Critical Heat Flux Look-up Table Research Articles

Investigation of Machine Learning Regression Techniques to Predict Critical Heat Flux Over a Large Parameter Space

A unifying and accurate model to predict critical heat flux (CHF) over a wide range of conditions has been elusive since wall boiling research emerged. With the release of the experimental data utilized in the development of the 2006 Groeneveld CHF lookup table (LUT), by far the most extensive public CHF database available to date (nearly 25 000 data points), the development of data-driven prediction models over a large parameter space in simple geometry (vertical, uniformly heated round tubes) can be achieved. Furthermore, the popularization of machine learning techniques to solve regression problems has led to more advanced tools for analyzing large and complex databases. This work compares three machine learning algorithms to predict the CHF database. For each selected regression algorithm (ν-Support vector, Gaussian process, and neural network), a set of optimized hyperparameters is applied. Among the investigated algorithms, the neural network emerges as the most effective, achieving a CHF predicted/measured factor standard deviation of 12.3%, three times less than that of the LUT. In comparison, the Gaussian process regression and the ν-support vector regression achieve a standard deviation of 17.7%, about two times lower than the LUT. Hence, all considered algorithms significantly outperform the LUT prediction performance. The neural network model and training methodology are designed to prevent overfitting, which is confirmed by data analyses of the CHF predictions. Finally, future development directions (including data coverage, transfer learning, and uncertainty quantification) are discussed.

Numerical study on the critical heat flux based on the two-phase multi-scale interface model using OpenFOAM

For the analysis of two-phase phenomena, this work addresses the implementation of the advanced multi-scale interface model of Tentner et al. (2006) into OpenFOAM-7 code, and its assessment for flow boiling in vertical pipes. The model considers the concentration and shape of the interfacial region, as well as the interphase interactions. Two-phase boiling-flow data were used to methodically evaluate this model and its overall propensity to predict the critical heat flux (CHF) was then assessed. Departure from nucleate boiling (DNB) was predicted based on a surface temperature rise, which served as the criterion. The impacts of exit quality, pressure and mass flow velocity on DNB were also addressed. The mean percentage discrepancy found between CHF lookup table and simulated results was 3%, indicating a satisfactory level of agreement. Findings indicate that the implemented two-phase multi-scale interface model in OpenFOAM-7 tool could be utilized in forecasting boiling flow involving flow topology transitions and adequately predict CHF.

Critical heat flux of water in vertical annular channel with a short heated rod under low pressure and low flow conditions

An experimental study on critical heat flux (CHF) has been conducted in a vertical annulus channel with a short heated rod at low pressure and low flow conditions. The heated rod of the test section was made of Inconel-625 with a diameter of 37.2 mm and a heated length of 390 mm. The pressure, inlet temperature and mass flux were varied in the range of 103–170 kPa, 63 −90℃and 59.6–131.9 kg m2 s−1. The CHF phenomenon was observed through the transparent quartz glass. It was found that the CHF positions firstly appeared in a small zone on the heated rod wall and the dry-out area would further expand if the power was not cut off immediately. The experimental results showed that most of CHF data were firstly detected at the upper thermocouple position near the outlet, while CHFs data were observed at lower positions with low mass flux. And based on Mishima and Ishii’s flow regime map, the analysis of experimental flow regime indicated that most of the CHF occurred in slug-churn and churn-annular flow regimes. Finally, the measured CHF data were compared with the results predicted by four commonly used correlations and the method of CHF look-up table, and a new correlation was developed. It was found that the new correlation can be better predicting experimental data with an error within ± 15%.

OpenFOAM CFD simulation of critical heat flux in vertical pipe under typically PWR conditions

This paper aims to see how well the open-source CFD code OpenFOAM can simulate the critical heat flux (CHF) in vertical pipe under extreme conditions, close to PWR operating conditions. The two-fluid approach combined with an extended wall boiling model was used to forecast CHF. The 2006 CHF look-up table was employed as benchmark data. The wall temperature jump was used as the criterion for predicting departure from nucleate boiling (DNB) type CHF. Good agreement was obtained between CHF from look-up table and calculated values. The effects of pressures, mass flow rates, and equilibrium qualities on CHF are investigated. CHF location and maximum volume fraction at corresponding CHF were also obtained. Most of the deviations are within 15% of error. The average absolute error of the simulated CHF was 7%. The findings indicate that OpenFOAM promises to forecast boiling flow and CHF in the PWR reactor fuel assembly geometry.

