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On the other hand, in a later stage of the LOCA and reflooding where liquid flow rate is extremely low, the pool entrainment phenomena play important roles in heat and mass transfer processes. Therefore, these phenomena were studied. Droplets which are suspended from a free surface are partly carried away by streaming gas and partly returned back to the free surface by gravity. A correlation is developed for the pool entrainment amount based on simple mechanistic modeling and a number of data. This analysis reveals that there exist three regions of entrainment in the axial direction from a pool surface. .In the first region (near surface region), entrainment is independent of height and gas velocity. In the second region (momentum controlled region), the amount of entrainment decreases with increasing height from the free surface and increases with increasing gas velocity. . In the third region (deposition controlled region), the entrainment increases with increasing gas velocity and decreases with increasing height due to deposition of droplets. The present correlation agrees well with a large number of experimental data over a wide range of pressure for air-water and steam-water systems. Along with the separate effects of the transient boiling and two-phase flow on the thermohydraulic characteristics of a nuclear reactor, the over- rall characteristics throughout the entire loop of a nuclear reactor com- prise another set of important problems. The phenomena correspond to the transient boiling and two-phase flow under extremely large t/dh e where t covers the entire loop. One of the most important applications of the above problems is the natural circulation coolability. The phenomena are particularly important associated with small break LOCA and subsequent pump trip in a nuclear reactor. A model facility is often used in evaluating the natural circulation coolability. In designing the model facility. which' simulates a prototype reactor, , scaling laws are impotant. Therefore, scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the 373
turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminaryconclu- sions on the feasibility of the facility have been obtained. Some of the results of this study on the transient boiling and two- phase flow have been incorporated into a large scale computor code such as TRAC which is commonly used to evaluate the safety of a nuclear reactor. accident. The author believes that this study will make some contribution to the improvement of such safety analyses of the nuclear reactor accidents. However, it is needless to say that much more research efforts on the transient boiling and two-phase flow phenomena should be done in order to acquire accurate understandings of the themohydraulics of nuclear power plants under normal and off-normal operational conditions. 374
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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
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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 -
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
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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: Concerning a LOCA and subsequent re
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