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iii Acknowledgements Abstract Introduction TABLE OF CONTENTS Chapter I. Forced Convective Boiling Heat Transfer under Power I.1 I.2 I.3 I.4 I.3.1 I.3.2 Transients Introduction Experimental Apparatus and Procedures Results and Discussions I.3.l.a I.3.l.c I.3.2.a I.3.2.b I.3.2.c Conclusions Steady State Performances Non-Boiling Heat Transfer Nucleate Boiling Heat Transfer Maximum Heat Flux Transient Performances Transient Non-Boiling Heat Transfer Transient Boiling Heat transfer Transient Maximum Heat Flux Chapter II. Analysis of Transient Forced Convective Heat Transfer by Boundary Layer Approximation II.1 Introduction 113 Page 12 14 14 15 16 17 21 21 23 25 29 1 9
II.3 II .2 II.4 II.5 II.6 II.7 II.8 II.9 II.10 Basic Equations Laminar Flow for Pr > 1 Laminar Flow for Pr = 1 Turbulent Flow for Pr > 1 Turbulent Flow for Pr = 1 Comparison with Experimental Data Conclusions Chapter III.. Generation and Size Distribution of Droplet in Gas Liquid III.1 III.2 III.3 III. 4 lII.5 Two-Phase Flow Introduction Droplet Generation Mechanism Droplet Generation by Entrainment Mean Droplet Size and Size Distribution Conclusions Chapter IV. Entrainment Rate in Annular Two-Phase Flow IV.1 IV.2 IV.3 IV.4 IV.5 Introduction Previous Works Basic Equation for Entrainment Rate Entrainment Rate Correlation Entrainment Rate in Entrance Region x 115 117- 121 123 126 .126 129 134 135 155 157 160 164 169 193 194 197 200 205
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: vni
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 and 22: • under zero liquid flow rate ( i
Page 24: CHAPTER I FORCED CONVECTIVE BOILING
Page 27 and 28: There have been two groups of works
Page 29 and 30: no direct interaction between the o
Page 31 and 32: On the other hand,the instantaneous
Page 33 and 34: - The properties were taken at film
Page 35 and 36: In Fig.9(a) is shown the effect of
Page 37 and 38: in a 19 mm i.d. tube with water and
Page 39 and 40: long heater. The transient non-boil
Page 41 and 42: shifts towards higher wall superhea
Page 43 and 44: Figures 27(a) and (b) show the effe
Page 45 and 46: where E is given by Eq.(8-2) E = 0
Page 47 and 48: decreasing period and increased wit
Page 49 and 50: gmax ,0 gmax ,st gmax ,st00 gmax ,t
Page 51 and 52: REFERENCES 1. Rosenthal,M.W.,"An ex
Page 53 and 54: (1954). 21. Kutateladze,S.S., Heat
Page 55 and 56: 0 obtained by consulting a text boo
Page 57 and 58: o Cooling Water Storage Tank Pump S
Page 59 and 60: Fig.3 Z 10 Comparative coefficient
Page 61 and 62: 0 E N lo' 106 105 Fig.4(b) The effe
Page 63 and 64: E N 107 106 105 1 Fig.4(d) P = 0.14
Page 65 and 66:
Z N. m a) EX m 10 Fig.5 O 0 Compara
Page 67 and 68:
0 N E X as E O' 15 0 0 Fig.6(b) 0.2
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N E 2 E 0 0 Fig.6(d) 0.396 MPa 1,2
Page 71 and 72:
X Ln '-S N E }---..... } 2 E 0 0 Fi
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Ui rn 1 N E X m E Q' 0 Fig.7(d) 1 T
Page 75 and 76:
x Ln Co N E ro E 0 Fig.8(b) 1 The v
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0 (N E x b E cr 15 10 0 0 Fig.9(a)
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j V c G 14 12 10 Fig .10 The variat
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E rn N rd E Cr Fig.12 7 6 5 4 3 2 1
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'.9 fS ~; x~ Photo.1 Steady state b
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^ CO TA 7 z D Z 10 1 0.1 \(1) (2) (
Page 87 and 88:
" E cr Fig.16(b) 107 106 1o5 1 The
Page 89 and 90:
N V 1 o 7 106 105 Fig.17(b) 1 10100
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E N 1 106 105 2 Fig.18(a) P=0.396 M
Page 93 and 94:
iv 15 E x E (710 0 0.0 01 A Fig.19(
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2 X CO 20 cy 15 ro E °10 5 0 0.001
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• CO 0 cv 15 E ' E °'10 0.001 Fi
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03 N E 2 rd E o- Fig.20(a) The and
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00 E15 x rtl E 0'10 20 5 0 0.001 Fi
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00 2 co E o- Fig,20(e) The variatio
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00 CO I' rd 20 15 cr 10 5 0.0 01 Fi
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0 20 c+ 15 E x rd oor 10 5 01------
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Ni C15 2 20 x ro E o10 5 0 0.001 Ty
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20 N 15 E 2 E °r10 5 0 0.0 01 Fig.
