Pseudo-critical Region Research Articles

Performance of a tube-in-tube CO2 gas cooler

In this study, a tube-in-tube heat exchanger model applicable to supercritical CO2 and water was developed. The developed model is first validated with some existing measurements. Normally, the variation of the heat transfer rate for a constant-property working fluid shows a monotonic decrease from the inlet of minimum heat capacity flow rate (Cmin). By contrast, the CO2 may present a local minimum and a local maximum along the length of the heat exchanger, provided CO2 passes through the pseudo-critical temperature, and this phenomenon becomes more and more pronounced when the pressure is close to the critical pressure. In contrast, it is possible for a local maximum heat transfer rate to occur near the inlet of Cmin even when the CO2 does not pass through the pseudo-critical point. This happens when Cmin is on the water side and the property variation of CO2 is taken into account. The calculation also shows that the effect of the inlet pressure on the variation of the CO2 temperature is not as apparent as the effect of the inlet pressure on the heat transfer rate, even when there is a significant change in the overall heat transfer coefficient, implying that the heat transfer characteristics of CO2 near the pseudo-critical region is similar to normal refrigerants, which show an invariant temperature at the condensation point. Hence, it would be beneficial to extend the influence of the pseudo-critical region when taking the heat transfer augmentation into consideration.

CO2 based natural circulation loops: New correlations for friction and heat transfer

Results obtained from CFD analysis of 3-dimensional natural circulation loops (NCL) that employ carbon dioxide and water as loop fluids are presented for various isothermal wall temperatures of source and sink in the range of 278–341K. Such a temperature range would be useful in various heat transfer applications of NCL, e.g. air conditioning, solar collectors, extraction of geothermal energy, etc. For the same wall temperature and geometrical parameters, comparison is made between CO2 and water in terms of heat transfer rate. Water is considered at atmospheric pressure whereas CO2 is either in subcritical (liquid) or supercritical state. Liquid CO2 exhibits very high heat transfer rate, approximately seven times higher than water, whereas performance of supercritical CO2 depends on the operating pressure and temperature. Effect of loop operating pressure on the system performance is also investigated. Results show that near pseudo-critical region, CO2 yields very high heat transfer rate, approximately seven times higher than water. Results also show that, due to the presence of bends and local buoyancy effects, fluid parameters such as local velocity and temperature vary in all three dimensions. Validation of simulation results against experimental results reported in the literature with respect to modified Grashof number (Grm) and Reynolds number (Re) exhibit good agreement. Additionally, new correlations are proposed for Re in terms of Grm, friction factor (f) in terms of Re, and Nusselt number (Nu) in terms of Re and Prandtl number (Pr).

CFD analysis of a CO2 based natural circulation loop with end heat exchangers

Abstract 3-D steady flow simulation of a CO2 based, single-phase (subcritical and supercritical) rectangular natural circulation loop (NCL) with end heat exchangers is presented. Viscous dissipation in fluid and axial conduction in fluid as well as in solid wall are considered. Results are obtained for various inlet temperatures of water in the hot heat exchanger, for a fixed inlet temperature of cooling water in the cold heat exchanger. Effect of loop operating pressure (60–100 bar) on system performance is also investigated. Results show that due to the presence of bends and strong buoyancy effects near pseudo-critical zone, local velocity and temperature vary in all three dimensions. It is noticed that at a given loop pressure, the variation of heat transfer rate with loop fluid temperature changes sign in the vicinity of pseudo-critical region. Steady-state Reynolds number and heat transfer coefficients obtained through the CFD analysis are compared with those calculated using available correlations. Although qualitative trends match, quantitative differences exist that may be attributed to difference in configuration. Additionally, new correlations are proposed for Re in terms of modified Gr, and Nu in terms of Re and Pr which are expected to be useful in the design and analysis of NCLs with end heat exchangers.

