4: Outer instrument Tube Failure ! (Shaded area represents computational domain for propagation calculation) f i t l 24 I t 1 l
r i I i i k i Figure III.5 ! Outer Instrument Tube Failure-Propagation : Fuel Volume Fraction
-( Ar = 3.0 cm,3: = 20.0 cm) r 27 27 27 l f
}
i l l i 18 . is - 18 - ' l M M g M . d d d I W W W , U . O O .'
! I I I I N N N .
I i ! 9 l 9 9 - - t l ' i t l l l > l l I f O 10 20 30 40 SO O 10 20 30 40 SO O 10 20 30 40 SC R-CELLS R-CELLS R-CELLS 2.5 ms 5.0 ms 7.5 ms H=0.2247 H =0.1080 H=0.1015 l L=0.0001 L=0.0001 L=0.0001 i j 25 i 4
. _ . . . _ . _ _ _ , , , . . . . _ _ ..,,,,,,-._.r.,. . . . . , _ . . _
4 l l l Figure III.5 (contd) Outer Instrument Tube Failure-Propagation Fuel Volume Fraction (3r = 3.0 cm, A2 = 20.0 cm) l i i 27 27 27 f l 18- 15 - 15 - O O M b W ' W W U U U
! l l 0 1 N N N
! l l 9 . . 9 - 9 - l 1 0 *O 20 30 40 SO O 10 20 30 40 SO O 10 20 30 40 50 R - C EL LS R - C E LLS R-CELLS 10.0 ms 12.5 ms 15.0 ms H=0.0951 H=0.0419 H=0.0469 L=0.0001 L=0.0001 L=0.0001 l l 1 26
i 1 1 J Figure III.6 Outer Instrument Tube Failure-Propagation Void Fraction ( Ar = 3.0 cm, A: = 20.0 cm) li 27 j 27 27 a l l !
\
T I
\ !
l l 18, 15 18- j i 1 l 0 ( 0 M ' J J J J J , J W W W U O O l i I N N N , 9 > 9- 9; i i ( i I O 10 20 .30 40 SO O 10 20 30 40 SO O 10 20 30 40 50 R - C E LLS R - C ELLS R-CELLS 2.5 ms 5.0 ms 7.5 ms H =0.9394 H =0.9871 H=0.9958 L=0.0000 L=0.0000 L=0.0000 27
l l 1 I Figure III.6 (contd) Outer Instrument Tube Failure-Propagation Void Fraction (Ar = 3.0 cm,3: = 20.0 cm) 27 27 27 i \ l I,! l f,. l f' ' ll l J l l 18 - 18 lI j f 15 - i l
)
l l
-{ I
'i '
l d d l l d , U U O i I l d3 1 f N N N )
\
\
9 - 9 ,
< 9 - -
i ; i i d l 4' O 10 20 30 40 LO O 10 20 30 40 SO O 10 20 30 40 50 R - C E L LS R-CELLS R - C E LLS 10.0 ms 12.5 ms 15.0 ms H=0.9982 H=0.9992 H=0.9997 L=0.0000 L=0.0000 L=0.0000 28
l Figure III.7 ) Outer Instrument Tube Failure-Propagation Pressure (bar) (_\r = 3.0 cm, _\: = 20.0 cm) 27 27 27 l M s..
,.g ,.
e m W s m W e m W ib , U U U l l l l N N N i-l 9 - 9 - 9V fi f f' fit 1ff ff fl' f11 f if O 10 20 30 40 SO O 10 20 JO 40 SO O '10 20 00 40 50 R-CELLS R - C ELLS R-CELLS 2.5 ms 5.0 ms 7.5 ms H = 61.26 H=63.46 H =38.99 L=2.061 L= 1.967 L=1.405 l l l 29 l <
l Figure III.7 (contd) l Outer Instrument Tube Failure-Propagation Pressure (bar) (3r = 3.0 cm,3: = 20.0 cm) I 27 27 27 ' ' u ,, , ar . .. 15 - 18 - 15 - h 9 .,e 9 9 - I c i,,, ,,,,,,,,i / 0 10 20 30 40 SO O 10 20 30 40 SO O 10 20 30 40 50 R-CELLS R-CELLS R-CELLS 10.0 ms 12.5 ms 15.0 ms i H =27.99 H = 16.67 H=12.69 l L=1.636 L=2.152 L=2.001 9 30 l l
I 1 I l Figure III.8 Outer Instrument Tube Failure-Propagation Pressure (bar) (3r = 3.0 cm, A: = 20.0 cm) 100.0 , , j i I i I l (1.19) 80.0 '- - - --
; (1,21)---! j
---H (1,23) i O p i -- (1.25) d 60.0 '---74
- --- (1,27)-- l
'm li j 1 5 ) i
$ 40.0 ,+ j --T ; l
- a. g ! l 4g
,Il ls ; !\ .
