Improvement of Supercritical Water Heat-Transfer Correlations for Vertical Bare Tubes

2014 ◽  
Author(s):  
Sarah Mokry ◽  
Igor Pioro
Keyword(s):  
Heat Transfer ◽  
Supercritical Water ◽  
Operating Conditions ◽  
Entrance Region ◽  
Fluid Temperature ◽  
Supercritical Conditions ◽  
Bulk Fluid ◽  
Wide Range ◽  
Heat Transfer Correlations ◽  
Region Effect

Currently, there are a number of Generation IV SuperCritical Water-cooled nuclear Reactor (SCWR) concepts under development worldwide. These high temperature, high pressure reactors will have much higher operating parameters compared to current Nuclear Power Plants (NPPs) (i.e., steam pressures of about 25 MPa and steam outlet temperatures up to 625°C). Additionally, SCWRs will have a simplified flow circuit in which steam generators, steam dryers, steam separators, etc. will be eliminated. In support of developing these SCWRs, studies are currently being conducted for heat transfer at supercritical conditions. Currently, there are no experimental datasets for heat transfer at supercritical conditions from power-reactor fuel bundles to a coolant (water) available in open literature. Therefore, for preliminary calculations, heat-transfer correlations obtained with bare-tube data can be used as a conservative approach. A number of empirical generalized correlations, based on experimentally obtained datasets, have been proposed to calculate Heat Transfer Coefficients (HTCs) in forced convective heat transfer for various fluids, including water at supercritical pressures. There have been a number of methods applied to correlate heat transfer data. The most conventional approach is to modify the classical Dittus-Boelter correlation for forced convection. The Bishop et al. correlation is an example of this type modification with an addition of an entrance-region term. The Mokry et al. correlation (2009) was developed as a Dittus-Boelter-type correlation with thermophysical properties taken at a bulk-fluid temperature. The derived correlation has shown a good fit for experimental data at supercritical conditions within a wide range of operating conditions in normal and improved heat-transfer regimes. This correlation has an uncertainty of about ±25% for HTC values and about ±15% for calculated wall temperature. However, this correlation does not take into account the entrance-region effect. The objective of this paper is an investigation of the entrance-region effect to be incorporated into the proposed Mokry et al. correlation (2009) in an attempt to further improve its accuracy.

Investigation of Characteristic-Temperature Approaches for Heat-Transfer Correlations at Supercritical Conditions

2013 ◽  
Author(s):  
Sarah Mokry ◽  
Igor Pioro
Keyword(s):  
Heat Transfer ◽  
Supercritical Water ◽  
Wall Temperature ◽  
Characteristic Temperature ◽  
Fluid Temperature ◽  
Transfer Coefficients ◽  
Supercritical Conditions ◽  
Bulk Fluid ◽  
Heat Transfer Coefficients ◽  
Bare Tube

It is expected that the next generation of water-cooled nuclear reactors will operate at supercritical pressures (∼25 MPa) and high coolant temperatures (350–625°C). In support of the development of SuperCritical Water-cooled Reactors (SCWRs), research is currently being conducted for heat-transfer at supercritical conditions. Currently, there are no experimental datasets for heat transfer from power reactor fuel bundles to the fuel coolant (water) available in open literature. Therefore, for preliminary calculations, heat-transfer correlations obtained with bare-tube data can be used as a conservative approach. A number of empirical generalized correlations, based on experimentally obtained datasets, have been proposed to calculate Heat Transfer Coefficients (HTCs) in forced convective heat transfer for various fluids, including water, at supercritical pressures. These bare-tube-based correlations are available in various literature sources. There have been a number of methods applied to correlate heat transfer data. The most conventional approach, which accounts for property variations in the data, is to modify the classical Dittus-Boelter equation for forced convection. However, analysis and comparison of these correlations has shown that differences in HTC values can be up to several hundred percent. In general, the familiar correlations of Dittus-Boelter and Bishop et al. have used the bulk-fluid temperature approach for characteristic temperature properties evaluations. However, at high heat fluxes, fluid near the tube-wall will have a temperature close to that of the wall temperature. This might be significantly different from the bulk-fluid temperature. Therefore, another approach can be used based on the wall temperature as the characteristic temperature. The Swenson et al. correlation is based upon this approach. Finally, a third approach has been considered in which the film-temperature is used as the characteristic temperature (Tf = (Tw+Tb) / 2). McAdams et al. based their correlation for annuli on this approach. Therefore, the objective of this paper is to evaluate the three characteristic temperature approaches, (1) Bulk-fluid temperature approach; (2) Wall-temperature approach; and (3) Film-temperature approach, and determine which characteristic temperature method can most accurately predict supercritical water heat transfer coefficients. Both classical correlations and more recently developed correlations are considered in this investigation.

