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experiments for transient forced convective boiling with an exponential power increase over a wide range of experimental variables) but the data of their experiments show considerable scatter' and fail to give quantitative information about the effects of period, velocity,pressure and subcooling on the transient boiling characteristics. In Martenson's experiment [16], the flow channel was so narrow (0.18 cm gap) that bubbles generated on the heater would interact violently with the outer wall and make the phenomena more complicated. Only a few data for transient maximum heat flux are reported in his paper. Aoki et al. [17] studied flow and boiling characteristics under transient conditions using an annular passage with the inner tube heated exponentially with time. As in Martenson's experiment [16],' the annular flow passage was narrow (0.15 cm gap), and the system pressure was limited to nearly atmospheric. Thus little is known about transient boiling characteristics under forced convection. As for transient maximum heat flux, knowledge is still limited particularly about the effects of period, velocity, pressure, subcooling and heater size, not to mention the mechanisms involved. As is well known, various flow patterns exist in flow boiling and heat transfer characteristics are more or less affected by them. It is there- fore necessary to study transient boiling taking these effects into con- sideration., In fact, a change of flow pattern along the flow direction, which is often encountered,makes transient boiling phenomena much more complicated. Since the purpose of this chapter is to clarify fundamental aspects of transient boiling under forced convection, the experimental setup was designed in such a way that there might be no change of flow pattern and 11
no direct interaction between the outer tube wall and vapor bubbles [18]. Under these flow conditions, effects of exponential period, velocity, subcooling, pressure and heater size were studied on transient boiling heat transfer. I. 2 EXPERIMENTAL APPARATUS AND PROCEDURES Figure 1 shows a schematic diagram of the experimental apparatus used in this work. Distilled and deionized water (specific resistivity was more than 5 MO-cm) is circulated by a pump (at a flow rate up to 300 L/min ,) and heated to the desired temperature level in a preheater . The flow, rate is controlled by a flow regulating valve and measured by a turbine flow meter. Water and steam are separated in a separator & expansion. tank, steam being then collected in condensers. , A cooler is used to cool down circulating water to the desired temperature if necessary. The test loop is made of stainless steel with a quartz glass window to allow visual observation. The test section is a round tube~ 1425 mm long and 38 mm in inner diameter. Water flows upward in this test section . The test loop is pressurized by steam in experiments at zero subcooling and by compressed air in those at subcooled conditions. Figure 2 shows a cross-sectional view of the heated section . The heater element is a_platinum wire of diameter 0.8, 1.2 and 1.5 mm and length 3.93, 7.12 and 10.04 cm. It is soldered to silver-coated copper electrodes at both ends,and located along the centerline of the flow channel at a position 1200 mm downstream from the test section inlet . Potential taps(0.2 mm diam platinum wires) are soldered at positions . about .12
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: There have been two groups of works
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 and 46: where E is given by Eq.(8-2) E = 0
Page 47 and 48: decreasing period and increased wit
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
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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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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
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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
Page 351 and 352:
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(
Page 357 and 358:
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
Page 371 and 372:
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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