Heat Transfer Measurements of Supercritical Carbon Dioxide in a Horizontal Circular Straight Tube

Supercritical fluids have been drawing attention to many researchers as heat transfer media for power plant cycles, for refrigeration and heat pump applications. The exceptional heat transfer characteristics of supercritical fluids are key parameters for those applications. Above critical pressure, especially, in pseudocritical region, small temperature and pressure variations can lead to significant changes in the thermo-physical properties of the fluids. The large variation of thermo-physical properties of the fluid in the near critical point can cause a different thermo-fluid behavior and an enhanced convection heat transfer characteristics in this region. This allows enormous potential for energy transfer, but also alters the turbulent flow due to changes in the turbulent shear stress, brought about by acceleration and buoyancy effects. These effects are not fully understood and require further research to be able to predict the dynamic behaviors for further design applications. A supercritical CO2 testing loop has been built at Texas A&M University at Qatar to perform detailed heat transfer and pressure drop measurements to investigate the thermo-physical and dynamic characteristics of supercritical fluid flows. As an initial test, the total heat transfer coefficient of the tube has been measured at the supercritical conditions and the results are compared with that of a sub-cooled fluid and discussed here.

Heat Transfer of Supercritical Carbon Dioxide in Printed Circuit Heat Exchanger Geometries

The increasing importance of improving efficiency and reducing capital costs has led to significant work studying advanced Brayton cycles for high temperature energy conversion. Using compact, highly efficient, diffusion-bonded heat exchangers for the recuperators has been a noteworthy improvement in the design of advanced carbon dioxide Brayton cycles. These heat exchangers will operate near the pseudocritical point of carbon dioxide, making use of the drastic variation of the thermophysical properties. This paper focuses on the experimental measurements of heat transfer under cooling conditions, as well as pressure drop characteristics within a prototypic printed circuit heat exchanger. Studies utilize type-316 stainless steel, nine channel, semi-circular test section, and supercritical carbon dioxide serves as the working fluid throughout all experiments. The test section channels have a hydraulic diameter of 1.16 mm and a length of 0.5 m. The mini-channels are fabricated using current chemical etching technology, emulating techniques used in current diffusion-bonded printed circuit heat exchanger manufacturing. Local heat transfer values were determined using measured wall temperatures and heat fluxes over a large set of experimental parameters that varied system pressure, inlet temperature, and mass flux. Experimentally determined heat transfer coefficients and pressure drop data are compared to correlations and earlier data available in literature. Modeling predictions using the computational fluid dynamics (CFD) package FLUENT are included to supplement experimental data. All nine channels were modeled using known inlet conditions and measured wall temperatures as boundary conditions. The CFD results show excellent agreement in total heat removal for the near pseudocritical region, as well as regions where carbon dioxide is a high or low density fluid.

Supercritical Water Heat Transfer in a Vertical Bare Tube: Normal, Improved, and Deteriorated Regimes

This paper presents selected results on heat transfer to supercritical water flowing upward in a 4-m-long vertical bare tube. Supercritical water heat transfer data were obtained at pressures of ~24 MPa, mass fluxes of 200 to 1500 kg/m2s, heat fluxes up to 874 kW/m2, and inlet temperatures from 320 to 460°C for several combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperatures.In general, the experiments confirmed that there are three heat transfer regimes for forced-convection heat transfer to water flowing inside tubes at supercritical pressures: (a) normal heat transfer regime characterized in general with heat transfer coefficients (HTCs) similar to those of subcritical convective heat transfer far from the critical region, which are calculated according to Dittus-Boelter-type correlations; (b) deteriorated heat transfer (DHT) regime with lower values of HTC and hence higher values of wall temperature within some part of a test section compared to those of the normal heat transfer regime; and (c) improved heat transfer regime with higher values of HTC and hence lower values of wall temperature within some part of a test section compared to those of the normal heat transfer regime.These new heat transfer data are applicable as a reference dataset for future comparison with supercritical water bundle data and for a verification of scaling parameters between water and modeling fluids.Also, these HTC data were compared to those calculated with the original Dittus-Boelter and modified Bishop et al. correlations. The comparison showed that the modified Bishop et al. correlation (i.e., the Bishop et al. correlation with the constant proposed by Kirillov et al.), which uses the cross-sectional averaged Prandtl number, represents HTC profiles more correctly along the heated length of the tube than the Dittus-Boelter correlation. In general, the modified Bishop et al. correlation shows good agreement with the experimental HTCs outside the pseudocritical region; however, it underpredicts the experimental HTCs within the pseudocritical region. The Dittus-Boelter correlation can also predict experimental HTCs outside the pseudocritical region but deviates significantly from experimental data within the pseudocritical region by up to four times.A reason for this deviation is that the Nusselt number in the Dittus-Boelter correlation and corresponding HTC values closely follow the regular Prandtl number (i.e., based on data from thermophysical properties tables), which in turn closely follows the peak in specific heat within the pseudocritical region. However, experimental HTC values show just a moderate increase within the pseudocritical region possibly due to significant variations of fluid temperature within the tube cross section. In this case, the bulk-fluid temperature might not be the best characteristic temperature at which all thermophysical properties should be evaluated. That is why the cross-sectional averaged Prandtl number is used in many supercritical heat transfer correlations instead of the regular one.A simple empirical correlation was proposed for calculating heat flux at the starting point of the DHT regime. However, it should be noted that both these correlations, i.e., the Dittus-Boelter and modified Bishop et al. correlations, cannot accurately predict HTCs within the DHT regime.

