An Semi-Empirical Model of Turbulent Convective Heat Transfer to Fluids at Supercritical Pressure

Recently, there has been a renewed interest in heat transfer to fluids at supercritical pressure because of the consideration now being given to the Supercritical Pressure Water-cooled Reactor (SPWR). This will supply high temperature ‘steam’ to turbines at pressures well above the critical value. The particular feature of fluids at pressures just above the critical pressure which makes them of special interest is that as they change from being liquid-like to gaseous the transition occurs in a continuous manner over a narrow band of temperature without the discontinuous behaviour encountered when phase occurs in fluids at sub-critical pressure. However, when heat takes place within fluids at supercritical pressure, extreme non-uniformities of physical and transport properties can be present. The governing equations for flow and convective heat transfer have to be written in a form which takes account of the temperature dependence of the properties. They are complicated, highly non-linear and strongly inter-dependent. The proportionality between heat flux and temperature difference found in constant property forced convection no longer exists. Also, the effectiveness of heat transfer can be very sensitive to imposed heat flux. Particular problems arise due to the non-uniformity of density by virtue of the fluid being caused to accelerate where the bulk density is falling or as a consequence of the flow field and turbulence being modified by the influence of buoyancy. Severe impairment on heat transfer can be encountered due to such effects. The requirements for achieving similarity and the approach to the correlation of data on heat transfer to fluids at supercritical pressure are matters that need to be carefully considered and soundly based. This necessitates representing the general form of the governing equations and the boundary conditions in non-dimensional form to identify the parameters that are involved. In this paper, an extended model of turbulent heat transfer to fluids at supercritical pressure is presented which utilises a semi-empirical multiplier to account for the combined effects of flow acceleration and buoyancy.