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SUMMARY AND CONCLUSIONS The thermohydraulic characteristics of transient boiling and two- phase flow have been studied experimantally and analytically. The main objectives of the study are to provide an accurate knowledge for the various thermohydraulic phenomena encountered under the accidental conditions of a nuclear reactor. In relation to the reactivity accident of a nuclear reactor, the transient boiling phenomena under rapid power increase have been studied experimentally. In this case, transient boiling and two-phase flow phenomena under small 2/dhe and low steam quality are particularly important and the boiling phenomena are considered to be localized. Experiments were conducted by exponentially increasing heat input to a platinum wire in water flowing vertically upward in a round tube, under mean water velocity from 1.35 to 4.04 m/s, inlet subcooling from 0 to 70 K, system pressure from 0.143 to 1.503 MPa, exponential period from 5 ms to 10 s, heater diameter from 0.8 to 1.5 mm and heater length from 3.93 to 10.04 cm. In most cases, the transient boiling curve after temperature overshoot coincided with the steady state boiling curve and/or its extrapolation. In these cases, the transient maximum heat flux intreased with increasing velocity, subcooling and pressure, and with decreasing period and heater diameter, independently of heater length. The difference between the transient maximum heat flux and the steady state maximum heat flux was satisfactori- ly correlated by the exponential period. Incidental to the transient boiling phenomena, the transient non- boiling heat transfer has been analysed. Based on integral method (boundary layer approximation), transient non-boiling heat transfer coefficients are obtained for a flat plate. The approximate but simple and analytic correlations obtained in this analysis cover various flow regimes (laminar, turbulent)and awide range of Prandtl number of a fluid. These transient heat transfer coefficients attain the asymptotic values. The ratio between the asymptotic heat transfer coefficient and the steady state one is correlated in terms of dimensionless parameter including a heat flux increasing rate. 371
Concerning a LOCA and subsequent rewetting and reflooding phenomena in a nuclear reactor, the transient boiling and two-phase flow under large Q/dhe and high steam quality are considerably important . In analysing the phenomena, an accurate knowledge of an annular and annular dispersed flow is essential. In an earlier stage of the LOCA and reflooding, the most important flow regime involved is counter-current annular dispersed flow where liquid flow rate is positive. Associated with the annular dispersed flow in the above case, droplet size and entrainment rate have been analyzed. The mean droplet size and size distribution are important for detailed mechanistic modeling of annular two-phase flow. A large number of experimental data indicate that the standard Weber number criterion based on the relative velocity between droplets and gas flow predicts far large droplet sizes. Therefore, it was postulated that the majority of the droplets were generated at the time of entrainment and the size distribution was the direct reflection of the droplet entrainment mechanism based in roll-wave shearing off. A detailed model of the droplet size in annular flow was then developed based on the above assumption. The correlations for the volume mean diameter as well as the size distrinution were obtained in collaboration with a large number of experimental data-.= A comparison with experimental data indicated that indeed the postulated mechanism has been the dominant factor in determining the droplet size. Furthermore, a large number of data can be successfully correlated by the present model . These correlations can supply accurate information on droplet size in annular flow which has not been available previously. As for the entrainment rate in annular dispersed flow , the correlations for entrainment rate covering both entrance region and equilibrium region have been developed from a simple model in collaboration with d ata. Results show that the entrainment rate varies considerably in the entrainment development region, however, at a certain distance from an inlet it attains an equilibrium state where entrainment rate and deposition rate becomes equal. The result indicates that the equilibrium entrainment rate is proportional to the Weber number based on the hydraulic diameter of the tube 372
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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
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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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Page 339 and 340: w CP CP -2 10 I0 I0 -3 -4 -6 10 Fig
Page 341 and 342: • • Fig. 19. M 0 CL. a 101 100
Page 343 and 344: N CD -2 I0 -3 177'10 c, -4 0 cn -5
Page 345 and 346: w co Table II. Summary of Various E
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Page 349 and 350: equations. However, the same approa
Page 351 and 352: The U. = ui/uo Li = t./to T = t U0i
Page 353 and 354: where ai' asi' ted perimeter di = 4
Page 355 and 356: uoRu uom opqoR(pCp =gaoR2 R doR'OR(
Page 357 and 358: In contrast to the design parameter
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Page 361 and 362: • For A scale model can be design
Page 363 and 364: The similarity criteria based on th
Page 365 and 366: m where the total flux j is given b
Page 367 and 368: By assuming an axially uniform heat
Page 369 and 370: t _ 0 to density change. In two-pha
Page 371 and 372: Negligible Effects of Viscosity Rat
Page 373 and 374: SR gRQR d = 1 R uR (AHsub)R 1 .(102
Page 375 and 376: It is noted that the above conditio
Page 377 and 378: In the present study, only general
Page 379 and 380: Pr P qs Qs q„ c R Re St t T Ts Ts
Page 381 and 382: 1. 2. 3 4 5 6 7 8. 9. • • • 1
Page 383 and 384: W 01 DOWN 1COMMER PUMP ,-. P1 SINGL
Page 385 and 386: L FROM PUMP H DOWN - COMMER UPPER C
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Page 391: turbulent flow regime. For a two-ph
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