Computational-fluid-dynamics study of a Kenics static mixer as a heat exchanger for supercritical carbon dioxide

The thermal efficiency of a Kenics ® KM static mixer used to pre-heat supercritical carbon dioxide, under high pressure conditions, is studied using computational fluid dynamics (CFD). A mesh sensitivity analysis is performed and the CFD model is validated against experimental results on heat transfer with conventional and supercritical fluids. Three turbulent models – standard k– ɛ, RNG k– ɛ, and k– ω – are employed to model the flow and heat transfer under high pressure conditions; the effects of large variations of the physical properties in the pseudo-critical region of the fluid are also studied. The RNG k– ɛ model gives results that are closer to the experimental data than the other two turbulence models. The numerical results show that the static mixer has a thermal efficiency more than three times higher than that of a conventional empty pipe heat exchanger with similar heat transfer area.

New correlation to predict the heat transfer coefficient in-tube cooling of supercritical CO 2 in horizontal macro-tubes

The heat transfer coefficient during gas cooling process of supercritical CO 2 without lubricating oil in horizontal macro-tubes has experimentally investigated. Investigation has done on two stainless steel circular tubes having inside-diameter of 4.55 mm and 7.75 mm and carried out for CO 2 mass fluxes of 200–600 kg/m 2 s, inlet fluid pressures of 7.5–10.0 MPa, and the inlet fluid temperatures of 90–100 °C. The experimental results indicate that the gas cooling pressure, the inner tube diameter, the mass flux and the temperature of CO 2 have significant effects on the heat transfer coefficient, especially near pseudo-critical region. The heat transfer coefficient decreases as the cooling pressure increases otherwise increases as mass flux increases. At any temperatures, smaller inner tube diameter shows higher heat transfer coefficient. In comparison between present experimental data and existing correlations from references, most of supercritical heat transfer correlations show large deviations with this present experimental data. Therefore, based on experimental data obtained in this present work, a new correlation is proposed to predict more accurate heat transfer coefficient of supercritical CO 2 in horizontal macro-tubes under cooling conditions. The majority of the experimental values are within 13% of the values predicted by the new correlation.

Self-organization without conservation: are neuronal avalanches generically critical?

Recent experiments on cortical neural networks have revealed the existence of well-definedavalanches of electrical activity. Such avalanches have been claimed to be generically scaleinvariant—i.e. power law distributed—with many exciting implications in neuroscience.Recently, a self-organized model has been proposed by Levina, Herrmann and Geisel toexplain this empirical finding. Given that (i) neural dynamics is dissipative and (ii) there isa loading mechanism progressively ‘charging’ the background synaptic strength, thismodel/dynamics is very similar in spirit to forest-fire and earthquake models, archetypicalexamples of non-conserving self-organization, which have recently been shown to lack truecriticality. Here we show that cortical neural networks obeying (i) and (ii) are notgenerically critical; unless parameters are fine-tuned, their dynamics is eithersubcritical or supercritical, even if the pseudo-critical region is relatively broad.This conclusion seems to be in agreement with the most recent experimentalobservations. The main implication of our work is that, if future experimental research oncortical networks were to support the observation that truly critical avalanchesare the norm and not the exception, then one should look for more elaborate(adaptive/evolutionary) explanations, beyond simple self-organization, to account for this.

