A methodology for including wall roughness effects in k-ɛ low-Reynolds turbulence models

A model accounting for wall roughness effects in k-ε low-Reynolds turbulence models is described in the present paper. In particular, the introduction in the transport equations of k and ε of additional source terms related to roughness, based on simple assumptions and dimensional relationships, is proposed. An objective of the present paper, in addition to obtaining more realistic predictions of wall friction, is the application of the proposed model to the study of heat transfer to supercritical fluids. A first validation of the model is reported. The model shows the capability of predicting, at least qualitatively, some of the most important trends observed when dealing with rough pipes in very different flow conditions. Qualitative comparisons with some DNS data available in literature are also performed. Further analyses provided promising results concerning the ability of the model in reproducing the trend of friction factor when varying the flow conditions, though improvements are necessary for achieving better quantitative accuracy. First applications of the model in simulating heat transfer to supercritical fluids are also described, showing the capability of the model to affect the predictions of these heat transfer phenomena, in particular in the vicinity of the pseudo-critical conditions. A more extended application of the model to relevant deteriorated heat transfer conditions will clarify the usefulness of this modelling methodology in improving predictions of these difficult phenomena. Whatever the possible success in this particular application that motivated its development, this approach suggests a general methodology for accounting for wall roughness effects in low-Reynolds number turbulence models