Fluid-to-Fluid modelling of CHF at High-Pressure subcooled water conditions

An experiment was carried out to obtain data on critical heat flux (CHF) in an 8-mm vertical heated tube cooled with Refrigerant (R-134a) at high-pressure subcooled and low-quality conditions. Parametric trends of the CHF data were examined and have been shown consistent with those obtained in experiments with water flow. Variations of CHF depends mainly on local flow conditions and the length effect appears to be diminished at length-to-diameter (L/D) ratios from 30 to 200. The Katto scaling law has been shown applicable for transforming R-134a CHF values into water CHF values at subcooled and low-quality conditions. The R-134a CHF data have been transformed using the Katto fluid-to-fluid scaling law and assessed against the water CHF values obtained from the 2006 CHF look-up table (LUT-2006). The results showed that the LUT-2006 is conservative and need further development.

Correction factor development for the 2006 Groeneveld CHF look-up table for rectangular channels under low pressure

Similar to commercial nuclear reactors, research reactors are recommended to be designed with sufficient safety margins for thermalhydraulic issues such as critical heat flux (CHF) in both normal and accident conditions. In the MARS-KS system code, developed based on RELAP5, the 2006 Groeneveld CHF look-up table (Groeneveld et al., 2007) is adopted to predict CHF for plate-type fuel. The applicability of this table to CHF in rectangular channels for high pressure conditions of over 40 bar has been confirmed (Choi et al., 2015); however, its applicability to pressure conditions under 40 bar has yet to be clarified. While Sudo and Kaminaga previously suggested a rectangular CHF model for a wide experimental range, some notifications have indicated the inclusion of flow excursion data in their model. In this paper, a rectangular channel CHF database was constructed for wide experimental ranges and used to assess the 2006 Groeneveld CHF look-up table and Sudo-Kaminaga correlation to confirm their applicability to rectangular channels under low pressure. Then, with several parameters selected by the Random Forest method in the R package (Reynolds number, quality, aspect ratio, diameter ratio, and length over diameter), a new correction factor was suggested by applying a non-linear regression method from a statistical software package to correct the CHF values in the CHF look-up table for rectangular channels. Results confirmed that the CHF LUT with the newly suggested correction factor is capable to predict CHF in rectangular channels.

Comparison of steady and transient flow boiling critical heat flux for FeCrAl accident tolerant fuel cladding alloy, Zircaloy, and Inconel

Steady and transient (with a heating rate of 685 °C/s) internal-flow CHF (Critical Heat Flux) experiments were conducted under atmospheric pressure at a fixed inlet temperature (40 °C or 60 °C) and mass flow (300 kg/m2 s) on Fe-13Cr-6Al alloy, Inconel 600 and Zircaloy-4 tube samples. Multiple experiments were repeated on the same specimen to investigate the effect of surface characteristic changes (i.e., roughness, wettability, and oxide scale morphology) on the occurrence of CHF. Despite notable changes of wettability, roughness, and oxide layer characteristics on samples that had already been subjected to CHF, measured flow CHF remained unchanged throughout repeated experiments for tested materials. This demonstrates that the surface effects on flow CHF are limited in the test conditions. In the steady-state flow boiling condition, Fe-13Cr-6Al alloy demonstrated a 22% and 14% increase in CHF compared to Zircaloy-4 and Inconel 600, respectively. Compared to the 2006 Groeneveld CHF lookup table, Fe-13Cr-6Al alloy gives a 13% increase in the tested flow boiling condition. Material properties are considered primarily responsible for the observed CHF differences among the tested materials. The surface thermal economy parameter (ρcp3/2k) is proposed as an explanation for the observed CHF differences; this parameter is related to material’s ability to avoid an irreversible dry spot formation. The apparent disagreement of Zircaloy-4 CHF with both the look up table predictions and Inconel 600 shows the limitation of departure of nucleate boiling (DNB) evaluations that do not consider cladding materials. The transient Fe-13Cr-6Al CHF is 39% and 23% higher than the lookup table prediction and the steady-state condition experimental result, respectively.

