Development of supercritical water heat-transfer correlation for vertical bare tubes

This paper presents an analysis of heat-transfer to supercritical water in bare vertical tubes. A large set of experimental data, obtained in Russia, was analyzed and a new heat-transfer correlation for supercritical water was developed. This experimental dataset was obtained within conditions similar to those in supercritical water-cooled nuclear reactor (SCWR) concepts.The experimental dataset was obtained in supercritical water flowing upward in a 4-m long vertical bare tube with 10-mm ID. The data were collected at pressures of about 24 MPa, inlet temperatures from 320 to 350 °C, values of mass flux ranged from 200 to 1500 kg/m² s and heat fluxes up to 1250 kW/m² for several combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperature.A dimensional analysis was conducted using the Buckingham Π-theorem to derive the general form of an empirical supercritical water heat-transfer correlation for the Nusselt number, which was finalized based on the experimental data obtained at the normal and improved heat-transfer regimes. Also, experimental heat transfer coefficient (HTC) values at the normal and improved heat-transfer regimes were compared with those calculated according to several correlations from the open literature, with CFD code and with those of the proposed correlation.The comparison showed that the Dittus-Boelter correlation significantly overestimates experimental HTC values within the pseudocritical range. The Bishop et al. and Jackson correlations tended also to deviate substantially from the experimental data within the pseudocritical range. The Swenson et al. correlation provided a better fit for the experimental data than the previous three correlations at low mass flux (∼500 kg/m² s), but tends to overpredict the experimental data within the entrance region and does not follow up closely the experimental data at higher mass fluxes. Also, HTC and wall temperature values calculated with the FLUENT CFD code might deviate significantly from the experimental data, for example, the k-? model (wall function). However, the k-? model (low Reynolds numbers) shows better fit within some flow conditions.Nevertheless, the proposed correlation showed the best fit for the experimental data within a wide range of flow conditions. This correlation has an uncertainty of about ±25% for calculated HTC values and about ±15% for calculated wall temperature. A final verification of the proposed correlation was conducted through a comparison with other datasets. It was determined that the proposed correlation closely represents the experimental data and follows trends closely, even within the pseudocritical range. Finally, a recent study determined that in the supercritical region, the proposed correlation showed the best prediction of the data for all three sub-regions investigated.Therefore, the proposed correlation can be used for HTC calculations in SCW heat exchangers, for preliminary HTC calculations in SCWR fuel bundles as a conservative approach, for future comparison with other datasets and for the verification of computer codes and scaling parameters between water and modelling fluids.