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acore ad • • co of 11g Pf Pg Ap a T. 1 Subsc Subscripts :f fe ff g i Fraction of gas core NOMENCLATURE (Cant'd) Droplet fraction in the gas core Film thickness Entrainment rate Equilibrium entrainment rate Dimensionless distance given-by Eq.. (24) Viscosity of liquid Viscosity of gas Liquid density Gas density Density difference between liquid and gas Surface tension Interfacial shear force Liquid phase Liquid entrainment Liquid film Gas phase Interface Equilibrium 217
1 2 3 4 5. 6. 7. 8. 9. 10 11 12 13 14 15. • Petrovichev, REFERENCES Hewitt, • G. F. and Hall-Taylor, N. S., "Annular Two-phase Flow," Pergamon Press, Oxford (1970). Ishii, M. and Mishima, K., "Correlation for Liquid Entrainment in Annular Two-phase Flow of Low Viscous Fluid," Report, ANL/RAS/LWR 81-2 (1981). Argonne National Laboratory Collier, J. G., "Burnout in Liquid Cooled Reactors," Nuclear Power, 5, 61 (1961). V. I., Kokorev, L. S:-, Didenko, A. Ya., and Dubvrovskiy, G. P., "Droplet Entrainment in Boiling of Thin Liquid Film," Heat Transfer-Soviet Res., 3, 19 (1971). Cousins, L. B.,'Denton, W. .H., and Hewitt, G. E., "Liquid Mass Transfer in Annular Two-phase Flow," Sym. on Two-phase Flow, Vol. 1, paper C4, Exter, England (1965). Tong, L. S., "Boiling Heat Transfer and Two-phase Flow," R. E. Krieger Publishing Co., NY (1975). Hsu, Y. Y. and Graham, R. W., "Transport Process in Boiling and Twophase Systems," Hemisphere Publishing Co., WA (1976). Hewitt, G. F., "Mechanism and Prediction of Burnout," NATO Advanced Study Institute on Two Phase Flows (1976). Yamanouchi, A., "Effects of Core Spray Cooling at Stationary State After Loss of Coolant Accident," J. Nuc. Sci. & Tech., 5(9), 498 (1968). Semeria, R. and Martinet, "Calefaction Spots on a Heating Wall; Temperature Distribution and Resorption," Sym. on Boiling Heat Trans. in Steam Generatina Unit and Heat Exchanaers 205 (1965). Duffey, R., "The Physics of Rewetting in Cooling," Nucl. Eng. Design, 25, 379 Bennett, A., "The Wetting of Hot Surfaces ment at High Pressure," Atomic Energy AERE-R5146 (1966). Ishii, M. and Grolmes, M. A., "Inception ment in Two-phase Concurrent Film F Kataoka, I., Ishii, M., and Mishima Distribution of Droplet in Annular J. of Fluid Eng., Vol. 105, 230 (1983) Alexander, L. G. and Coldren C. L., Transfer from Suspending Air to Duct Walls," Ind. Eng. Chem. , Proc. AIChE Water Criteria 1325 "Generation Inst. (1951). Reactor J., Mech. earch for Establishment, 21, Droplet and Engs. Emergency 308 Size (1975). Flow,"Trans. 180, Harwell, Entrain- ASME, Two-Phase Core 192- by "Drop Water '3) in rfaces a Steam Environ- 218
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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
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: a W C C D E E ., g jf 'fe Jg k Ref
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)
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dv pfD a€-f = Ti - opgD ,(43) whe
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liquid level is very low, i.e., 5-6
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Substituting Eq. (63) into Eq. (54)
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and Y jr (vr+j g )dt (72) Equation
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Equation where vh vh (79) 0 2h* can
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On is the other hand, in annular-di
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In Fig. 6, the general trend of the
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* ~ • This Efg(h,jg) = 2.213 N1.5
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f(DJj) =C1()fl5j*1.5 D*0.5(105) gp3
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-4 *3 0.5p ()_1.0 Efg(h,jg) = 7.13
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h* = 1.038 x 103 jgN095 0.23 DH0.42
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E fg (h,jg ) =2. 213 N1.5D*1 jigH .
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(1) Total Droplet Flux- In this wor
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intermediate gas flux regimes given
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g(v. h h* hm h+ m d *qc jfe jf 'fd
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REFERENCES 1. Ishii, M. and Grolmes
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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
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and Here pool and Equation gas phas
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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
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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 -
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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(
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
Page 363 and 364:
The similarity criteria based on th
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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
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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
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
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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
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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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