Developing New Heat-Transfer Correlation for SuperCritical-Water Flow in Vertical Bare Tubes
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Bibliographic record
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.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it