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Heat Transfer and Fluid Flow of Supercritical Fluids in Advanced Energy Systems
Abstract
This chapter aims to clarify the supercritical fluids thermal hydraulics characteristics including heat transfer, pressure drops and flow instabilities for the purpose of accurate design and efficient safe operation of advanced energy systems. At first, the convection heat transfer models considering the effect of nonlinear properties and the effect of buoyancy and acceleration have been provided and discussed. Secondly, the hydraulic resistance models for supercritical fluids have been selected and suggested for different conditions. Thirdly, the published models for supercritical flow instabilities based on four different regional partitions are summarized and clarified. At last, two typical case studies have been provided to further intuitively elaborate the thermal hydraulics of supercritical fluids within the advanced energy systems.
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Competitive cycles must have a minimal initial cost and be inherently efficient. Currently, the supercritical carbon dioxide (S-CO2) Brayton cycle is under consideration for these very reasons. This paper examines one major challenge of the S-CO2 Brayton cycle: the complexity of heat exchanger design due to the vast change in thermophysical properties near a fluid's critical point. Turbulent heat transfer experiments using carbon dioxide, with Reynolds numbers up to 100 K, were performed at pressures of 7.5-10.1 MPa, at temperatures spanning the pseudocritical temperature. The geometry employed nine semicircular, parallel channels to aide in the understanding of current printed circuit heat exchanger designs. Computational fluid dynamics was performed using FLUENT and compared to the experimental results. Existing correlations were compared, and predicted the data within 20% for pressures of 8.1 MPa and 10.2 MPa. However, near the critical pressure and temperature, heat transfer correlations tended to over predict the heat transfer behavior. It was found that FLUENT gave the best prediction of heat transfer results, provided meshing was at a y(+) similar to 1. [DOI: 10.1115/1.4006108]
Heat transfer from supercritical carbon dioxide flowing in horizontal mini/micro circular tubes cooled at a constant temperature has been investigated experimentally. Six stainless steel circular tubes having inside-diameters of 0.50 mm, 0.70 mm, 1.10 mm, 1.40 mm, 1.55 mm, and 2.16 mm were tested. Measurements were carried out for the pressures ranging from 74 to 120 bar, the temperatures ranging from 20 to 110°C, and the mass flow rates ranging from 0.02 to 0.2 kg/min. It is found that the buoyancy effect was still significant, although supercriticalCO2 was in forced motion through the horizontal tubes at Reynolds numbers up to 10 5. The experimental results also indicate that the existing correlations developed in the previous studies for large tubes deviate significantly from the experimental data for the present mini/micro tubes. Based on the experimental data, a correlation was developed for the axially averaged Nusselt number in terms of appropri- ate dimensionless parameters for forced convection of supercritical carbon dioxide in horizontal mini/micro tubes cooled at a constant temperature. @DOI: 10.1115/1.1423906#
Experiments on turbulent heat transfer by supercritical CO2 in a vertical upward flow were conducted in a tube with an inner diameter of 4.5 mm. The experiments were performed for bulk fluid temperatures ranging from 29 to 115 °C, pressures ranging from 74.6 to 102.6 bar, local wall heat fluxes ranging from 38 to 234 kW/m2, and mass fluxes ranging from 208 to 874 kg/m2 s. The wall temperature distributions were significantly influenced by wall heat flux and mass flux. The wall temperature had a noticeable peak value when the wall heat flux was moderate and the mass flux was low. To determine the buoyancy and flow acceleration effects on heat-transfer characteristics, the ratios of the Nusselt numbers obtained from the experimental data and from a reference correlation are compared with Bo* and q+ along the test section. To analyze the changes in the shear stress distribution due to flow acceleration and buoyancy effects, the ratios of the shear stress reduction to wall shear stress due to flow acceleration and buoyancy effects are derived from approximate considerations. A new heat-transfer correlation is proposed, which could be used to predict heat transfer phenomena in a vertical upward flow of a supercritical fluid. The correlation is assessed by comparison with various experimental data.
This literature survey is devoted to the problem of heat transfer of fluids at supercritical pressures including near critical region.The objectives are to assess the work that was done in the area of heat transfer at supercritical pressures, to understand the specifics of heat transfer at these conditions, to compare different prediction methods for supercritical heat transfer in tubes and bundles, and to choose the most reliable ones.The comparisons showed there is a significant difference in heat transfer coefficient values calculated according to various correlations. Only some correlations show similar results, which are quite close to the experimental data for normal supercritical heat transfer in water and carbon dioxide. Also, no one correlation can accurately predict the magnitude and onset of deteriorated heat transfer.The exhaustive literature search, which included hundreds of papers, showed that the majority of correlations were obtained in tubes and just few of them in other flow geometries including bundles.The variations in the prediction of supercritical heat transfer are related to the significant changes in thermophysical properties near the critical and pseudocritical points. Therefore, a discussion on the general trends of various thermophysical properties at near critical and pseudocritical points is also included.Based on several chosen correlations, the heat transfer coefficients and temperature profiles in the CANDU-X reactor cooled with supercritical water were calculated.
