Pseudo-critical Region Research Articles

Hydraulic resistance of in-tube cooling supercritical water accompanying out-tube pool boiling

The experiment was conducted by immersing a smooth horizontal tube in a pool tank to simulate the flow condition of Passive Residual Heat Removal System (PRHRS) in a SuperCritical Water-cooled Reactor (SCWR). Hydraulic resistance and friction factor of in-tube cooling supercritical water accompanying out-tube pool boiling were investigated in this study with test pressure ranging from 23 to 28 MPa and mass flux ranging from 600 to 1000 kg·m−2·s−1. The influence of pressure and mass flux on pressure drop in adiabatic and cooling flows was analyzed. This paper also discussed the effect of deceleration in the cooling flow and assessed various friction-factor correlations by employing the experimental data. Results showed that the friction factor of the adiabatic flow exists a steep “pit” approaching to pseudocritical region. A noticeable “Λ-shaped” profile was observed in the vicinity of the pseudocritical temperature, due to deceleration-effect of frictional pressure drop in the cooling flow. The deceleration factor of supercritical cooling flow led to the axial fluid element shrinkage and radial bulk fluid velocity parabolic distribution. Taking into account the effect of deceleration-factor, a modified correlation was proposed for in-tube cooling supercritical water accompanying out-tube pool boiling, of which the average error and root mean square error are −2.51% and 15.28% respectively.

Density Measurements of Propellant EHF-TU at (3 to 7) MPa Supercritical Pressures

Endothermic Hydrocarbon Fuel-Tianjin University (EHF-TU) is one advanced propellant and fractionated from RP-3 extensively used in China. The density of propellant EHF-TU at supercritical pressures is measured using the flow conservation method. The measurement covers temperatures from (303 to 765) K and pressures of (3 to 7) MPa using three tubes with different sizes, and the density varies from (759 to 134) kg·m–3. The n-decane is used for calibration, and the relative uncertainty of density measurement is 1.1%. A series of measures were adopted to improve the measurement accuracy including flexible sizes of test tubes, the lumped parameter method, and the advanced data process. The results indicate that density decreases with the decline of temperature and pressure. Dramatic variation of density occurs in the pseudocritical region at 3 MPa pressure. Density data is fitted using polynomials, and the average absolute deviation (AAD) between the experimental data and the fitted data is 0.7%. Additionally,...

Low-grade heat utilization by supercritical carbon dioxide Rankine cycle: Analysis on the performance of gas heater subjected to heat flux and convective boundary conditions

The design and optimization of gas heater in supercritical carbon dioxide Rankine cycles faces some challenges, among which an urgent one is the effect of thermal boundary condition on the performance of gas heater. This work focused on performance comparison and effects of major operating parameters under two most common thermal boundary conditions regarding to low-grade heat sources, by employing a modified Shear-Stress Transport model where a variable turbulent Prandtl formulation was incorporated. Results show that in the pseudo-critical region thermal boundary condition obviously affected the performance of supercritical carbon dioxide gas heater. Compared with the uniform heat flux condition, at convective boundary condition impairment occurred in both the local enhancement at high mass flux and local deterioration at low mass flux, due to the self-regulation in local heat input. A nearly uniform thermal field under convective boundary condition was achieved by increasing the mass flux of heat source fluid, while increasing the inlet temperature of source fluid was ineffective to that end. Opposite to constant-property fluid heater, flow arrangement dramatically affected axial profiles of local heat transfer coefficient while had a much weaker effect on local heat flux in supercritical gas heater. Temperature distribution of supercritical carbon dioxide along the heater was insensitive to the flow arrangement. Further studies reveal that thermal boundary effect was closely related to the buoyancy effect. Thermal boundary condition has a minimal effect on heat transfer of supercritical carbon dioxide when buoyancy effect is negligible. Under heavy influence of buoyancy, thermal boundary effect was obvious in the form of much weaker local deterioration under convective boundary. Finally, the Jackson Nusselt correlation was found applicable to the prediction of overall heat transfer rate under convective boundary condition, with relative deviations within ±15%.

