KURENAI : Kyoto University Research Information Repository

More documents

Recommendations

Info

the CHF under natural circulation conditions. For example , if the CHF occurs due to the local condition such as given by Eq. (73), it cannot be simulated by the above scaling criteria. VI.3..5 Sample Calculations As an example, a preliminary consideration on the simulation of LWR by the LOFT facility is presented. In this case, as stated above it is not possible to operate in the real time scale. Therefore, the time scale should be distorted in order to have a meaningful simulation. From Eqs. (60) and (105)- tR = 0.4 L 0.44 uR = 0.63 ti 0.66 .(106) qR = 1.58 ti 1.51 The geometrical similarity criteria given by Eqs. (44) and (45) requires that (SR= dR = 0.8 .(107) The subcooling or the secondary loop temperature is limited by (eHsub)R = 1 .(108) Furthermore, for an accurate simulation, it is necessary that in two-phase sections the friction and orifice number satisfy and(109) (ft -)R=1 or fR2ti8 KR = 1 3 where it was assumed that (ai/ao)R = 1 based on dR = constant. On the other hand, for single phase sections the overall friction similarity is sufficient. 357
It is noted that the above conditions also satisfies the single phase natural circulation requirements. The exception is the simulation of the turbulent boundary layer. As mentioned above the time scale is distorted by tR • 2.R 17,-R--= 0.63ti0.66 .(110) Therefore, the time events will be accelerated in the model. The above similarity requirement can be compared to the parameters given in Table I. It is clear that the geometrical condition given by Eq. (107) is only met approximately. Furthermore, Eq. (106) shows that the power should be higher in the LOFT facility by 50% or more. It is necessary to adjust the frictional pressure drop coefficients by installing several orifices in the two-phase flow sections. For modifications of the facility or designing ex- periments, much more detailed analysis may be needed. In the present analysis only the general similarity criteria and the feasibility of using the LOFT facility are examined. VI. 4 CONCLUSIONS Scaling criteria for a natural' circulation loop under single phase and two-phase.flow conditions have been derived from the fluid balance equations, boundary conditions, and solid energy equations. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area averaged forms have been used. The solid heat conduction is considered only in a direction normal to the flow, therefore, the effect of axial conduction has been neglected. For a two-phase natural convection case the one-dimensional drift-flux model obtained from the short time temporal averaging the sectional area averaging has been used. The set of balance equations and boundary conditions is nondimensional- ized by using reference scales and steady state solutions. From this, impor- tant similarity groups have been identified. The natural circulation in a closed loop is induced by the density changes due to heating up of liquid and due to boiling. Therefore, special attention has been paid to the driving head of the gravitational term in the differential and integral momentum equations. The coupling of this gravitational driving force with the solution of the fluid energy equation is the particular characteristic of a natural circulation loop. 358
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 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
Page 69 and 70:
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
Page 73 and 74:
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
Page 77 and 78:
0 (N E x b E cr 15 10 0 0 Fig.9(a)
Page 79 and 80:
j V c G 14 12 10 Fig .10 The variat
Page 81 and 82:
E rn N rd E Cr Fig.12 7 6 5 4 3 2 1
Page 83 and 84:
'.9 fS ~; x~ Photo.1 Steady state b
Page 85 and 86:
^ 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
Page 91 and 92:
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(
Page 95 and 96:
2 X CO 20 cy 15 ro E °10 5 0 0.001
Page 97 and 98:
• CO 0 cv 15 E ' E °'10 0.001 Fi
Page 99 and 100:
03 N E 2 rd E o- Fig.20(a) The and
Page 101 and 102:
00 E15 x rtl E 0'10 20 5 0 0.001 Fi
Page 103 and 104:
00 2 co E o- Fig,20(e) The variatio
Page 105 and 106:
00 CO I' rd 20 15 cr 10 5 0.0 01 Fi
Page 107 and 108:
0 20 c+ 15 E x rd oor 10 5 01------
Page 109 and 110:
Ni C15 2 20 x ro E o10 5 0 0.001 Ty
Page 111 and 112:
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
