Developing New Heat-Transfer Correlation for SuperCritical-Water Flow in Vertical Bare Tubes

Abstract

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.

An assessment of correlations of forced convection heat transfer to water at supercritical pressure

“…The accuracies of the Gupta et al (2010) and Swenson et al (1965) correlations are very close, having the MAD less than 18.5% and predicting about 80% of the experimental data in the deteriorated heat transfer regime within ±20%. The Xu et al (2005) correlation has the smallest RMSD (31.3%) and SD (31.1%) and predicts 66.2% of the deteriorated data within ±20%.…”

“…The McAdams (1942) correlation has the smallest MAD (10.3%), RMSD (14.2%), and SD (11.1%), predicting 82.8% of the experimental data in the enhanced heat transfer regime within ±20% and 94.4% within ±30%. (4) For the deteriorated heat transfer regime, the correlations of Gupta et al (2010), Swenson et al (1965), and Xu et al (2005) are the most promising ones. The Gupta et al (2010) correlation has the smallest MAD of 18.1%, predicting 77.6% of the experimental data in the deteriorated heat transfer regime within ±20%, and 86.8% within ±30%.…”

“…(4) For the deteriorated heat transfer regime, the correlations of Gupta et al (2010), Swenson et al (1965), and Xu et al (2005) are the most promising ones. The Gupta et al (2010) correlation has the smallest MAD of 18.1%, predicting 77.6% of the experimental data in the deteriorated heat transfer regime within ±20%, and 86.8% within ±30%. The Xu et al (2005) correlation has the smallest RMSD (31.3%) and SD (31.1%), predicting 66.2% of the deteriorated heat transfer data within ±20% and 84.6% within ±30%.…”

Developing empirical heat-transfer correlations for supercritical CO2 flowing in vertical bare tubes

“…7 and 8). New correlations developed for SCW - Mokry et al (2009b and Gupta et al (2011), which show good results for SCW data, cannot be directly applied to SCCO 2 , as thermophysical properties of these two fluids differ significantly (refer to discussion in Section 2). Therefore, empirical heat-transfer correlations based on bare-tube SCCO 2 data and its latest thermophysical properties should be developed.…”

“…Please refer to previous publications by Gupta et al (2010Gupta et al ( , 2011, Figs. 1 and 2 and Appendix A, for explanation of these terms.…”