Numerical investigation of spacer effects on heat transfer of supercritical fluid flow in an annular channel

This paper conducts a numerical investigation of spacer effects on heat transfer of supercritical R-134a flows in a vertical annular channel. The simulations are conducted with SST k-ω turbulent model in Fluent 15.0. The investigation range is in the normal and improved heat transfer region at supercritical pressure. The results show that the spacer end enthalpy has remarkably influence on the spacer effects at supercritical pressure, which is different from that at subcritical pressure. In the liquid-like region, the enhancement effectiveness of spacers increases with increasing spacer end bulk enthalpy. However, in the in the gas-like region, the enhancement effectiveness of spacers decreases with increasing spacer end bulk enthalpy. The enhancement effectiveness reaches a peak value near the pseudo-critical enthalpy. For the parameters sensitivity, besides the blockage ratio, spacer end enthalpy and dimensionless distance to the spacer end, the flow parameters and local enthalpy also have significant influences on the spacer effects. Mechanism analysis shows that the characteristic of the mechanism of disruption of boundary layer is the main cause for the appearance of peak value of enhancement effectiveness near the pseudo-critical region at supercritical pressure. The HTC ratio of bare channels can be used to help the prediction of the HTC ratio in the corresponding spacer downstream.

The trans-critical heat transfer characteristics of LNG in a submerged combustion vaporizer under different operating pressures

It has been reported that trans-critical LNG vaporization process always occurs on the tube-side of typical submerged combustion vaporizer (SCV). In-depth analysis of this complex physical process is crucial for the stable operation of efficient SCV. In the present paper, a three-dimensional CFD numerical model was developed to analyze the flow and heat transfer characteristics of trans-critical LNG in the horizontal tube. Based on the numerical simulation results, the velocity, temperature and heat flux along the tube length were obtained. The distributions of local heat transfer coefficients under different operating pressures were also analyzed. The calculated results displayed that the representative phenomenon of “flow acceleration” occurs inside the horizontal serpentine tube. Affected by the variation of the physical properties, the heat transfer coefficient under the lower operating pressure was higher around pseudo-critical region, but decreased lower in the later field. Totally, the higher operating pressure may bring faster temperature rising and lower energy expenditure to reach the similar outlet temperature.

Entropy generation of supercritical water in a vertical tube with concentrated incident solar heat flux on one side

This paper presents the results of a numerical investigation of entropy generation of supercritical water in a vertical tube with concentrated incident solar heat flux on one side. The characteristics of heat transfer and pressure drop in the tube are analyzed first. The decrease in shear stresses near the pseudo-critical region results in the decrease in turbulence production and the increase in friction factor. It is the common cause of heat transfer deterioration and an abrupt increase in pressure drop near the pseudo-critical region. Entropy generation mainly depends on the temperature gradient along the vertical tube’s radial direction which is due to the thickness of the thermal boundary layer and the intensity of secondary flow. The results further show that entropy generation of supercritical water in a vertical tube with concentrated incident solar heat flux on one side decreases with increasing mass flux and decreasing incident heat flux. In addition, to balance the minimum irreversible losses and hydraulic resistance in the tube in a central receiver, the relationship between incident flux and mass flux is determined.

Thermal performance analysis of a parabolic trough solar collector using supercritical CO2 as heat transfer fluid under non-uniform solar flux

