Pseudo-critical Region Research Articles

Experimental studies on heat transfer to supercritical water in 2 × 2 rod bundle with two channels

The experiment of heat transfer to supercritical water in 2×2 rod bundle is performed at Shanghai Jiao Tong University. The test section consists of two channels separated by a square steel assembly box with rounded corners. Water flows downward in the first channel and then turns upward in the second channel to cool the 2×2 rod bundle installed inside the assembly box. The bundle consists of four heated rods of 10mm in O.D. and 1.18 in pitch-to-diameter ratio. The fluid enthalpy in the first channel increases due to the heat transfer through the assembly box when flowing downward. The minimum fluid enthalpy increase in the first channel appears at the pseudo-critical region due to the small temperature difference between the two channels. Effects of various parameters on heat transfer behavior inside the 2×2 rod bundle are similar to those observed in tube or annuli. No special phenomenon in heat transfer is observed during the mass flux and power transient. The steady-state heat transfer correlation is applicable to predict the heat transfer in the mass or power transient sequence. In addition, the importance of several dimensionless numbers and the accuracy of 20 heat transfer correlations are assessed. It is concluded that the buoyancy parameter proposed by Cheng et al. (2009) shows unique effect on heat transfer coefficient. Among the 20 selected heat transfer correlations, the correlations of Jackson and Fewster (1975) and Bishop et al. (1964) give the best predictions when compared with the experimental data.

Heat transfer to supercritical water in a 2 × 2 rod bundle

An experimental study on heat transfer to supercritical water flowing in a 2×2 rod bundle test section with two channels is carried out at Shanghai Jiao Tong University. The bundle consists of four heated rods with an OD of 10mm and a pitch-to-diameter ratio of 1.18. The 2×2 rod bundle is inserted into a square assembly box with rounded corners by which the test section is separated into two channels. Water flows downward in the first channel between the pressure tube and the assembly box and then turns upward in the second channel inside the assembly box to cool the four heated rods, which are directly heated by DC power. The experimental conditions are as follows: pressure ranging from 23 to 26MPa, mass flux ranging from 400 to 1200kg/m2s, heat flux between 300 and 1000kW/m2, and bulk fluid temperatures ranging from 200 to 480°C. The heat transfer through the assembly box is strongly affected by the temperature difference between the two channels. The minimum fluid enthalpy increase in the first channel appears near the pseudo-critical temperature region. Non-uniformity of circumferential wall-temperature distribution around the heated rod is observed. The effects of various parameters on heat transfer behavior inside the 2×2 rod bundle are similar to effects observed in tubes. Six developed correlations are compared with the test data. The correlations of Jackson and Fewster (1975) and Bishop et al. (1964) provide the best predictions of the test data among the selected correlations.

Modifications of heavy-flavor spectra insNN=62.4GeV Au-Au collisions

We calculate open heavy-flavor (HF) production in Au+Au collisions at $\sqrt{s_{\rm NN}}$=62.4 GeV utilizing a nonperturbative transport approach as previously applied in nuclear collisions at top RHIC and LHC energies. The effects of hot QCD matter are treated in a strong-coupling framework, by implementing heavy-quark diffusion, hadronization and heavy-flavor meson diffusion within a hydrodynamic background evolution. Since in our approach the heavy-flavor coupling to the medium is strongest in the pseudo-critical region, it is of interest to test its consequences at lower collision energies where the sensitivity to this region should be enhanced relative to the hotter (early) fireball temperatures reached at top RHIC and LHC energies. We find that the suppression and flow pattern of the non-photonic electrons from heavy-flavor decays at 62.4 GeV emerges from an intricate interplay of thermalization and initial-state effects, in particular a Cronin enhancement which is known to become more pronounced toward lower collision energies.

ICONE23-1743 HTC CORRELATION APPLICATIONS TO SUPERCRITICAL WATER FLOWING UPWARD IN A VERTICAL ANNULAR CHANNEL AND 3-ROD BUNDLE

There have been relatively few publications detailing correlations for heat-transfer in SuperCritical Water (SCW) flowing inside bundle geometry compared to SCW heat-transfer in bare-tubes. Since flow geometry is impeded by bundle geometry, heat-transfer to the coolant occurs differently in bundles than in bare tubes. In this paper, results of heat-transfer to supercritical water flowing upward in a vertical 1-rod annular channel and 3-rod bundle (rods are equipped with helical ribs) are discussed. The data obtained in this study could be applicable for a reference estimation of heat transfer in future designs of fuel bundles. The Jackson (2002) bare-tube heat-transfer correlation most accurately predicted Heat Transfer Coefficients (HTCs) in annular channel trials at heat fluxes less than 2.5 MW/m2. However, this correlation (along with others) did not predict HTCs accurately in annular channel trials at heat fluxes above 2.5 MW/m2 and in 3-rod bundle geometry at all values of heat flux tested. Changes in thermophysical properties of a coolant, especially, within the pseudocritical region, caused discontinuity in the calculated HTC profiles in most correlations.

