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More precise measurements on transient heat transfer coefficient have been made by Kataoka et al. [27] for a cylindrical wire located parallel to turbulent water flow. In their experiment, the transient heat transfer coefficient averaged over the whole heater length, 2., with exponentially increasing heat generation rate has been measured. The result indicates that the transient heat transfer coefficient approaches a asymptotic value k" and it is correlated in term of Q, by; h*0.97' h= 1 + 0.1448Q(94) st On the other hand, present analysis shows that for small xand for turbulent flow and Pr = 1, the ratio of h a/hst can be approximated by h a = 1 + 0 .0824 x(95) h Averaging Eq.(95) over heater length, 2,, one obtains, h st• ha = 1 + 0.0412Q,(96) st The difference of the proportionality constant between Eqs.(94) and (96) can be attributued to the difference of heater configuration (wire and plate). It is northworthy that turbulent boundary layer approximation in present analysis gives similar functional form to the exprimental correlation. II. 10 CONCLUSIONS Transient heat transfer coefficients for a flat plate with exponentially increasing heat flux under forced convection condition have been analysed by using boundary layer approximation. The results indicate that the 135
the transient heat flux attains the asymptotic value. The ratio between the asymptotic value of the transient heat transfer coefficient and steady state one is larger than unity. It increases with increasing x , a dimensionless parameter composed of distance from inlet, velocity and in— creasing rate of heat flux. The transient heat transfer coefficient for laminar flow and Pr > 1 by Eqs...(39) and (40), for laminar flow and Pr=1 by Egs:(55) and (56). For turbulent flow and Pr > 1 by Eqs.(65) and(66), and for turbulent flow and Pr = 1 by Eqs.(89) and (90). The results for turbulent flow and Pr = 1 can predict general trends and parametric dependence obtained in experiments for water using flat plate and cylindrical wire heaters. More experimental data will be neccessary in order to acquire accurate knowledge for transinet heat transfer coefficient under forced convection condition along with analytical approaches carried out in present analysis. 136 tl'
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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
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 and 136: One assumes temperature distributio
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: The asymptotic value of the transie
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
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
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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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