In this paper, an integrated numerical model was established to solve the complex energy transfer in a parabolic trough collector (PTC) by combining Monte Carlo ray tracing and finite volume method. Based on the model, the thermal performance of the PTC using supercritical CO2 (s-CO2) as the heat transfer fluid (HTF) was studied and analyzed. The results indicate that the solar fluxes on the receiver walls are non-uniform, which results in the non-uniform temperatures on the walls and in the s-CO2. Moreover, the optical efficiency of 84.19% is achieved at normal incidence. The circumferential temperature difference (ΔTc) of the absorber is found to be within 18–60K under typical conditions, and it decreases with increasing inlet velocity (vin) and decreasing inlet temperature (Tin). Studies on the flow and heat transfer characteristic indicate that the secondary flow occurs on the cross-section due to the buoyancy. The velocity of the secondary flow in the pseudo-critical region can be one magnitude order larger than that in the high temperature region, which leads to strong heat transfer enhancement in the former. Studies on the energy conversion performance indicate that the PTC can achieve the collector efficiencies of 18.78–84.17% and 81.93–84.17% at the typical conditions for Brayton and Rankine cycles, respectively, where the efficiency increases with decreasing Tin and increasing vin. Additionally, corresponding efficiency equations have also been obtained. The information from this study will provide a reference for the design and operation of the PTCs using s-CO2 as HTF.

Numerical study of the heat transfer to carbon dioxide in horizontal helically coiled tubes under supercritical pressure

The cooling heat transfer and pressure drop characteristics of supercritical CO2 in the horizontal helically coiled tube are numerically simulated using RNG k-ε turbulent model. The results show that the heat transfer coefficient and pressure drop in the helically coiled tube are larger than that in the straight tube because of the secondary flow. The heat transfer coefficient and pressure drop increase with the increase of mass flux and the peak value of heat transfer coefficient is shifted to high temperature region with the increase of pressure. The gravitational Richardson number decreases with the increase of the mass flux and the centrifugal Richardson number increases with the fluid temperature and mass flux increasing. The Nusselt number correlations are presented by using the numerical simulation values. The pressure distribution in helically coiled tube fluctuates from top to bottom like a wave because of the gravitational buoyancy force. When the fluid temperature is higher than the pseudo-critical temperature, the pressure is mainly affected by the fluid pressure and when the fluid temperature is lower than the pseudo-critical temperature, the pressure is mainly affected by the fluid temperature. The static pressure difference has the minimum values in the pseudo-critical temperature region. The wall temperature and the heat transfer coefficient close to the inner region are lower than the other regions.

High-Flux Thermal Management With Supercritical Fluids

A novel thermal management approach is explored, which uses supercritical carbon dioxide (sCO2) as a working fluid to manage extreme heat fluxes in electronics cooling applications. In the pseudocritical region, sCO2 has extremely high volumetric thermal capacity, which can enable operation with low pumping requirements, and without the potential for two-phase critical heat flux (CHF) and flow instabilities. A model of a representative microchannel heat sink is evaluated with single-phase liquid water and FC-72, two-phase boiling R-134a, and sCO2. For a fixed pumping power, sCO2 is found to yield lower heat-sink wall temperatures than liquid coolants. Practical engineering challenges for supercritical thermal management systems are discussed, including the limits of predictive heat transfer models, narrow operating temperature ranges, high working pressures, and pump design criteria. Based on these findings, sCO2 is a promising candidate working fluid for cooling high heat flux electronics, but additional thermal transport research and engineering are needed before practical systems can be realized.

Analysis of Computational Fluid Dynamics Code FLUENT Capabilities for Supercritical Water Heat-Transfer Applications in Vertical Bare Tubes

In this paper, the computational fluid dynamics (CFD) code FLUENT was used to predict wall-temperature profiles inside vertical bare tubes with supercritical water (SCW) as the cooling medium, to assess the capabilities of FLUENT for SCW heat-transfer applications. Numerical results are compared to experimental data and current one-dimensional (1D) models represented by existing heat-transfer empirical correlations. Wall-temperature and heat-transfer coefficients were analyzed to select the best model to describe the fluid flow before, at, and after the pseudocritical region. k−ϵ and k−ω turbulent models were evaluated in the process, with variations in the submodel parameters such as viscous heating, thermal effects, and low-Reynolds-number correction. Results of the analysis show a fit of ±10% for wall temperatures using the SST k−ω model within the deteriorated heat-transfer regime and less than ±5% within the normal heat-transfer regime. The accuracy of the model is higher than any empirical correlation tested in the mentioned regimes and provides additional information about the multidimensional effects between the bulk-fluid and wall temperatures.