Turbulent convective heat transfer of CO 2 in a helical tube at near-critical pressure

Abstract Experiments of carbon dioxide flowing in a helical pipe at near-critical pressure were performed at constant heat flux boundary condition. The helical curvature diameter, helical pitch and tube diameter were 283.0 mm, 32.0 mm and 9.0 mm, respectively. The inlet Reynolds number was larger than 104 to ensure the turbulent flow. The renormalization group RNG k–e model simulated the three-dimensional turbulent heat transfer of CO2 in the helical pipe. Much attention was paid to the combined effects of the centrifugal force and buoyancy force on the heat transfer. The RNG k–e model reasonably simulates the complicated heat transfer. The wall temperatures near the tube exit were slightly over-predicted, due to the suppression of the increased wall temperatures near the tube exit by axial thermal conduction in the experiment. Before and near the pseudocritical temperature region, the varied physical properties caused significantly non-uniform velocity and temperature distributions over the tube cross section. The larger axial velocities appear at the outer-bottom location, and the higher wall temperatures appear at the inner-top location. Thus, the outer-bottom locations hold larger heat transfer coefficients. The turbulent kinetic energies are increased along the axial angles and larger in the inner-top region of the tube cross section. The effective viscosities are decreased along the axial angles, and the larger effective viscosities are shifted to the tube center with the axial flow development. Beyond the pseudocritical temperature region, the decreased buoyancy force suppressed the non-uniformity of the heat transfer coefficients over the tube circumference.

Finite-size scaling analysis of pseudocritical region in two-dimensional continuous-spin systems.

At low temperatures, the two-dimensional continuous-spin systems exhibit large correlation lengths. Some of them show the Berezinskii-Kosterlitz-Thouless-like transitions, and some others show pseudocritical behaviors for which correlation lengths are extremely large but finite. To distinguish pseudo and genuine critical behaviors, it is important to understand the nature of spin-spin correlations and topological defects at low temperatures in continuous-spin systems. In this paper, I develop a finite-size scaling analysis which is suitable for distinguishing the critical behavior and its applications to the two-dimensional XY, Heisenberg, and RP(2) models.

The transition to turbulence of buoyant near-critical water jets

Observations of near-critical water jets are reported in the injection Reynolds number range of approximately 300–3000 to characterize their transition to turbulence. Three types of cases are described: (i) subcritical jet injected into subcritical water, (ii) supercritical jet injected into supercritical water, and (iii) supercritical jet injected into subcritical water. In each case, the working pressure was kept above the critical value to eliminate two-phase effects. For cases (i) and (ii), the transition behavior follows well known characteristics with transition to turbulence initially occurring near the tip of the jet with the transition location moving upstream nearer to the nozzle exit with an increase in injection Reynolds number. However, the transition behavior for case (iii) is quite different with significant buoyant effects leading to turbulent behavior at lower Reynolds numbers. Consideration of the pseudocritical region with strongly varying fluid properties, which is established in the mixing region between the jet and the cell fluid, yields an effective Froude number that is useful to elucidate this difference. The effective Froude number incorporates the Prandtl number of the mixing region to account for the large disparity between viscous and thermal length scales.

Properties of thermal photons at RHIC and LHC

We study the emission characteristics of thermal photons at RHIC and LHC as affected by both the space-time evolution of the bulk medium and the thermal emission rates. For the former we compare the results of two evolution models (expanding fireball and hydrodynamics). For the latter, we detail the influence of hadronic emission components and study a speculative scenario by upscaling the default QGP and hadronic rates around the pseudo-critical region.