5 20.0 ! t, N, A'-~ p\ 's ,. , l
!! j q %. i
.,1 -~..~.~=__ _______=
0.0 /.0 8.0 12.0 16.0 20 0 Time (ms) (a) Pressures along melt jet center line ; I 50.0 , - ;- I i I l (5,19) 40.0 -- - - - - -
- l-(E21)--
---4 (5,23) f s e r* 11 . --4
$ 30.0 - ------ \-- --- \-((5,25) 5.27) -
E s
-,,-}\(l\
I\ t 8 20.0 --AI+ ll \l ,N'- i g ,\ l
- i' !
10.0 ~[l gg l '-- x.%g. -f-i l/e :l i' s . ,' ~, _.. l ~ , - . . m= - 0.0 ' - 0.0 4.0 8.0 12.0 16.0 20.0 Time (ms) (b) Pressures along corbel support 31
1 l Figure III.9 Outer Instrument Tube Failure impulse (KPa s) (ar = 3.0 cm, ._\: = 20.0 cm) 20.0 16.0 ~~~-l- --- I I 12.0 -- E i 8.0 E i 4.0 --~-- 4 0.0 18.0 21.0 24.0 27.0 Axial Location (node) Bottom of initial corbel support water level (a) Impulse Distribution Along Center Line l 20.0 l 16.0 ---- -
?
$ 12.0 - - - - - - - ~ ~ - -
--- h- -- ~ ~ ~ -
t x I i 18.0 E 1 i l i 4.0 - 4 l i i
' ~
0.0 I 18.0 21.0 24.0 27.0 Axial Location (node) Bottom of initial corbel support water level (b) Impulse Distribution Along Corbel Support 32 l
1 RESPONSE TO CO.\1.\IENTS l I.
GENERAL COMMENT
l l The water pool was assumed to be initially saturated in [1]. We have repeated 1 the calculations for the central instrument rupture and the outer instrument rupture 1 scenarios, using a subcooled water pool temperature of 353 K [2}. In the repeated ! calculations re have also modified the location of triggering (see response to Comment 11.4 below). We did not repeat calculations for the multipleinstrument tube rupture, because, as discussed in our report, 2-D calculations for this case do not provide i realistic predictions, and 3-D calculations may be required. ! l II. CENTRAL INSTRUMENT TUBE FAILURh j i I Comment II.1 i The boundary conditions imposed on the top of the computational domain are: a) a constant pressure of 2 bars; and b) a constant, downward velocity for fluid 3, representing the incoming molten fuel jet, and its associated volume fraction, as in the innermost radial node. The boundary conditions in item b provide sufficient in- 4 l l formation for the specification of the velocity and mass flow rate of the molten fuel. Throughout the simulated transient, furthermore, the top of the computational do-main is an open port, through which fluids 1 and 2, representing gas and liquid coolant phases, respectively, are allowed to flow as required by the conservation equations. 1
Comment II.2 The velocity and the path of the fuel particles in the water pool represent the so-lutions of the momentum conservation equations. The molten fuel has a significantly 1 higher density than water, and velocity of the fuel particles remains high due to their large inertia. One can, of course, manipulate this by modifying the drag coefficient correlations in the code. This however, would be inappropriate. During premixing, when there is no significant convective flow in the water pool, the fuel particles are predicted by the code to move straight downward in the water j pool, and they undergo significant radial distribution only after they impact the bottom of the pool. This is expected. Heavy particles sinking in quiescent liquids may move zigzag as they sink, nevertheless, their overall path should remain vertical. Comment II.3 In the referenced figures contours of equal void fractions are shown. The contours i i indicate that void fraction is.very high along the path, and at the immediate vicinity, of the fuel jet, and remains very small far away from the fuel jet.The code's predictions are reasonable. By " cell-like" structures the reviewers may be referring to the contours in some of the figures, e.g. Figures 2.4 and 3.4 of [1],in which some of the contours are closed curves. During premixing and propagation in saturated water, near-complete local evaporation results in the establishment of a two-dimensional flow field, leading to 2
i l l l
. l l
the curvature of some of the constant void fraction contours due to lateral motion of l l the fluid. Note also that the sum of the volume fractions of all fluids at each node i should be equal to one, therefore the vapor void fraction in this case has to decrease near the fuel jet centerline due to the presence of fuel. The enclosed new calculation results obtained with an initially subcooled water pool [2], as noted, generally indicate lower void fractions than the results with an l 1 initially saturated water pool, and do not include such " cell-like" structures. i Comment II.4 l In the repeated calculations for the centralinstrument and outer instrument tube l rupture scenarios (see response to General Comment I) we have assumed that trigger-j ing takes place in node (1,23) 4.5 m above the pool bottom. This location correctly l l represents the midplane of the submerged portion of the corbel support structure. Regarding the etTect of the triggering strength on the predicted results, please l l see Section II.3 of the enclosed supplement report [2], where we have compared re-sults obtained assuming 10(7c and 20% fuel fragmentation in one time step (2 ps), in the triggered node. These results, as noted, indicate that the pressure histories far away from the triggering location are relatively insensitive to the triggering strength. They also indicate that the impulse distribution in the explosion zone is only slightly affected. l The assumed size and strength of the trigger are arbitrary, nevertheless. The im-3