Optimum Operating Conditions for Subcritical/Supercritical Fluid-Based Natural Circulation Loops

Natural circulation loop (NCL) is simple and reliable due to the absence of moving components and is preferred in applications where safety is of foremost concern, such as nuclear power plants and high-pressure thermal power plants. In the present study, optimum operating conditions based on the maximum heat transfer rate in NCLs have been obtained for subcritical as well as supercritical fluids. In recent years, there is a growing interest in the use of carbon dioxide (CO2) as loop fluid in NCLs for a variety of heat transfer applications due to its excellent thermophysical environmentally benign properties. In the present study, three-dimensional (3D) computational fluid dynamics (CFD) analysis of a CO2-based NCL with isothermal source and sink has been carried out. Results show that the heat transfer rate is much higher in the case of supercritical phase (if operated near pseudocritical region) than the subcritical phase. In the subcritical option, higher heat transfer rate is obtained in the case of liquid operated near saturation condition. Correlations for optimum operating condition are obtained for a supercritical CO2-based NCL in terms of reduced temperature and reduced pressure so that they can be employed for a wide variety of fluids operating in supercritical region. Correlations are also validated with different loop fluids. These results are expected to help design superior optimal NCLs for critical applications.

Structure, dielectric property and impedance spectroscopy of La2/3Cu3Ti4O12 ceramics by sol–gel method

La2/3Cu3Ti4O12 (LCTO) precursor powders were synthesized by the sol–gel method. Effect of sol conditions and sintering process on microstructure and dielectric properties of LCTO powders or ceramics were investigated systematically. The optimum sol conditions for the synthesis of precursor powders were as follows: the Ti4+ concentration of 1.00 mol/L, the molar ratio of water and titanium of 5.6:1 and the sol pH of 1.0, respectively. After sintered at 1105 °C for 15 h, the LCTO ceramics exhibited more homogeneous microstructure, much higher dielectric constant (ca 09–1.6 × 104) and lower dielectric loss (ca 0.057). The higher dielectric constant of the LCTO ceramics might be due to the internal barrier layer capacitor effect. The LCTO ceramics showed two kinds of conductivity activation energy for grain boundary conductivity from complex impedance analysis. The transition temperature of two activation energy values occured between 170 and 210 °C. The temperature range of 170–210 °C was critical pseudocritical region of the dielectric constant, dielectric loss and activation energy. Furthermore, it was concluded that the grain boundary play an important role for electrical properties.

Flow and heat transfer characteristics of high-pressure water flowing in a vertical upward smooth tube at low mass flux conditions

An experiment that covered a wide range of parameters was conducted to investigate the flow and heat transfer characteristics of water flowing in a vertical upward smooth tube. The effects of the operating parameters on flow and heat transfer were analyzed, and the corresponding empirical correlations were presented. Results show that at subcritical pressures, dryout dominates heat transfer deterioration. This phenomenon can be delayed by reducing pressure and heat flux; however, the effect of mass flux on dryout occurrence is nonmonotonic. At near-critical pressures, departure from nucleate boiling (DNB) occurs at low vapor qualities under high heat fluxes and low mass fluxes. When heat flux increases, DNB occurs early, and peak wall temperature increases significantly. At supercritical pressures, heat transfer is enhanced within the pseudo-critical region, and the heat transfer coefficient peaks correspondingly. When pressure approaches the critical value, heat transfer deterioration occurs at high heat fluxes when the bulk fluid temperature is below and the wall temperature is above the pseudo-critical temperature. Three hydraulic resistance correlations were evaluated using the experimental data, and all three correlations underestimated the frictional pressure drop.