Experimental and numerical investigations on forced convection heat transfer of supercritical CO2 within a semi-circular printed circuit heat exchanger have been performed in the present study. Primary operational parameters included inlet pressure of 7.5 MPa to 8.5 MPa, mass fluxes ranged from 160 kg/m2s to 760 kg/m2s and the average heat fluxes of 20 kW/m2 to 90 kW/m2. A physically improved semi-empirical correlation for the forced convection heat transfer of supercritical CO2 within the PCHE was developed by implementing probability density function (PDF)-based property revised technique for more reasonably interpreting the influence of the instantaneous turbulent temperature and fluctuating properties. The comparison results showed that the simple DB correlation could not reproduce the experiments and the Jackson correlation with the properties ratio correction terms could qualitatively capture the heat transfer features under different working conditions, however, it still overestimated the average value of the heat transfer coefficients in the whole range of the working conditions. The predictions of the PDF-based new developed correlation are significantly improved so that more than 96% data in the heating mode and more than 92% data in the cooling mode with various heat fluxes are captured and collapsed to an ideal straight line within an accuracy of 25%.
CATHARE is the French best estimate code used for safety analysis of Light Water Reactors. Two-phase flow is modelled with a two-fluid six-equation model in 0-D, 1-D and 3-D modules. A few months ago, the range of applications was limited to the sub-critical two-phase region, but thanks to the extension of the water and steam properties up to 26 MPa and recent modifications of the standard code version, it is now possible to simulate transients where both supercritical and sub-critical regimes are encountered. This paper describes these recent developments in the modelling of supercritical water flows using the two-fluid model implemented into the CATHARE code and shows the results of the preliminary assessment of this model successfully achieved by running several calculations for 1-D applications: - Steady state in supercritical conditions followed by blow-down - Stationary isenthalpic expansion - Stationary heat-up of supercritical fluid Then, using the modified CATHARE version, first steady-state and transient calculations of a Supercritical Light Water Reactor operating above the critical point were carried out, among them, Loss of Coolant Accidents (LOCAs) considering simple sequences of events. The predicted transient behaviours seem to be correct from supercritical to sub-critical regimes, which confirms the CATHARE capabilities.
Properties of supercritical water will undergo drastic changes near the "pseudo critical" point which gives rise to a serious concern about flow instabilities under supercritical conditions. To investigate the fluid flow behaviors, experiments with different system pressures (near-critical and supercritical pressure) were conducted on the Xi'an Jiao tong University's (XJTU) supercritical water test facility. Large amplitudes of mass flow flux as well as inlet pressure were found in various operation conditions. Mechanism of this unusual flow instability behavior is discussed. The oscillation behavior occurring in the present work has also been compared with that under the subcritical pressures and parameters effects are also studied.
A new model is presented in this paper to study the density wave instabilities of supercritical water (SCW) flowing in tubes. A new regional partition of SCW is proposed in this model for better dealing with the great variations of physical properties of SCW in the neighborhood region of pseudo critical point, based on the analyses of the physical properties of SCW. According to the frequency domain method, the new model is employed to study the density wave instabilities of SCW flowing in tubes, and the calculation results are compared with the experimental data in literature, together with the calculation results of three previous models proposed by different researchers. According to the comparisons, the present model is proved to be more reasonable and accurate than the other three models. The relative error of the present model is less than 26%, while that of the other three models are all greater than 30%. Hence, it is believed that the present model can provide well guidance for the design and operation of supercritical boilers, steam generators and other relevant heat exchangers.
With a view to better utilizing and further expanding the experimental results recently obtained on supercritical flow instability, an in-house code has been developed applying time-domain approach. Different ways of geometrical modeling of the test section in the experiments are studied. Comparison between the numerical and experimental results shows that the numerical code is capable to predict well the stability boundaries. Based on the validated code, the geometrical simplification is further discussed and a relatively simple as well as common geometrical configuration is proposed. Discussions also indicate that the entrance and riser sections cannot be eliminated with respect to numerical modeling of flow stability. Effects of inlet temperature and total mass flow rate are numerically analyzed. Results show that the inlet temperature has a non-monotonic effect on the threshold power, while the threshold power is roughly proportional to the total mass flow rate no matter the system is symmetrical or not. Moreover, the results indicate that it would be more difficult to perform flow instability experiments at higher inlet temperature or total mass flow rate.
