46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 • • • • • • • • • • • • • • • Rozen, A. M., Golub, S. I., and Votintseva, T. I., "Calculating Droplet Carryover with Bubbling," Teploenergetika 23(11), 59 (1976). Rozen, A. M., Golub, S. I., and Votintseva, T. I., "On the Nature of Degree of Dependence of Transported Carryover on Vapor Velocity with Bubbling," Teploenergetika 23(9), 55 (1976). Rozen, A. M., Gostinin, G. I., Davydov, I. F., Golub, S. I., and Krasikov, A. N., "On the Problem of Effects of Salt Content in Water on Moisture Carryover with Bubbling," Izv. Akad. Nauk, Energetika and Transport, No. 6, p. 164 (1973). Kolokoltsev, V. A., "Investigation of the Operation of the Steam Space of ISV Evaporator," Trudy MEI (1952) (quoted from Ref. 40). Ishii, M. and Zuber, N., "Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows," AIChE J. 25, 843 (1979). Davis, R. F., "The Physical Aspect of Steam Generation at High Pressure and Problem of Steam Contamination," Proc. Inst. Mech. Engs., Vol. 144, p. 198 (1940). Woodcock, A. H., Kientzler, C. F., Arons, A. B., and Blanchard, D. C., "Giant Condensation Nuclei from Bursting Bubbles ," Nature 172(4390), 1144 (1953). Knelman, F., Dombrowski, N., and Newitt, D. M., "Mechanism of the Bursting of Bubbles," Nature 173(4397), 261 (1954). Newitt, D. M., Dombrowski, N., and Knelman, F. M., "Liquid Entrainment, 1. The Mechanism.of Drop Formation from Gas or Vapor Bubble," Trans. Inst. Chem. Engs. 32, 245 (1954). Gleim, V. G., "On the Problem for General Theory on Moisture Entrainment from Boiling Mixture," Zhurnal Prikladnoi Khimii 28(1), 12 (1955). Gleim, V. G., Shelomov, I. K., and Shidlovskii, B. R., "Process Leading to Generation of Droplets in Rupture of Bubbles at Liquid-Gas Interface," J. of Applied Chem. USSR 32(1), 222 (1959). Aiba, S. and Yamada, T., "Studies on Entrainment," AIChE J. 5(4), 506 (1959). Wallis, G. B., "One Dimensional Two-Phase Flow," McGraw-Hill Publishing Co., NY, 261-263 (1969). Ishii, M., "One-Dimensional Drift-Flux Model and Constitutive Equations for Relative Motion between Phases in Various Flow Regimes," ANL-77-47 (1977). Ishii, M. and Mishima, K., "Study of Two-Fluid Model and Interfacial Area," ANL-80-111, NUREG/CR-1873 (1980). 301
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 • . • • • • . Nielsen, R. D., Tek, M. R., and York, J. L., "Mechanism of Entrainment Formation in Distillation Columns," <strong>University</strong> of Michigan, Ann Arbor, MI. • • • . Akselrod, L. S. and Yusova, G. M., "Dispersity of the Liquid in the Interplate Space in Bubble Tower," J.--of Applied Chem. USSR 30, 739 (1959). . Muller, R. L. and Prince, R. G. H., "Regimes of Bubbling and Jetting from Submerged Orifices," Chem. Eng. Sci. 27, 1583 (1972). . Margulova, T. H., "An Experimental Investigation of the Relative Velocity of Vapor in Bubbling through a Layer of Water at High Pressures,".Trans. of Power Inst., M. V. Molotov, Vol.--11 Moscow (1953) (quoted from Ref. 33). Kurbatov, A. V., "The Bubbling and the Problem of Critical Load in Steam Separation," Trans. of the POwer Inst., M. V. Molotov, Vol. 11, Moscow (1953) (quoted from Ref. 33). Sterman, L. S., "The Generalization of Experimental Data Concerning the Bubbling of Vapor Through Liquid," Soviet Physics - Technical Physics, 1479 (1957). Wilson, J. F., Grenda, R. J., and Patterson, J. F., "Steam Volume Fraction in a Bubbling Two-Phase Mixture," Trans. ANS 5 Ser. 25, 151 (1962). Lapple, C. E. and Shepherd, C: B., "Calculation of Particle Trajectory," Ind. Eng. Chem. 32(5), 605 (1940). Golub, S. I., Rozen, A. M., Vaislat, M. B., and Votintseva, T. I., "On the Height of Thrown Liquid Droplet under Vertical Gas Flow," Teor. Osnovy Khim. Tekhnol. 6(3), 484 (1972). Hinze,•J. 0., "Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Process," AIChE J. 1, 289 (1955). Antonov, A. I. and Panasenko, M. D., "The Influence of the Vapor Volume Fraction upon the Critical Height of Vapor Space in Boiler," Teploenergetika 4(8), 39 (1957). Panasenko, M. D. and Antonov, A. I., "Correlation of Mechanical Carryover by Steam," Teploenergetika 6(10), 44 (1959). Zuber, N. and Findley, J. A., "Average Volumetric Concentration in Twophase Flow Systems," J. Heat Trans. 87, 453 (1965). Orth, K. W., Epstein, M., Linehan, J. H., Lambert, G. A., and Stachyra, L. J., "Hydrodynamic Aspects of Volume Boiling," ANL/RAS 80-6 (1980). Paleev, I. I. and Filipovich, B. S., "Phenomena of Liquid Transfer in Two-Phase Dispersed Annular Flow," Int. J. Heat Mass Trans. 9, 1089 (1966).— 302
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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
- Page 47 and 48:
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
- Page 141 and 142:
v v Here, S is a thickness of veloc
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*1.5* for -ln[1-{1-exp(-5.67Pr x )}
- Page 145 and 146:
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
- Page 153 and 154:
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
- Page 185 and 186:
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
- Page 195 and 196:
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 ;:
- Page 199 and 200:
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
- 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
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B I 00 NA D vm D max *_ D 10' D 20'
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192
- Page 211 and 212:
IV. 2 PREVIOUS WORKS In annular two
- Page 213 and 214:
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
- Page 223 and 224:
where the equilibrium rate is given
- Page 225 and 226:
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
- Page 231 and 232:
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
- Page 259 and 260:
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
- 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: 30. 31. 32. 33. 34. 35. 36. 37. 38.
- 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 and 374:
SR gRQR d = 1 R uR (AHsub)R 1 .(102
- Page 375 and 376:
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
- 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