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P terminal h due to velocity is deposition less and is E fg (h,jg) = 7.13 x 10-4 than the given by gas Eq. velocity. Efg (114) as p )-1.0 j*3 9NO.5 ( ug oexp (-0. (4) Entrainment rate and droplet size distribution- From the above development for entrainment, now obtain the entrainment rate and droplet size distribution surface. By integrating Eq. (106) over D with the limit one gets E(jg) PgJ g f(D,jg )dD = 4.84 x 10-3 In view of Eq. (20), the entrainment rate becomes E(jg) = 4. Thus the droplet f(D,j which applies additional important V. When g 84 x 10-3 pg jg A (fa)-1.0 P size distribution becomes Lp decreases gradually with 205(h/DH)) it is possible to at the pool given by Eq. (122), (124) (125) = 0 . 077 jgl .5 D°.5Ig y op (126) to D Dmax where Dmax = 7.24 j-. 12 SUPPLEMENTARY REMARKS ON APPLICATION TO PRACTICAL CASES the correlations developed here are applied to a considerations may be necessary for each case. " cases are discussed below. 291 practical system, Some of the
(1) Total Droplet Flux- In this work, the entrainment is correlated in terms of the upward droplet flux jfe. This parameter itself is very important in studying the carryover droplet mass. However, it is noted that the total liquid volumetric flux jf may be different from the upward droplet flux jfe due to the droplets and liquid film which are falling back to the pool. For quasi-steady state conditions, it is straight forward to extend the present analysis to obtain the total liquid flux as discussed below. For simplicity, the effect of the deposition is neglected. In this case, it can easily be shown from the continuity relation that the total liquid flux can be given by the droplet flux at the end of the momentum controlled region, thus from Eq. (107) P —f f = 2 .0 x 10-3j*35Pg-1.0 N0.(127) PgJgg ug AP This is because all the droplets arriving at the end of momentum controlled region-are fully suspended and cannot fall back without the deposition. Then the droplet volumetric flux of the falling drops are given by 3fd = Jf 3fe(128) which is geherally negative in the near surface or momentum controlled regions. this indicates that there are a definite number of droplets falling downward in these regions. (2) Burnout in Steady State In the case where vapor is produced by pool boiling , the critical heat flux (CHF) gives an additional limit for j9. The pool boiling CHF criterion developed by Zuber [77] or Kutateladze [78] is given by 1/4 PeHf--------- = 0.16ag2P(129) 99Pg 292
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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
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29. Brodkey, R. S., "The Phenomena
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N 9 W 'W C) 67 -z 10 103 -4 10 105
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•W 0.1 0.01 0 0 0.2 Fig. 3. Entra
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s •w 10 1 0.1 0.01 0 0 a 0.2 Fig.
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.W 10 I o .) L1I 0 0.2 0.4 E/Em Fig
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I. _ I J w W a W 4 '4d 0.1 0.01 Fig
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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
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1.0 0.8 0.6 04 0.2 8 0.0 1.0 0.8 0.
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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: E fg (h,jg ) =2. 213 N1.5D*1 jigH .
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
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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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