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TRANSIENT BOILING AND TWO-PHASE FLOW PROBLEMS ASSOCIATED WITH NUCLEAR REACTOR SAFETY ISAO KATAOKA INSTITUTE OF ATOMIC ENERGY KYOTO UNIVERSITY
Page 2: TRANSIENT BOILING AND TWO-PHASE FLO
Page 8 and 9: ABSTRACT The transient boiling and
Page 10 and 11: Therefore, the knowledge of hydrody
Page 12 and 13: has become one of the most importan
Page 14 and 15: iii Acknowledgements Abstract Intro
Page 16 and 17: IV . 5 IV.5.1 IV.5.2 Conclusions Ge
Page 18 and 19: INTRODUCTION The safety of a nuclea
Page 20 and 21: of the transient non-boiling heat t
Page 22: -ti actor core by natural circulati
Page 26 and 27: I.1 INTRODUCTION One of the most im
Page 28 and 29: experiments for transient forced co
Page 30 and 31: 10 tam from both ends of platinum w
Page 32 and 33: I.3.l.a. Non-Boiling Heat Transfer
Page 34 and 35: where NuB = 7.0 x 10-4 PX0•7 ReB
Page 36 and 37: 6 The value of K in Eq.(6) was dete
Page 38 and 39: Visual observations were made of st
Page 40 and 41: where _$ () ------1(13-2) RePr Here
Page 42 and 43: As mentioned above, the transient b
Page 44 and 45: the transient maximum heat flux. It
Page 46 and 47: stances, after the heat flux reache
Page 48 and 49: a -- e C C P d dh e D g G Hf 9 AH.
Page 50 and 51: Xthermal conductivity; pdensity; dy
Page 52 and 53: 9. Sato,T., Michiyoshi,I. and Takeu
Page 54 and 55:
APPENDIX Consider a semi-infinite r
Page 56 and 57:
From Nutr Nust Eq.(A-8) and Eq.(A-9
Page 58 and 59:
I------------ Fig.2 Electrode 0-Rin
Page 60 and 61:
N E a- 107 106 105 Fig.4(a) 1 The e
Page 62 and 63:
N E CT 107 106 los ' 1 Fig.4(c) 4.0
Page 64 and 65:
E 107 106 105 Fig.4(e) 1 U =1,35 AT
Page 66 and 67:
X N rd E o- 15 E 1 5 0 0 it 0.143 M
Page 68 and 69:
E N 2 x rd E O" 15 10 0 0 Fig.6(c)
Page 70 and 71:
Ln W N E X rd E o- 15 10 5 1 0 0 Fi
Page 72 and 73:
01 E N } X b E 0- 0 0 Fig.7(c) 1,0
Page 74 and 75:
Ul N E X Id E Cr 15 10 0 Fig.8(a) 1
Page 76 and 77:
X Ln (N E rd E 0 15 0 Fig.8(c) The
Page 78 and 79:
I-, (N E X rd E 0 1 10 5 0 0 Fig.9(
Page 80 and 81:
n Lt.) CD Ij E CT 10-2 10-3 Fig.11
Page 82 and 83:
Ui E Q rn x rd E o.. 1 0.1 Fig.13 C
Page 84 and 85:
U CS E 8 7 6 5 4 3 2 1 0 1 100ms 30
Page 86 and 87:
0 1 E Fig.16(a) 1 0 7 106 105 1 The
Page 88 and 89:
0 107 106 10 Fig.17(a) 1 The effect
Page 90 and 91:
a- l o' 106 05 1 Fig.17(c) The effe
Page 92 and 93:
U, Fig.18(b) The N 107 E U 106 effe
Page 94 and 95:
V v 20 (C'15 _E 2 E O10 5 0 0.001 F
Page 96 and 97:
ln ti E 2 x it E Cr 20 0.001 Fig.19
Page 98 and 99:
00 20 N 15 E 2 E 0 10 5 0 0.001 0.0
Page 100 and 101:
X 00 W N E 2 ris E Cr 20 0.001 0.01
Page 102 and 103:
o U, 21 x 20 1 E cr 10 5 01 I 1 I 0
Page 104 and 105:
m 20 E15 x m E 0- 10 5 0 Fig.20(f)
Page 106 and 107:
CO 20 E 15 x cr 10 5 0' I I 0,001 F
Page 108 and 109:
20 N 15 E 2 E o10 5 0 0.001 0.01 0.
Page 110 and 111:
x Lo N 15 E 2 ro E Er10 Type-B Fig.
