On the mechanism of final heat transfer restoration at the transition to gas-like fluid at supercritical pressure: A description by CFD analyses

A successful general fluid-to-fluid similarity theory for heat transfer at supercritical pressure

“…The RANS analyses presented hereafter were performed by following (or rather establishing) the similarity rules reported as guideline for future applications in the next section. The adopted CFD code is STAR-CCM+, in one of its latest versions [30] , and the turbulence model is the k-ε low-Reynolds one by Lien [31] , modified by the adoption of available user features, equipping it with an additional transport equation necessary for the use of an Algebraic Heat Flux model (AHFM) (see, e.g., [ 20 , 22 , 23 ] for details). The discretisation techniques are typical of the applications of low-Reynolds number models and are quite the same as described in previous mentioned works, in which the reader can find thorough descriptions.…”

“…A passive scalar equation was introduced to represent the transport of the averaged square temperature fluctuations, while an algebraic equation was used for its dissipation. Again, for further details the reader may consider references [ 20 , 22 , 23 ].…”

“…16 from the carbon dioxide database by Kline [29] were selected both for the good prediction obtained by the adopted model (see [23] for a through discussion of model capabilities and limitations in relation to these data) and because they represent bounding phenomena. On the one side, the case with lower inlet temperature exhibits a severe deterioration, beyond the pseudocritical threshold, with wall temperature oscillations and the occurrence of a final recovery of heat transfer at the transition to the gas-like phase (see [23] for a discussion of the phenomenon). The second case is instead characterised by the lack of deterioration phenomena, since the inlet subcooling is very low and buoyancy forces have not enough strength to produce laminarisation and the subsequent deterioration.…”

“…it improved the predictive capabilities of CFD models, successfully trying the use of Algebraic Heat Flux Models (AHFM) suggested in previous literature [19] : this made more reliable the CFD predictions performed for comparing the behaviour of different fluids (see, e.g.,[ 20 , 21 ] and the more recent works [ 22 , 23 ]);…”

“…A turning point in the research was represented by the doctoral thesis of one of the co-authors of this paper (A.P.) [18] which provided a contribution in two key areas for the establishment of a similarity theory: it improved the predictive capabilities of CFD models, successfully trying the use of Algebraic Heat Flux Models (AHFM) suggested in previous literature [19] : this made more reliable the CFD predictions performed for comparing the behaviour of different fluids (see, e.g.,[ 20 , 21 ] and the more recent works [ 22 , 23 ]); it revised and updated the old rationale for similarity proposed in previous works, also abandoning the preservation of geometrical similarity in circular pipes (in terms of the equality of the length over diameter ratio); in fact, it was noted that its effects for heated fluids at supercritical pressure are weaker in view of the continuous development of the flow due to property changes: this led to a first publication proposing an extended rationale for heat transfer similarity [24] . Then, a recent paper presented by the group of Prof.…”