Supercritical-water heat transfer in a vertical bare tube

This paper presents selected results on heat transfer to supercritical water flowing upward in a 4-m-long vertical bare tube. Supercritical-water heat-transfer data were obtained at pressures of about 24 MPa, mass fluxes of 200–1500 kg/m 2 s, heat fluxes up to 884 kW/m 2 and inlet temperatures from 320 to 350 °C for several combinations of wall and bulk-fluid temperatures that were below, at or above the pseudocritical temperature. In general, the experiments confirmed that there are three heat-transfer regimes for forced-convective heat transfer to water flowing inside tubes at supercritical pressures: (1) normal heat-transfer regime characterized in general with heat transfer coefficients (HTCs) similar to those of subcritical convective heat transfer far from critical or pseudocritical regions, which are calculated according to the Dittus-Boelter type correlations; (2) deteriorated heat-transfer regime with lower values of the HTC and hence higher values of wall temperature within some part of a test section compared to those of the normal heat-transfer regime; and (3) improved heat-transfer regime with higher values of HTC and hence lower values of wall temperature within some part of a test section compared to those of the normal heat-transfer regime. This new heat-transfer dataset is applicable as a reference dataset for future comparison with supercritical-water bundle data and for a verification of scaling parameters between water and modeling fluids. Also, these HTC data were compared to those calculated with the original Dittus-Boelter and Bishop et al. correlations. The comparison showed that the Bishop et al. correlation, which uses the cross-section average Prandtl number, represents HTC profiles more correctly along the heated length of the tube than the Dittus-Boelter correlation. In general, the Bishop et al. correlation shows a fair agreement with the experimental HTCs outside the pseudocritical region, however, overpredicts by about 25% the experimental HTCs within the pseudocritical region. The Dittus-Boelter correlation can also predict the experimental HTCs outside the pseudocritical region, but deviates significantly from the experimental data within the pseudocritical region. It should be noted that both these correlations cannot be used for a prediction of HTCs within the deteriorated heat-transfer regime.

Experimental investigation on heat transfer from a heated rod with a helically wrapped wire inside a square vertical channel to water at supercritical pressures

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/m 2 s, heat fluxes of 200–800 kW/m 2, 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.

Experimental study of critical flow of water at supercritical pressure

Experimental studies of the critical flow of water were conducted under steady-state conditions with a nozzle 1.41 mm in diameter and 4.35 mm in length, covering the inlet pressure range of 22.1–26.8 MPa and inlet temperature range of 38–474°C. The parametric trend of the flow rate was investigated, and the experimental data were compared with the predictions of the homogeneous equilibrium model, the Bernoulli correlation, and the models used in the reactor safety analysis code RELAP5/MOD3.3. It is concluded that in the near or beyond pseudo-critical region, thermal-dynamic equilibrium is dominant, and at a lower temperature, choking does not occur. The onset of the choking condition is not predicted reasonably by the RELAP5 code.

Static mixers as heat exchangers in supercritical fluid extraction processes

The performance of a Kenics static mixer as a heat-transfer device for supercritical carbon dioxide (CO 2) flow is studied and compared with conventional tube-in-tube heat exchangers. Measurements were carried out at pressures ranging from 8 to 21 MPa, temperatures from 283 to 323 K, and mass flowrates from 2 to 15 kg/h. The corresponding Reynolds and Prandtl numbers, at bulk conditions, ranged between 10 3 and 2 × 10 4 and between 2 and 7, respectively. The temperature increase experienced by the supercritical CO 2 stream varied between 10 and 35 K. The heat fluxes obtained with the static mixer are one order of magnitude higher than the ones observed with a tube-in-tube heat exchanger for the same set of operating conditions. The heat-transfer enhancement is caused by the cross-sectional mixing of the fluid and to a lesser extent by conduction across the metallic mixing elements. Heat-transfer is also affected by temperature-induced variation of physical properties, especially in the pseudocritical region of the fluid. From the experimental data, a correlation was developed for convective heat-transfer to supercritical CO 2 in terms of the Nusselt number.

Transient convective heat transfer to water near the critical region in a vertical tube

Numerical analysis has been carried out to investigate transient forced convective heat transfer to water near the critical region in developing flow through a vertical tube. With large variations of thermophysical properties such as density, specific heat, viscosity, and thermal conductivity near the thermodynamic critical point, heat transfer in the tube is strongly coupled with fluid flow. Buoyancy force parameter has also large variation with fluid temperature and pressure in the tube. Time dependent characteristics of fluid velocity, temperature, and heat transfer coefficient with water properties are presented and analyzed. Transient Nusselt and Stanton number distributions along the tube are also compared for various pressures in the tube. Because of heat transfer from the wall transition behavior from liquid-like phase to gas-like phase of heat transfer coefficient occurs when the fluid passes through pseudocritical temperature region in the tube. Turbulent viscosity ratio also has steep variation near the pseudocritical temperature close to the wall.

