Boiling Heat Transfer Correlations Research Articles

A knowledge gap analysis for transient CHF prediction within RELAP5-3D

We compare several experimental pool and flow boiling critical heat flux experiments with corresponding computational models developed with RELAP5-3D. Encompassed within this paper are several sensitivity analyses for the boiling heat transfer correlations, critical heat flux (CHF) prediction within RELAP5-3D and the thermal properties of the cladding for experiments in the Transient Reactor Test Loop (TRTL) and Transient Reactor Test (TREAT) facilities. The sensitivity analyses were consistent in determining that there is a large contribution from the critical heat flux multiplier which in this application, accounts for the effects of power transient critical heat flux. Comparison to experimental results of both the TREAT CHF-SERTTA experimental campaign and a University of New Mexico (UNM) pool boiling experimental campaign demonstrate both the under-prediction of transient CHF and nucleate boiling heat transfer. To address the gaps in knowledge regarding the transient heating effect for both boiling heat transfer and CHF prediction, we present an experimental test matrix for the TRTL facility that will isolate the power transient effect under PWR relevant operational conditions. The test matrix will incorporate 6 power pulses with a constant energy deposition and a timescale that spans over several orders of magnitude, including a steady state test with an exponential period of 10 s.

Experimental study on single- to two-phase flow and heat transfer of water in a small tube

Experimental investigation on flow boiling heat transfer in a small tube under high system pressure has been conducted in this study. The test-section is constructed with a 316L stainless steel tube. The inner diameter and heated length of the test-section are 5 mm and 930 mm, respectively. The working fluid is deionized water. The operating conditions of the experiments are as follows, the mass flux from 548 to 978 kg/(m2·s), the wall heat flux from 136 to 238 kW/m2, and the system pressure from 1.0 to 2.9 MPa. The experimental results showed that the inlet subcooling mainly affects the onset of nucleate boiling, but its impact on the heat transfer coefficient at the same vapor quality is almost negligible. The heat transfer coefficient increases with the increase of mass flux and wall heat flux, especially in the region where xe < 0.02. The average heat transfer coefficient is higher under high system pressure owing to the variation of the thermophysical properties. Additionally, the existing flow and heat transfer correlations cannot predict the flow boiling heat transfer coefficient and frictional pressure drop in the experiments accurately enough. Therefore, the new flow and heat transfer correlations are developed based on the experimental data in this paper, and the mean absolute deviation of the flow boiling heat transfer correlation and frictional pressure drop correlation are 13.3% and 12.1%, respectively.

Numerical investigation and data-driven prediction of flow boiling heat transfer in manifold microchannels with slopes

The manifold microchannels (MMC) with high heat transfer coefficient and low pressure drop has received much attention. Flow boiling heat transfer inside MMC is promising for dissipating heat of high-power devices. In this study, flow boiling heat transfer inside MMC is further numerically studied with slopes added in the upstream and downstream corners of MMC. The results show that downstream slope leads to lower local temperature and thermal resistance by removing the upstream vapor more easily, and upstream slope leads to higher heat flux corresponding to the turning point in the flowing boiling curve by restraining the local high temperature at upstream corner. The combination of the upstream and downstream slopes can reduce the thermal resistance by 5.45% and increase the heat flux related to the turning point by 14.28% compared to the MMC without slopes. A new flow boiling heat transfer correlation considering the slopes is developed with prediction accuracy of mean absolute deviation (MAD) of about 0.05%. An artificial neural network (ANN) is further built to predict the vapor saturation inside the MMC based on the outside temperature at the MMC bottom surface, which presents high accuracy of 97.03%.

Study of flow pattern transition criterion and heat transfer characteristics in vertical rectangular narrow channel for steam heating

