Considerations on CFD studies about heat transfer to supercritical fluids

The paper reports on the activities performed in the last years at the University of Pisa. Heat transfer to supercritical fluids has been a relevant topic since 2005 when it was selected as the main subject of research in the frame of a PhD programme. RANS calculations were performed both adopting commercial and in-house codes. The capabilities of different turbulence models were evaluated highlighting both interesting features and weaknesses. In particular, heat transfer deterioration proved to be the most difficult phenomenon to be predicted as it seems showing a threshold behaviour. In fact, even little changes in the boundary conditions may trigger it and, in addition, further difficulties are due to the fact that, depending on the selected turbulence model, the phenomenon may be predicted whether or not. In the frame of the latest studies, advanced models for the calculation of the turbulent heat fluxes, such as AHFM were considered. At the beginning AHFM was adopted for calculating the production terms of turbulence due to buoyancy only, obtaining interesting results; nevertheless, problems still appear for cases in correspondence of the pseudo-critical temperature. In later analyses, AHFM was also adopted in the energy equation. A full use of the relation was allowed only with the in-house code while when adopting commercial codes the simple gradient approach had to be maintained. Consequently, in the latter case AHFM was used as an advanced tool for calculating the turbulent Prandtl number. Improvements were obtained in particular for near critical conditions, suggesting that the considered approach could be the best one for dealing with supercritical fluids. After this long time of studies, it is time to make a summary of the performed work and learn the lessons drawn, in order to pave the way for further improvements and understandings to be reached in the next years. This is the main purpose of this paper.