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-ti actor core by natural circulation cooling, treatment of transient heat transfer and two-phase flow throughout the entire loop of the reactor is indespensable. This is because in natural circulation, the driving force,isdetermined by the density difference between the hot and cold sections throughout the entire loop. The importance of natural circulation cooling has been recognized since the accident of Three Mile Island Power Plant. In view of these, the final chapter (Chapter VI. ) of this thesis is devoted to the natural circulation problem. The scaling criteria for the natural circulation under single and two-phase flow have been developed based on the basic formulations'of the phenomena. Of cource, the results obtained in the previous chapters are closely related to this analysis. The knowledge of the non-boiling transient heat transfer ( Chapter IL) can be used in the single phase natural_circulation and the knowledges of the transient boiling and two-ohase. low (Chapter I, DI-V) are necessary to the two-phase natural circulation. The results obtained in this chapter can be used in designing a model plant which simulates a prototype power plant. They are also needed in interpreting the experimental data obtained in the model facilities. 5
Page 2: TRANSIENT BOILING AND TWO-PHASE FLO
Page 6: ACKNOWLEDGEMENTS I would like to ex
Page 9 and 10: parallel to the water flow. The eff
Page 11 and 12: entrance and developed region of th
Page 13 and 14: vni
Page 15 and 16: II.3 II .2 II.4 II.5 II.6 II.7 II.8
Page 17 and 18: VI.3 VI.4 VI.2.1 VI.2.2 VI.2.3 VI.2
Page 19 and 20: high. The boiling phenomena under v
Page 21: • under zero liquid flow rate ( i
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
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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
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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
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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
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m 20 E15 x m E 0- 10 5 0 Fig.20(f)
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CO 20 E 15 x cr 10 5 0' I I 0,001 F
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20 N 15 E 2 E o10 5 0 0.001 0.01 0.
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x Lo N 15 E 2 ro E Er10 Type-B Fig.
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U, 20 E 15 ro 0- 10 5 0(-----------
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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
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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 .
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"1,5~c for -ln[1-{1-exp(-4.91Pr x )
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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
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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
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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
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* -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
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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.
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8 GAS FLOW a LIQUID FLOW a" ED Fig.
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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 --
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) N 0—IQ ._ M CV a) (Y (0 a ul—
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N rr) Q I L r) N C (0 CD CL) 100 10
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M N °'1 ~}-- 10-I \ -----1 ~IQ M N
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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
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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
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1.0 0.8 0.6 0.4 0.2 Jac) ' I .0 0.8
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1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6
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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
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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
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terminal velocity is equal to the g
Page 282 and 283:
This implies that for D < Dc E o(D,
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V. 5 DROPLET VELOCITY AT INTERFACE
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• 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
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f h+ = op M Jg h a Vr W • T rm +
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Efg(h,jg ) = 0. 5963 + 0. 5963 0 D
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E 15*1.5-3n4/2 fg(hjg) = 0.398 Cm'
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* ' As shown in Figs . 7 through 17
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In the regime where (jg/h*) exceeds
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dEfg _ 4 a(108) dh DHpg g Here a is
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' Measuring the entrainment amount
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H* In this surface In this (1) o< h
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P terminal h due to velocity is dep
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• jgc=jgc Here qc is the vaporiza
Page 312 and 313:
• Ad AH Av CD C CE CK Cm Cl a D D
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v of vfe v~ vg vh(D,jg,h) vh vi * v
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16. Duffey, R ., "The Cooling," Nuc
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46 47 48 49 50 51 52 53 54 55 56 57
Page 320 and 321:
76 77 78 79 80 • • • • Gill
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Jfe acE=J g • Substituting Eq. (A
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Z=0 k Fig. 2. Schematic Diagram of
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y=0 y iq, Pg A F D V POOL SURFACE F
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w cn NEAR REGION /SURFACE MOMENTUM
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w Cn CT I0 -2 -3 I0 -4 -10 -5 l0 Fi
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4 Q1 Qi wal -2 10 I0 -3 -4 I0 -5 10
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w cn cn -2 I0 -3 10 • -4 I0 -5 10
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CP L.1.1 Cn -2 I0 -3 I0 -4 I0 -5 I0
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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
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o • v an L.I.J cri 10 -1 —2 I0
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a N Q1 QI ccCl VI O i so 4-- CU CU
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CHAPTER VI SCALING CRITERIA FOR AND
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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
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i sR CpsR = ksR = asR = 1 .(20) The
Page 356 and 357:
B.111 hRS.R= 1 (31) QsoR = (PC)R3oR
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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
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Mixture ap mum • at Mixture apmHm
Page 366 and 367:
Katto's correlation [16] for low fl
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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
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the CHF under natural circulation c
Page 376 and 377:
The above similarity analysis shows
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a as A B Cp Cps Co f d F f(x) g Gr
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6(z) AT AHfg AHsub Lp Ap ou e P PS
Page 382 and 383:
16. Y. Katto, "A Generalized Correl
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• 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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