position of a strong local fragmentation is a reasonable way of simulating spontaneous triggering in computations. Sensitivity studies are needed to examine the effect of both the strength and location of the triggering event. Comment II.5 l In the repeated calculations for centralinstrument tube and outer instrument tube failure scenarios discussed in the enclosed supplement report [2] (see also response to General Comment I) we have included the calculated pressure impulse distributions I l for both the molten fuel jet centerline and the corbel support surface. The calculated ! l results for both the initially saturated and subcooled water pool cases are once again i l lower than those predicted by the TEXAS code. ! t j Comment II.6 This is a matter of degree. We agree with the comment that a 10-20% difference j in the calculated results is well within the uncertainties of such calculations. Comment II.7 l The new calculation results representing an initially subcooled water pool, de-picted in Figure 11.7 of the enclosed supplement report (2) give somewhat different numbers. The maximum depicted pressure at corbel support (node (50,19) in Figure 11.7 b) is approximately 6.5 bars, compared with a maximum pressure of approxi-mately 26 bars at the same elevation on the centerline (node (1,19) in Figure ll.7a). One should remember that the explosion zone is approximately a cylinder. Follow-4 l
i l ' 1 mg triggermg, the code predicts multiple explosions at various heights. The apparent flat pressure histories at the corbel support surface are due to the arrival of pressure waves, resulting from these multiple explosions, at different times. The arrivmg pres-sure waves tend to overlap and hence it is not a straightforward matter to attenuate the calculated pressure histories from 1-D calculations to the outer boundaries of the i l calculated domain. We agree that the calculated impulse on the corbel support would be somewhat higher, had the caiculation been performed for a longer period. How-ever, as can be seen in Figure II.7 and III.8, the calculated impulse values along the molten fuel jet centerline are reasonable since, within 20 ms after triggering (which represents the integration time period for calculated impulses), the pressures have decreased to the base pressure value. l III. OUTER INSTRUMENT TUBE FAILURE Comment III.1 Please see responses to comments II.1,11.2, and 11.3. Comment III.2 We agree with the reviewers' comment regarding the conservative nature of pres-sure histories predicted by using a 30 cm-diameter cylindrical computational zone. In the enclosed supplement report [2] we have repeated the simulation of outer instrument rupture scenario where we have used a computational domain 300 cm in diameter (Figure 111.4 in the supplement report), as suggested by the reviewers. 5 4
l l 1
* . l l
l The computational domain is entirely fluid, however, and does not include any flow ' I obstruction. In these calculations, furthermore, the initial pool temperature was assumed to be 353 K, and triggering was simulated 4.5 m above the pool bottom. l 1 The predicted pressure histories for the molten fuel jet centerline and the radial nodes representing the physicallocation of the corbel support surface are shown in Figures III.8a and III.8b of the supplement report [2]. Comparing these figures with the i results representing the central tube failure case (Figures II.7 a and II.7 b in the supplement report (2]),it can be noted that the predicted peak pressures in the two cases are comparable, and the differences can be attributed at least partially to the differences between the two systems at the end of premixing (the molten fuel jet has l a slightly lower velocity in the outer instrument tube failure scenario). The predicted pressures along the corbel support surface, as expected, are significantly higher for the outer instrument tube failure, due to the proximity to the explosion zone. It should be noted that placing a flow obstruction in a large computational domain I in order to simulate the geometry of this system will make the problem three dimen-sional. Simulation of the problem using a 2-D (r,z) coordinate system, as suggested I by the reviewers, is not possible. Rigorous and realistic simulation of this scenario l will need a 3-D analysis. I 6 l l
,,u . -, ,-,, , . -- , , ~ ,
