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4 = 0 .022 Ref-0.26E0.74 (_11)0.26 Pf By substituting Eq. (17) into Eq. (6), the entrainment rate becomes • =DPf--------f 1E\+0 .022pfjfRef-0.260.26E0.74 Equation (18) indicates that knowing the entrainment fraction distribution along the flow direction, one can calculate the entrainment rate. In the following sections, entrainment rate is calculated from the existing entrainment fraction correlation in collaboration with experimental data. 199 f (17) (18)
IV. 4 ENTRAINMENT RATE CORRELATION Ishii and Mishima [2] developed a correlation for entrainment fraction based on the mechanistic model of shearing-off of roll wave crest by a stream- ing gas. The fraction of liquid flux flowing as droplets, E, is correlated in terms of two dimensionless groups given by; Weber Number for Entrainment We =gq(19) pj2D (4)1/3 Total Liquid Reynolds Number Ref Qg D =puJf f(20) The entrained fraction reaches a quasi-equilibrium value, E., at points far removed from the tube entrance where the entrainment and deposition proc- esses attain an equilibrium condition. The distance necessary to reach this condition is given approximately by z = 440 D We0.25/Ref.5 '(21) forcases with smooth liquid injection. At this entrance length the entrain- 'z > 440 D We0'25/Ref'S the correlation becomes ment has reached within about 2% of its ultimate value. _ Then for the region E = E = tanh (7.25 x 10-7 We1.25 Ref0.25)(22) This correlation has been compared to many experimental data for airwater systems in the ranges of 1 < p < 4 atm, 0.95 < D < 3.2 cm, 370 < Ref < 6400, and jg < 100 m/sec, and the result has shown to be satisfactory. The various parametric dependencies have been explained in terms of physical mechanisms. Some experimental data indicated the strong entrance effect as well as the gas expansion effect due to the axial pressure drop in a low pressure system. For the correlation development it was essential to use a local gas velocity or volumetric flux based on a local pressure in evaluating data. By separating these two effects, an additional correlation for the entrance 200
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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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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 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: C = pf j Jfevq1 gvfe+ ifevg(10) or
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
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.
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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
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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(
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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
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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
show all

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