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This paper presents an analysis of heat-transfer to SuperCritical Water (SCW) in bare vertical tubes. A large set of experimental data, obtained in Russia, was analyzed and a new heat-transfer correlation for SCW was developed. This experimental dataset was obtained within conditions similar to those for proposed SuperCritical Water-cooled nuclear Reactor (SCWR) concepts. Thus, the new correlation presented in this paper can be used for preliminary heat-transfer calculations in SCWR fuel channels. The experimental dataset was obtained for SCW flowing upward in a 4-m-long vertical bare tube. The data was collected at pressures of about 24 MPa for several combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperature. The values ranged for mass flux from 200–1500 kg/m2s, for heat flux up to 1250 kW/m2 and for inlet temperatures from 320 to 350°C. Previous studies have confirmed that there are three heat-transfer regimes for forced convective heat transfer to water flowing inside tubes at supercritical pressures: (1) Normal Heat-Transfer (NHT) regime; (2) Deteriorated Heat-Transfer (DHT) regime, characterized by lower than expected Heat Transfer Coefficients (HTCs) (i.e., higher than expected wall temperatures) than in the NHT regime; and (3) Improved Heat-Transfer (IHT) regime with higher-than-expected HTC values, and thus lower values of wall temperature within some part of a test section compared to those of the NHT regime. Also, previous studies have shown that the HTC values calculated with the Dittus-Boelter and Bishop et al. correlations deviate quite substantially from those obtained experimentally. In particular, the Dittus-Boelter correlation significantly over predicts the experimental data within the pseudocritical range. A new heat-transfer correlation for forced convective heat-transfer in the NHT regime to SCW in a bare vertical tube is presented in this paper. It has demonstrated a relatively good fit for HTC values (±25%) and for wall temperature calculations (±15%) for the analyzed dataset. This correlation can be used for supercritical water heat exchangers linked to indirect-cycle concepts and the co-generation of hydrogen, for future comparisons with other independent datasets, with bundle data, as the reference case, for the verification of computer codes for SCWR core thermalhydraulics and for the verification of scaling parameters between water and modeling fluids.

This paper presents an analysis of heat transfer in water at supercritical conditions in bare vertical tubes. A large dataset within conditions similar to those of SuperCritical Water-cooled nuclear Reactors (SCWRs) was obtained from the Institute for Physics and Power Engineering (Obninsk, Russia). This dataset was compared to existing heat-transfer correlations from the open literature. This comparison is an extension to the previous studies done with this dataset. Previous studies have shown that existing correlations, such as the Dittus-Boelter correlation significantly overestimates the experimental heat transfer coefficient (HTC) values within the pseudocritical range; the Bishop et al. and Jackson’s correlations were also found to deviate significantly from the experimental data. The Swenson et al. correlation provided a better fit for the experimental data, as compared to the previous three correlations within some flow conditions, but deviates from data for other conditions. HTC and wall temperature values calculated with the FLUENT CFD code also deviate from the experimental data within some conditions. After analyzing the existing correlations, it was decided to develop a better correlation for predicting HTC. Since the Swenson et al. correlation seems to be the best candidate for predicting the experimental data; it was selected as a basis for developing a new empirical correlation. The primary difference of the Swenson et al. approach is that it uses the majority of thermophysical properties at the wall temperature as opposed to those used at bulk-fluid temperatures in other models. Calculating various thermophysical properties based on wall temperature seems to give much better results in terms of accuracy. To obtain a basic empirical correlation, a dimensional analysis was conducted using a combination of various dimensionless terms. This approach was combined with the experimental dataset at the normal heat-transfer regime using statistical analysis. The final correlation showed the best fit for the experimental dataset within a wide range of flow conditions. The calculated wall temperatures were within (±15%) for the analyzed dataset, which is a considerable improvement from the previous correlations. The accuracy of calculated values was further improved when a term was added to the correlation that accounted for the entrance effect in bare tubes. Thus, the new correlation presented in this paper can be used for HTC calculations in supercritical-water heat exchangers at SCW Nuclear Power Plants (NPPs) in case of the indirect cycle, in heat exchangers for co-generation of hydrogen from supercritical water side, for a preliminary heat-transfer calculations in SCWR fuel channels as a conservative approach. It can also be used for future comparisons with other independent datasets, with bundled data, for the verification of computer codes for SCWR core thermalhydraulics and for the verification of scaling parameters between water and modeling fluids.

Generation-IV SuperCritical Water-cooled Reactors (SCWRs) are expected to have high thermal efficiencies within the range of 45–50% owing to the reactor’s high pressures and outlet temperatures. The behavior of supercritical water however, is not well understood and most of the methods available to predict the effects of the heat transfer phenomena within the pseudocritical region are based on empirical one-directional correlations which do not capture the multi-dimensional effects and do not provide accurate results in regions such as the deteriorated heat transfer regime. Computational Fluid Dynamics (CFD) is a numerical approach to model fluids in multidimensional space using the Navier-Stokes equations and databases of fluid properties to arrive at a full simulation of a fluid dynamics and heat transfer system. In this work, the CFD code, FLUENT-12, is used with associated software such as Gambit and NIST REFPROP to predict the Heat Transfer Coefficients at the wall and corresponding wall temperature profiles inside vertical bare tubes with SuperCritical Water (SCW) as the cooling medium. The numerical results are compared with experimental data and 1-D models represented by existing empirical correlations. Analysis of the individual heat-transfer regimes is conducted using an axisymmetric 2-D model of tubes of various lengths and composed of different nodalizations along the heated length. Wall temperatures and heat transfer coefficients were analyzed to select the best model for each region (below, at and above the pseudocritical region). Two turbulent models were used in the process: k-ε and k-ω, with variations in the sub-model parameters such as viscous heating, thermal effects, and low-Reynolds number correction. Results of the analysis show a fit of ±10% for the wall temperatures using the SST k-ω model in the deteriorated heat transfer regime and less than ±5% for the normal heat transfer regime. The accuracy of the model is higher than any empirical correlation tested in the mentioned regimes, and provides additional information about the multidimensional effects between the bulk-fluid and wall temperatures.

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