HEAT TRANSFER AT SUPERCRITICAL PRESSURES (SURVEY) 1 Igor Pioro*, Hussam Khartabil and Romney Duffey Chalk River Laboratories, AECL, Chalk River, ON, Canada K0J 1J0 Keywords: Supercritical pressure, forced convective heat transfer, water, carbon dioxide. Objectives The objectives are to assess the work that was done in the area of heat transfer at supercritical pressures, to understand the specifics of heat transfer at these conditions, to compare different prediction methods for supercritical heat transfer in tubes and bundles, and to choose the most reliable ones. Preliminary Findings The exhaustive literature search, which included hundreds of papers, showed that the majority of correlations were obtained in tubes and just few of them in other flow geometries including bundles. The use of supercritical steam-water in nuclear reactors (Generation IV Nuclear Energy Systems Report 2001) will: Significantly increase thermal efficiency up to 40–45%; Decrease reactor coolant pumping power; Lower containment loadings during loss-of-coolant accidents; Eliminate dryout; and Eliminate steam dryers, steam separators, re-circulation pumps, and steam generators. 1 The presentation is based on the following papers: 1. Pioro, I.L., Khartabil, H.F. and Duffey, R.B., Heat Transfer at Supercritical Pressures (Survey), Proceedings of the 11 th International Conference on Nuclear Engineering (ICONE-11), Shinjuku, Tokyo, Japan, April 20–23, 2003, Paper No. 36454, 13 pages. 2. Duffey, R.B., Khartabil, H.F., Pioro, I.L. and Hopwood, J.M., The Future of Nuclear: SCWR Generation IV High Performance Channels, Proceedings of the 11 th International Conference on Nuclear Engineering (ICONE-11), Shinjuku, Tokyo, Japan, April 20–23, 2003, Paper No. 36222, 8 pages.
THERMOPHYSICAL PROPERTIES AT CRITICAL AND SUPERCRITICAL PRESSURES 700 p=22.1 MPa p=25.0 MPa 600 500 Density, kg/m3 400 300 200 100 0 350 360 370 380 390 400 Temperature, oC
3000 p=22.1 MPa p=25.0 MPa Specific Enthalpy, kJ/kg 2500 2000 1500 350 360 370 380 390 400 Temperature, oC
p=22.1 MPa p=25.0 MPa 600 500 Specific Heat, kJ/kg K 400 300 200 100 0 350 360 370 380 390 400 Temperature, oC
p=22.1 MPa p=25.0 MPa 1 Volume Expansivity, 1/K 0.1 0.01 0.001 300 350 400 450 500 550 600 650 Temperature, oC
0.7 Thermal Conductivity, W/m K 0.6 0.5 0.4 0.3 0.2 p=22.1 MPa 0.1 p=25.0 MPa 0.0 350 360 370 380 390 400 Temperature, oC
8 p=22.1 MPa Dynamic Viscosity * 105, Pa s p=25.0 MPa 7 6 5 4 3 2 350 360 370 380 390 400 Temperature, oC
p=22.1 MPa p=25.0 MPa 35 30 25 Prandtl Number 20 15 10 5 0 350 360 370 380 390 400 Temperature, oC
KRASNOSHCHEKOV AND PROTOPOPOV (1959, 1960) FOR TUBES − 0 . 35 0 . 11 0 . 33 µ k � c � � � � � = p b b Nu Nu � � � � � � µ 0 � � � � k � c � � � � � w w p b � � ξ Re Pr b 8 = Nu 0 ξ 2 − + 12 . 7 ( Pr 1 ) 1 . 07 3 8 1 ξ = − 2 ( 1 . 82 log Re 1 . 64 ) 10 b − µ ( ) H H = w b b Pr − ( T T ) k w b b − H H = w b c p − T T . w b
DYADYAKIN AND POPOV (1977) FOR TIGHT 7-ROD BUNDLE WITH HELICAL FINS 0 . 45 0 . 2 ρ µ 0 . 7 � � � � = × 0 . 8 w b Nu 0 . 021 Re Pr � � � � x ρ µ x x � � � � � � � � b in x x 0 . 1 � + ρ D � � � hy b 1 2 . 5 � � � � ρ � � � � x � � � � in x
