HEAT TRANSFER AT SUPERCRITICAL PRESSURES (SURVEY) 1 Igor Pioro*, - - PDF document

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 11th 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 11th 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

Temperature, oC 350 360 370 380 390 400 Density, kg/m3 100 200 300 400 500 600 700 p=22.1 MPa p=25.0 MPa

Temperature, oC 350 360 370 380 390 400 Specific Enthalpy, kJ/kg 1500 2000 2500 3000 p=22.1 MPa p=25.0 MPa

Temperature, oC 350 360 370 380 390 400 Specific Heat, kJ/kg K 100 200 300 400 500 600 p=22.1 MPa p=25.0 MPa

Temperature, oC 300 350 400 450 500 550 600 650 Volume Expansivity, 1/K 0.001 0.01 0.1 1 p=22.1 MPa p=25.0 MPa

Temperature, oC 350 360 370 380 390 400 Thermal Conductivity, W/m K 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 p=22.1 MPa p=25.0 MPa

Temperature, oC 350 360 370 380 390 400 Dynamic Viscosity * 105, Pa s 2 3 4 5 6 7 8 p=22.1 MPa p=25.0 MPa

Temperature, oC 350 360 370 380 390 400 Prandtl Number 5 10 15 20 25 30 35 p=22.1 MPa p=25.0 MPa

KRASNOSHCHEKOV AND PROTOPOPOV (1959, 1960) FOR TUBES

35 . 33 . 11 .

• =

− b p p w b w b

c c k k Nu Nu µ µ

2 10 3 2

64 1 82 1 1 07 1 1 8 7 12 8 ) . Re log . ( . ) Pr ( . Pr Re Nu

b b

− = + − = ξ ξ ξ

b b b w b w

k T T H H µ ) ( ) ( Pr − − =

b w b w p

T T H H c − − =

.

DYADYAKIN AND POPOV (1977) FOR TIGHT 7-ROD BUNDLE WITH HELICAL FINS

• +
• ×
• =

x D Nu

hy x in b x in b x b w x x x

5 . 2 1 Pr Re 021 .

1 . 2 . 45 . 7 . 8 .

ρ ρ µ µ ρ ρ

Fluid Enthalpy, kJ/kg 1200 1300 1400 1500 1600 1700 1800 Heat Transfer Coefficient, kW/m2K 5 10 15 20 25 30 35 40 45 50 Heated Length, m 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Bulk Temperature, oC 280 300 320 340 360

Experiment (Shitsman, 1963) Correlation (Dittus-Boelter) Correlation (Shitsman, 1959) Correlation (Kondrat'ev, 1969) Correlation (Krasnoshchekov- Protopopov, 1960) Correlation (Ornatsky et al., 1970) Correlation for finned bundle (Dyadyakin and Popov, 1977) Correlation (Bishop et al., 1964) Correlation (Kitoh et al., 1999)

Water, circular vertical tube, D=8 mm, L=1.5 m, P=23.3 MPa, q=1084 kW/m2, G=1500 kg/m2s, tpc=378.6oC, Hpc=2148 kJ/kg

Heated Length, m 0.00.51.01.52.02.53.03.54.04.55.05.56.0 Sheath Wall Temperature, oC 350 400 450 500 550 600 650 700 750 800 850 900

Gorban' et al., 1990 Kondrat'ev, 1969 Krasnoshchekov-Protopopov, 1960 Dyadyakin-Popov, 1977 Bishop et al., 1964 Kitoh et al., 1999 Kirillov et al., 1990

Pseudocritical Temperature

CANDU-X Pressure 25 MPa, Mass flux 860 kg/m2s Heat flux 670 kW/m2 Uniform axially and radially Dhy=7.71 mm Heated length 5.772 m 43-element bundle 12 bundles in string

B u l k F l u i d T e m p e r a t u r e

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 CO2 LOOP (NORMAL HEAT TRANSFER)

Axial Location, mm 500 1000 1500 2000 2500 Temperature, oC 10 20 30 40 50 60 70 Fluid Bulk Enthalpy, kJ/kg 250 260 270 280 290 Heat Transfer Coefficient, W/m2K 1000 3000 1500 2500 2000

Heated length Bulk fluid temperature (calculated) Tin Tout Tout mixer I n s i d e w a l l t e m p e r a t u r e ( r e c a l c u l a t e d f r

• m

T

w ext

) Heat transfer coefficient (calculated)

Carbon dioxide, Pout=8.36 MPa, ∆P=1.5 kPa, G=726 kg/m2s, Q=1.5 kW, q=26.8 kW/m2 (uniform heat flux) C . T

• cal

pc

5 36 =

Tin, Tout, Tout mixer, Tw ext are measured values HTC (Krasnoshchekov- Protopopov, 1960)

(NORMAL, DETERIORATED AND IMPROVED HEAT TRANSFER)

Axial Location, mm 500 1000 1500 2000 2500 Temperature, oC 40 80 120 160 200 240 280 Fluid Bulk Enthalpy, kJ/kg 250 300 350 400 450 500 550 Heat Transfer Coefficient, W/m2K 1000 1500 2500 2000

Heated length Bulk fluid temperature (calculated) Tin Tout Tout mixer Inside wall temperature (recalculated from Tw ext) H e a t t r a n s f e r c

• e

f f i c i e n t ( c a l c u l a t e d )

Carbon dioxide, Pout=8.37 MPa, ∆P=1.7 kPa, G=823 kg/m2s, Q=12.0 kW, q=214.3 kW/m2 (uniform heat flux) C . T

• cal

pc

5 36 =

Tin, Tout, Tout mixer, Tw ext are measured values DHT, q/G= 0.26 kJ/kg IHT