Heat transfer characteristics of supercritical pressure water in vertical upward annuli

Heat transfer characteristics of supercritical pressure water in vertical-upward annuli with annular gaps of 4mm and 6mm were investigated experimentally. The inner heated rod has an outer diameter of 8mm with an effective heated length of 1400mm. Experimental parameters covered the pressures of 23–28MPa, mass fluxes of 350–1000kg/m2s, heat fluxes of 200–1000kW/m2 and inlet bulk temperature up to 400°C. According to the experimental data, the effects of heat flux and mass flux on heat transfer of supercritical water were analyzed. Experimental results showed that heat transfer of various heat fluxes and mass fluxes in annuli are similar with those in tubes. Compare the heat transfer differences in the two annular gaps, it was found that heat transfer in 6mm gap channel is better than that in 4mm gap channel, especially in the pseudo-critical enthalpy region. Experimental results also showed that the spiral spacer, which was arranged on the outer surface of the heated rod, has a positive effect on enhancing local heat transfer. However, this enhanced phenomenon seems stronger in 4mm gap compared to that in 6mm gap. The criterion of Jackson–Hall was selected to distinguish the effect of buoyancy in annular channels. Predicted results demonstrated that this criterion achieves good agreements against the experimental data at various mass fluxes and pressures. The present paper compared the experimental data with eight heat transfer correlations for supercritical pressure water. It was found that the correlations of Jackson, Bishop and Cheng are most close to the test data for normal heat transfer region, whereas only the correlation of Cheng seems acceptable when heat transfer deterioration occurs.

Natural convective flow and heat transfer studies for supercritical water in a rectangular circulation loop

A closed Supercritical Pressure Natural Circulation Loop (SPNCL) has been set up to generate data on flow and heat transfer behavior for supercritical fluids (i.e. water and carbon dioxide) under natural circulation conditions. Experiments were conducted in SPNCL with water as working fluid. Instability was observed over a narrow window of power in the pseudo-critical temperature region for horizontal heater horizontal cooler orientation. Instability was observed at low supercritical pressure range of 22.1–22.9MPa, however it got suppressed at higher pressures. An in-house developed computer code NOLSTA has been used to perform steady state and stability analysis of SPNCL and predictions are compared with experimental data. The heat transfer data generated in the test facility has been compared with various heat transfer correlations for supercritical fluids available in literature. The present paper describes the experimental results and comparisons in detail.

Performance evaluation of a tube-in-tube CO2 gas cooler used in a heat pump water heater

In this study, investigation of the performance of a tube-in-tube counter-flow water-cooled CO2 gas cooler operating above and near critical pressure is presented using a heat pump water heater with CO2 flowing in the annulus side. A tube-in-tube heat exchanger model applicable for supercritical fluid CO2 and water was also developed and validated. The measured total heat transfer capacity ranged from 1.31 to 4.06kW at various test conditions. The calculations show good agreement with the experimental results. The results demonstrate that the variation of CO2 temperature tends to show very slow decreasing near the pseudo-critical region when compared to the inlet region. Yet this phenomenon becomes more pronounced as the inlet pressure is close to the critical pressure (73.8bar). The calculation also reveals a peculiar phenomenon that the local heat transfer rate of the heat exchanger peaks within the heat exchanger near the pseudo critical region due to the drastic rise of specific heat (CP value).

Evaluation of the Heat Transfer Correlations for Supercritical Pressure Water in Vertical Tubes

A large number of studies have been carried out on the flow and heat transfer of supercritical pressure fluids in the past decades. However, there are still some uncertainties and deficiencies in the accurate prediction for supercritical fluid heat transfer coefficient due to the large and fast variations of fluids properties in the so-called pseudo-critical region. In this paper, 15 correlations were selected from the literature and were compared with each other to verify their capability in predicting heat transfer coefficient of supercritical pressure water in vertical tubes. Based on the comparison between the calculation results of the existing heat transfer correlations and the experimental data obtained from the open literature, it was found that the Swenson et al. correlation and the Hu correlation can reasonably predict the heat transfer coefficient of supercritical water in the pseudo-critical region. After evaluating these correlations, the authors conducted polynomial fitting for the collected experimental data and got a new correlation for heat transfer coefficient of water at supercritical pressures. The new correlation can fit well with the experimental data even in the neighborhood of pseudo-critical temperature.

