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v of vfe v~ vg vh(D,jg,h) vh vi * vi yr vr~ + v ri Wemax y z Greek Symbols a aE • 6(x) Mfg Op of (jg) vg of vg pf Pg a Ti Velocity NOMENCLATURE (Cont'd) Velocity of element of liquid ligament Droplet velocity Gas velocity Dimensionless gas velocity defined by Eq. (52) Initial velocity of droplet (diameter D) necessary to rise more than height h under gas velocity jg Dimensionless form of vhdefined byEq.(81) ' Initial velocity of droplet at pool surface Dimensionless initial velocity defined by Eq. (51) Relative velocity•between droplet and gas defined by Eq. (69) Terminal velocity of droplet given by Eq. (78) Dimensionless relative velocity of droplet defined by Eq. (7.7) Weber number based on maximum droplet diameter defined by Eq. (85) Vertical position above pool surface Vertical coordinate attached to the liquid ligament Void fraction in liquid pool Liquid fraction of droplet in gas space Parameter defined by Eq. (113) Delta function defined by Eq. (66) Latent heat of vaporization Density difference between gas and liquid Entrainment rate at pool surface for jg (Kg/m2/s) Viscosity of liquid Viscosity of gas Kinematic viscosity of liquid Kinematic viscosity of gas Density of liquid Density of gas Surface tension Interfacial shear stress between gas and liquid ligament 297
REFERENCES 1. Ishii, M. and Grolmes, M. A., "Inception Criteria for Droplet Entrainment in Two-Phase Cocurrent Film Flow," AIChE J. 21, 308 (1975). 2. Hewitt, G. F. and Hall-Taylor, N. S., "Annular Two-Phase Flow," Pergamon Press, Oxford (1970). 3. Brodkey, R. S., "The Phenomena of Fluid Motion," Addison-Wesley, Reading, MA (1967). 4. Ishii, M. and Mishima, K., "Liquid Transfer and Entrainment Correlation for Droplet-Annular Flow," Proc. 7th Intl. Heat Trans. Conf., TF 20, Munich (1982) 5. Kataoka, I., Ishii, M., and Mishima, K., "Generation and Size Distribution of Droplet in Annular Two-Phase Flow,"Trans. ASME, J. of Fluid Eng., Vol. 105, 230 (1983) 6. Kataoka, I., and Ishii, M., "Mechanism and Correlation of Droplet , Entrainment and Deposition in Annular Two-Phase Flow," ANL 82-44, NUREG/CR-2885 (1982) 7. Ishii, M., "Thermo-fluid Dynamic Theory of Two-phase Flow," Eyrolles, Paris, Scientific and Medical Publication of France, NY (1975). 8. Collier, J. G., "Burnout in Liquid Cooled Reactors," Nuclear Power 5, 61 (1961). 9. Petrovichev, 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). 10. 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)- 11. Tong, L. S., "Boiling Heat Transfer and Two-phase Flow," R. E. Krieger Publishing Co., NY (1975). 12. Hsu, Y. Y. and,Graham, R. W., "Transport Process in Boiling and Two-phase Systems," Hemisphere Publishing Co., WA (1976). 13. Hewitt, G. F., "Mechanism and Prediction of Burnout," NATO Advanced Study Institute on Two Phase Flows (1976). 14. Yamanouchi,-A., "Effects of Core Spray Cooling at Stationary State After Loss of Coolant Accident," J. Nuc. Sci. & Tech. 5(9), 498 (1968). 15. Semeria, R. and Martinet, "Calefaction Spots on a Heating Wall; Temperature Distribution and Resorption," -Sym. on Boiling Heat Trans. in Steam Generating Unit and Heat Exchangers, Proc. Inst. Mech. Engs. 180, 192-205 (1965)- 298
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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.
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 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: g(v. h h* hm h+ m d *qc jfe jf 'fd
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
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
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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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