The feature of fluids at pressures just above the critical value which makes them of particular interest is that they change in a continuous manner from being liquid-like to gas-like with increase of temperature at constant pressure. As a consequence of the extreme dependence of fluid properties on temperature, non-uniformity of density can lead to important effects on the mean flow and turbulence fields and heat transfer effectiveness. When the author and his colleagues first commenced research on supercritical pressure fluids many years ago it was decided to begin with a novel experiment specifically designed to include effects of strong non-uniformity of fluid properties whilst avoiding other complications associated with the temperature dependence of density. This fundamental experiment on stably stratified turbulent flow of supercritical pressure carbon dioxide between two horizontal planes, with the upper one heated and the lower one cooled, in such a way that there was no net heat transfer to the fluid, yielded evidence of a special mechanism for enhancement of turbulent mixing. Later, experiments with uniformly heated vertical tubes using carbon dioxide at pressures very near to the critical value gave results, which exhibited further striking features. Severe localized non-uniformity of heat transfer developed in the case of upward flow, but was not found with downward flow. Gravitationally induced motion caused effects on heat transfer which could only be explained by postulating drastic modification of turbulence. Such results stimulated the development of physically based ideas concerning the mechanisms which might be involved and led to the development of a semi-empirical model of buoyancy-influenced turbulent flow and heat transfer. The main aim of this paper is to show how such early work is now providing a basis for correlating experimental data and enabling the complicated phenomena encountered in those early experiments to be properly accounted for in thermal design procedures.
A new mathematical model was proposed in this paper based on the frequency domain theory to investigate two-phase flow instabilities in internally-ribbed tubes. Two significant improvements were made to conventional models, one of which was that the heat storage of the tube wall metal, the internal wall heat flux and the external wall heat flux were considered as dynamic parameters, and another one was that a new feedback relationship was established. The new model was verified by comparing the prediction results to both the corresponding experimental data in literature and the results obtained with SIMULINK. Then the two-phase flow instabilities in internally-ribbed tubes were studied systematically. It was shown that the stability of two-phase flows increased with pressure, mass flux or inlet resistance coefficient. It was also found that there existed a worst point of the stability (WPS) of the two-phase flows when the inlet fluid subcooling increased. Two-phase flows in the 6-head ribs internally-ribbed tube (ϕ38.1 × 7.5 mm) was more stable than that in the 4-head ribs internally-ribbed tube (ϕ28 × 5.41 mm). The present model and results could provide guidance for the design and operation of boilers.
Due to the urgent need for validation data in supercritical flow instability analysis, an experimental study has been performed in Nuclear Power Institute of China (NPIC) on flow instability in two parallel channels with supercritical water. The heated pipes have a length of 3000 mm and inner and outer diameters of 6 mm and 11 mm. Experimental conditions included pressures of 23–25 MPa, mass fluxes of 600–800 kg/m2 s, and inlet temperatures of 180–260 °C. In the experiments heat flux was increased gradually to obtain possible parallel instability boundaries while other parameters were adjusted in advance to desired values and kept constant. The evolution of flow rates during the heat flux increase has been analysed and divided into four stages. Discussions indicate that the asymmetry of flow rate between the parallel channels would be enlarged with relatively higher fluid temperature or total mass flow rate, subsequently making the occurrence of parallel flow instability more difficult in the experiments. The way of defining the onset of parallel instabilities has been proposed for supercritical water based on the experimental phenomena. Short-life transients are disregarded and only the sustained out-of-phase oscillations accompanied by evident amplitude enlargement are considered. Parametric studies show that the flow becomes more stable with increasing pressure or decreasing inlet temperature in the range of present experiments, and the mechanisms have been discussed compared to that for two-phase flow. Finally, the stability boundaries are illustrated in a two-dimensional plane using two dimensionless parameters proposed for supercritical flow.
The specifics of the thermophysical properties of single-phase supercritical pressure (SCP) coolants and the typical ranges of their thermodynamic state that determine the peculiarities of their turbulent heat transfer are considered. An assessment of the effect that dissolved gases with low critical parameters have on water and carbon dioxide properties is given. A brief analysis is presented of experimental studies on heat transfer of turbulent flows of SCP fluids in tubes when heating. Specific features of typical heat transfer modes (normal, deteriorated, and improved) are pointed out. The existing concepts concerning the nature of heat transfer deterioration are discussed. A simple classification of heat transfer regimes under high heat loads is proposed, which makes it possible to determine the reasons for and assess the degree of danger of heat transfer deterioration
This paper summarizes the analysis results of the thermal-hydraulic stability of a high-temperature reactor cooled and moderated by supercritical-pressure light water (SCLWR-H). A linear stability analysis code in the frequency domain was developed to study the thermal-hydraulic stability of SCLWR-H at constant supercritical pressure. The analysis method is based on linearization by perturbation of numerically-discretized one-dimensional single-channel single-phase conservation equations. The effect of water rods on stability is considered. The thermal-hydraulic stability of SCLWR-H for full-power and partial-power normal operations was investigated by frequency domain method. Our analysis reveals that though SCLWR-H has low coolant flow rate and large density change in the core, the thermal-hydraulic stability can be maintained both at normal operation and during power raising phase of constant pressure startup by applying an orifice pressure drop coefficient at the inlet of the fuel assemblies. A parametric study was also carried out to determine the parameters affecting the stability.