Page 112 and 113:
U, 20 E 15 ro 0- 10 5 0(-----------
Page 114 and 115:
20 ;715 x E cr10 5 0 0.001 Fig.24(c
Page 116 and 117:
20 cN 15 E 2 E 0'10 5 0 0.001 Fig.2
Page 118 and 119:
0 1 20 c. 15 E 2 x rd E Cr10 5 0 0,
Page 120 and 121:
I-, O W "L ...- K rd E o- 20 1 0.01
Page 122 and 123:
X 0 Ln " E rd E 0 20 15 10 5 0 0.01
Page 124 and 125:
E 0 N x E CT 20 15 10 5 0 Fig.27(b)
Page 126 and 127:
O 20 r,"` 15 E 2 -o a) `- 10 U) rti
Page 128 and 129:
CHAPTER II ANALYSIS OF TRANSIENT FO
Page 130 and 131:
lI . 1 INTRODUCTION As described in
Page 132 and 133:
will take considerable time for com
Page 134 and 135:
q0 is initial value of exponentiall
Page 136 and 137:
• S*-ATS t t t = tw * xw x = —
Page 138 and 139:
atio increases with increasing x .
Page 140 and 141:
"1,5~c for -ln[1-{1-exp(-4.91Pr x )
Page 142 and 143:
not make serious errors when one as
Page 144 and 145:
oundary layer. However, when Prandt
Page 146 and 147:
*0.4.2 hNux Pro,i7(u)0.1 _a _a co h
Page 148 and 149:
errors. In view of this, one can ob
Page 150 and 151:
t= [0.623{ 1 - exp(-1.318 x)}]7/8 (
Page 152 and 153:
More precise measurements on transi
Page 154 and 155:
a A h h Q,' Q Nu Pe x Pr q qw q0--
Page 156 and 157:
1. 2 3 4. 5. 6 7 8. 9. • • •
Page 158 and 159:
20 21 22 23 24 25 26 27 Trans. ASME
Page 160 and 161:
U uco ,Tco --› 0 ///111// v~ qW.
Page 162 and 163:
s 4 s N ro Fig.4 i 3 2 1 0.01 Ratio
Page 164 and 165:
* -C Fig.6 6 5 4 3 2 1 0 0.01 Lamin
Page 166 and 167:
w 3 2 1 0 0.001 Fig.8 Thermal bound
Page 168 and 169:
0 I- LO co 1/4/a 0.8 0.7 0.6 0.5 0.
Page 170 and 171:
CHAPTER III GENERATION AND SIZE DIS
Page 172 and 173:
M. 1 INTRODUCTION A loss of coolant
Page 174 and 175:
• by BI. 2 DROPLET GENERATION MEC
Page 176 and 177:
this case, the entrainment mechanis
Page 178 and 179:
T 1 adAd ai Vd 4(12) where ai is th
Page 180 and 181:
Then CD, is T. = 0.005C 1g in view
Page 182 and 183:
proportional to jg2. This differenc
Page 184 and 185:
0 D= 3.13 D(37) max vm and D is cor
Page 186 and 187:
III. 5 CONCLUSIONS (1) Based on the
Page 188 and 189:
v g v r v Vd V w We We c We (D) X G
Page 190 and 191:
17. 18. 19. 20. 21. 22. 23. 24. 25.