Page 119 and 120:
O N N E 2 X rd' E 0 20 15 10 5 0 U.
Page 121 and 122:
0E 0 -P- N 2 x g E 0' 20 15 10 0 5
Page 123 and 124:
• O 0' N E 2 rd E ET' 20 0.01 Fig
Page 125 and 126:
• F-' O m 0 o0.1 QIQ rd CT 4- I c
Page 127 and 128:
110
Page 129 and 130:
112
Page 131 and 132:
of these works, the transient heat
Page 133 and 134:
Y pendicular to the flat plate. v i
Page 135 and 136:
One assumes temperature distributio
Page 137 and 138:
u for x*>t*h* = -------------------
Page 139 and 140:
value oft and is given by solving f
Page 141 and 142:
v v Here, S is a thickness of veloc
Page 143 and 144:
*1.5* for -ln[1-{1-exp(-5.67Pr x )}
Page 145 and 146:
previous cases St =)76{ 1 - exp(-t*
Page 147 and 148:
' u = (i)l/7 u~ S 1.7(69) T -TT= 1
Page 149 and 150:
Equation (79) was derived based on
Page 151 and 152:
The asymptotic value of the transie
Page 153 and 154:
the transient heat flux attains the
Page 155 and 156:
Greek Letters dtThermal boundarylay
Page 157 and 158:
10. 11. 12. 13. 14. 15. 16. 17. 18
Page 159 and 160:
C a) . V F-- 4- 3 ~~U -~xL . (1.;L
Page 161 and 162:
s 10 - s \ 6- 4- 2- 0- 0.01 Slug Fl
Page 163 and 164:
ON Fig.5 3 2 1 0 0.01 Thermal bound
Page 165 and 166:
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
Page 169 and 170:
Ln N N O I X a) CC Ln N O X (0 CD N
Page 171 and 172:
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
Page 181 and 182:
Ia. 4 MEAN DROPLET SIZE AND SIZE DI
Page 183 and 184:
and the volume fraction oversize A
Page 185 and 186:
p-1/3u2/3 We(D ~) = 0.0099 Reg/3pgu
Page 187 and 188:
a a. 1 a. 1W Ad A. iw CD C g C w D
Page 189 and 190:
1. 2. 3. 4. 5. 6. 7- 8. 9. 10. 11.
Page 191 and 192:
34. Mugele, R. A. and Ind. Eng. Che
Page 193 and 194:
n WAVE REG Ti 0' r ION VOLUME Vw SU
Page 195 and 196:
I pr) M M \ N CO a) a) 100 10-2 10-
Page 197 and 198:
N Io° - J 10-1 M N CO M iCI_ CT ;:
Page 199 and 200:
N C\J C311 us-- N) QQ CS' I 1.4 C\J
Page 201 and 202:
C '14- cacri N C:51 N CC I0~ 10-I 1
Page 203 and 204:
• N ~-1 M J,~-- ~ I Q. M N a) C C
Page 205 and 206:
M rr) ..I~ N IQ Cr) CD Fig. 14. 100
Page 207 and 208:
B I 00 NA D vm D max *_ D 10' D 20'
Page 209 and 210:
192
Page 211 and 212:
IV. 2 PREVIOUS WORKS In annular two
Page 213 and 214:
it has been thought that a sufficie
Page 215 and 216:
C = pf j Jfevq1 gvfe+ ifevg(10) or
Page 217 and 218:
IV. 4 ENTRAINMENT RATE CORRELATION
Page 219 and 220:
• E= 0 .022 pfjfRef-0.26E0.74_(26
Page 221 and 222:
• 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
Page 229 and 230:
droplet impingements and deposition
Page 231 and 232:
where E is given by For The E = tan
Page 233 and 234:
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
Page 251 and 252:
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
Page 257 and 258:
1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 8 0
Page 259 and 260:
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.
Page 263 and 264:
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
Page 269 and 270:
252
Page 271 and 272:
254
Page 273 and 274:
satisfactory correlations which pre
Page 275 and 276:
a j* 99 =jagOp1/4(3) 2 pg where a,
Page 277 and 278:
P Then where Dc r 4j p)2]1/3 g the
Page 279 and 280:
o Droplets ejected from the interfa
Page 281 and 282:
height from the pool surface. Howev
Page 283 and 284:
Substituting Eqs. (32) through (35)
Page 285 and 286:
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.
Page 319 and 320:
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
Page 325 and 326: * 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
Page 329 and 330: w Cn Cn I0 -2 -3 10 I0 -4 -5 I0 -4
Page 331 and 332: U../ -2 10 -3 10 -4 10 -5 I0 -4 10
Page 333 and 334: W -2 10 -3 10 -4 10 I05 Fig. 11. Co
Page 335 and 336: CP Q1 .4w I0 -2 -3 10 -4 I0 105 Fig
Page 337 and 338: 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
Page 343 and 344: N CD -2 I0 -3 177'10 c, -4 0 cn -5
Page 345 and 346: 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: SR gRQR d = 1 R uR (AHsub)R 1 .(102
Page 377 and 378: In the present study, only general
Page 379 and 380: Pr P qs Qs q„ c R Re St t T Ts Ts
Page 381 and 382: 1. 2. 3 4 5 6 7 8. 9. • • • 1
Page 383 and 384: W 01 DOWN 1COMMER PUMP ,-. P1 SINGL
Page 385 and 386: 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
show all

KURENAI : Kyoto University Research Information Repository

Create successful ePaper yourself

Delete template?

Save as template?