Bulk Temperature, o C 280 300 320 340 360 50 Experiment (Shitsman, 1963) Correlation (Dittus-Boelter) 45 Correlation (Shitsman, 1959) Heat Transfer Coefficient, kW/m 2 K Correlation (Kondrat'ev, 1969) Correlation (Krasnoshchekov- 40 Protopopov, 1960) Correlation (Ornatsky et al., 1970) Correlation for finned bundle 35 (Dyadyakin and Popov, 1977) Correlation (Bishop et al., 1964) Correlation (Kitoh et al., 1999) 30 25 20 15 10 Water, circular vertical tube, D=8 mm, L=1.5 m, P=23.3 MPa, q=1084 kW/m 2 , 5 G=1500 kg/m 2 s, t pc =378.6 o C, H pc =2148 kJ/kg 0 1200 1300 1400 1500 1600 1700 1800 Fluid Enthalpy, kJ/kg 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Heated Length, m
900 Gorban' et al., 1990 Kondrat'ev, 1969 850 Krasnoshchekov-Protopopov, 1960 Dyadyakin-Popov, 1977 Bishop et al., 1964 800 Kitoh et al., 1999 Kirillov et al., 1990 Sheath Wall Temperature, o C 750 CANDU-X Pressure 25 MPa, Mass flux 860 kg/m 2 s 700 Heat flux 670 kW/m 2 Uniform axially and radially 650 D hy =7.71 mm e Heated length 5.772 m r u 43-element bundle t 600 a r 12 bundles in string e p m 550 e T d i 500 u l F k l u 450 B 400 Pseudocritical Temperature 350 0.00.51.01.52.02.53.03.54.04.55.05.56.0 Heated Length, m
FINAL REMARKS AND CONCLUSIONS • A comparison of various correlations for supercritical heat transfer showed that several correlations can be used for preliminary estimations of heat transfer in tubes and bundles. However, no one correlation is able to describe deteriorated heat transfer in tubes. • Preliminary calculations of heat transfer and temperature profiles in a CANDU- X supercritical water-cooled reactor operating conditions showed that the proposed concept of this reactor is feasible for future development.
CURRENT EXPERIMENTAL DATA FOR CO 2 LOOP (NORMAL HEAT TRANSFER) Carbon dioxide, P out =8.36 MPa, ∆ P=1.5 kPa, G=726 kg/m 2 s, Q=1.5 kW, q=26.8 kW/m 2 (uniform heat flux) Fluid Bulk Enthalpy, kJ/kg 250 260 270 280 290 70 3000 Heat Transfer Coefficient, W/m 2 K 2500 Heat transfer coefficient (calculated) 60 2000 1500 ) T w ext HTC (Krasnoshchekov- m Temperature, o C o 50 r 1000 f d e a t l u Protopopov, 1960) c l a c e r ( e r u t a r e p m e t l l a w 40 e d = i s cal o n T 36 . 5 C I pc T out T out mixer 30 Bulk fluid temperature (calculated) T in 20 T in , T out , T out mixer , T w ext are measured values 10 Heated length 0 0 500 1000 1500 2000 2500 Axial Location, mm
(NORMAL, DETERIORATED AND IMPROVED HEAT TRANSFER) Carbon dioxide, P out =8.37 MPa, ∆ P=1.7 kPa, G=823 kg/m 2 s, Q=12.0 kW, q=214.3 kW/m 2 (uniform heat flux) Fluid Bulk Enthalpy, kJ/kg 250 300 350 400 450 500 550 280 2500 Heat Transfer Coefficient, W/m 2 K DHT, q/G= 2000 d ) e 0.26 kJ/kg a t u l a l c c t ( n c i e f i e f c o r f e n s a 240 t r a t H e 1500 1000 IHT Temperature, o C 200 Inside wall temperature (recalculated from T w ext ) 160 120 T in , T out , T out mixer , T w ext are measured values T out mixer T out 80 Bulk fluid temperature (calculated) = cal o T 36 . 5 C 40 pc T in Heated length 0 0 500 1000 1500 2000 2500 Axial Location, mm
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