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1 206 Development of Heat Transfer Models for Gap Cooling * * * RPV RPV CCFL CHF CHF Kutateladze CCFL CCFL CHF CHF Kutateladze CCFL CHF 3 4,,,, Abstract In a severe accident of a light water reactorlwr, heat transfer models in a narrow annular gap between superheated core debris and a reactor pressure vesselrpvare important to evaluate the integrity of RPV and emergency procedures. This paper discusses the effects of superheat on the heat flux based on exisisting data. In low superheat conditions, the heat flux in the narrow gap is higher than the heat flux in pool nucleate boiling due to restricted flow area. It approaches the nucleate boiling heat flux as superheat increasing and reaches a critical value subject to the countercurrent flow limitingccflat the top end of the gap. A heat transfer correlation was derived as a function of dimensionless superheat and a Kutateladze-type CCFL correlation was deduced for critical heat fluxchfrestricted by CCFL, which gave good prediction for a wide range of the CHF data. Effect of an angle of inclination of the gap could also be incorporated in the CCFL correlation. In high superheat conditions, the heat flux in the narrow gap maintains a similar shape to the pool boiling curve but shifts the position to a higher superheated side than the pool boiling except film boiling, which could be expressed by the typical pool film boiling correlation. Incorporating quench test data, the heat flux correlation was derived as a function of dimensionless superheat using the same formula for the low superheat and the Kutateladze-type CCFL correlation was deduced for CHF. The CHF at the high superheat was 3-4 times as large as CHF at the low superheat and this difference was well predicted by different flow patterns in the gap and the balance of pressure gradients between gas and liquid phases. Keywords critical heat flux, narrow gap, superheat, counter-current flow limiting, angle of inclination

2 207 1 TMI-2 RPV RPV 1400 K K/ (1) RPV RPV RPV CHF (2) (3) (4) RPV CHF (5) RPV (6) CCFL CHF Chang Yao (7) CHF CCFL (8) Jeong (9) Schmidt TMI-2 RPV () CHF (11) 200 CCFL Henry Hammersley (12) 600 RPV CCFL CHF (6)(12) CHF A [m 2 ] f [-] g [m/s 2 ] h fg [J/kg] J [m/s] K k* = J k [ 2 k /g( f )] 1/4 L [m] = {/g ( f )} 1/2 P [Pa] q [W/m 2 ] T SAT [K] [-] [m] [W/m K] [m 2 /s] [kg/m 3 ] [N/m] [Pa] RPV g J g A CS = f J f A CS g, f CS

3 208 q H,A A H = q CS A CS = g J g h fg A CS q H,A H 1 RPV (6), (7) CCFL q H,A CHFq H,C CCFL Jg q H,C CHF CCFL 2 CCFL CHF CHF 1 1 CCFL CHF CCFL A H q H q cs A cs RPV j f 3 CCFL 3.1 CCFL CHF (6) Chang Yao (7) CHF Kutateladze (13) CHF Kutateladze (13) Nu = (q H /T SAT ) (L / f ) = C ( f T SAT / g h fg f ) n1 (PL /) n2 L = {/g ( f )} 1/2 C n1 0.1 MPa (6) n2 Schmidt MPa () C = 1.1, n1 = 0.3, n2 = Chang Yao CHF 0.6

4 209 CHF CHF kwm CCFL CHF CHF K CCFL Wallis (14) ( Jg * ) 1/2 + m ( J f* ) 1/2 = C w m C w J k*, k=f or g J k* = J k [ k /g D ( f )] 1/2, k=f or g Kutateladze (13) K k* = J k [ 2 k /g ( f )] 1/4, k=f or g Collier (15) H k* = J k [ k /g w ( f )] 1/2, k=f or g w = D (1-) L D L =0 =1 Bankoff (16) (6) Chang Yao (7) RPV (K g* ) 1/2 + m (K f* ) 1/2 = C k, m = 1 11 m = 1 11 CHF q H,C = q CS (A CS /A H ) = C e g h fg [ g( f )/ g 2] 1/4 (A CS /A H ) 12 C e = [C K / {1+( g / f ) 1/4 }] 2 13 C K CHF q H,C C K D C K = C K =1.2 C K = Chang 7 / / PMPa 0.1 R-113/ m 2 A H , 0.8, 2.58 CHF 6 / , 0.6, 2, 5 Jeong 9 / , 2 Schmidt / 1, 5, TMI-2 RPV , 3, 5 8 R-113/ , 1, 2, 5 4 K k* =(D * ) 1/2 J * k 15 D * = D/L 16 (8) C K (D * ) 1/2 Kutateladze 11