Experimental investigation on heat transfer characteristics of smooth tube with downward flow

In the range of pressure from 11.5 to 28MPa, mass flow rate from 450 to 1550kgm−2s−1, and heat flux at inner wall from 50 to 585kWm−2, an experiment was conducted to investigate the heat transfer characteristics of water in a vertical downward tube. The temperature distribution in the tube wall was obtained. The effects of heat flux on heat transfer coefficient and wall temperature were analyzed and the corresponding empirical correlations were presented. The heat transfer coefficients of vertical downward flow were compared with that of vertical upward flow. The experimental results show that at subcritical and near critical pressure, dryout and departure from nucleate boiling (DNB) can occur in vertical downward tube. With the increase of heat flux, heat transfer deterioration occurs ahead and the peak wall temperature after heat transfer deterioration increases obviously. At supercritical pressure, the wall temperature increases slowly with fluid enthalpy when the bulk temperature is lower than the pseudo-critical temperature and increases considerably when the bulk temperature is higher than the pseudo-critical temperature. In the pseudo-critical enthalpy region, the heat transfer is enhanced.

Experimental investigation on convective heat transfer from a horizontal miniature tube to methane at supercritical pressures

Heat transfer of supercritical cryogenic methane in miniature tube has been experimentally investigated. Experimental conditions included pressures of 5–15 MPa, mass velocities of 6000–150,000 kg m−2 s−1 and heat fluxes of 1–16 MW m−2. The mass flux, heat flux and pressure effect were analyzed. A physically reasonable property averaging technique, Probability Density Function (PDF)-based time-averaged properties, were proposed for accounting for the effect of highly nonlinear dependency of properties on instantaneous turbulent temperature. A semi-empirical new correlation evaluated by PDF-based time-averaged properties for convection heat transfer of supercritical cryogenic methane was developed. The experimental Nusselt numbers were compared with those calculated with empirical correlations. The Dittus–Boelter and Gnielinski correlations overestimate the measurements in the pseudo-critical region since they could not accurately reflect the properties variations.The newly developed PDF correlation works so well that more than 85% experimental data are captured within an accuracy of 25%. Jackson acceleration criterion is found valid in evaluating the acceleration effect and works well in predicting heat transfer deterioration occurring in present experiments.

Developing empirical heat-transfer correlations for supercritical CO2 flowing in vertical bare tubes

This paper presents an analysis of three new heat-transfer correlations developed for SuperCritical (SC) carbon dioxide (CO2) flowing in vertical bare tubes. These correlations were developed from the large set of experimental data obtained at Chalk River Laboratories (CRL), AECL (2003). The dataset consists of tests performed in upward flow of CO2 inside 8-mm ID vertical Inconel-600 tube with a 2.208-m heated length. Data points compiled lie within a wide range of thermodynamic parameters – outlet pressures ranging from 7.4 to 8.8MPa, mass fluxes from 900 to 3000kg/m2s, inlet fluid temperatures from 20 to 40°C, and heat fluxes from 15 to 615kW/m2; and for several combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperature.The objective of our research is to obtain reference dataset on heat transfer in SCCO2 and improve fundamental knowledge of the heat-transfer processes and handling of supercritical fluids. In general, heat-transfer process to a supercritical fluid is difficult to model, especially, when a fluid passes through the pseudocritical region, as there are very rapid variations in thermophysical properties of the fluid. Thus, it is important to investigate SC-fluid behaviour within these conditions.In general, SCCO2 was and is used as a modelling fluid instead of SC water due to its lower critical parameters. Also, SCCO2 is proposed to be used as a working fluid in the Brayton gas-turbine cycle as a secondary power cycle for some of the Generation-IV nuclear-reactor concepts such as Sodium-cooled Fast Reactor (SFR), Lead-cooled Fast Reactor (LFR) and Molten-Salt-cooled Reactor (MSR). In addition, SCCO2 was proposed to be used in advanced air-conditioning and geothermal systems.Previous studies have shown that existing correlations deviate significantly from experimental Heat Transfer Coefficient (HTC) values, especially, within the pseudocritical range (for both SCCO2 and SC water data–see Section 4 for more details). Moreover, the majority of correlations were mainly developed for supercritical water, and our latest results indicate that they cannot be directly applied to SCCO2 with the same accuracy.There is still a great reliance on 1-D correlations for basic heat transfer calculations. We need to develop better empirical models that can predict SCF thermodynamic/heat-transfer behavior more accurately. Therefore, new empirical correlations to predict HTC values were developed based on CRL – SCCO2 dataset. These correlations calculate HTC values with an accuracy of ±30% (wall temperatures with accuracy of ±20%) for the analyzed dataset.

