Fluid Flow and Heat Transfer at Supercritical Pressure
NURETH-14 - 2011 September 25-30

Presented at:
2011 September 25-30
Toronto, Canada
Session Title:
A12-1 Introductory Session on Non-Unity Prandtl Number Flows

J. D. Jackson (University of Manchester)


The feature of fluids at supercritical pressure which makes them of special interest is, continuous transition from a liquid-like to a gas-like state with increase of temperature at constant pressure accompanied by variation of properties over a particular band of temperature within which the specific heat reaches its peak value (the pseudocritical point). At pressures just above the critical value this band of temperature is very narrow, the peak is high and it is very sharp. As a consequence of the extreme dependence on temperature of fluid properties under such conditions the equations which govern fluid flow and heat transfer are very non-linear and strongly inter-linked. Thus, some of the simplifying concepts and assumptions which are widely employed in the case heat transfer to conventional fluids (such as fully developed flow and negligible influence of buoyancy and thermal expansion) no longer apply. Non-uniformity of density, can lead to important effects on the mean flow and turbulence fields and the effectiveness of heat transfer. When the author and his colleagues commenced work on supercritical pressure fluids almost fifty years ago they were very conscious of these challenges. Therefore, after carrying out a careful review of the literature they made the decision to begin with a novel experiment specifically designed to include effects of strong non-uniformity of fluid properties on heat transfer without involving the particular complications identified above. This very challenging experiment on stably-stratified turbulent flow of carbon dioxide at slightly supercritical pressure between two horizontal planes, with the upper one heated and the lower one cooled in such a way that there was no net heat transfer, yielded interesting results and some evidence of a special mechanism for enhancement of turbulent mixing. Non-dimensional representation of the governing equations and boundary conditions for flow and heat transfer in vertical tubes of fluids with highly temperature dependent properties enabled the appropriate dimensionless groups to be identified and the conditions for similarity to be rigorously specified. Experiments with uniformly heated vertical tubes using carbon dioxide at pressures very near to the critical value produced results, which in some cases exhibited very striking features. On increasing the imposed heat flux or reducing mass flow rate, severe localized non-uniformity of heat transfer developed in the case of upward flow. This was manifested by sharp, wall temperature peaks which were not observed with downward flow. These observations, provided clear evidence of gravitationally-induced motion leading to effects on heat transfer which could only be explained by postulating drastic modification of turbulence. This stimulated the development of a physically-based criterion for determining the conditions under which such effects might occur and led, eventually, to the development of a physically-based, semi-empirical model of buoyancy-influenced heat transfer with effects of thermal expansion. The aim of this lecture is to show how such early work is now providing a basis for correlating experimental data on heat transfer to supercritical pressure fluids and enabling the complicated phenomena encountered with such fluids to be better understood and properly accounted for in thermal design procedures.

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