5 2 Wallis Schmidt () MPa 11P= MPa D * =1 1 C K = MPaR CHF kwm 2 MPaR Ck CHF kwm 2 CHF D DL 3.4 CHF CCFL 3.3 CCFL 1214 CHF CHF C K CHF 60% 150% 0.1 MPa m CHF 0.15 CHF CHF 2 5 CHF K

6 211 kwm CHF CHF CHF CCFL CHF : q 90 CHF : q /2 q = q /2 (sin) 1/2 17 CHF C K 2 C K 90 C K : 14 C K = 1.2(sin) 1/ CCFL K CHF CHF 3 CHF Horner (18) R-134a Jeong (9) Schmidt () 11 CHF % 150% (19) 4.1 (11) CCFL Henry Hammersley (12) Kutateladze (13) Bromley (20) q FB = C FB [{g g ( f )H 3 / g2 } Pr g {h fg / Cp g T SAT + 0.5}] 1/4 ( g T SAT /H ) 19 C FB = H Cp 8 CHF

7 212 C n1 12 [] C = 2.2, n1 = 0.1, n2 = 0.32 [] 21 C = 1.2X 14, n1 = 5.5, n2 = n2 (21) kwm 2 Henry K kwm K CCFL CCFL CCFL Henry Hammersley (12)

8 Ck2.1 Ck1.2 CCFL 12 Ck2.1 Ck1.2 kwm 2 1 ms K 0 1 K CCFL C K C K = C K =1.2 C K =2.1 (5) C K =1.2 5 CCFL Henry Hammersley (12) CCFL 25m/s C K =1.2 7m/s C K =2.1 21m/s (W : P : )

9 CCFL (22) CHF 11 -(dp/dz ) = g g + ( wg L wg + j L j )/A g ) ={ g + f (1-)}g +( wg L wg - wf L wf )/A 24 Z w j L w L j A 24 wg = (f w /8) g ( J g /) 2 25 wf = (f w /8) f { J f /(1-)} 2 26 j = (f j /8) g { J g /- J f /(1-)} 2 27 J f = - ( g / f ) J g /( J g* ) 2 = (f w / 2 ) (L wg D h /A) + {f w /(1 -) 3 } ( g / f ) (L wf D h /A) + {f j / 3 /(1 -)}{1+( g / f )/ ( 1 -)} 2 (L j D h /A) 29 J g* = J g /{D h g ( f )/ g } D h = D or 2 31 D h D w p 11 w A L wg L wf L j D h D 2 /4 0 D D 0.5 D 29 2 J g [] 2/( J g* ) 2 = f w ( g / f )/(1 -) 3 + f j {1+( g / f )/(1-)} 2 /{ 2.5 (1-)} 32 [ 11 (1)] 4/( J g* ) 2 = f w {1+( g / f ) 3 /(1 -) 3 } / 3 + f j {1+( g / f )/(1 -)} 2 /{ 3 (1-)} 33 [ 11 (2)] 2/( Jg * ) 2 = f w {1+( g / f ) 2 /(1-) 2 } / 2 + f j (/p) {1+( g / f )/(1 -)} 2 /{ 3 (1 -)} 34 f w f j Wallis (14) f w = 0.02 W W W W 2 f j = {1+75 (1 -)} P 2P 2P MPa p = CHF CHF CCFL

10 215 ms CCFL CHF CHFCHF kwm 2 CHF 1 0 K CHF CHF C K =2.1 (5) 1214 C K = CCFL CHF Chun (17) 14 Chun K CHF CHF C K =2.1 (5) CHF 34 CHF CHF 36 CCFL CHF CCFL C K =2.1 Chun (17) CHF CCFL CHF

11 216 Chun17 Ck2.1 Monde kwm MPa 14 CHF 7 CHF 1Kutateladze 16K CHF Kutateladze CCFL C K =1.2 CHF MPa m CHF 60% 150% CHF CCFL CHF CHF CCFL 3 CHF CHF (5) CHF INEEL Dr. Joy L. Rempe (1)Wolf, J. R., Rempe, J. L., Stickler, L. A., Korth,

