Abstract
The recent advancements achieved in the development of a fluid-to-fluid similarity theory for heat transfer with fluids at supercritical pressures are summarised. The prime mover for the development of the theory was the interest in the development of Supercritical Water nuclear Reactors (SCWRs) in the frame of research being developed worldwide; however, the theory is general and can be applied to any system involving fluids at a supercritical pressure. The steps involved in the development of the rationale at the basis of the theory are discussed and presented in a synthetic form, highlighting the relevance of the results achieved so far and separately published elsewhere, with the aim to provide a complete overview of the potential involved in the application of the theory. The adopted rationale, completely different from the ones in the previous literature on the subject, was based on a specific definition of similarity, aiming to achieve, as much as possible, similar distributions of enthalpies and fluid densities in a duct containing fluids at a supercritical pressure. This provides sufficient assurance that the complex phenomena governing heat transfer in the addressed conditions, which heavily depend on the changes in fluid density and in other thermophysical properties along and across the flow duct, are represented in sufficient similarity. The developed rationale can be used for planning possible counterpart experiments, with the aid of supporting computational fluid-dynamic (CFD) calculations, and it also clarifies the role of relevant dimensionless numbers in setting up semi-empirical correlations for heat transfer in these difficult conditions, experiencing normal, enhanced and deteriorated regimes. This paper is intended as a contribution to a common reflection on the results achieved so far in view of the assessment of a sufficient body of knowledge and understanding to base successful predictive capabilities for heat transfer with fluids at supercritical pressures.
Highlights
Fluids at supercritical pressures exhibit a complex variety of convective heat transfer behaviours, ranging from “normal heat transfer”, similar to the one observed in fluids with little property changes, to “enhanced heat transfer”, mainly caused by the larger specific heat occurring at a pressure-dependent temperature threshold defined as “pseudocritical”, to “deteriorated heat transfer”, occurring owing to a combination of factors mainly depending on the fluid property changes
This situation could not be considered satisfactory, and subsequent works concentrated on the assessment and the development of more reliable turbulence models; this effort was rewarded by better predictions at least in some operating ranges [16,17,18,19,20] owing to the use of an algebraic heat flux model (AHFM) and to its implementation in a low-Re turbulence model adopted in a commercial code [21]
The trends of the fluid properties at supercritical pressures for the two relevant fluids shown in Figures 1 and 2, water at 25 MPa as the coolant proposed for most Supercritical Water nuclear Reactors (SCWRs) concepts and used in the experimental data by Watts [27] and CO2 at 8.35 MPa, adopted in some of the experiments taken into account in a recent work [28], justify the complexities exhibited by the observed heat transfer phenomena
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The use of CFD models was, at that time, highly unreliable, since the deficiencies in two-equation turbulence models were well-known, with k-ε models showing a tendency to overestimate heat transfer deterioration, while, in many instances, k-ω models showed some degree of insensitivity to the onset of heat transfer deterioration [14,15] This situation could not be considered satisfactory, and subsequent works concentrated on the assessment and the development of more reliable turbulence models; this effort was rewarded by better predictions at least in some operating ranges [16,17,18,19,20] owing to the use of an algebraic heat flux model (AHFM) and to its implementation in a low-Re turbulence model adopted in a commercial code [21]. The predicted phenomena were assessed both in dimensional and dimensionless forms, in order to assure that both qualitative and quantitative features of the bulk and wall temperature trends were sufficiently well-represented This rationale requests, firstly, a check of the RANS model in front of reliable experimental data and, the extrapolation to other fluids with “similar” boundary conditions. Since the theory may be considered for planning confirmatory experiments, independent checks are expected to be made by other research groups in order to possibly confirm and refine the similarity principles at the basis of the present rationale
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