This study clarifies the heat transfer characteristics of flow boiling in a narrow vertical rectangular channel at each stage and optimizes the performance of a heat exchanger. The flow pattern and local heat transfer characteristics in a narrow vertical rectangular channel of steam heating with dimensions of 1400 × 250 × 2.75 mm (l × w × s) were experimentally investigated using deionized water as the working medium. Based on the visualization data, the mechanical model and empirical formulas in previous literature, a preliminary derivation of the flow pattern transition criterion for steam heating in a vertical rectangular narrow channel was obtained. The effects of the inlet temperature, mass flux, and heating power on the local heat transfer characteristics were analyzed in conjunction with the flow patterns. Based on the parametric analysis of the experimental data, a new flow boiling heat transfer correlation formula was obtained and applied to the experimental conditions. The results showed that an increase in the inlet temperature had a positive effect on the nucleate boiling section, whereas the effect on the local heat transfer coefficient was minimal after entering the churn flow phases. The increase in mass flux decreased the local heat transfer coefficient in the nuclear state boiling stage and enhanced the local heat transfer coefficient in the evaporation zone of the liquid film flow. The peak of the local heat transfer coefficient tended to shift to the left as the heating power increased. The proposed heat transfer correlation equation could well predict the local heat transfer coefficient of flow boiling in a vertical rectangular narrow channel heated by steam under these experimental conditions.

A Comparative Analysis of Two-Phase Flow Boiling Heat Transfer Coefficient and Correlations for Hydrocarbons and Ethanol

This study will present a comprehensive review of the two-phase flow boiling heat transfer coefficient of hydrocarbons such as propane (R-290), butane (R-600), iso-butane (R-600a), and ethanol at various experimental conditions. Studying the multiphase flow heat transfer coefficient is crucial for many types of heat transfer equipment to achieve higher efficiency for more compact design and cost reduction. One reason we chose hydrocarbons as refrigerants in this study is that they are of an ozone depletion potential equal to zero (ODP = 0) and a deficient level of direct global warming potential (GWP = 3). Moreover, hydrocarbons’ thermodynamic and thermophysical characteristics qualify them to be a strong candidate for more heat transfer applications, initially, by constructing a database for the working fluids using multiple existing experimental work. The current data that this study have collected for the flow boiling spans a wide range of parameters, such as mass flux, heat flux, operating pressure, saturation temperature, etc. Furthermore, by comparing the experimental multiphase heat transfer coefficient database with the anticipated values of each correlation, the prediction performance of 26 correlations found in the literature was assessed. This study allows the best prediction method to be selected based on the minimum deviation of predicted results from the experimental database provided based on the mean absolute error (MAE) calculated from the assessed correlations. The conclusions of such a study can also be helpful for developing more accurate correlation methods for these fluids and improving the prediction of their flow boiling characteristics.

Saturated/subcooled flow boiling heat transfer inside micro/mini-channels: A new prediction correlation and experiment evaluation

In this study, a new general heat transfer correlation was developed for predicting the saturated/subcooled flow boiling heat transfer coefficient in micro/mini-channels. The collected database included 4250 data points, which covered eleven different working fluids. These included deionized water, new electronic fluorinated solutions, and refrigerants, among others. The temperature range of the experimental operation was from 0 to 100 °C with a saturated pressure of 101 to 775 kPa. The hydraulic diameter of micro/mini-channels varied from 0.1 to 3 mm, and the liquid sub-cooling was between 0 and 80 K. The database included various operation conditions, such as mass flux, heat flux, vapor quality, and reduced pressure. The liquid and vapor Reynolds numbers were calculated based on the hydraulic diameter. Six existing flow boiling heat transfer correlations were employed to evaluate the present data points in micro/mini-channels. However, it was observed that these correlations were unable to predict the present data points accurately due to high liquid sub-cooling and heat flux. Therefore, a new prediction correlation based on the present database was developed by dividing flow boiling into three stages, including subcooled boiling, developed nucleate boiling and nucleate boiling deterioration. This new prediction model can predict more than 80% of data points within ±30% error band.

Deep learning-based assessment of saturated flow boiling heat transfer and two-phase pressure drop for evaporating flow

This work proposes new correlations as well as deep learning based modeling of saturated flow boiling heat transfer and two-phase pressure drops for evaporating flow. First, existing saturation flow boiling heat transfer correlations are compared to experimental database (2,500 data points) of numerous refrigerants for tube diameters ranging from 1 to 7 mm. The newly developed correlation for heat transfer outperformed the existing correlations resulting in an MAE =11.28%. For two-phase pressure drop of the evaporating flow, 1,954 measurement data points of 7 refrigerants were used, for the experimental tube diameter ranged from 0.509 to 14 mm. The newly developed correlation for pressure drop outperformed the existing correlations resulting in an MAE =19.07%. An optimal deep learning model (DL) was developed that further improved the accuracy of the prediction in terms of both heat transfer and pressure drop (R2=0.984 and MAE=4.5 % in terms of heat transfer and R2=0.994 and MAE=7.39 % in terms of two-phase pressure drop). The proposed correlations and deep learning models significantly improve microchannel prediction in terms of heat transfer and two phase pressure drop. Besides, explainable artificial intelligence highlights the dependence and interaction between various features affecting the heat transfer and pressure drop.