Experimental Investigation on Critical Heat Flux for Water Flowing in a Vertical Uniformly Heated Rifled Tube under Near-critical Pressures

This study experimentally investigated the critical heat flux (CHF) of departure from nucleate boiling (DNB) of water flowing under near-critical pressures in a 2 m-long vertical upward rifled tube with the size of ϕ35 × 5.67 mm. Operating conditions included pressures of 18–21 MPa, mass fluxes of 475–1000 kg·m−2·s−1, inlet subcooling temperatures of 3–5°C, and wall heat fluxes of 40–960 kW·m−2. Tube wall temperature distribution and heat transfer performance in different test conditions were obtained. The effects of the operating parameters on CHF were analyzed. Four heat transfer coefficient correlations were evaluated against our experimental data for further investigation of the two-phase heat transfer characteristics. A heat transfer correlation based on Martinelli number utilized in two-phase region and two empirical correlations used to predict the CHF in rifled tube at near-critical pressures were proposed. Meanwhile, experimental CHF data in rifled tube were compared with six widely used correlations and a CHF look-up table. The CHF enhancement effect in rifled tube is obvious as compared with the CHF data in smooth tube. Results show that DNB occurs at low vapor quality and subcooled region in the rifled tube at near-critical pressures. The increase in pressure leads to the early occurrence of DNB and the decrease in CHF, whereas the increase in mass flux delays the occurrence of DNB and results in the increase in CHF. DNB presents a tendency to move toward the inlet of the rifled tube. At individual operating conditions, DNB and dryout coexist at different sections of the rifled tube.

Transient Heat Transfer in an Out-of-Pile SCWR Fuel Assembly Test at Near-Critical Pressure

While supercritical water is a perfect coolant with excellent heat transfer, a temporary decrease of the system pressure to subcritical conditions, either during intended transients or by accident, can easily cause a boiling crisis with significantly higher cladding temperatures of the fuel assemblies. These conditions have been tested in an out-of-pile experiment with a bundle of four heated rods in the supercritical water multipurpose loop (SWAMUP) facility coconstructed by CGNPC and SJTU in China. Some of the transient tests have been simulated at KIT with a one-dimensional (1D) matlab code, assuming quasi-steady-state flow conditions, but time dependent temperatures in the fuel rods. Heat transfer at supercritical and at near-critical conditions was modeled with a recent look-up table of Zahlan (2015, “Derivation of a Look-Up Table for Trans-Critical Heat Transfer in Water Cooled Tubes,” Ph.D. dissertation, University of Ottawa, Ottawa, ON, Canada.), and subcritical film boiling was modeled with the look-up table of Groeneveld et al. (2003, “A Look-Up Table for Fully Developed Film Boiling Heat Transfer,” Nucl. Eng. Des., 225(1), pp. 83–97.). Moreover, a conduction controlled rewetting process was included in the analyses, which is based on an analytical solution of Schulenberg and Raqué (2014, “Transient Heat Transfer During Depressurization From Supercritical Pressure,” Int. J. Heat Mass Transfer, 79(12), pp. 233–240.). The method could well reproduce the boiling crisis during depressurization from supercritical to subcritical pressure, including rewetting of the hot zone within some minutes, but the peak temperature was somewhat under-predicted. Tests with a lower heat flux, which did not cause such phenomena, could be predicted as well. In another test with increasing pressure, however, a boiling crisis was also observed at a heat flux, which was significantly lower than the critical heat flux (CHF) predicted by the CHF look-up table of Groeneveld et al. (2007, “The 2006 CHF Look-Up Table,” Nucl. Eng. Des., 237(15–17), pp. 1909–1922.). The paper is summarizing the physical models and the numerical approach. Comparison with experimental data is used to discuss the applicability of the method for the design of supercritical water-cooled reactors (SCWR).

