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• S*-ATS t t t = tw * xw x = — u Equation (13) can be rewritten in dimensionless form by St2.4_ a(St2)+a(St2) = 6 at* t-- ax The initial and boundary conditions are given by St(x ,0) = 0 for x > 0 t(0,t ) = 0 for t > 0 The solution of Eq.(15) under the conditions of Eqs.(16) and (17) by method of characteristic equation and given by for x < t* St { 1'- exp(-x )} for x> tSt=/-6{ 1 — exp(-t*)} From Eq.(10), heat transfer coefficient is given by h=qw _2Xh~_h" -T w- T~StX Then the transient heat transfer coefficient for laminar and Pr
u for x*>t*h* = ----------------------2 *(22) { 1 - exp(-t )} Equations (21) and (22) indicate that for large time, heat transfer coeffi- * cient attains a asymptotic value, h a, which is given by * h a= ----------------------2*(23) { 1 - exp(-x )} On the other hand, steady state heat transfer coefficient, h st, can be obtained by putting w 0 in Eqs.(21)and (22), since for small value of w heat flux increases slowly enough to be regarded as quasi-steady state. Then steady state heat transfer coefficient is given by or in dimensionless form by Here Nu st and Pex are defined by. h=2(--)(24) stxa • Nut= 0.82 Pe x(25) Nu -hstx st A u x•(26) Pe E — x a From Eqs.(23) and (26), the ratio between asymptotic transient heat transfer coefficient and steady state one, h a/hst, can be obtained h Nu*' a ( _a) = -----------------------h st - Nust{ 1 - exp(-x*)} • This ratio is expressed in term of dimensionless parameter , x (=xw/u .), and shown in Fig. 4 in h a/hst vs. x plot. As shown in this figure, the 120 (27)
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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
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 and 134: Y pendicular to the flat plate. v i
Page 135: One assumes temperature distributio
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
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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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