Page 192 and 193:
8 GAS FLOW a LIQUID FLOW a" ED Fig.
Page 194 and 195:
9n I 300 100 10 20 0 0 x WICKS & CO
Page 196 and 197:
o N r() crl roll M N an a) f CD --
Page 198 and 199:
0 10 N N) On Cl.„.IQ_ Po a) (0 --
Page 200 and 201:
) N 0—IQ ._ M CV a) (Y (0 a ul—
Page 202 and 203:
N rr) Q I L r) N C (0 CD CL) 100 10
Page 204 and 205:
M N °'1 ~}-- 10-I \ -----1 ~IQ M N
Page 206 and 207:
CIO VD Reference Table I. _ Wicks a
Page 208 and 209:
CHAPTER IV ENTRAINMENT RATE IN ANNU
Page 210 and 211:
N. 1 INTRODUCTION As mentioned in t
Page 212 and 213:
T46 C m = C. a(3) where, 8 and a ar
Page 214 and 215:
IV. 3 BASIC EQUATION FOR ENTRAINMEN
Page 216 and 217:
4 = 0 .022 Ref-0.26E0.74 (_11)0.26
Page 218 and 219:
effect on entrainment have been dev
Page 220 and 221:
Thus 7.25 x 10WeRe(32) 71.25 ffo.0.
Page 222 and 223:
IV.5.1 General Formulation ot of En
Page 224 and 225:
f f(E/E m ) takes the by the follow
Page 226 and 227:
• as a film are obtained. In calc
Page 228 and 229:
And for E/Em > 1 u0.26 - 0.088 Ref
Page 230 and 231:
u • In IV. 5 CONCLUSIONS A correl
Page 232 and 233:
1 The present model is based on the
Page 234 and 235:
acore ad • • co of 11g Pf Pg Ap
Page 236 and 237:
16 17 18 19 20 21 22. 23. 24. 25. 2
Page 238 and 239:
Appendix A Derivation of Equation (
Page 240 and 241:
10 o,_ 3 x10 5 4 cc 9 3 W N O C7 3
Page 242 and 243:
0 .w 10 1 0.1 0.01 0 o • 0 Ref =4
Page 244 and 245:
0 • W 10 0.1 0.01 1 0 0.2 Fig. 6.
Page 246 and 247:
J F W 2 W a Ui W W i0 0.I COUSINS e
Page 248 and 249:
° / J w 0 w Cl- >C •W 0.1- 0.01
Page 250 and 251:
Zri i— io Z W M CC W CL X W w 0 '
Page 252 and 253:
1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 8 0
Page 254 and 255:
1.0 0.8 0.6 0.4 0.2 8 00 w -- I.0 0
Page 256 and 257:
1.0 0.8 0.6 04 0.2 0.0 1.0 0.8 we 0
Page 258 and 259:
1.0 0.8 0.6 0.4 0.2 8 0.0 Ui 1.0 0.
Page 260 and 261:
w 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 9
Page 262 and 263:
1.0 0.8 0.6 0.4 0.2 Jac) ' I .0 0.8
Page 264 and 265:
1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6
Page 266 and 267:
w w 8 I.0 0.8 0.6 0.4 0.2 0.0 I.0 0
Page 268 and 269:
N Cousins Gill & Gill Table I. Summ
Page 270 and 271:
MECHAN I ST I C POOL CHAPTER V MODE
Page 272 and 273:
V. 1 INTRODUCTION As already descri
Page 274 and 275:
The experimental data show that the
Page 276 and 277:
of N uf (pf~~Q/gop)1/2(8) Equation
Page 278 and 279:
As'shown above, these semi-empirica
Page 280 and 281:
terminal velocity is equal to the g
Page 282 and 283:
This implies that for D < Dc E o(D,
Page 284 and 285:
V. 5 DROPLET VELOCITY AT INTERFACE
Page 286 and 287:
• Equation £ ^ D Substituting Eq
Page 288 and 289:
where by DH Wilson, Sterman' a = 0.