Assessment of RELAP5 CHF prediction methods against experimental tube data

Under particular conditions, boiling may lead to sudden and catastrophic phenomena called critical heat flux (CHF). Therefore, better CHF predictions by system codes such as RELAP5 are seen to be important for system safety and operations. Hence, a set of 1145 water CHF data points for vertical up flow covering a wide range of different parameters have been used to assess the CHF prediction methods in RELAP5. The RELAP5 code uses two methods: the 1986 AECL-UO critical heat flux lookup table method and the PG-CHF correlations. In addition, results obtained from the recent lookup tables of 1995 and 2006 are included in the plots and used to support the conclusions and to perform a comparative study of the methods used by the code. Compared to the look-up tables and correlations, the present study showed a good agreement with the experimental data for the basic form of the PG-CHF correlations illustrated by a good statistics (99.4% of predictions are within ±20% and with a root mean square error of 6.44%).

An empirical correlation for the entrainment fraction at the onset of annular flow based on 2006 CHF look-up table

The critical heat flux (CHF) of gas-liquid flow plays an important role in the safety of industrial equipment. At present, the liquid film dryout model is widely used for predicting CHF in gas-liquid annular flow. Most parameters in this model can be determined by some empirical correlations which are valid under different conditions. However, up to now, the entrainment fraction at the onset of annular flow is always assumed due to the lack of relevant experimental data. In this paper, the normalized data of the 2006 CHF look-up table (LUT) which has been adopted widely, especially in the nuclear industry, were used. Firstly, the empirical correlations, provided for the onset of annular flow and the limiting quality, were employed. In the valid pressure and mass flux range of these correlations, the selected database from LUT was confirmed. Secondly, the liquid film model was built. The entrainment fraction at the onset of annular flow was obtained when the calculated CHF by the model agreed with the corresponding value in LUT. A parallel look-up table for it was developed. Its correlation including the Weber and the liquid Reynolds number at outlet was proposed. The errors are mostly within ±30%. Finally, its reliability on the other conditions in LUT, which are beyond the valid range of the empirical correlations used for determining the database, was discussed. All the conditions whose errors are outside ±30% of the predictions by the provided correlation were marked in the tables.

Evaluation of a uranium zirconium hydride fuel rod option for conversion of the MIT research reactor (MITR) from highly-enriched uranium to low-enriched uranium

The conversion of the Massachusetts Institute of Technology Reactor (MITR) from the use of highly-enriched uranium (HEU) fuel-plate assemblies to low-enriched uranium (LEU) by replacing the HEU fuel plates with specially designed General Atomics (GA) uranium zirconium hydride (UZrH) LEU fuel rods is evaluated. The margin to critical heat flux (CHF) in the core, which is cooled by light water at low pressure, is evaluated analytically for steady-state operation. A form of the Groeneveld CHF lookup table method is used and described in detail. A CHF ratio of 1.41 was found in the present analysis at 10MW with engineering hot channel factors included. Thus, the nominal reactor core power, and neutron flux performance, would need to be reduced by at least 25% in order to meet the regulatory requirement of a minimum CHF ratio of 2.0.

A Discussion of Uncertainty Quantification for CHF as Performed in COBRA-IE

An assessment of the predictive capability of Coolant Boiling in Rod Arrays—Integrated Environment (COBRA-IE) for critical heat flux (CHF) using the 2005 Groeneveld CHF lookup table is presented. The assessment was performed against 13 different open literature CHF experiments that were conducted over a wide range of conditions in various internal flow geometries. Overall, approximately 1300 data points were evaluated.Different methodologies to quantify the uncertainty inherent in the CHF models are discussed in this paper. The simulation techniques, uncertainty methods, and results of two of the methods are provided. A discussion of the appropriate use of the CHF uncertainty methods is included. The results indicate that for the method associated with the largest uncertainty, the average measured/predicted value in CHF is 1.19, and the standard deviation is 0.62. For the second method, similar to the critical power ratio used for boiling water reactors, the average ratio is 0.98, and the standard deviation is 0.13. Finally, a method to translate between the methods is proposed and shown to be accurate. The use of this transformation could permit significant time and cost savings by allowing a single uncertainty assessment to serve two very different analytical needs.