A novel integrated PDB-FDB model for the prediction of flow boiling heat transfer under high sub-cooling and very high heat flux conditions

Although numerous studies on subcooled flow boiling heat transfer have been conducted, those evaluating very high heat fluxes of several MW/m2 under one-side heating conditions are limited. In this study, the heat transfer characteristics of a circular smooth channel are evaluated under one-sided heating conditions with a high heat flux of up to 11.82 MW/m2. An experiment to measure the heat transfer (including boiling performance) from single-phase to critical heat flux (CHF) under an inlet pressure of 0.1–1 MPa, mass flux of 2000–6000 kg/m2s, and inlet bulk temperature conditions of 30–140 °C is conducted. The boiling regime is analyzed by dividing it into a partially developed nucleate boiling (PDB) regime and fully developed nucleate boiling (FDB) regime, using the onset of the nucleate boiling (ONB) point and onset of the fully developed nucleate boiling (OFDB) point. A total of 15 existing subcooled flow boiling heat transfer correlations for the PDB and FDB regimes are evaluated with the experimental results. In the PDB regime, the Liu and Winterton correlation reveal good predictability within 11%. However, all the evaluated existing correlations of the FDB regime exhibit high error rates. In this study, a new FDB correlation is developed by considering the agitation heat flux (an expected heat transfer characteristic in the FDB regime) in the Liu and Winterton correlation with Python code and the AI regression method. An evaluation of the developed correlation with the data of other previous studies, such as those of Araki et al. and Jianguo Yan et al. reveals that the newly proposed correlation can predict the FDB heat transfer under conditions of higher pressure (approximately 5 MPa) and higher flow rate (approximately 10,000 kg/m2s) with a low error rate of 17%.

Development of transient flow film boiling heat transfer correlations for energy efficient cryogenic fluid management during feed line quenching operation

Currently, there is considerable interest in constitutive relations for accurate heat transfer prediction during cryogenic feed line chill-down to optimize the cryogen requirement and quench time. The present work develops a new database for transient quench flow film boiling with 14,143 inverted annular (IAFB), 9299 inverted slug (ISFB), and 3257 dispersed flow (DFFB) film boiling data from LH2, LN2, LAr, LOX, and LCH4 chill-down experiments with transfer line length ranging from 0.11 m to 11 m, inner diameter from 0.4 cm to 2.2 cm, and under various orientations and gravity levels. Moreover, in the collected data, mass flux spans 8.8–1805 kg/m2s and local pressure from 72.3 kPa to 1246.2 kPa. The database is used to analyze 33 existing film boiling correlations to understand their predictive performances and limitations. Accordingly, new IAFB, ISFB, DFFB, and combined IAFB and ISFB inverted flow regime heat transfer correlations are proposed using mutual information and conditional mutual information statistical filter algorithms and genetic algorithm-based optimization. The predictions from the new correlations are in good agreement with the experimental results with a mean absolute error of less than 29%. Hence the proposed correlations can be added to thermal-hydraulic codes to support the design of reliable and energy-efficient cryogenic fluid transfer.

Investigation of quench flow boiling heat transfer correlations for liquid oxygen feed line chill-down with outlet contraction