A Natural Convection Fin with a Solution-Determined Nonmonotonically Varying Heat Transfer Coefficient

1981 ◽  
Vol 103 (2) ◽  
pp. 218-225 ◽  
Author(s):  
E. M. Sparrow ◽  
S. Acharya
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Transfer Coefficient ◽  
First Principles ◽  
Numerical Solutions ◽  
Flow Direction ◽  
Operating Conditions ◽  
Fluid Temperature ◽  
Wide Range

A conjugate conduction-convection analysis has been made for a vertical plate fin which exchanges heat with its fluid environment by natural convection. The analysis is based on a first-principles approach whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, and energy in the fluid boundary layer adjacent to the fin. The natural convection heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. For a wide range of operating conditions, the local heat transfer coefficients were found not to decrease monotonically in the flow direction, as is usual. Rather, the coefficient decreased at first, attained a minimum, and then increased with increasing downstream distance. This behavior was attributed to an enhanced buoyancy resulting from an increase in the wall-to-fluid temperature difference along the streamwise direction. To supplement the first-principles analysis, results were also obtained from a simple adaptation of the conventional fin model.

Effects of Various Parameters on Supercritical-Pressure Heat Transfer and Limits for Heat Transfer Correlations Obtained in Vertical Bare Tubes

2017 ◽  
Author(s):  
Hakim Maloufi ◽  
Hanqing Xie ◽  
Andrew Zopf ◽  
William Anderson ◽  
Christian Langevin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Nuclear Power ◽  
Nuclear Reactor ◽  
Heat Fluxes ◽  
Operating Conditions ◽  
Transfer Coefficients ◽  
Wide Range ◽  
Heat Transfer Correlations ◽  
Bare Tube

Currently, there is a number of Generation-IV SuperCritical Water-cooled nuclear-Reactor (SCWR) concepts under development worldwide. These high temperature and pressure reactors will have significantly higher operating parameters compared to those of current water-cooled nuclear-power reactors (i.e., “steam” pressures of about 25 MPa and “steam” outlet temperatures up to 625 °C). Additionally, SCWRs will have a simplified flow circuit in which steam generators, steam dryers, steam separators, etc. will be eliminated, as the steam will be flowing directly to a steam turbine. In support of developing SCWRs studies are being conducted on heat transfer at SuperCritical Pressures (SCPs). Currently, there are very few experimental datasets for heat transfer at SCPs in power-reactor fuel bundles to a coolant (water) available in open literature. Therefore, for preliminary calculations, heat-transfer correlations developed with bare-tube data can be used as a conservative approach. Selected empirical heat-transfer correlations, based on experimentally obtained datasets, have been put forward to calculate Heat Transfer Coefficients (HTCs) in forced convective in various fluids, including water at SCPs. The Mokry et al. correlation (2011) has shown a good fit for experimental data at supercritical conditions within a wide range of operating conditions in Normal and Improved Heat-Transfer (NHT and IHT) regimes. However, it is known that a Deteriorated Heat-Transfer (DHT) regime appears in bare tubes earlier than that in bundle flow geometries. Therefore, it is important to know if bare-tube heat-transfer correlations for SCW can predict HTCs at heat fluxes beyond those defined as starting of DHT regime in bare tubes. The Mokry et al. (2011) correlation fits the best SCW experimental data for HTCs and inner wall temperature for bare tubes at SCPs within the NHT and IHT regimes. However, this correlation might have problems with convergence of iterations at heat fluxes above 1000 kW/m2.