Critical heat flux of highly subcooled water flow boiling in circular tubes with and without internal twisted tapes under high mass fluxes

This study focuses on the critical heat flux (CHF) of highly subcooled water flow boiling under high mass fluxes, particularly with respect to the thermal–hydraulics analysis in fusion reactor components. The experiments were performed in vertical circular tubes those were uniformly heated by a large AC power supply. Twisted tape was employed to induce swirl flow in order to further enhance the subcooled CHF. This study obtained several high CHF data points in both smooth tubes and twisted-tape tubes, which can enhance relevant high-CHF databases. The influences of thermodynamic quality, mass flux, pressure, and twisted tape on subcooled CHF were discussed. The results show that twisted tapes can allow significant increase in subcooled CHF under high mass fluxes. The CHF enhancement effect is more obvious when using twisted tapes with smaller twist ratios. Available existing subcooled CHF correlations were compared with the experimental data from the present and others’ studies for both smooth tubes and twisted-tape tubes. For smooth tubes, the CHF look-up table has satisfactory prediction accuracy. For twisted-tape tubes, a modified correlation of Arment et al. was proposed to predict the swirl-flow subcooled CHF.

Application of the Critical Heat Flux Look-Up Table to Large Diameter Tubes

The critical heat flux look-up table was applied to a large diameter tube, namely 67 mm inside diameter tube, to predict the occurrence of the phenomenon for both vertical and horizontal uniformly heated tubes. Water was considered as coolant. For the vertical tube, a diameter correction factor was directly applied to the 1995 critical heat flux look-up table. To predict the occurrence of critical heat flux in horizontal tube, an extra correction factor to account for flow stratification was applied. Both derived tables were used to predict the effect of high heat flux and tube blockage on critical heat flux occurrence in boiler tubes. Moreover, the horizontal tube look-up table was used to predict the safety limits of the operation of boiler for 50% allowable heat flux.

Applications of genetic neural network for prediction of critical heat flux

In this study, the data set of the 2006 CHF look-up table is partitioned into five subsets by using Fuzzy c-means (FCM) clustering algorithm. The elements of the same subset are ‘similar’ to each other in some sense while those assign to different subsets are ‘dissimilar’. At the same time, a Genetic Neural Network (GNN) model for predicting critical heat flux (CHF) is set up. It has some advantages of its globe optimal searching, quick convergence speed and solving non-linear problem. The methods of establishing the model and training of GNN are discussed particularly in the article. Local condition type CHF is predicted by GNN on the basis of 6930 CHF data from the 2006 CHF look-up table. The prediction results are consistent with database very well. Next, the mainly parametric trends of the CHF are analyzed by applying GNN. At last, prediction of dryout point is investigated by GNN with distilled water flowing upward through narrow annular channel with 0.95 mm and 1.5 mm gaps, respectively. The prediction results by GNN have a good agreement with experimental data. Simulation and analysis results show that the network model can effectively predict CHF.

