A new heat transfer correlation for supercritical fluids

Abstract

A new method of heat transfer prediction in supercritical fluids is presented. Emphasis is put on the simplicity of the correlation structure and its explicit coupling with physical phenomena. Assessment of qualitative behaviour of heat transfer is conducted based on existing test data and experience gathered from open literature. Based on phenomenological analysis and test data evaluation, a single dimensionless number, the acceleration number, is introduced to correct the deviation of heat transfer from its conventional behaviour, which is predicted by the Dittus-Boelter equation. The new correlation structure excludes direct dependence of heat transfer coefficient on wall surface temperature and eliminates possible numerical convergence. The uncertainty analysis of test data provides information about the sources and the levels of uncertainties of various parameters and is highly required for the selection of both the dimensionless parameters implemented into the heat transfer correlation and the test data for the development and validation of new correlations. Comparison of various heat transfer correlations with the selected test data shows that the new correlation agrees better with the test data than other correlations selected from the open literature.

Keywords

super critical fluids / heat transfer / circular tubes / prediction method

References

[1] Bishop A A, Sandberg L O, Tong L S. Forced convection heat transfer to water at near critical temperatures and supercritical pressures. WCAP-2056-P, Part-III-B, 1964

[2] Swenson H S, Caever J R, Kakarala C R. Heat transfer to supercritical water in smooth-bore tube. Journal of Heat Transfer, 1965, 87(4): 477-484

[3] Krasnoshchekov E A, Protopopov V S. Experimental study of heat exchange in carbon dioxide in the supercritical range at high temperature drops, Teplofizika Vysokikh Temperatur, 1966, 4(3): 389-398

[4] Yamagata K, Nishikawa K, Hasegawa S, . Forced convection heat transfer to supercritical water flowing in tubes. International Journal of Heat and Mass Transfer, 1972, 15(12): 2575-2593

[5] Griem H. Untersuchungen zur thermohydraulik innenberippter verdampferrohre. <DissertationTip/>. Technical University of Munich, 1995

[6] Cheng Xu, Schulenberg T. Heat transfer at supercritical pressures—literature review and application to an HPLWR. <DissertationTip/>Wissenschaftliche Berichte (Tech. Report) FZKA 6609, Forschungszentrum Karlsruhe, Mai, 2001

[7] Pioro I L, Duffey R B. Experimental heat transfer in supercritical water flowing inside channels. Nuclear Engineering and Design, 2005, 235(22): 2407-2430

[8] Jackson J D. Semi-empirical model of turbulent convective heat transfer to fluids at supercritical pressure. Procceding of 16th International Conference on Nuclear Engineering, ICONE16, Orlando, Florida, USA, 2008, Paper No. 48914

[9] Kuang B, Zhang Y Q, Cheng X. A new, wide-ranged heat transfer correlation of water at supercritical pressures in vertical upward ducts. The 7th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Operation and Safety (NUTHOS-7), Seoul, Korea, 2008, Paper No. 189

[10] Herkenrath H, Mörk-Mörkenstein P, Jung U, . Forced convection Heat transfer to water at the pressure range from 140 to 250 bar, <patent>EUR 3658d</patent>, EURATOM, 1967

[11] Koshizuka S, Takano N, Oka Y. Numerical analysis of deterioration phenomena in heat transfer to supercritical water. International Journal of Heat and Mass Transfer, 1995, 38(16): 3077-3084

[12] Jackson J D, Hall W B. Influences of buoyancy on heat transfer to fluids in vertical tubes under turbulent conditions. In: Turbulent Forced Convection in Channels and Bundles, Vol.2, New York: Hemisphere Publishing Corporation, 1979, 613-640

[13] Jackson J D. HTFS design report No. 34 – Heat transfer to supercritical pressure fluids, Part 1 – Summary of design recommendation and equations. <patent>AERE-R8157</patent>, 1975

Acknowledgements

The authors would like to thank the National Basic Research Program of China (No. 2007CB209804) for providing the financial support for this study.

Notation

CP	specific heat/(J•kg-1•K-1)
D	diameter/m
e	error of various parameters
F	correction factor
G	mass flux/(kg•m-2•s-1)
Gr	Grashof number
h	enthalpy/(J•kg-1)
Nu	Nusselt number
p	pressure/MPa
pc	critical pressure/MPa
Pr	Prandtl number
q	heat flux/(W•m-2)
Re	Reynolds number
T	temperature/°C
Tc	critical temperature/°C
y	coordination in radial direction/m
z	coordination in axial direction/m
a	heat transfer coefficient/(W•m-2•K-1)
a0	reference heat transfer coefficient/(W•m-2•K-1)
b	thermal expansion coefficient/K-1
l	Thermal conductivity/(W•m-1•K-1)
m	Dynamic viscosity/(kg•m-1•s-1)
pa	acceleration number
pb	buoyancy number
pc	ratio of specific heat
r	density/( kg•m-3)
subscripts
B	bulk
C	calculated
m	measured
W	wall
pc	pseudo-critical

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