Direct numerical simulation of turbulent supercritical flows with heat transfer

Turbulent heat transfer to CO2 at supercritical pressure flowing in heated vertical tubes is investigated using direct numerical simulation at the inlet Reynolds number Re0=5400, which is based on inlet bulk velocity and tube diameter. Temperature range within the flow field covers the pseudocritical region, where very significant fluid property variations are involved. Both upward and downward flows are considered. The wall temperature distribution shows well-known heat transfer deterioration characterized by the localized peak in upward flows, while no such anomaly is observed in downward flows. The deterioration occurs at the region where turbulence is attenuated significantly, and is followed by the enhancement with restoration of turbulence caused by complicated interactions with a buoyancy effect. Further investigation of turbulence statistics indicates that ρux″ux″¯, ρux″ur″¯, and ρux″h″¯ are significantly affected by their respective buoyancy production terms due to ρ′ux′¯, ρ′ur′¯, and ρ′h′¯ which are proven to be significant in vertical supercritical flows. Combined with the deformation of mean velocity profile into an M-shaped one in upward flow, ρ′ux′¯ becomes negatively correlated from a certain downstream region so that ρux″h″¯ undergoes a very complicated transition changing both in sign and magnitude, causing severe impairment of heat transfer in upward supercritical flows.

An experimental investigation of convection heat transfer to supercritical carbon dioxide in miniature tubes

Experimental results of convection heat transfer to supercritical carbon dioxide in heated horizontal and vertical miniature tubes are reported in this paper. Stainless steel circular tubes having diameters of 0.70, 1.40, and 2.16 mm were investigated for pressures ranging from 74 to 120 bar, temperatures from 20 to 110 °C, and mass flow rates from 0.02 to 0.2 kg/min. The corresponding Reynolds numbers and Prandtl numbers ranged from 10 4 to 2×10 5 and from 0.9 to 10, respectively. It is found that the buoyancy effects were significant for all the flow orientations, although Reynolds numbers were as high as 10 5. The experimental results reveal that in downward flow, a significant impairment of heat transfer was discerned in the pseudocritical region, although heat transfer for both horizontal and upward flow was enhanced. The experimental results further indicate that in all the flow orientations, the Nusselt numbers decreased substantially as the tube diameter shrunk to <1.0 mm. Based on the experimental data, correlations were developed for the axially-averaged Nusselt number of convection heat transfer to supercritical carbon dioxide in both horizontal and vertical miniature heated tubes.

Pseudocritical heat transfer inside vertical tubes

Heat transfer to fluids with pressures slightly above the critical is strongly influenced by the variation of the fluid properties occurring in the so-called pseudocritical region. The heat transfer can either be improved or reduced, depending on the flow conditions. The improvement is due to the enhanced heat transport caused by the increased heat capacity of the fluid. In the case of reduced heat transfer the turbulence is weakened by gravitational effects. In the present paper the heat transfer due to the complex interaction between gravity and turbulence in the so-called pseudocritical region is predicted by a numerical solution of the conservation equations for a turbulent pipe flow. The numerical results are compared with published experimental data for an electrically heated vertical pipe with the fluid R12.

Forced convective heat transfer to supercritical water flowing in tubes

Experimental investigations were made of heat transfer to supercritical water flowing in a horizontal tube and vertical tubes. A comprehensive set of data was obtained for pressures from 226 to 294 bar, bulk temperatures from 230 to 540°C, heat fluxes from 116 to 930 kW/m 2 and mass velocities from 310 to 1830 kg/m 2s. Because the physical properties of supercritical fluids change rapidly with temperature in the pseudocritical region, the heat transfer coefficients show unusual behavior depending upon the heat flux. At low or modetate heat fluxes relatively to the flow rate, a satisfactory correlation was obtained, which predicts reasonably well the enhanced heat transfer coefficients near the pseudocritical point. The several characteristics of the deterioration in heat transfer which occurs at high heat fluxes were clarified, and the limit heat flux for the occurrence of the deterioration was determined in connection with the flow rate.

An Analytical Investigation of Free Convection Heat Transfer to Supercritical Water

Heat transfer to supercritical water (at 3400 psia in the pseudocritical region) by stable laminar free convection from an isothermal, vertical flat plate was analytically investigated. The actual variations with temperature of all or some of the thermophysical properties of supercritical water were taken into consideration. Fair agreement was found between the analytical values of this paper and existing experimental data.