Performance analyses of transcritical organic Rankine cycles with large variations of the thermophysical properties in the pseudocritical region

This study analyzed the influence of the thermophysical properties variations in the pseudocritical region on the transcritical organic Rankine cycles (ORCs) performance. An optimization method is proposed using the net power output, the thermal efficiency and the total vapor generator area as indicators. The effect of the turbine inlet temperature and the vapor generation pressure is investigated for transcritical ORCs. The variations of the vapor generator area are discussed based on the thermophysical property changes. The results show that the total vapor generator area varies with the turbine inlet temperature along an N-shaped curve. For any heat source temperature, the suitable working fluid should have a pronounced N-shaped curve of the total vapor generator area to guarantee the existence of the optimal parameter region in which selected indicators are optimized. This provides a working fluid selection criterion for heat sources of different temperatures. The analysis simplifies the selections of the operating parameters and the working fluids.

Heat transfer to supercritical water in a vertical tube with concentrated incident solar heat flux on one side

A solar tower power plant with supercritical water as a heat-transfer medium in the central receiver is potentially one of the most promising solar thermal power technologies due to its high solar-to-electric efficiency. In this paper, the heat transfer of supercritical water in a vertical tube of a solar tower receiver has been investigated. A 3D mathematical model has been developed to investigate the distribution of heat flux in the circumferential direction of a circular tube heated by concentrated incident solar flux on one side. The RNG k–ε model with the standard wall function is employed to describe the turbulent flow of water from a liquid-like state to a gas-like state, and the results are validated with experimental data. For supercritical water in a tube heated on one side by concentrated incident solar heat flux, the maximum wall temperature is located on the sunward outside wall where the incident heat flux is at a maximum. In the pseudo-critical flow region, due to the drastic turbulent diffusion of supercritical water, the temperature distribution of the supercritical water in the tube is evenly distributed at the same flow cross section. To avoid deterioration in the heat transfer of supercritical water, the relation between the threshold incident solar heat flux and mass flux for the supercritical water has been provided. Furthermore, the Nusselt correlation which can be used to predict heat transfer coefficient of the vertical tube heated non-uniformly on one side by concentrated solar flux has been confirmed.

Effect of Oxidation Chemistry of Supercritical Water on Stress Corrosion Cracking of Austenitic Steels

Austenitic steel is a candidate material for supercritical water-cooled reactor (SCWR). This study is to investigate the stress corrosion cracking (SCC) behavior of HR3C under the effect of supercritical water chemistry. A transition phenomenon of the water parameters was monitored during a pseudocritical region by water quality experiments at 650°C and 30 MPa. The stress–strain curves and fracture time of HR3C were obtained by slow strain rate tensile (SSRT) tests in the supercritical water at 620°C and 25 MPa. The concentration of the dissolved oxygen (DO) was 200–1000 μg/kg, and the strain rate was 7.5×10−7/s. The recent results showed that the failure mode was dominated by intergranular brittle fracture. The relations of the oxygen concentration and the fracture time were nonlinear. 200–500 μg/kg of oxygen accelerated the cracking, but a longer fracture time was measured when the oxygen concentration was increased to 1000 μg/kg. Chromium depletion occurred in the oxide layer at the tip of cracks. Grain size increased and chain-precipitated phases were observed in the fractured specimens. These characteristics were considered to contribute to the intergranular SCC.

Assessment of Computational Tools in Support of Heat-Transfer Correlation Development for Fuel Assembly of Canadian Supercritical Water-Cooled Reactor

Experimental data and correlations are not available for the fuel-assembly concept of the Canadian supercritical water-cooled reactor (SCWR). To facilitate the safety analyses, a strategy for developing a heat-transfer correlation has been established for the fuel-assembly concept at supercritical pressure conditions. It is based on an analytical approach using a computational fluid dynamics (CFD) tool and the ASSERT subchannel code to establish the heat transfer in supercritical pressure flow. Prior to the application, the CFD tool was assessed against experimental heat transfer data at the pseudocritical region obtained with bundle subassemblies to identify the appropriate turbulence model for use. Beyond the pseudocritical region, where the normal heat transfer behavior is anticipated, the ASSERT subchannel code also was assessed with appropriate closure relationships. Detailed information on the supporting experiments and the assessment results of the computational tools are presented.