IV. MULTIPLE INSTRUMENT TUBE FAILURE Comment IV.1 We agree that the calculated results for this case were unrealistic, as stated in our report [1]. Furthermore, as we mentioned in [1], we believe that this scenario needs a 3-D calculation. Comment IV.2 i The calculations were presented in crder to demonstrate the inadequacy of coarse nodahzation, and convey the conclusion that this problem requires a 3 D simulation. V. RECOMMENDATIONS FOR FUTURE WORK Comment V.1 . Calculations where the effect of the location of triggering is parametrically varied are recommended because the location of triggering rnay affect the pressure histories and pressure impulses. In the absence of an external trigger, triggering due to the impact of the molten material on solid surfaces is a well-recognized and experimentally-observed phenomenon. This type of triggering is likely to happen in the real systems. Parametric examination of the effect of the locatice of triggering should of course l l be done using a realistic simulation of the propagation phase. We therefore agree with the reviewers that such parametric calculations using the small 30 cm-diameter cylindrical computational domain will not be adequate. These parametric calculation, 7 e
however, can be done with the large computational domain used in the supplement report [2], and should certainly be done with a 3-D simulation, should such simulation be deemed necessary. Comment V.2 Realistic quantification of the consequences of the failure of multiple instrument tube penetrations needs a 3-D simulation. A 2-D simulation, even with very small I radial nodes, will not be quite adequate since replacing circular jets with annuli is inappropriate. Performing a 3-D calculation with a small segment of the system, say 1/4 of the circular cross-section of a large computational zone which includes blocked flow areas, can be a reasonable compromise for addressing multi-dimensionality and maintain-ing the computational cost under control. The nonuniformity of the distribution of tube penetration locations can be dealt with by approximating the geometry with an equivalent symmetric distribution. Such an approximation would be far more re-alistic than replacing the jets with circular annuli. Furthermore, by performing two l parametric calculations, representing upper and lower bounds for the concentration l of the penetrations in the assumed symmetric geometry, one can bracket the exact solution results within a rather small bound. Regarding adequate experimental validation of parametric fine fragmentation model in CT3F , lack of sufficient validation applies to all the results and is not limited 8 l l l i 6
- - ~ . - - , ,##.
to the multi-penetration case. It also applies to all existing steam explosion models. VI. PARTICLE BREAKUP AND FINE FRAGMENTATION MODELS IN GT3F COMPUTER CODE Comment VI.1 Both typographical errors have been corrected. Comment VI.2 i The method for calculating the molten fuel surface area in GT3F will be ex-plained in the following paragraph. However, the reviewers should be reminded that the intention of providing Appendix A, as clearly stated in Reference [1], was to 'de-scribe details of the breakup model only. Further modeling details, relevant to the issue raised in this comment or otherwise, should be obtained from References [3,4} (References [2,3] in the supplement report [2]). The total surface area of the fuel is calculated from: 6a3 a33 + a23 = ( D3 where ai3 and a23 are specific surface areas (surface areas per unit mixture volume) between fluids 1 and 3, and between fluids 2 and 3, respectively, and a3 is the volume fraction of the molten fuel in the mixture. Thus, the total surface area of the molten materialis calculated by assigning an average, hydrodynamically-controlled diameter to the fuel particles. Now, the way this specific area is distributed among a33 and 9
i l l an depends on which one of the two fluids 1 (gas) and 2 (liquid) is continuous. The reviewers should consult References [3A] (References [2,3) of the supplement report) for further details. Comment VI.3 The specification of I cm as the lower bound on fuel particle diameter only applies to the premixing calculations, and is based on comparison of model-predicted pressure i peaks during the subsequent propagation phase with KROTOS-21 test results. Equation 19 in [1] represents the GT3F hydrodynamic breakup model for: a) the premixing phase, as long as the fuel particles are larger in diameter than 1 cm; and b) for the propagation phase, without any bound. Comment VI.4 Freezing of the melt particles is included in the simulation. Frozen particles are not allowed to undergo fine fragmentation. In Equation (18) of [1] the critical Weber number is the only adjustable parameter. GT3F does not consider thermal effects in its modeling of fine fragmentation. VII. SLMULATION OF KROTOS-21 STEAM EXPLOSION EXPERIMENT Comment VII.1 KROTOS-21 was a 1-D test, and was therefore simulated using a 1-D nodalization. Radial nodalization is thus irrelevant. 10
I I i i . l
- Comment VII.2 !
