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v g v r v Vd V w We We c We (D) X Greek S. Symbols y Gas velocity Relative velocity between phases Terminal velocity Volume of a particle Volume of wave regime Weber number Critical Weber number Weber number based on volume median Parameter defined by Eq. (31) Parameter defined by Eq. (33) ad Volume fraction of a particle 6Average film thickness AVolume fraction oversize Op ; Density difference Pf Liquid viscosity ug Gas viscosity Pf Liquid density pg Gas density Distribution parameter in upper aSurface tension T iInterfacial shear stress Subscripts dParticle DDrag iInterface fLiquid gGas wWave 171 diameter limit log-normal 1 distribution
1. 2. 3. 4. 5. 6. 7- 8. 9. 10. 11. 12. 13. 14. 15. 16. REFERENCES Hewitt, G. F. and Hall-Taylor, N. S., "Annular Two-phase Flow," Per- gamon Press, Oxford (1970). Ishii, M. and Mishima, K., "Correlation for Liquid Entrainment in Annular Two-phase Flow of Low Viscous Fluid," Argonne National Laboratory report, ANL/RAS/LWR 80-3 (1980). Collier, J. G., "Burnout in Liquid Cooled Reactors," Nuclear Power, 5, 61 (1961). Petrovichev, V. I., Kokorev, L. S., Didenko, A. Ya. and Dubvrovskiy, G. P., "Droplet Entrainment in Boiling"bf 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 Two- phase Systems," Hemisphere Pub. Co., Washington (1976). Yamanouchi, A., "Effects of Core Spray Cooling at Stationary State After Loss of Coolant Accident," J. Nuclear 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 Generating Unit and Heat Exchangers, Proc. Inst. Mech. Engs. 180, 192- 205 (1965). Duffey, R., "The Physics of Rewetting in Water Reactor Emergency Core Cooling," Nucl. Eng. Design, 25, 379 (1973). Bennett, • A., "The Wetting of Hot Surfaces by Water in a Steam Environment at High Pressure," R5146 (1966). Atomic Energy <strong>Research</strong> Establishment , Harwell, AERE- Brodkey, R. S., . "The Phenomena of Fluid Motion," Addison-Wesley , Reading, (1967) MA Hinze, J. 0., "Fundementals of the Hydrodynamic Mechanism of Splitting in Dispersion Process," AIChE J., 1, 289 (1955). Ishii, M. and Grolmes, M. A., "Inception Criteria for Droplet Entrainment in Two-Phase Concurrent Film Flow," AIChE J., 21, 308 (1975) . Lamb. H., "Hydrodynamics," Dover, NY (1945). Levich, V. G., "Physicochemical Hydrodynamics," Prentice-Hall 172 , NY (1962).
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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
Page 137 and 138: u for x*>t*h* = -------------------
Page 139 and 140: value oft and is given by solving f
Page 141 and 142: v v Here, S is a thickness of veloc
Page 143 and 144: *1.5* for -ln[1-{1-exp(-5.67Pr x )}
Page 145 and 146: previous cases St =)76{ 1 - exp(-t*
Page 147 and 148: ' u = (i)l/7 u~ S 1.7(69) T -TT= 1
Page 149 and 150: Equation (79) was derived based on
Page 151 and 152: The asymptotic value of the transie
Page 153 and 154: the transient heat flux attains the
Page 155 and 156: Greek Letters dtThermal boundarylay
Page 157 and 158: 10. 11. 12. 13. 14. 15. 16. 17. 18
Page 159 and 160: C a) . V F-- 4- 3 ~~U -~xL . (1.;L
Page 161 and 162: s 10 - s \ 6- 4- 2- 0- 0.01 Slug Fl
Page 163 and 164: ON Fig.5 3 2 1 0 0.01 Thermal bound
Page 165 and 166: 00 * s Fig. 6 5 4 3 2 1 0 0.01 Lami
Page 167 and 168: ln 0 * Fig.9 J 6 P. 4 3 2 1 0 Turbu
Page 169 and 170: Ln N N O I X a) CC Ln N O X (0 CD N
Page 171 and 172: 154
Page 173 and 174: icantly influenced by the amount of
Page 175 and 176: Substituting Eqs. (3) and (4) into
Page 177 and 178: ]]I. 3 DROPLET GENERATION BY ENTRAI
Page 179 and 180: In the entrainment regime of entrai
Page 181 and 182: 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: a a. 1 a. 1W Ad A. iw CD C g C w D
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 and 234: a W C C D E E ., g jf 'fe Jg k Ref
Page 235 and 236: 1 2 3 4 5. 6. 7. 8. 9. 10 11 12 13
Page 237 and 238: 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
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252
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254
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satisfactory correlations which pre
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a j* 99 =jagOp1/4(3) 2 pg where a,
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P Then where Dc r 4j p)2]1/3 g the
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o Droplets ejected from the interfa
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height from the pool surface. Howev
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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
Page 347 and 348:
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
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
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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
Page 373 and 374:
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
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L FROM PUMP H DOWN - COMMER UPPER C
Page 387 and 388:
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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