Page 113 and 114:
CN 20 (C" 15 E x CT 10 5 0t- 0.001
Page 115 and 116:
CO Fig.24(d) The variation and velo
Page 117 and 118:
0 0 0.001 Fig.25(b) 0.01 The variat
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O N N E 2 X rd' E 0 20 15 10 5 0 U.
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0E 0 -P- N 2 x g E 0' 20 15 10 0 5
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• O 0' N E 2 rd E ET' 20 0.01 Fig
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• F-' O m 0 o0.1 QIQ rd CT 4- I c
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110
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112
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of these works, the transient heat
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Y pendicular to the flat plate. v i
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One assumes temperature distributio
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u for x*>t*h* = -------------------
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value oft and is given by solving f
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v v Here, S is a thickness of veloc
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*1.5* for -ln[1-{1-exp(-5.67Pr x )}
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previous cases St =)76{ 1 - exp(-t*
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' u = (i)l/7 u~ S 1.7(69) T -TT= 1
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Equation (79) was derived based on
Page 151 and 152:
The asymptotic value of the transie
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the transient heat flux attains the
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Greek Letters dtThermal boundarylay
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10. 11. 12. 13. 14. 15. 16. 17. 18
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C a) . V F-- 4- 3 ~~U -~xL . (1.;L
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s 10 - s \ 6- 4- 2- 0- 0.01 Slug Fl
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ON Fig.5 3 2 1 0 0.01 Thermal bound
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00 * s Fig. 6 5 4 3 2 1 0 0.01 Lami
Page 167 and 168:
ln 0 * Fig.9 J 6 P. 4 3 2 1 0 Turbu
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Ln N N O I X a) CC Ln N O X (0 CD N
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154
Page 173 and 174:
icantly influenced by the amount of
Page 175 and 176:
Substituting Eqs. (3) and (4) into
Page 177 and 178:
]]I. 3 DROPLET GENERATION BY ENTRAI
Page 179 and 180:
In the entrainment regime of entrai
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Ia. 4 MEAN DROPLET SIZE AND SIZE DI
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and the volume fraction oversize A
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p-1/3u2/3 We(D ~) = 0.0099 Reg/3pgu
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a a. 1 a. 1W Ad A. iw CD C g C w D
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1. 2. 3. 4. 5. 6. 7- 8. 9. 10. 11.
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34. Mugele, R. A. and Ind. Eng. Che
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n WAVE REG Ti 0' r ION VOLUME Vw SU
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I pr) M M \ N CO a) a) 100 10-2 10-
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N Io° - J 10-1 M N CO M iCI_ CT ;:
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N C\J C311 us-- N) QQ CS' I 1.4 C\J
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C '14- cacri N C:51 N CC I0~ 10-I 1
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• N ~-1 M J,~-- ~ I Q. M N a) C C
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M rr) ..I~ N IQ Cr) CD Fig. 14. 100
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B I 00 NA D vm D max *_ D 10' D 20'
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192
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IV. 2 PREVIOUS WORKS In annular two
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it has been thought that a sufficie
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C = pf j Jfevq1 gvfe+ ifevg(10) or
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IV. 4 ENTRAINMENT RATE CORRELATION
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• E= 0 .022 pfjfRef-0.26E0.74_(26
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• uD= 6.6 x 10-7 Re0.74 Re0.185 W
Page 223 and 224:
where the equilibrium rate is given
Page 225 and 226:
f uD= 1.2 x 103RefReff..Reffm-0.25W
Page 227 and 228:
f Figures 8 through 12 show the com
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droplet impingements and deposition
Page 231 and 232:
where E is given by For The E = tan
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a W C C D E E ., g jf 'fe Jg k Ref
Page 235 and 236:
1 2 3 4 5. 6. 7. 8. 9. 10 11 12 13
Page 237 and 238:
29. Brodkey, R. S., "The Phenomena
Page 239 and 240:
N 9 W 'W C) 67 -z 10 103 -4 10 105
Page 241 and 242:
•W 0.1 0.01 0 0 0.2 Fig. 3. Entra
Page 243 and 244:
s •w 10 1 0.1 0.01 0 0 a 0.2 Fig.
Page 245 and 246:
.W 10 I o .) L1I 0 0.2 0.4 E/Em Fig
Page 247 and 248:
I. _ I J w W a W 4 '4d 0.1 0.01 Fig
Page 249 and 250:
4 E•- 1- U.! CC w w CL X w 'W I0
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w w 9 1.0 0.8 0.6 0.4 0.2 0.0 I.0 0
Page 253 and 254:
1.0 0.8 0.6 04 0.2 8 0.0 1.0 0.8 0.