Pressure Drop Studies on Supercritical Helium Flowing in Horizontal Tubes

Supercritical helium owing to its single-phase characteristics and enhanced heat transfer near the pseudo-critical region is envisaged as a potential coolant for superconducting magnets used in particle accelerators and fusion devices. However, near the transposed critical line, there is a wide fluctuation of thermophysical properties like specific heat at constant pressure, density, thermal conductivity, viscosity, etc. As a consequence of this fluctuation, heat transfer and fluid flow studies become difficult for accurate prediction of heat transfer coefficient and friction factor. In this paper, numerical simulation of supercritical helium flowing under turbulent conditions in a horizontal heated tube is performed using computational fluid dynamics (CFD) software ANSYS FLUENT v12.0.16. It is found that results of pressure drop obtained from simulation closely match experimental data in case of fluctuation free regimes. The friction factor indicating the frictional pressure drop occurring in a horizontal tube can be matched to existing correlations within given accuracies for fluctuation regimes. A correlation for friction factor that yields better results than those in literature is proposed based on the simulation data obtained. The accurate determination of the overall pressure drop in the tubes along with the optimum flow rates gives the estimation of pumping power required for enhanced heat transfer with flow of supercritical helium.

Heat transfer characteristics of water flowing in a vertical upward rifled tube with low mass flux

This paper presents an experimental investigation on heat transfer characteristics of water flowing upward in a 2-m long vertical rifled tube with an hydraulic diameter of 19.1mm. The experiment was conducted at pressures ranged from 11 to 32MPa, values of mass flux from 170 to 800kgm−2s−1 and heat fluxes up to 600kWm−2. The results show that at subcritical pressures, dryout occurs at high vapor qualities and is delayed by decreasing heat flux. The influence of mass flux on the onset of dryout is non-monotonic. Compared to smooth tube, rifled tube can effectively prevent the occurrence of departure from nucleate boiling (DNB). Whereas, at near-critical pressures, the enhancement disappears and DNB even occurs in sub-cooling region. But the peak wall temperature is remarkably reduced. Based on the experimental data, correlations were obtained to predict heat transfer in single-phase, two-phase and post-dryout regions. At supercritical pressures, heat transfer is enhanced within the pseudo-critical region due to drastic variations of thermo-physical properties. Both buoyancy and flow acceleration have little effect on heat transfer. Five heat transfer correlations were evaluated with the experimental data divided into forced convection and mixed convection. The Mokry et al. correlation shows the best performance in predicting heat transfer with forced convection and the Jackson correlation gives the best prediction in mixed convection region.

Experimental investigation on heat transfer characteristics of water in inclined downward tube of a supercritical pressure CFB boiler

In this study, experiments have been performed for an investigation on heat transfer of water in an inclined downward tube with an inner diameter of 20 mm and an inclined angle of 45° from the horizon, with the range of pressure from 11.5 to 28 MPa, mass flux from 450 to 1550 kg/(m2 s), and heat flux from 50 to 585 kW/m2. Based on the experimental data, the temperature distribution in the tube wall was derived. The heat transfer characteristics of inclined downward flow were compared with that of vertical downward flow. The effects of heat flux on wall temperature were analyzed and the corresponding empirical correlations were presented. The results show that heat transfer characteristics of water in the inclined downward tube are not uniform along the circumference from the top surface to the bottom surface. An increase in heat flux exacerbates the non-uniformity. At subcritical pressures, both dry-out and departure from nucleate boiling (DNB) occur at the top surface of the inclined downward tube; inversely, only dry-out takes place on the bottom surface of the inclined downward tube and in the vertical downward tube. At near-critical pressures, DNB and dry-out occur in the comparing tubes with greater possibility. At supercritical pressures, heat transfer gets enhanced in the pseudo-critical enthalpy region; in the high enthalpy region, the top surface temperature of the inclined downward tube decreases obviously.