Analysis of Updated SuperCritical Water Heat Transfer Correlations for Vertical Bare Tubes

2010 ◽  
Author(s):  
Sarah Mokry ◽  
Sahil Gupta ◽  
Amjad Farah ◽  
Krysten King ◽  
Igor Pioro
Keyword(s):  
Heat Transfer ◽  
Supercritical Water ◽  
Thermophysical Properties ◽  
Vertical Tube ◽  
Large Set ◽  
Conservative Approach ◽  
Bulk Fluid ◽  
Heat Transfer Correlations ◽  
Vertical Tubes ◽  
Bare Tube

In support of developing SuperCritical Water-cooled Reactors (SCWRs), studies are currently being conducted for heat-transfer at supercritical conditions. This paper presents an analysis of heat-transfer to SuperCritical Water (SCW) flowing in bare vertical tubes as a first step towards thermohydraulic calculations in a fuel-channel. A large set of experimental data, obtained in Russia, was analyzed. Two updated heat-transfer correlations for forced convective heat transfer in the normal heat transfer regime to SCW flowing in a bare vertical tube were developed. It is expected that the next generation of water-cooled nuclear reactors will operate at supercritical pressures (∼25 MPa) with high coolant temperatures (350–625°C). Currently, there are no experimental datasets for heat transfer from power reactor fuel bundles to the fuel coolant (water) available in open literature. Therefore, for preliminary calculations, heat-transfer correlations obtained with bare tube data can be used as a conservative approach. The analyzed 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 for mass flux ranged from 200–1500 kg/m2s, for heat flux up to 1250 kW/m2 and inlet temperatures from 320–350°C. The Mokry et al. correlation was developed as a Dittus-Boelter-type correlation, with thermophysical properties taken at bulk-fluid temperatures. Alternatively, the Gupta et al. correlation was developed based on the Swenson et al. approach, where the majority of thermophysical properties are taken at the wall temperature. An analysis of the two updated heat-transfer correlations is presented in this paper. Both correlations demonstrated a good fit (±25% for Heat Transfer Coefficient (HTC) values and ±15% for calculated wall temperatures) for the analyzed dataset. Thus, these correlations can be used for preliminary HTC calculations in SCWR fuel bundles as a conservative approach, for SCW heat exchangers, for future comparisons with other independent datasets and for the verification of computer codes for SCWR core thermohydraulics.

Development and Comparison of a Heat-Transfer Correlation for Supercritical Refrigerants

2017 ◽  
Author(s):  
Nicholas Tarsitano ◽  
Khalil Sidawi ◽  
Igor Pioro
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Fluxes ◽  
Critical Parameters ◽  
Future Research ◽  
Supercritical Conditions ◽  
Wide Range ◽  
Heat Transfer Correlations ◽  
R 134A ◽  
Correlation Accuracy