12 217 G. E., Diercks, D. R., Neimark, L. A., Akers, D. W., Schuetz, B. K., Shearer, T. L., Chavez, S. A., Thinnes, G. L., Witt, R. J., Corradini, M. L. and Kos, J. A., TMI-2 Vessel Investigation Project Integration Report, NUREG/CR-6197, TMI V(93) EG, EGG-2734, Idaho National Engineering Laboratory, EG&G Idaho, Inc., March (2),,, (B ), , pp , (3),,, (B ),56 531, No A, pp , (4),,, (B ), , No , pp , (5)Monde, M., Kusuda, H. and Uehara, H., Critical Heat Flux during Natural Convective Boiling in Vertical Rectangular Channels Submerged in Saturated Liquid, Transactions of the ASME, Vol. 4, pp , May (6)Fujita, Y., Ohta, H., Uchida, S. and Nishikawa, K., Nucleate Boiling Heat Transfer and Critical Heat Flux in Narrow Space between Rectangular Surfaces, Int. J. Heat Mass Transfer, Vol. 31, No. 2, pp , (7)Chang, Y. and Yao, S., Critical Heat Flux of Narrow Vertical Annuli with Closed Bottoms, Transactions of ASME, Vol. 5, pp , February (8),,,, 36, D221, pp , (9)Jeong, J. H., Park, R. J., Kang, K. H., Kim, J. H., Kim, S. B. and Kim, H. D., SONATA- Experiments on In-Vessel Debris Coolability and Retention, JAERI-Conf , SARJ-97 Workshop, pp , October 6-8, 1997, Yokohama, Japan. () Schmidt, H., Kohler, W., Herbst, O. and Kratzer, W.,Experiments on Heat Removal in a Gap between Debris Crust and RPV Wall, 1st European-Japanese Two-Phase Flow Group Meeting, 36th European Two-Phase Flow Group Meeting, Portoroz, 1-5 June (11),, ( ), (B ), , No , pp , (12) Henry, R. E. and Hammersley, R. J., Quenching of Metal Surfaces in a Narrow Annular Gap,Paper Presented at the 5th International Conference on Simulation Methods in Nuclear Engineering, (13) Kutateladze, S. S., Heat Transfer in Condensation and Boiling, United States Atomic Energy Commision, Technical Information Service, AEC-tr-3770, (14) Wallis, G. B., One-Dimensional Two-Phase Flow, McGraw-Hill, (15) Collier, R. P., Bishop, T. A., Dworak, J. A., Flanigan, L. J., Kurth, R. E., Liu, J. S. and Segev, A., Steam-Water Mixing and System Hydrodynamics Program, NUREG/CR-0897, BMI-2029, Battelle Columbus Laboratories, June (16) Bankoff, S. G., Tankin, R. S., Yuen, M. C. and Hsieh, C. L.,Countercurrent Flow of Air/Water and Steam/Water through a Horizontal Perforated Plate, Int. J. Heat Mass Transfer, Vol. 24, No. 8, pp , (17) Chun, S. Y., Moon, S. K., Hong, S. D., Yang, S. K. and Chung, M. K., Critical Heat Flux in a Uniformly Heated Vertical Annulus at Zero Inlet Flow under Various Pressures, Proceedings of the 4th JSME- KSME Thermal Engineering Conference, E114, pp , October 1-6, 2000, Kobe, Japan. (18) Horner, P., Zeisberger, A. and Mayinger, F.,

13 218 Boiling and Flow Regimes in a Gap with Adjustable Inclination and Heating from the Top, Ninth International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH- 9), San Francisco, California, October 3-8, (19),,,,, 2001 ( 39 ), (, ), I28, p. 439, ,. (20) Bromley, L. A., Heat Transfer in Stable Film Boiling, Chemical Engineering Progress, Vol. 46, No. 5, pp , May (21),,, 2000, (, ), E1, p. 242, ,. (22),, ( ), (B ), , No , pp ,

J. Jpn. Inst. Light Met. 65(6): 224-228 (2015)

J. Jpn. Inst. Light Met. 65(6): 224-228 (2015) 65 62015 224 228 ** Journal of The Japan Institute of Light Metals, Vol. 65, No. 6 (2015), 224 228 2015 The Japan Institute of Light Metals Investigation of heat flow behavior on die-casting core pin with