Page 255 and 256:
1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6
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1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 8 0
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1.0 0.8 0.6 0.2 0.4 I.0 0.8 8 0 .6
Page 261 and 262:
LO 0.8 0.6 0.4 0.2 0.0 1.0 0.8 8 0.
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1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 8 0
Page 265 and 266:
. 1.0 0.8 0.4 0.2 1.0 0.8 8 0 .6 0.
Page 267 and 268:
w 8 2.0 L8 1.6 I.4 1.2 1 .0 0.8 0.6
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252
Page 271 and 272:
254
Page 273 and 274:
satisfactory correlations which pre
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a j* 99 =jagOp1/4(3) 2 pg where a,
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P Then where Dc r 4j p)2]1/3 g the
Page 279 and 280:
o Droplets ejected from the interfa
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height from the pool surface. Howev
Page 283 and 284:
Substituting Eqs. (32) through (35)
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dv pfD a€-f = Ti - opgD ,(43) whe
Page 287 and 288:
liquid level is very low, i.e., 5-6
Page 289 and 290:
Substituting Eq. (63) into Eq. (54)
Page 291 and 292:
and Y jr (vr+j g )dt (72) Equation
Page 293 and 294:
Equation where vh vh (79) 0 2h* can
Page 295 and 296:
On is the other hand, in annular-di
Page 297 and 298:
In Fig. 6, the general trend of the
Page 299 and 300:
* ~ • This Efg(h,jg) = 2.213 N1.5
Page 301 and 302:
f(DJj) =C1()fl5j*1.5 D*0.5(105) gp3
Page 303 and 304:
-4 *3 0.5p ()_1.0 Efg(h,jg) = 7.13
Page 305 and 306:
h* = 1.038 x 103 jgN095 0.23 DH0.42
Page 307 and 308:
E fg (h,jg ) =2. 213 N1.5D*1 jigH .
Page 309 and 310:
(1) Total Droplet Flux- In this wor
Page 311 and 312:
intermediate gas flux regimes given
Page 313 and 314:
g(v. h h* hm h+ m d *qc jfe jf 'fd
Page 315 and 316:
REFERENCES 1. Ishii, M. and Grolmes
Page 317 and 318:
30. 31. 32. 33. 34. 35. 36. 37. 38.
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61 62 63 64 65 66 67 68 69 70 71 72
Page 321 and 322:
and Here pool and Equation gas phas
Page 323 and 324:
0 0 uJ -3 I0 -4 10 -5 10 -6 I0 104
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* N vt v- M Sc CP } 10 4 103 2 I0 0
Page 327 and 328:
ca._ a cri E cl:- cv ._ > 1 .2 1 .0
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w Cn Cn I0 -2 -3 10 I0 -4 -5 I0 -4
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U../ -2 10 -3 10 -4 10 -5 I0 -4 10
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W -2 10 -3 10 -4 10 I05 Fig. 11. Co
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CP Q1 .4w I0 -2 -3 10 -4 I0 105 Fig
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Q, v CT W 10 I0 -2 -3 -4 I0 -5 I0 -
Page 339 and 340:
w CP CP -2 10 I0 I0 -3 -4 -6 10 Fig
Page 341 and 342:
• • Fig. 19. M 0 CL. a 101 100
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N CD -2 I0 -3 177'10 c, -4 0 cn -5
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w co Table II. Summary of Various E
Page 347 and 348:
330
Page 349 and 350:
equations. However, the same approa
Page 351 and 352:
The U. = ui/uo Li = t./to T = t U0i
Page 353 and 354:
where ai' asi' ted perimeter di = 4
Page 355 and 356:
uoRu uom opqoR(pCp =gaoR2 R doR'OR(
Page 357 and 358:
In contrast to the design parameter
Page 359 and 360:
• R _Hydraulic Diameter Ratio diR
Page 361 and 362:
• For A scale model can be design
Page 363 and 364:
The similarity criteria based on th
Page 365 and 366:
m where the total flux j is given b
Page 367 and 368:
By assuming an axially uniform heat
Page 369 and 370:
t _ 0 to density change. In two-pha
Page 371 and 372:
Negligible Effects of Viscosity Rat
Page 373 and 374:
SR gRQR d = 1 R uR (AHsub)R 1 .(102
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It is noted that the above conditio
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In the present study, only general
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Pr P qs Qs q„ c R Re St t T Ts Ts
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1. 2. 3 4 5 6 7 8. 9. • • • 1
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W 01 DOWN 1COMMER PUMP ,-. P1 SINGL
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L FROM PUMP H DOWN - COMMER UPPER C
Page 387 and 388:
370
Page 389 and 390:
Concerning a LOCA and subsequent re
Page 391:
turbulent flow regime. For a two-ph
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