A model of developing mixed convection heat transfer in vertical tubes to fluids at supercritical pressure

The physical and transport properties of fluids at pressures just above the critical value change very rapidly with temperature over a particular range where such fluids make the transition from being liquid-like to gas-like. Consequently, when heat transfer takes place within them, strong spatial non-uniformity of density can be encountered. Problems can then arise as a result of the influence of buoyancy on mean flow, turbulence and heat transfer. Partial laminarisation of the flow accompanied by severe deterioration of heat transfer and localised overheating sometimes occur. The empirical equations currently available for calculating heat transfer to fluids at supercritical pressure are not able to account for such effects. Thus, with the aim of achieving an improved understanding of the physics of such flows and also constructing a sound, theoretically-based, empirical framework able to support reliable calculational procedures, the author has extended an existing semi-empirical model of fully developed mixed convection in vertical tubes to account for, non-uniformity of fluid properties, inertia and axial development of the effect of buoyancy on heat transfer. Firstly, the approach used to incorporate non-uniformity of fluid properties into the model is presented. Next the method adopted for bridging the discontinuous heat transfer behaviour exhibited by the model is described. Finally, two possible approaches designed to capture the observed axial development of buoyancy-influence on heat transfer are presented. Computational work is in progress using the extended model to try to reproduce the heat transfer behaviour found in experiments with water at supercritical pressure. Preliminary results have indicated that the extended model is valid for downward flow and that it is capable of reproducing the impairment of heat transfer found with upward flow. The work is ongoing and an interim report on it is presented here. (author)