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q0 is initial value of exponentially increasing heat flux and w is a reci- procal of the period of exponetially increasing heat flux, respectively. In the momentum and energy equations (Eqs. (2) and (3)), the momentum trans- 22 port in x direction, 1, and energy transport in x direction, k5-177, are assumed to be negligible. Above equations are applied to laminar flow. For turbulent flow case, a and v in above equations will be replaced by (a+CH) and (v+cm). respectively. Here, ca and EM are turbulent diffusivi- ty of heat and momentum, respectively. II. 3 LAMINAR FLOW FOR Pr
One assumes temperature distribution within the thermal boundary layer is given by parabolic distribution, Eq. (10), Which is adopted by Adams et al. [15] for step heat flux change. This temperature distribution agrees well with experimental data under steady state condition cl w6 T - T co=Xt( 1-S)2 (10) t Here, St represents the thickness of thermal boundary layer. Under transient state, the thickness of thermal boundary layer changes with time. In this analysis,it is assumed that temperature distribution is given by Eq. (10.) even in transient state. Of course, as pointed out by Hanawa [23-26], this assumption may not be strictly accurate. However, in view of the success in step heat flux change [15], as a first approximation, above assumption can be applied to transient heat transfer with exponential heat flux increase without serious errors. one obtains, Integrating Eq.(3) from 0 tot' and in view of Eqs.(1) and (2), Sq 2tItTdy+3x,tuTdy=CW(11) '00 Here, p and C are density and specific heat of fluid, respectively. Substituting Eqs.(9) and (10) into Eq.(11), one obtains, 6aat(Stgw)+6a ax(Stq) -Cp(12) • Considering q w = q0 exp(wt), Eq.(12) becomes, we+at(St) + u 8 x(St) = 6a(13) Introducing following dimensionless parameters, 118 pp
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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
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
Page 97 and 98: • CO 0 cv 15 E ' E °'10 0.001 Fi
Page 99 and 100: 03 N E 2 rd E o- Fig.20(a) The and
Page 101 and 102: 00 E15 x rtl E 0'10 20 5 0 0.001 Fi
Page 103 and 104: 00 2 co E o- Fig,20(e) The variatio
Page 105 and 106: 00 CO I' rd 20 15 cr 10 5 0.0 01 Fi
Page 107 and 108: 0 20 c+ 15 E x rd oor 10 5 01------
Page 109 and 110: Ni C15 2 20 x ro E o10 5 0 0.001 Ty
Page 111 and 112: 20 N 15 E 2 E °r10 5 0 0.0 01 Fig.
Page 113 and 114: CN 20 (C" 15 E x CT 10 5 0t- 0.001
Page 115 and 116: CO Fig.24(d) The variation and velo
Page 117 and 118: 0 0 0.001 Fig.25(b) 0.01 The variat
Page 119 and 120: O N N E 2 X rd' E 0 20 15 10 5 0 U.
Page 121 and 122: 0E 0 -P- N 2 x g E 0' 20 15 10 0 5
Page 123 and 124: • O 0' N E 2 rd E ET' 20 0.01 Fig
Page 125 and 126: • F-' O m 0 o0.1 QIQ rd CT 4- I c
Page 127 and 128: 110
Page 129 and 130: 112
Page 131 and 132: of these works, the transient heat
Page 133: Y pendicular to the flat plate. v i
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
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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 -
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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
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