Large eddy simulation of turbulent heat transfer at supercritical pressures

The paper presents results of large eddy simulation of turbulent heat transfer for water at supercritical pressures. Two cases are considered; the downward and the upward flow in an externally heated pipe. The temperature range for both considered cases entails the pseudo-critical region, where physical properties of the working fluid change significantly. The upward case, in particular, features the heat transfer deterioration, characterized by large increase in wall temperature. The numerical framework consists of staggered finite volume method, defined on Cartesian grids, integrated in time with a projection method. Variable physical properties of the working fluid are implemented as look-up tables, based on the NIST database. Turbulent statistics were gathered for a range of 55 large-eddy turn-over times. The results for first and second moment statistics are presented. Wall temperature, in particular, compares favorably with measurements. The authors believe that insight into turbulent statistics presented in this work can be useful to improve Reynolds-averaged Navier–Stokes based models.

Numerical simulation and comparison of turbulent heat transfer in supercritical and subcritical water

In this study, the heat transfer of supercritical water in uniformly heated vertical tube is numerically investigated with three different turbulence models, i.e., the renormalisation group (RNG) k-e model, the shear stress transport (SST) k-ω model and the Reynolds stress model (RSM). In order to find suitable turbulence models for engineering applications, for example, the supercritical water-cooled reactor (SCWR), the results are compared with experimental results by Yamagata et al. (1972) firstly. It has been found that, as the physical properties of supercritical water change rapidly with temperature in pseudo-critical region, these turbulence models, which are simplified, based on isotropic flow and constant physical properties, do not agree well with the experimental results, and even fail in some cases. The numerical results of RSM are also not good enough as expected near critical point. To further explore the flow and heat transfer mechanism in supercritical water, sub-cooled nucleate boiling under subcritical pressure is also numerically investigated in order to find the similarities and differences with those under supercritical pressure.

The pseudocritical regions for supercritical water

Vapour pressure curves and stability lines can be extended beyond the critical points into the supercritical domain by so-called Widom lines, along which some thermodynamic property undergoes a rapid change and liquid-like behaviour turns to vapour-like one. Knowledge about such lines is therefore important for thermohydraulic calculations and design. There are several properties that can be chosen as defining property of a Widom line. In this short note we calculate and compare several kinds of Widom lines for water.

Investigation on the Properties of Supercritical CO<sub>2 </sub>Fluid and its Heat Transfer Characteristics

The obvious characteristics of transcritical CO2 cycle are that the heat rejection process takes place in the supercritical region. The thermophysical properties of supercritical CO2 change dramatically with the temperature and pressure near the critical region, which results in the momentum and energy exchange and buoyant force change in the heat flux direction, so it should be treated as “variable properties”. According to the characteristics of CO2 specific heat, the correlation of the pseudocritical temperature is obtained and the pseudocritical region is defined. The heat transfer features of CO2 under supercritical pressure are different from those of the conventional refrigerants. In order to compare the heat transfer performance of supercritical CO2 fluid and the conventional refrigerants, the contrast investigation on the heat transfer treatment principle, the heat transfer mechanism and the thermophysical properties are mainly presented in this paper.

Flow frictional resistance characteristics of kerosene RP-3 in horizontal circular tube at supercritical pressure

The flow frictional resistance characteristics of kerosene RP-3 have been experimentally investigated in the horizontal circular tube that is isothermal and has the inner diameter of 1.78mm at supercritical pressures. Both frictional pressure drop and friction factor of RP-3 were investigated under the pressures of 3–6MPa, temperatures from 329K to 810K and mass flow rates from 2g/s (803.71kg/m2s) to 4g/s (1607.4kg/m2s). The results demonstrate that the operating pressure, mass flow rate and fluid temperature have considerable effects on the fluid flow frictional resistance. The frictional pressure drop increases with the mass flow rate, and also increases significantly with the promoting temperature of RP-3 in the critical region. At relatively low operating pressure in the decreasing process, the friction factor presents a prominent peak, near the pseudo-critical temperature, with the increasing fluid temperature. Both the frictional pressure drop and friction factor variation decrease with increasing operating pressure in the critical and pseudo-critical regions. Based on a large amount of experimental data, we have proposed a new friction factor correlation that fits the sub- and super-critical kerosene RP-3 studied in this work, and the correlation shows much less deviation of friction factor than previous models.