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76 77 78 79 80 • • • • Gill, L. E. and Hewitt, G. F., "Sampling Probe Studies of the Gas Core in Annular Two-phase Flow - Part 3. Distribution of Velocity and Droplet Flowrate after Injection through Axial Jet," AERE-M1202 (1967). Zuber, N., "On the Stability of Boiling Heat Transfer," Trans. ASME 80, 711 (1958). Kutateladze, S. S., "Heat Transfer During Condensation and Boiling," AECtr-3770 (1952). Tien, C. L., "A Simple Analytical Model for Counter-current Flow Limiting Phenomena with Vapor Condensation," Letters in Heat and Mass Transfer 4, 231 (1977). Bankoff, S. G., Tankin, R. S., Yuen, M. C., and Hsieh, C. L., "Countercurrent Flow of Air/Water and Steam/Water through a Horizontal Perforated Plate," Intl. J. Heat Mass Trans. 24, 1381 (1981). 303
and Here pool and Equation gas phase. CE = aE is . On Here vfe the P f aE the (110) 3 fe vfe aE The can mass droplet volumetric other hand, in the APPENDIX A Derivation of Eq. (110) be obtained by considering concentration of droplet fraction deposition in"the gas controlled mass CE is balance of given by space above region the liquid (A.1) (A.2) Jg=V (1-ar) (A.3) From and vg Eqs. are (A.2) vfe aE 3 fe + Sig the and velocity of (A.3) one droplets obtains Here S is the velocity ratio between droplet and gas When Eq. S =vfe v g j >> g 3fe (A.4) can and S = 1, be rewritten which as and gas in gas space. may be applicable in the present analysis, 304 (A.4) (A.5)
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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
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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
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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
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. 1.0 0.8 0.4 0.2 1.0 0.8 8 0 .6 0.
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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: 61 62 63 64 65 66 67 68 69 70 71 72
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
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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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