A successful local fluid-to-fluid similarity theory for heat transfer to supercritical pressure fluids: merits and limitations

A similarity theory, proposed with a limited success some years ago and subsequently refined in a more complex form in further efforts, has been applied in a recent published work to perform Direct Numerical Simulations (DNS) of heat transfer to turbulent flow, with four different fluids at supercritical pressure. The obtained results showed an exceptionally good behaviour of the theory in the addressed cases, sug- gesting that the initial proposal, though it had only limited success in the cases considered at that time, possibly caught some of the basic features to be preserved in scaling. The theory, based on dimensionless definitions that provided a reasonable degree of universality in the analysis of flow stability, found immediate difficulties to be applied with a comparable success to heat transfer problems. These difficulties mainly stemmed from the fact that, while it is relatively easy to scale fluid density, having a major role in stability analyses, it is definitely much harder to scale at a comparable level of accuracy the fluid thermo-physical properties, relevant in heat transfer. The very good results obtained in the recent work by DNS stimulated new reflections that shed light on the merits and limitations on the old theory. The present paper, starting from these recent results and discussing them in front of RANS calculations, is aimed to highlight the promising features of this theory, envisaging the missing steps that should be completed to make it more general, in order to give to its consequences a higher level of universality.