Linear stability analysis is being widely used in exploring gas-liquid stratified/non-stratified transitions. As the present study relates to liquid-liquid two-phase systems, the stability characteristics of stratified layers are considered. In parallel, the conditions necessary for real characteristics are also explored. The relations between stability conditions and those for well-posedness are discussed in view of the implications for flow pattern transitions. The convergence of the stability conditions to various extremes is discussed. The integrated considerations of stability and well-posedness shed light on the physical sequences in flow pattern transitions, which so far have been studied by stability analysis alone. As liquid-liquid systems are involved, wide ranges of density and viscosity ratios are studied for various operational conditions.
The thermal-hydraulic stability of a uniformly heated channel at supercritical water pressure has been investigated to help understand the system instability phenomena which may occur in supercritical water nuclear reactors (SCWRs). We have extended the modeling approach often used for the stability analysis of phase change systems to supercritical pressure operation conditions and have developed rigorous new non-dimensional groups for the stability maps. We have also shown that while density-wave oscillations (DWO) can occur, Ledinegg excursive instabilities and pressure drop oscillations (PDO) will not occur in supercritical water systems. The linear stability characteristics of a typical uniformly heated channel were computed by evaluating the eigenvalues of a one-dimensional model. An analysis of non-linear instability phenomena was also performed in the time domain and the dynamic bifurcations were evaluated.
This paper presents the fluid flow and heat transfer characteristics of supercritical CO2 in a horizontal multi-port extruded aluminum test section consisting of 10 circular channels with an inner diameter of 1.31 mm. Both local and average pressure drop and heat transfer coefficients were measured as CO2 was cooled in the multi-port circular channels with pressures ranging from 7.4 to 8.5 MPa, inlet fluid temperatures ranging from 22 to , and mass velocity ranging from 113.7 to 418.6 kg/m2 s. The results indicate that the operating pressure, the mass velocity and the temperature of CO2 had significant effects on fluid flow and heat transfer characteristics. The pressure drop and the average heat transfer coefficient increased greatly with increasing the average temperatures of CO2 in the near-critical region; the average heat transfer coefficient attained a peak value near the corresponding pseudocritical temperature; and the maximum heat transfer coefficient decreased as the pressure increased. Both the pressure drop and the heat transfer coefficient increased with the mass velocity, but decreased with the operating pressure. The measured average heat transfer coefficients were compared with the experimental data reported in the literatures and a large discrepancy was observed. Based on the experimental data collected in the present work, a new correlation was developed for forced convection of supercritical CO2 in horizontal multi-port mini channels under cooling conditions.
A supercritical water heat transfer test section has been built at Xi’an Jiaotong University to study the heat transfer from a 10 mm rod inside a square vertical channel with a wire-wrapped helically around it as a spacer. The test section is 1.5 m long and the wire pitch 200 mm. Experimental conditions included pressures of 23–25 MPa, mass fluxes of 500–1200 kg/m2 s, heat fluxes of 200–800 kW/m2, and inlet temperatures of 300–400 °C. Wall temperatures were measured with thermocouples at various positions near the rod surface. The experimental Nusselt numbers were compared with those calculated by empirical correlations for smooth tubes. The Jackson correlation showed better agreement with the test data compared with the Dittus-Boelter correlation but overpredicted the Nusselt numbers almost within the whole range of experimental conditions. Both correlations cannot predict the heat transfer accurately when deterioration occurred at low mass flux and relatively high heat flux in the pseudocritical region. Comparison of experimental data at two different supercritical pressures showed that the heat transfer was more enhanced at the lower supercritical pressure but the deterioration was more likely to occur at the higher pressure, meaning increased safety. Based on a comparison with an identical channel without the helical wrapped wire, it was found that the wire spacer does not enhance the heat transfer significantly under normal heat transfer conditions, but it contributes to the improvement of the heat transfer in the pseudocritical region and to a downstream shift of the onset of the deterioration. The Jackson buoyancy criterion is found to be valid and works well in predicting the onset of heat transfer deterioration occurring in the experiments without wire.
An analysis of thermally induced flow oscillations in the near-critical and super-critical thermodynamic region
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Hydrodynamic flow instabilities in power equipment components
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