Diameter effect on critical heat flux

The critical heat flux look-up table (CHF LUT) is widely used to predict CHF for various applications, including design and safety analysis of nuclear reactors. Using the CHF LUT for round tubes having inside diameters different from the reference 8 mm involves conversion of CHF to 8 mm. Different authors [Becker, K.M., 1965. An Analytical and Experimental Study of Burnout Conditions in Vertical Round Ducts, Aktiebolaget Atomenergie Report AE 177, Sweden; Boltenko, E.A., et al., 1989. Effect of tube diameter on CHF at various two phase flow regimes, Report IPE-1989; Biasi, L., Clerici, G.C., Garriba, S., Sala, R., Tozzi, A., 1967. Studies on Burnout, Part 3, Energia Nucleare, vol. 14, pp. 530–536; Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. AECL-UO critical heat flux look-up table. Heat Transfer Eng., 7, 46–62; Groeneveld et al., 1996; Hall, D.D., Mudawar, I., 2000. Critical heat flux for water flow in tubes – II subcooled CHF correlations. Int. J. Heat Mass Transfer, 43, 2605–2640; Wong, W.C., 1996. Effect of tube diameter on critical heat flux, MaSC dissertation, Ottawa Carleton Institute for Mechanical and Aeronautical Engineering, University of Ottawa] have proposed several types of correlations or factors to describe the diameter effect on CHF. The present work describes the derivation of new diameter correction factor and compares it with several existing prediction methods.

Investigation on the characteristic of CHF in various flow pattern regimes based on look-up table data

The critical heat flux (CHF) is one of the important phenomena limiting the maximum rate of heat transfer and hence power rating of nuclear reactors. The thermal hydraulic phenomena like pressure drop, heat transfer, stability, etc. depends upon the flow pattern in the system. The CHF phenomenon is also closely related to the two-phase flow patterns. It is important to investigate the dependence of CHF on the flow pattern regimes to understand the underlying mechanisms. The present investigation reveals that CHF generally increases with mass flux in the churn/slug region. However, in the annular region the CHF decreases with increase in mass flux. Considering the dependency of the CHF trend on the flow pattern regime, it will be useful to develop CHF models, which are specific to the flow pattern regime. The data of CHF look-up table has been considered in this investigation since this approach is one of the most reliable methods for the prediction of CHF and is being used in several best-estimate thermal-hydraulic system codes, such as RELAP5, CATHARE and CATHENA. The pressure, mass flux and quality have been considered as important thermal hydraulic parameters to characterize the flow pattern during CHF under various operating condition.

The 2006 CHF look-up table

CHF look-up tables are used widely for the prediction of the critical heat flux (CHF). The CHF look-up table is basically a normalized data bank for a vertical 8 mm water-cooled tube. The 2006 CHF look-up table is based on a database containing more than 30,000 data points and provides CHF values at 24 pressures, 20 mass fluxes, and 23 qualities, covering the full range of conditions of practical interest. In addition, the 2006 CHF look-up table addresses several concerns with respect to previous CHF look-up tables raised in the literature. The major improvements of the 2006 CHF look-up table are: • An enhanced quality of the database (improved screening procedures, removal of clearly identified outliers and duplicate data). • An increased number of data in the database (an addition of 33 recent data sets). • A significantly improved prediction of CHF in the subcooled region and the limiting quality region. • An increased number of pressure and mass flux intervals (thus increasing the CHF entries by 20% compared to the 1995 CHF look-up table). • An improved smoothness of the look-up table (the smoothness was quantified by a smoothness index). A discussion of the impact of these changes on the prediction accuracy and table smoothness is presented. The 2006 CHF look-up table is characterized by a significant improvement in accuracy and smoothness.

Modeling capability of R134a for a critical heat flux of water in a vertical 5 × 5 rod bundle geometry

Critical heat flux (CHF) tests have been performed for a vertically upward R134a flow in a 5 × 5 rod bundle in the following parameter ranges: outlet pressure 1.5–3.0 MPa, mass flux 50–2500 kg m −2 s −1, inlet quality −0.08 to −0.75 and critical quality −0.17 to 1.58. Parametric trends of the CHF data agree well with the general understanding. Water equivalent CHF data is generated using a set of well-established modeling parameters, then compared with (a) the EPRI/Colombia University’s water CHF database for similar geometry and experimental conditions and (b) commonly used CHF prediction methods. The water equivalent CHF data generated from the present tests shows a good agreement with the actual water CHF data for both Katto’s and Ahmad’s modeling methods when considering the differences in the detailed geometric and flow conditions. They are also predicted well by the 1995 CHF look-up table. These results indicate that R134a can be a good modeling fluid for the CHF of water in rod bundles at least in the investigated parameter ranges.