The objective of this paper is to act as a collection of multiple different heat-transfer correlations and to check their accuracy when compared to experimental data obtained in supercritical-pressure refrigerants (R-22 and R-134a). This paper is also intended to collect as much relevant data of heat transfer in supercritical refrigerants as possible for future research. The experimental data have been retrieved from graphs within a wide range of operating parameters. This study is in support of potential use of supercritical refrigerants as modeling fluids instead of supercritical water. The use of refrigerants as modelling fluids instead of water will allow to decrease costs and technical difficulties during experiments at supercritical pressures and widen operating ranges, because the critical parameters of refrigerants are significantly lower than those of water. The research was completed by collecting graphed data from several different experimental series using both R-22 and R-134a data. The advantage of comparing different refrigerants for determining correlation accuracy is to increase the predictability for other potential experiments using refrigerants. All data are taken from bare-tube experiments to produce a relative baseline for heat-transfer characteristics. These experiments have been performed within the following range: Inner tube diameter ranging between 4.4 mm to 13 mm, pressure ranging between 4.3 MPa to 5.5 MPa, and at a number of various mass and heat fluxes. Sixteen potential heat-transfer correlations have been selected and used in this assessment. The correlation by Watts and Chou [1] and Cheng et al. [2] were shown to have the lowest root-mean-square error. Other correlations with the reasonable accuracy include Mokry et al. [3] and Swenson et al. [4] correlations. However, it was decided to develop a new correlation based on these refrigerant data in an attempt to increase the prediction accuracy. Therefore, based on the Mokry et al. [3] correlation a modified correlation was developed, which generalized the experimental Freon data with higher accuracy than the know correlations. This correlation is intended to create a basis for further study on the use of refrigerants as modeling fluids. While Freon has similar properties to water at supercritical conditions, the different molecular properties causes factors to affect each fluid differently. For refrigerants at supercritical conditions, the factors that seem to have the most effect are the dynamic viscosity and density of a fluid.

Comparison of Selected Forced-Convection Supercritical-Water Heat-Transfer Correlations for Vertical Bare Tubes

2010 ◽  
Author(s):  
Amjad Farah ◽  
Krysten King ◽  
Sahil Gupta ◽  
Sarah Mokry ◽  
Wargha Peiman ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Supercritical Water ◽  
Heat Exchangers ◽  
Power Plants ◽  
Heat Fluxes ◽  
Operating Conditions ◽  
Transfer Coefficients ◽  
Heat Transfer Correlations ◽  
Bare Tube

This paper presents an extensive study of heat-transfer correlations applicable to supercritical-water flow in vertical bare tubes. A comprehensive dataset was collected from 33 papers by 27 authors, including more than 125 graphs and wide ranges of parameters. The parameters ranges were as follows: pressures 22.5–34.5 MPa, inlet temperatures 85–350°C, mass fluxes 250–3400 kg/m2s, heat fluxes 75–5,400 kW/m2), tube heated lengths 0.6–27.4 m, and tube inside diameters 2–36 mm. This combined dataset was then investigated and analyzed. Heat Transfer Coefficients (HTCs) and wall temperatures were calculated using various existing correlations and compared to the corresponding experimental results. Three correlations were used in this comparison: Bishop et al., Mokry et al. and modified Swenson et al. The main objective of this study was to select the best supercritical-water bare-tube correlation for HTC calculations in: 1) fuel bundles of SuperCritical Water-cooled Reactors (SCWRs) as a preliminary and conservative approach; 2) heat exchangers in case of indirect-cycle SCW Nuclear Power Plants (NPPs); and 3) heat exchangers in case of hydrogen co-generation at SCW NPPs from SCW side. From the beginning, all these three correlations were compared to the Kirillov et al. vertical bare-tube dataset. However, this dataset has a limited range of operating conditions in terms of a pressure (only one pressure value of 24 MPa) and one inside diameter (only 10 mm). Therefore, these correlations were compared with other datasets, which have a much wider range of operating conditions. The comparison showed that in most cases, the Bishop et al. correlation deviates significantly from the experimental data within the pseudocritical region and actually, underestimates the temperature at most times. On the other hand, the Mokry et al. and modified Swenson et al. correlations showed a relatively better fit within the most operating conditions. In general, the modified Swenson et al. correlation showed slightly better fit with the experimental data than other two correlations.