Cryogenic feed lines used for ground-based liquid transfer, thermal management in space flight, as well as the one with an injector at the outlet used for supplying propellants to the cryogenic engine combustion chamber, undergo an initial transient cool-down operation before vapor free liquid supply can be established through them. Accurate prediction of the thermal and hydraulic transients during this period has critical importance in the safe operation and efficient utilization of the cryogen. In the present work, a one-dimensional non-homogeneous two-phase model is used for simulating the chill-down operation in feed lines with and without outlet contraction. For transport feed lines without outlet constriction, the obtained transient wall temperature profiles indicate good prediction when the heat transfer correlations proposed based on recent chill-down experiments are employed as constitutive relations. Subsequently, the numerical model is applied for predicting the wall temperature transients during outlet contracted LOX feed line chill-down. It was noted that built-in heat transfer correlations in thermal–hydraulic code SINDA/FLUINT need revision, especially for rewetting point and heat transfer correlation during post rewetting regimes, for accurate thermal transient predictions during end constrained feed line chill-down. Hence, recent chill-down correlations reported in the literature and the correlations employed in previous chill-down numerical models are tested for their applicability. The recent cryogenic chill-down correlations reported in the literature performed well when applied within the correlation range. However, these correlations over predict the heat transfer at a very high mass flux (order of 3412 kg/m2 s). Hence, modified correlations are proposed for film and nucleate boiling heat transfer coefficients and rewetting temperature.

Numerical simulation research on two-phase flow boiling heat transfer in helically coiled tube

In this paper, the partial geometric models of helically coiled tube type heat exchanger with different tube diameters (d = 12, 19, 25 mm), tube pitches (P = 50, 100, 150 mm) and helical radius (R = 100, 150, 200 mm), were established. Numerical simulation and performance comparison were carried out using water and water vapor as the working fluid. The gas–liquid phase distribution in the helically coiled tube, the gas volume fraction at different cross-sections, and the changes of heat transfer coefficient and pressure drop along the length of the helically coiled tube were analyzed. The results showed that the gas phase was concentrated in the inner side (near the side of the central axis) and the upper side of the helically coiled tube under boiling condition, and the liquid phase was concentrated in the bottom of the helically coiled tube and is stratified with the gas phase. As the helical radius and tube diameters increased, the heat transfer coefficient and unit pressure drop decreased gradually. Based on the simulated data, the boiling heat transfer correlation was fitted by the method of multiple nonlinear regression, and the mean absolute error was 4.5% compared with the modified Chen's correlation. Therefore, the numerical results were correct and trustable.

Heat transfer evaluation of saturated pool boiling outside slender tube bundle in passive residual heat removal system of molten salt reactor

In order to study the operation feasibility and safety margin of the water-cooled passive residual heat removal system applied to 2 MW molten salt reactor (MSR), the heat transfer characteristics of some local components in the system were experimentally investigated thoroughly. In the later stage of system operation, the water in the tank will reach saturation. In this paper, the overall and local pool boiling heat transfer characteristics outside the tube bundle of condenser are studied. A special local boiling heat transfer coefficient (HTC) distribution is found and the formation mechanism is explained. The experimental results are compared with four empirical correlations for local boiling HTCs. The errors between the four correlations and their applicability to the experimental results are discussed. A new boiling heat transfer correlation is proposed based on the experimental data.

Boiling Heat Transfer and Visualization for R717 in a Horizontal Smooth Mini-tube

The paper presents an experimental and theoretical investigation on the two-phase flow boiling heat transfer with ammonia (R717) as the refrigerant in a horizontal smooth mini-tube with inner diameter of 3mm. The experimental data were obtained in the following condition, the heat flux density is 10∼30 kW · m − 2 , the mass flux is 40∼200 kg · m − 2 · s − 1 , the saturation temperature is -10∼10 ℃, and the range of vapor quality is 0.1 ∼1. The experimental results show that the heat transfer coefficient before dryout phenomenon increases and gradually reaches a peak with the increase of vapor quality, but occurs heat transfer deterioration after dryout phenomenon. Combined with the transform of flow patterns, the effect of mass flux, heat flux density, and saturation temperature on the heat transfer coefficient and friction pressure drop are analyzed. The theoretical gas phase flow velocity of ammonia is much higher than other refrigerants, and the flow boiling heat transfer for ammonia is more dependent on convective boiling. The existing correlations of two-phase flow are compared with the measured data of ammonia. According to the experimental and comparative results, Kew and Conwell correlation and Müller-Steinhagen and Heck correlation were updated respectively, and new boiling heat transfer correlation and frictional pressure drop correlation were obtained.

