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where by DH Wilson, Sterman' a = 0.67 j *2/3 Pf -1/3 -2/9 * -1/6 ofDH DH is the dimensionless hydraulic diameter of = D HJ,(gop. The correlation of Sterman [66] a = 1.07 j*0.8 D et s; a = 0.68 al. [67] Ap These correlations dimensionless velocity, where *n1 a - j ni, n2, *-n2 DH and n3 ni = 0.62 - 0.8 *-0 H .25 (fa proposed a -0.14 Ap *-0 .1 H indicate hydraul ic Ap (Pg )-n3 -0.23 dimensionless j*0.62 9 have the ranges of correlation that the void fraction diameter and density vessel is given defined by similar to depends on ratio as n2 = 0.1 -- 0.25 (62) n3 = 0.14 - 0.23 Yeh and Zuber [33] recommend satisfactory agreements with above correlations. Then Eq. a j*g2/3 *-n2 DH 3 the value of n1 = 2/3 which gives a number of experimental data used in (61) becomes 271 the the (58) (59) (60) (61) (63)
Substituting Eq. (63) into Eq. (54), one obtains = C j/4 **- N4 D (:9)1/2 DH2p(64) 3n3/4 f Here C is a proportionality constant which should be determined in collaboration with experimental data. It is noted here that actually the initial velocity of droplet at the pool interface should have its distribution as discussed in Section V.3, However, apparently no data are available due"to experimental , difficulties. Therefore, as a first approximation, only the mean value of the initial velocities expressed by the above correlation is used in this analysis. This may also be justified for the simplicity of the model which can be checked by experimental data. Then droplet velocity distribution function, g(vi,D,jg) is given by the delta function in the following form where- In others droplets * *1/41/4*-1/4 g(vi ,D,jg)dvi=dvi- CjgNu9D - Pg1/2 *3n2/4[pg 3n3/4* x PfDHopdvi(65) f6(x)dx = 1 •(66) 6(x) = 0 for x # 0 words, the initial velocity distribution over the same size is neglected. 272
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TRANSIENT BOILING AND TWO-PHASE FLO
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ACKNOWLEDGEMENTS I would like to ex
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parallel to the water flow. The eff
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entrance and developed region of th
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vni
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II.3 II .2 II.4 II.5 II.6 II.7 II.8
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VI.3 VI.4 VI.2.1 VI.2.2 VI.2.3 VI.2
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high. The boiling phenomena under v
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• under zero liquid flow rate ( i
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CHAPTER I FORCED CONVECTIVE BOILING
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There have been two groups of works
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no direct interaction between the o
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On the other hand,the instantaneous
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- The properties were taken at film
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In Fig.9(a) is shown the effect of
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in a 19 mm i.d. tube with water and
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long heater. The transient non-boil
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shifts towards higher wall superhea
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Figures 27(a) and (b) show the effe
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where E is given by Eq.(8-2) E = 0
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decreasing period and increased wit
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gmax ,0 gmax ,st gmax ,st00 gmax ,t
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REFERENCES 1. Rosenthal,M.W.,"An ex
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(1954). 21. Kutateladze,S.S., Heat
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0 obtained by consulting a text boo
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o Cooling Water Storage Tank Pump S
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Fig.3 Z 10 Comparative coefficient
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0 E N lo' 106 105 Fig.4(b) The effe
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E N 107 106 105 1 Fig.4(d) P = 0.14
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Z N. m a) EX m 10 Fig.5 O 0 Compara
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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
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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
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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) (
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" E cr Fig.16(b) 107 106 1o5 1 The
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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
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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.
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CN 20 (C" 15 E x CT 10 5 0t- 0.001
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CO Fig.24(d) The variation and velo
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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
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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
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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
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icantly influenced by the amount of
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Substituting Eqs. (3) and (4) into
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]]I. 3 DROPLET GENERATION BY ENTRAI
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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
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where the equilibrium rate is given
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f uD= 1.2 x 103RefReff..Reffm-0.25W
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f Figures 8 through 12 show the com
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droplet impingements and deposition
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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
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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: liquid level is very low, i.e., 5-6
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 -
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w CP CP -2 10 I0 I0 -3 -4 -6 10 Fig
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• • 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
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330
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equations. However, the same approa
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The U. = ui/uo Li = t./to T = t U0i
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where ai' asi' ted perimeter di = 4
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uoRu uom opqoR(pCp =gaoR2 R doR'OR(
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In contrast to the design parameter
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• R _Hydraulic Diameter Ratio diR
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• For A scale model can be design
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The similarity criteria based on th
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m where the total flux j is given b
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By assuming an axially uniform heat
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t _ 0 to density change. In two-pha
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Negligible Effects of Viscosity Rat
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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
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370
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Concerning a LOCA and subsequent re
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turbulent flow regime. For a two-ph
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