, We agree with the reviewers on their point that the fragmentation model in : GT3F" needs further validation. We plan to perform more validation calculations, d in which we will include more KROTOS tests. 1 REFERENCE i l
- 1. Analysis of Ex vessel Steam Explosionsfor the Combustion Engineering System r i 1
i Jo+ using the GT3F Computer Code, Attachment to letter from S. I. Abdel-Khalik and S. M. Ghiaasiaan to M. Khatib-Rahbar (June 3,1994).
- 2. H. Esmaili and M. Khatib-Rahbar, Analysis of Ez-vessel Steam Explosions for the Combustion Engineering System 80+, ERI/NRC 94-201, Energy Research, Inc.
March 1994.
- 3. W. M. Ren, S. M. Ghiaasiaan, and S. I. Abdel-Khalik, CT3F: An Im, -it Finite-Diference Computer Codefor Transient Three-Dimension < Three-Phase Flow i
Part I: Governing Equations and Solution Scheme, Numerical Heat Transfer, Part B: Fundamental, Vol. 25, pp.1-20,1994.
- 4. W. M. Ren, S. M. Ghiaasiaan, and S. I. Abdel-Khalik, CT3F: An Implicit Finite-Diference Computer Code for Transient Three-Dimensional Three-Phase Flow l Part II: Applications, Numerical Heat Transfer, Part B: Fundamental, Vol. 25, pp.
21-38, 1994. 11
Figure II.9 Central Instrument Tube Failure-Propagation 1 l Pressure (bar) ! ( Ar = 3.0 cm A: = 20.0 cm,20% Triggering) l 100.0 i I lg (1,19)
--+ ~---F(1,21) - !
80.0 -ll-- ;-
--- 4 (1,23) l II l e iI i ---i (1,25) d 2
60.0
-fi-{-- - - - ' --
- (1.27)-
l 3 i'ii I l.i . m e
)I l
E 40.0I ,yl -l8 ; 3-+l-1 20.0 y!-*IV $ ,v:
\ .
' %. ~,._ ' -
0.0 0.0 5.0 10.0 15.0 20.0 25.0 i Time (ms) 1 (a) Pressures along melt jet center line 1 l 20.0 , . j t j i I r (50,19) j 16.0 [I ~ l ~ (5021)~ i [ -- -- (50,23) W t 6-
-- - (50,25)
~~ ~ - " " ~ ~ ~ " '
I
~~
a 12.0 _ ._- -(50~,27)"
?n $ 8.0 '- .
- c. t i
[ . 4.0 ~ - '- ~ ' t "I TN7I ' T. .f> ; k.d _ . f -- - . . . ~ .- i,t
. l
' i 0.0 (-- 5.0 10.0 15.0 20.0 25.0
! 0.0 l Time (ms) (b) Pressures along corbel support l l l 20 l 4
i 1 l 2 I 4 1 i^ l i 1 1 1 I i i m e J =O
<t
<n u J ,? 'G < oc h 3n
- g, m 6o
-"+
e e dU g C Mw wM r k e O n ""
- II ll 5773 3- Z -
M to ,
- n. . x -
- m n- G e J o J r-v u k e Q
*n
<~
u v moo
.!'. '~~~ O o
~~ - -- - -M -
u, qt v - e e o* g c4 "- O
~ t~
r-
- u.
C o N - s, iso- z C Il {l
. av _a
" es r e-ll sc 4 -& n ,
- y
- .4
=
-o F .: : u
.., -/ a ~c- m u <$ N O t
? 5-: ~~~ - - F .n u 'r, mo -
,-N a.n. u o q. -x j
- :- 2. 11
, o i ; l e o e Q.