Comparison of Heat-Transfer Correlations Obtained in Supercritical-Water-Cooled Bundles

2017 ◽  
Author(s):  
Hanqing Xie ◽  
Hakim Maloufi ◽  
Andrew Zopf ◽  
William Anderson ◽  
Christian Langevin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Supercritical Water ◽  
Nuclear Power ◽  
Annular Channel ◽  
Bulk Fluid ◽  
Efficient Operation ◽  
Normal Heat ◽  
Flow Geometry ◽  
Heat Transfer Correlations ◽  
Bare Tube

SuperCritical Water-cooled Reactor (SCWR) as one of the six Generation-IV nuclear-power-reactor concepts will have increased thermal efficiency compared to that of current Nuclear Power Plants (NPPs) equipped with water-cooled reactors by operating the reactor coolant at supercritical conditions: Coolant pressure of about 25 MPa, inlet temperatures between 300–350°C, and outlet temperatures between 550–625°C. The major flow geometry inside the reactor core is the bundle flow geometry. For safe and efficient operation of an SCWR heat transfer coefficients should be calculated with minimum uncertainties. Unfortunately, the vast majority of experimental datasets were obtained in vertical bare tubes cooled with SCW. Experiments in a bundle flow geometry are even more complicated and expensive compared to that in bare tubes. Due to this very few experiments have been performed in bundles. According to the abovementioned, the vast majority of heat-transfer correlations are based on bare-tube data, and only one currently known correlation is based on a 7-element bundle cooled with SCW (the so-called, Dyadyakin and Popov correlation (1977)). Rods in this bundle are equipped with four helical ribs to enhance the heat transfer. However, the authors have not provided any dataset(s) associated with this bundle and correlation. In the current paper a number of bare-tube heat-transfer correlations obtained in SCW and the Dyadyakin and Popov correlation were compared with two datasets obtained in an annular channel with the heated central rod and 3-element bundle. The central rod in this annular channel and rods in the 3-element bundle have the same heated length as those in the 7-element bundle tested by Dyadyakin and Popov in 1977, and are also equipped with four helical ribs. The comparison showed that the Jackson correlation (2002) is the most accurate one in predicting Heat-Transfer-Coefficient (HTC) profiles in the annular channel at normal heat-transfer regime. The Dittus and Boelter correlation (1930) is the most accurate in predicting HTC profiles in the 3-element bundle at normal heat-transfer regime. No one correlation is capable to follow closely HTC profiles at the deteriorated heat-transfer regimes in both flow geometries. Aloo, it should be mentioned that bare-tube heat-transfer correlations, which have thermophysical properties based on bulk-fluid and wall temperatures, might have problems with convergence at high heat fluxes, i.e., above the heat flux at which the deteriorated heat-transfer regime starts in bare tubes.

Experimental Heat Transfer in an Annular Channel and 3-Rod Bundle Cooled With Upward Flow of Supercritical Water

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
V. G. Razumovskiy ◽  
Eu. N. Pis’mennyi ◽  
Kh. Sidawi ◽  
I. L. Pioro ◽  
A. Eu. Koloskov
Keyword(s):  
Heat Transfer ◽  
Supercritical Water ◽  
Annular Channel ◽  
Fluid Temperature ◽  
Bulk Fluid ◽  
Experimental Heat ◽  
Rod Bundle ◽  
Fuel Bundle ◽  
Experimental Heat Transfer ◽  
Heated Length

There have been relatively few publications detailing heat transfer to supercritical water (SCW) flowing through a channel with a bundle or just with a single rod (annular channel) as compared to heat transfer to SCW in bare tubes. In the present paper, results of experimental heat transfer to SCW flowing upward in an annular channel with a heated rod equipped with four helical ribs and a 3-rod bundle (rods are also equipped with four helical ribs) are discussed. The experimental results include bulk-fluid-temperature, wall-temperature, and heat-transfer-coefficient (HTC) profiles along the heated length (485 mm) for these flow geometries. Data obtained from this study could be applicable as a reference estimation of heat transfer for future fuel-bundle designs.

