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stances, after the heat flux reaches the steady state maximum heat flux, it will continue to increase for a time duration needed for the growth of hydro- dynamic instability and the evaporation of liquid layer under vapor blanket. The present study gives quantitative information about forced convective transient boiling heat transfer with fine wires. However, much remains to be studied. The mechanisms of forced convective transient boiling phenomena need to be clarified based on more detailed observations of flow characteristics and bubble behavior under transient conditions. I. 4 CONCLUSIONS Forced convective transient boiling heat transfer for exponential heat input using platinum wire heaters were studied. And the following conclusions are drawn. (1) The steady state non-boiling heat transfer coefficient is correlated within ±15 % by Eq .(3), where the heater length, L, appears as a characteristic length instead of diameter. (2) The steady state heat transfer coefficient in fully-developed nucleate boiling region was 40 % higher than Kutateladze's prediction. (3) The steady state maximum heat flux increased with increasing velocity, pressure and subcooling and with decreasing heater diameter. The steady,state maximum heat flux is correlated by Eq.(10) within ±10 errors. Equation(10) agrees wellwith Borishansky et al.'s data for water and ethyl alcohol. (4) The transient non-boiling heat transfer coefficient increased with • 29
decreasing period and increased with an increase in velocity and heater length for constant period. The transient non-boiling heat transfer coefficient is correlated by Eq.(12) within ±20 % . Equation(13), an analytical correlation obtained based on slug flow model, predicts the exurimental trends. (5) Two types of transient boiling were observed. In A-type boiling, the transient boiling curve coincided at higher heat flux with the steady state boiling curve and/or its extrapolation. In B-type boiling, the wall superheat remained higher than that on the steady state boiling curve and/or its extrapolation until the maximum heat flux was reached.. Under most of the experimental conditions tested, A-type boiling was observed. (6) In A-type boiling, the transient maximum heat flux increased with decreasing period and with increasing pressure,velocity and subcooling. The difference between the transient maximum heat flux and the steady state flux varied approximately as the -0.6 power of the period over the pressure, velocity, subcooling and heater size ranges of this experiment. (7) The nondimensional correlation for the transient maximum heat flux, Eq.(17), is presented for A-type boiling. Equation(17) correlates experimental data within ±20 % . For water at pressures from 0.1 to 5 MPa, Eq.(15) can be approximated by Eq.(18)_ 30
Page 2: TRANSIENT BOILING AND TWO-PHASE FLO
Page 6: ACKNOWLEDGEMENTS I would like to ex
Page 9 and 10: parallel to the water flow. The eff
Page 11 and 12: entrance and developed region of th
Page 13 and 14: vni
Page 15 and 16: II.3 II .2 II.4 II.5 II.6 II.7 II.8
Page 17 and 18: VI.3 VI.4 VI.2.1 VI.2.2 VI.2.3 VI.2
Page 19 and 20: high. The boiling phenomena under v
Page 21 and 22: • under zero liquid flow rate ( i
Page 24: CHAPTER I FORCED CONVECTIVE BOILING
Page 27 and 28: There have been two groups of works
Page 29 and 30: no direct interaction between the o
Page 31 and 32: On the other hand,the instantaneous
Page 33 and 34: - The properties were taken at film
Page 35 and 36: In Fig.9(a) is shown the effect of
Page 37 and 38: in a 19 mm i.d. tube with water and
Page 39 and 40: long heater. The transient non-boil
Page 41 and 42: shifts towards higher wall superhea
Page 43 and 44: Figures 27(a) and (b) show the effe
Page 45: where E is given by Eq.(8-2) E = 0
Page 49 and 50: gmax ,0 gmax ,st gmax ,st00 gmax ,t
Page 51 and 52: REFERENCES 1. Rosenthal,M.W.,"An ex
Page 53 and 54: (1954). 21. Kutateladze,S.S., Heat
Page 55 and 56: 0 obtained by consulting a text boo
Page 57 and 58: o Cooling Water Storage Tank Pump S
Page 59 and 60: Fig.3 Z 10 Comparative coefficient
Page 61 and 62: 0 E N lo' 106 105 Fig.4(b) The effe
Page 63 and 64: E N 107 106 105 1 Fig.4(d) P = 0.14
Page 65 and 66: Z N. m a) EX m 10 Fig.5 O 0 Compara
Page 67 and 68: 0 N E X as E O' 15 0 0 Fig.6(b) 0.2
Page 69 and 70: N E 2 E 0 0 Fig.6(d) 0.396 MPa 1,2
Page 71 and 72: X Ln '-S N E }---..... } 2 E 0 0 Fi
Page 73 and 74: Ui rn 1 N E X m E Q' 0 Fig.7(d) 1 T
Page 75 and 76: x Ln Co N E ro E 0 Fig.8(b) 1 The v
Page 77 and 78: 0 (N E x b E cr 15 10 0 0 Fig.9(a)
Page 79 and 80: j V c G 14 12 10 Fig .10 The variat
Page 81 and 82: E rn N rd E Cr Fig.12 7 6 5 4 3 2 1
Page 83 and 84: '.9 fS ~; x~ Photo.1 Steady state b
Page 85 and 86: ^ CO TA 7 z D Z 10 1 0.1 \(1) (2) (
Page 87 and 88: " E cr Fig.16(b) 107 106 1o5 1 The
Page 89 and 90: N V 1 o 7 106 105 Fig.17(b) 1 10100
Page 91 and 92: E N 1 106 105 2 Fig.18(a) P=0.396 M
Page 93 and 94: iv 15 E x E (710 0 0.0 01 A Fig.19(
Page 95 and 96: 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
Page 289 and 290:
Substituting Eq. (63) into Eq. (54)
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and Y jr (vr+j g )dt (72) Equation
Page 293 and 294:
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
Page 321 and 322:
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
Page 353 and 354:
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
Page 387 and 388:
370
Page 389 and 390:
Concerning a LOCA and subsequent re
Page 391:
turbulent flow regime. For a two-ph
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