~2
.- ~
c
~
s7,33 - z
=Ti C
o, j M
- u Q
.* s-
# .E
-e
=
0 Ew e J .,n
*w l
<e ,a 4D & W Q n N .) - -
M ,m ne l D 'n) . - X A e e o23 g C N df n - - ll s,,3 o- z o .Il .. - 1 6
e ue Ja 3 - w Pw o lm o eo a -
, 4- u, ea oO g ca - C A
e N -c c 11 ll , s773o-z n M
~
ho ,
.a .- ~r. .x -
- M : 4( d --
o 0 o: O 6 m 4m 4N w e- C o
'a ""* <- v, sa
=
.e O i y
~ s, e
o a 1 e, wa o g o n - g u a O _.I.l. 1,1
- s773o-z w . 7"4
- C ;
g 1j II v N
.= cm.
M A w N bd 0*-: J
=
B Laj
'{*
2' C a
,ee aa ., - -
o, y y C-- O 6 o, - y - 6 4, m.. z cf x 0,- k {l k Q
-c e o* hCe A -
v .a M 4
" S7730-Z d -ll -
ll, 04 m . 6 v v" u
=e 0 Cw e J M
<e J - *"*
4M w .M O O C j"o U, N *c - O h' d d m * % N I 57733-2 Cll ll
Figure 111.3 (Corresgionuling to Figure 3.5 in [1]) Outer Instruinent Tube Failure-l'reinixing l'ressuie (liar) (Ar = :).O cin, A: = 20.0 cin) , 2 7 e- 27 - 27 w 27- vv-t-3- I m1 A g ~ m - k C v tAAA. se . te. le. D se-J J C J J d d d h d U U O M U I 1 W l l N LA11-
\ N N N
9 9- 9- 9 - 3-tui.
- - p sII
+
s2AA. ss.a A. d$N$5 dibs d$IS d 'S R-CELLS R-CELLS R-CELLS R-CELLS 0.50 sec 0.75 sec 1.00 sec 0.25 sec 11=2.828 11=2.290 II=4.601 ll=2.381 1,=2.014 1,=l.878 I,=!.921 1,=1.971 _ _ _ - _ . _ . _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ .._ _ ______________._.__u_.-_-_____-__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ ______.. __
l
\
i i
)
l l 1 i l l \ l / l
\ j / !
W;J \ l 1 4 15 cm 4
; : 1 g
n
- n
~$
i : l i l 300 cm i Figure III.4: Outer instrument Tube Failure (Shaded area represents computational domain for propagation calculation) l t l 24
l l Figure III.5 Outer Instrument Tube Failure-Propagation Fuel Volume Fraction (3r = 3.0 cm,3: = 20.0 cm) 27 27, 27 l ! [ l l l I l' f 1 i iel 15; 18 -
, r M M M J J J J J J U W i W s u o o l l l l l N N N l 9 9< 9 -
! l I
O 10 20 30 40 SO O 10 20 30 40 SO O 10 20 30 40 50 R-CELLS R- L C' . S R-CELLS 2.5 ms 5.0 ms 7.5 ms H=0.2247 H =0.1080 H=0.1015 L=0.0001 L=0.0001 L=0.0001 25
1 l l Figure III.5 (contd) Outer Instrument Tube Failure-Propagation Fuel Volume Fraction (.1r = 3.0 cm,3: = 20.0 cm) 27 27 27 I
)
1 15 - 18 - 15-O d M J J J J J J l W W W U ' O U ( 1 I l 3 1 l l N N N g . 9 - 9 - I O 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 R-CELLS R-CELLS R-CELLS 10.0 ms 12.5 ms 15.0 ms i H=0.0951 H=0.0419 H=0.0469 L=0.0001 L=0.0001 L=0.0001 i 26 l l
i I
~
l I
)
Figure III.G j Outer Instrument Tube Failure-Propagation i Void Fraction (3r = 3.0 cm,3: = 20.0 cm) ; I 27, 27 27 f I Il 4 I
)
) {
. s j
l . I l I l ,! l 18 - 18' 15 , , ) i O d M J I J J 1 J J J W W W U U U l 1 I b-N N N , t 9 - 9- Si l f l I I h
.I r 0