Investigation of ATHLET System Code for Supercritical Water Applications

2014 ◽  
Author(s):  
J. Samuel ◽  
G. Lerchl ◽  
G. D. Harvel ◽  
I. Pioro
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Supercritical Water ◽  
Nuclear Reactor ◽  
High Pressures ◽  
Computer Code ◽  
Fluid Temperature ◽  
Bulk Fluid ◽  
Water Reactors ◽  
First Time

SuperCritical Water-cooled Reactors (SCWRs) are one of six Generation-IV nuclear-reactor concepts. They are expected to have high thermal efficiencies within the range of 45–50% owing to the reactor’s high pressures and outlet temperatures. Efforts have been made to study the supercritical phenomena both analytically and experimentally. However, codes that have been used to study the phenomena analytically have not been validated for supercritical water. The thermal-hydraulic computer code ATHLET (Analysis of THermal-hydraulics of LEaks and Transients) is used for analysis of anticipated and abnormal plant transients, including safety analysis of Light Water Reactors (LWRs) and Russian Graphite-Moderated High Power Channel-type Reactors (RBMKs). The range of applicability of ATHLET has been extended to supercritical water by updating the fluid- and transport-properties packages, thus enabling a transition from subcritical to supercritical fluid states. This extension needs to be validated using experimental data. In this work, the applicability of ATHLET code to predict supercritical-water behaviour in various heat-transfer conditions is assessed. Several well-known heat-transfer correlations for supercritical fluids are added to the code and applied for the first time in ATHLET simulations of experiments. A numerical model in ATHLET is created to represent an experimental test section and results for the heat transfer coefficient, bulk fluid temperature, and the tube inside-wall temperature are compared with the experimental data. The results from the ATHLET simulations are promising in the Normal and Enhanced Heat-Transfer Regimes. However, important phenomena such as Deteriorated Heat Transfer are currently not accurately predicted. While ATHLET can be used to develop preliminary design solutions for SCWRs, a significant effort in analysis of experimental work is required to make further advancements in the use of ATHLET for SCW applications.

Preliminary Investigation of Heat-Transfer Correlation for Upward Flow of CO2 at Supercritical Pressure

2013 ◽  
Author(s):  
Eugene Saltanov ◽  
Igor Pioro ◽  
Glenn Harvel
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Supercritical Water ◽  
Preliminary Investigation ◽  
Convection Heat Transfer ◽  
Theoretical Models ◽  
Supercritical Pressure ◽  
Operational Parameters ◽  
Bulk Fluid ◽  
Wide Range

The development of Generation IV nuclear reactors is an ongoing worldwide interdisciplinary effort. Canada is involved with the development of the SuperCritical Water-cooled Reactor (SCWR). One of the numerous engineering challenges associated with this development is to ensure intensive and stable heat transfer to SuperCritical Water (SCW) in a core. It is very important to develop sophisticated theoretical models to improving understanding of physical processes behind forced-convective heat transfer and its deterioration in near-critical region. However, not all turbulent models implemented in Computational Fluid Dynamics (CFD) codes are applicable to heat transfer at supercritical pressures. Additionally these codes should be first tuned on the basis of experimental data and, after that, used in similar calculations. Therefore, there is still a great reliance on 1D heat-transfer correlations for preliminary calculations. Performing experiments in SCW is extremely expensive due to the high temperatures and pressures involved. Therefore, it is reasonable to study the general properties of SuperCritical Fluids (SCF) by running experiments with modelling fluids; for example, carbon dioxide, which is widely used as a modeling fluid. In view of this, there is a need to compile a large database that will include experimental data on forced-convection heat-transfer to SuperCritical (SC) CO2 within a wide range of operational parameters. To date, a part of this database has been produced. It contains the bulk-fluid and wall temperatures of CO2 flowing upward in a vertical bare tube. CO2 is at supercritical pressure and the bulk-fluid and wall temperatures are below or above the pseudocritical temperature at the inlet of the test-section. Therefore, the objectives of this paper are: 1) to propose a correlation in a standard non-dimensional form, which will generalize data within ±25%; 2) to compare this correlation with the most recent, as well as previous 1D correlations for SC CO2 and SCW (appropriate scaling is performed).

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