Novel Saturated Flow Boiling Correlations for R600a and R717 Refrigerants

This research study provides a detailed analysis of the two-phase flow boiling heat transfer coefficients of R600a and R717. In addition, it proposes novel saturated flow boiling heat transfer correlations for these two refrigerants. In this context, 1306 experimental data points for R600a and 885 data samples for R717 are extracted from the literature works to develop new flow boiling models. Two different correlations are constructed under different forms of baseline frameworks for each refrigerant. The proposed flow boiling model for R600a utilizes the dimensionless numbers and operational parameters of the best performing literature correlations for this refrigerant while the model developed for R717 takes the advantage of piecewise continuous correlation form which successfully trace the tendencies of heat transfer coefficient with varying vapor qualities. It is found that the new model for R600a has a mean absolute error of 12.4% and mean relative error of 0.1, predicting 78.5% of the entire database within ±20.0% error band whereas the proposed correlation for R717 has an absolute error value of 17.3% having 65.3% of the data within ±20.0% error band, which are much better and accurate estimations compared to those obtained by the existing flow boiling models for R717 refrigerant.

Evaluation of Correlations of Flow Boiling Heat Transfer of R600a in a Flat-Plate Solar Collector/Evaporator

In the current research work, the behavior of the boiling heat transfer coefficient in a flat-plate solar collector/evaporator, component of a direct-expansion solar-assisted heat pump (DX-SAHP) was studied using a hydrocarbon refrigerant with zero Ozone Depletion Potential (ODP) and low Global Warming Potential (GWP). The main dimensions of the collector/evaporator are 0.8, 3.8, and 1000 mm of the fin thickness, internal diameter, and length, respectively. Five experimental tests were realized at different times of the day for obtaining the results, with mass velocities varying between 197.59 and 267.26 kg·m-2·s-1, and the heat flux having values between 72.83 and 488.27 W·m-2. The operating values in tests, such as refrigerant pressure and temperature, were taken in a built prototype. The numerical analysis was carried out considering different correlations proposed by Chen, Wojtan, and Kattan. The Wojtan mathematical model offered the best projection of the heat transfer effect for the different transition zones of a two-phase flow along the pipeline. The boiling heat transfer coefficients had approximate maximum values of 8.2, 8.5, 7.8, 6.7, and 5.8 kW·m-2·K-1 for the A, B, C, D, and E tests prediction by Wojtan. Moreover, the boiling heat transfer coefficients increased as the mass velocity enhanced and the rise of vapor quality as the mass velocity was fixed. In this study, the effect of solar radiation, vapor quality on the measured heat transfer coefficient was analyzed.

A New Saturated Two-Phase Flow Boiling Correlation Based on Propane (R290) Data

There are plenty of literature research studies investigating two-phase heat transfer characteristics of propane under varying operational conditions. Based on the collected data retrieved from the experimental measurements, several flow boiling heat transfer correlations have been proposed up to now. However, the prediction accuracy of the proposed correlations for propane refrigerant is still in question as most of the correlation is developed for their measurements or derived for a limited range of operational conditions. To conquer this drawback, this study proposes a new flow boiling heat transfer model for smooth tubes based on a propane experimental database compiled of 2179 points obtained from different eighteen laboratories around the world. Operational conditions of the database cover mass fluxes between 50 and 600 kg/m2s, saturation temperatures between − 35.0 and 43.0 °C, heat fluxes between 2.5 and 227.0 kW/m2, hydraulic diameters between 0.3 and 7.7 mm, and thermodynamic qualities 0.01 to 0.99. Estimations performed by the new flow boiling model have been compared to those obtained by the literature correlations, and comparative results indicate that the proposed model surpasses the existing flow boiling in terms of prediction accuracy with a mean absolute error of 19.1% and mean relative error of 1.7%.

Heat-transfer characteristics of screw tube in one-side high heat load condition for fusion reactor divertor application