o 10 20 30 40 50 0 10 20 30 40 Do 0 10 20 30 40 50 R-CELLS R-CELLS R - C ELLS 2.5 ms 5.0 ms 7.5 ms H =0.9394 H =0.9871 H=0.9958 L=0.0000 L=0.0000 L=0.0000 27 r i
) ) Figure III.6 (contd) Outer Instrument Tube Failure-Propagation
- Void Fraction (ar = 3.0 cm, a
- = 20.0 cm) 27 27 27
< ij I
l !l F ) ,e -l ,e
/f i ;
,e- ,
1 l M M 'f' M d d , d w i u I w U i U r' U 1 I I l d i N N , N
' i 9 -
j 9 , 9 - - 3 i l i ! ! l j 'l l i :
',' l 4
i o ,o 20 so 40 30 o ,o ao 20 40 so o ,o 20 so 40 so { R-CELLS R - C E LLS R - C E LLS 4 i 10.0 ms 12.5 ms 15.0 ms i H =0.9982 H=0.9992 H=0.9997 L=0.0000 L=0.0000 L=0.0000 , 1 1 J 28 s
l i Figure III.7 Outer Instrument Tube Failure-Propagation Pressure (bar) (.1r = 3.0 cm, .1: = 20.0 cm) l l l i i 27 27 27 9 is-Q 18 I 15 M M M J J J f J J J ,j W W W s O U U - 1 I l ,g , N N N La is , 9 - 9 - 9 # D 11 tet tf III It fl 1 Y I Et ! O 10 20 30 40 SO O 10 20 30 40 SO O 10 20 30 40 50 R-CELLS R - C E LLS R-CELLS 2.5 ms 5.0 ms 7.5 ms H = 61.26 H =63.46 H=38.99 L= 1.405 I L=2.061 L= 1.967 1 1 l l l l l 29 I l i 1
l Figure III.7 (contd) Outer Instrument Tube Failure-Propagation Pressure (bar) ' (._\r = 3.0 cm, .1: = 20.0 cm) 27 27 27 .
,, , .10:ii i I
l . l 18- 18r 18 - 0 0 O i % L ~! 68 x i L v (-
~ ~
9 - *e
. 9 9 .\
1 l J c ; m O 10 20 30 40 50 O 10 20 30 40 SO O 10 20 30 40 SC R-CELLS R - C E LLS R-CELLS 10.0 ms 12.5 ms 15.0 ms H =27.99 H=16.67 H = 12.69 L=1.636 L= 2.152 L =2.001 l 30
t l l 1 . 1 Figure III.8 Outer Instrument Tube Failure-Propagation
- Pressure (bar)
(.ir = 3.0 cm, .1: = 20.0 cm) 100.0 . l . I l (1,19) i 80.0 E - - - - - ! 1,21)- : f - - - - - - - - --- d. ((1,23) 8 e ,b ---i (1,25) l do 60.0 h , 1 0 - --E -(1,27)- - 5 llj' I l @ 40.0 4-j,*)-lg-l C- . i :
,ll , j\
A l > 20.0t ' t, gf ,,'- Hi ~A -
!)! -
0.0 4.0 8.0 12.0 16.0 20.0 Time (ms) 1 (a) Pressures along melt jet center line l ! 50.0 l f i
+
! (5,19) 40.0 r -- - ;-45,21)_ ,
- -- * (5,23)
I g e f Il . --- (5,25) d 30.0 " -]I-g -
----l- (5,27) ---
o
,s
,t I \f \
1 4-'
$ 20.0f. r- l'l \*)
d[ ,e b9" i 10.0 ll f. j - r l l O.0 '
-fl71i-(4 ip/ i t_. (.N . N'b_ _== m m _ __ __
O.0 4.0 8.0 12.0 16.0 20.0 l Time (ms) t (b) Pressures along corbel support 31 l
I l l l Figure III.9 i Outer Instrument Tube Failure i Impulse (KPa s) ( Ar = 3.0 cm, A: = 20.0 cm) l 20.0 l 1 l 16.0 E 12.0 ,
+
i E ' 8 i l ( l 8.0 , 5 4.0 b t l t 0.0 . 18.0 21.0 24.0 27.0 ' Axial Location (node) [ Bottom of initial i corcel support water level (a) Impulse Distribution Along Center Line 20.0 e 16.0 - -- +
?
E 12.0 -
---+- --k - ----
U i i
.E N E, 8.0 2
4.0 h
+
i' 0.0 18.0 21.0 24.0 27.0 Axial Location (node) Bottom of initial corbel support water level (b) Impulse Distribution Along Corbel Support 32 l
, y _ -~,,-,,,-,/.1 r-}}