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= D V. 6 MAXIMUM HEIGHT OF RISING D
Page 292 and 293:
f h+ = op M Jg h a Vr W • T rm +
Page 294 and 295:
Efg(h,jg ) = 0. 5963 + 0. 5963 0 D
Page 296 and 297:
E 15*1.5-3n4/2 fg(hjg) = 0.398 Cm'
Page 298 and 299:
* ' As shown in Figs . 7 through 17
Page 300 and 301:
In the regime where (jg/h*) exceeds
Page 302 and 303:
dEfg _ 4 a(108) dh DHpg g Here a is
Page 304 and 305:
' Measuring the entrainment amount
Page 306 and 307:
H* In this surface In this (1) o< h
Page 308 and 309:
P terminal h due to velocity is dep
Page 310 and 311:
• jgc=jgc Here qc is the vaporiza
Page 312 and 313:
• Ad AH Av CD C CE CK Cm Cl a D D
Page 314 and 315:
v of vfe v~ vg vh(D,jg,h) vh vi * v
Page 316 and 317:
16. Duffey, R ., "The Cooling," Nuc
Page 318 and 319:
46 47 48 49 50 51 52 53 54 55 56 57
Page 320 and 321:
76 77 78 79 80 • • • • Gill
Page 322 and 323:
Jfe acE=J g • Substituting Eq. (A
Page 324 and 325:
Z=0 k Fig. 2. Schematic Diagram of
Page 326 and 327:
y=0 y iq, Pg A F D V POOL SURFACE F
Page 328 and 329:
w cn NEAR REGION /SURFACE MOMENTUM
Page 330 and 331:
w Cn CT I0 -2 -3 I0 -4 -10 -5 l0 Fi
Page 332 and 333:
4 Q1 Qi wal -2 10 I0 -3 -4 I0 -5 10
Page 334 and 335:
w cn cn -2 I0 -3 10 • -4 I0 -5 10
Page 336 and 337:
CP L.1.1 Cn -2 I0 -3 I0 -4 I0 -5 I0
Page 338 and 339:
UJ tar CP CP I0 _2 -3 I0 -4 10 I0 -
Page 340 and 341:
A 101 -2 10 2 p 00 Fig. 18. .Compar
Page 342 and 343:
o • v an L.I.J cri 10 -1 —2 I0
Page 344 and 345:
a N Q1 QI ccCl VI O i so 4-- CU CU
Page 346 and 347:
CHAPTER VI SCALING CRITERIA FOR AND
Page 348 and 349:
VI. 1 INTRODUCTION In the preceedin
Page 350 and 351:
i a Jr) the following analysis, sub
Page 352 and 353:
d In cal S. are and The similarity
Page 354 and 355:
i sR CpsR = ksR = asR = 1 .(20) The
Page 356 and 357:
B.111 hRS.R= 1 (31) QsoR = (PC)R3oR
Page 358 and 359:
particularly in the case of a force
Page 360 and 361:
' From In cal and Eq. (16), a as R
Page 362 and 363:
• uR=0.4•,0.44 qR = 0.4 ti 0.44
Page 364 and 365:
Mixture ap mum • at Mixture apmHm
Page 366 and 367:
Katto's correlation [16] for low fl
Page 368 and 369:
x o-= f2e(82) A similar pressure d
Page 370 and 371:
AH AT= o C sub In view of the Eqs.
Page 372 and 373:
= 2 uR (NFr)R=A ,RR= 1 .(96) (Nf)Rd
Page 374 and 375:
the CHF under natural circulation c
Page 376 and 377:
The above similarity analysis shows
Page 378 and 379:
a as A B Cp Cps Co f d F f(x) g Gr
Page 380 and 381:
6(z) AT AHfg AHsub Lp Ap ou e P PS
Page 382 and 383:
16. Y. Katto, "A Generalized Correl
Page 384 and 385:
• FROM PUMP 6,89 H UPPER CORE STR
Page 386 and 387:
Table I. Basic Geometrical Paramete
Page 388 and 389:
SUMMARY AND CONCLUSIONS The thermoh
Page 390 and 391:
On the other hand, in a later stage
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