In this study, the heat transfer characteristics of one-side heated screw tubes were analyzed using subcooled flow boiling experiments. The experiments were performed until the critical heat flux was reached, while the applied heat flux was gradually increased. Subsequently, the boiling curves derived from the experimental results were divided into partial nucleate boiling (PDB) and fully developed nucleate boiling (FDB) regimes. As the flow rate increases, the forced convective heat transfer is enhanced, improving the single-phase heat transfer performance. However, as the FDB region is approached, most of the heat transfer proceeds via nucleate boiling heat transfer, so the heat transfer coefficient curve converges into the same straight line. The same trend was observed when analyzing the effect of the degree of subcooling. However, as the system pressure increased, and the liquid surface tension and latent heat decreased, a faster transition was observed from the single-phase regime to the PDB regime. From evaluating the prediction performance of the existing subcooled flow boiling heat transfer correlations, among the PDB regime; Liu and Winterton correlation, a kind of Chen-type correlation, showed the highest accuracy with mean absolute error (MAE) of 13.62% and root mean square error (RMSE) of 16.13%. However, most of the FDB correlations did not accurately predict the heat transfer performance of the one-side heated screw tube under a high heat flux load of several MW/m2. Therefore, a new screw tube FDB correlation was developed using Python code combined with artificial intelligence technology. The authors believe that the proposed correlation will be useful for not only predicting the heat transfer performance in the FDB region, but also establishing an operating map of the screw tube in the future.

Experimental study of hypervapotron channel with square fin structure for divertor cooling by one-side, electric joule heating system

The lack of cooling capacity to maintain the thermal steady state of the divertor is becoming a severe engineering problem in preparation for DEMO fusion reactor. But, there is not much literature comparing with the existing sub-cooled flow boilng heat transfer correlation and analyzing the Hypervapotron boiling curve. To simulate the fusion thermal condition, experimental loop that can withstand high temperature (150℃) and high pressure (20 bar) was constructed. And one-side electric joule heating system that can apply heat flux of up to 10.4 MW/m2 was developed. In addition, it was verified that stable operation is possible by confirming that the flow rate and the channel inlet temperature fluctuation rate are 1% or less, respectively. This experiment was carried out to evaluate the boiling heat transfer of Hypervapotron cooling channel at 10 bar, 40 ∼ 80 subcooling, 0.108 ∼ 0.284 kg /s and maximum effective heat flux of 6.87 MW/m2. Among the sub-cooled flow boiling heat transfer correlations, Thom correlation (1965), Jens & Lottes correlation (1951), and Aaladiev correlation (1957) differed significantly from the experimental data. But Shah 1977 (error rate: 4.75 %) and Kandlikar 1998 (error rate: 16.57 %) correlations were well predicted.

Two-phase flow boiling in a microfluidic channel at high mass flux

We report the experimental investigations of two-phase flow boiling heat transfer characteristics of a refrigerant in a microfluidic channel at a high mass flux (more than 1000 kg/m2 s). We investigate the heat transfer coefficients at a heat flux range of 7.63 kW/m2–49.46 kW/m2, mass flux range of 600 kg/m2 s–1400 kg/m2 s (high mass flux), and saturation temperature range of 23 °C–31 °C. We propose the new two-phase flow boiling heat transfer correlation of a refrigerant, which is used as the working fluid for the present experiments, at the microfluidic scale. We experimentally establish the functional relationship of two-phase flow boiling heat transfer correlation of the refrigerant during flow boiling in a rectangular microchannel with the Reynolds number, the boiling number, and the Weber number. We believe that the inferences of this study may provide a design basis for the micro-heat exchanger, typically used for thermal management in electronic devices, micro-electro-mechanical systems, and electric vehicle battery cooling system.

A Modified Correlation for Flow Boiling Heat Transfer in Plate Heat Exchangers

Abstract Corrugated plate heat exchangers are increasingly used in two-phase flow applications for their flexible compact size and efficient heat transfer performance. This paper presents a brief review of recent studies on the flow boiling in plate heat exchangers and creates a database containing 533 data points from previous experimental studies. The collected database covers seven working fluids, a wide range of vapor quality (both mean and local) 0.01–0.94, heat flux 0.5–46 kW m−2, mass flux 5.5–137 kg m−2 s−1, chevron angle 30–70 deg, and hydraulic diameter 1.7–4.0 mm. Based on the database a brief comparison between several previous correlations are discussed. A new prediction method for flow boiling heat transfer coefficient is developed by multiple regression analysis and modifying an existing correlation. A criterion proposed by Li and Wu about the transition from micro- to macroscale was introduced with a combined dimensionless number Bd·Rel0.5 which attempts to comprehensively consider four types of forces during flow boiling. It was observed that the modified correlation shows a better agreement and predicts 74.3% and 94.9% of total data points within ±30% and ±50% error bands, respectively.