Pseudo-critical Region Research Articles

Finite temperature QCD with $$N_f=2+1+1$$ Wilson twisted mass fermions at physical pion, strange and charm masses

We discuss recent progress in studying Quantum Chromodynamics at finite temperature using $N_f=2+1+1$ Wilson twisted mass fermions. Particular interest is in QCD symmetries and their breaking and restoration. First, we discuss the behaviour of the $\eta'$ meson at finite temperature, which is tightly connected to the axial and chiral symmetries. The results suggest a small decrease of the $\eta'$ mass in the pseudo-critical region coming close to the non-anomalous contribution and subsequent growth at large temperatures. Second, we present the first results of lattice simulations of Quantum Chromodynamics with $N_f=2+1+1$ twisted mass Wilson fermions at physical pion, strange and charm masses. We estimate the chiral pseudo-critical temperatures for different observables. Our preliminary results are consistent with a second order transition in the chiral limit, however other scenarios are not excluded.

Experimental study on heat transfer in vertical cooling tube cooled by downward flow in the passive heat removal system of SCWR

Experimental investigations were conducted into the heat transfer characteristics of supercritical water in a downward flowing cooling tube surrounded by pool boiling for the passive cooling system of the Generation-IV Supercritical-Water-Cooled Reactor (SCWR). The experimental parameters cover the extreme high ranges of pressure (23–27 MPa), mass flux (600–1000 kg·m−2·s−1), bulk fluid temperature (150–500 °C), and inner heat flux (98–1143 kW·m−2). A new thermal amplification system was applied to measure the heat transfer coefficient near the pseudocritical region under various mass fluxes and pressures. A sharp jump in the wall temperature and maximum heat transfer coefficient was observed at the pseudocritical point, and the mass flux and pressure exhibited different influences below and above the pseudocritical point. Based on the experimental data, a new heat transfer correlation for predicting the Nu is proposed for the subject cooling scenario. The proposed heat transfer correlation includes the density ratio and requires only the fluid properties at the bulk temperature. The mean absolute and root-mean-square error of the proposed correlation were about 7.94% and 9.60%, respectively. The proposed correlation can serve as a reference in the design of the passive cooling system of the SCWR.

Supercritical CO2 conjugate heat transfer and flow analysis in a rectangular microchannel subject to uniformly heated substrate wall

In this paper, a conjugate heat transfer and fluid flow analysis for supercritical CO2 (sCO2) was numerically investigated in a rectangular microchannel subject to uniform heat flux on the bottom of the substrate wall. The study was conducted to explore and quantify the effect of a sharp variation of sCO2 transport properties, Reynolds number and operational pressure conditions on the fluid flow and heat transfer in the pseudo-critical region and within close range of the Critical Point (CP). The numerical results indicate that the large variation of sCO2 properties within close range of the CP affects the heat transfer and flow along the channel. The local flow and heat transfer analyses demonstrate that the wall shear stress and heat flux are an increasing function of operating conditions especially for operational pressures higher than the critical pressure. The results show that the large variation of Nusselt number disappears for high operating pressures. It was also shown that the Nusselt Number is not affected by the Reynolds number in the laminar regime at high operating pressures.

Numerical investigation on convective heat transfer of supercritical aviation kerosene in a horizontal tube under hyper gravity conditions

The present study numerically investigates the convective heat transfer characteristics of supercritical aviation kerosene in a horizontal tube under hyper gravity conditions with various gravitational accelerations. Effects of mass flow rate (1.5 g/s∼2.5 g/s) and heat flux (500 kW/m∼2700 kW/m2) on heat transfer under hyper gravity conditions are discussed. Analyses focused on the influences of buoyancy force on heat transfer characteristics of the top and bottom wall under hyper gravity conditions. The model is simplified as a horizontal tube with the diameter of 1.8 mm and the length of 250 mm. The results show that the gravity plays a dominant role and the secondary flow structure is induced due to the drastic decrease in density in the pseudo-critical region. Two types of deterioration occur when the wall temperature and bulk temperature reaches the pseudo-critical point respectively. The onset of the deterioration occurs earlier with the increase of gravitational acceleration. As the gravitational acceleration increases, the difference between the top and bottom wall heat transfer coefficient (HTC) becomes larger. The criterion Grq/Grth<1 proposed by Petukhov is proved to be applicable to evaluate the effects of buoyancy.

Experimental study on heat transfer of supercritical CO2 flowing in a mini tube under heating conditions

Supercritical carbon dioxide (S-CO2) power cycles hold great potential applications in various energy utilization systems, in which the heat transfer of S-CO2 is one of the most important issues. However, due to the complex thermophysical properties, it is still insufficient to predict heat transfer coefficient of S-CO2, especially under the heating conditions with high ratios of heat flux to mass flux (q/G). In this study, the heat transfer of S-CO2 is experimentally investigated in a mini tube (d = 2 mm) in the range of p = 7.6–8.4 MPa, q = 100–200 kW/m2 and G = 400–700 kg/m2 s, in which the ratio of q/G is within 250–500 J/kg. The parameter influences on heat transfer coefficient of S-CO2 are analyzed. It is found that the heat transfer coefficient decreases with increasing heat flux and decreasing mass flux, but is little affected by pressure. Under high q/G conditions, buoyancy effect is significant and heat transfer is deteriorated in the whole test section. Available heat transfer correlations for S-CO2 are compared with the experimental data; however, the prediction errors of these correlations are relatively high, especially in pseudo-critical regions. As a result, a new heat transfer correlation is developed for S-CO2 under high q/G conditions, in which buoyancy effect and variations in thermophysical properties are both taken into account.

Mechanism analysis of the buoyancy effects on heat transfer of supercritical nitrogen in horizontal serpentine tube

In this paper, the buoyancy effects on heat transfer performance of cryogenic supercritical fluid in the submerged combustion vaporizer (SCV) are studied experimentally and numerically. Supercritical nitrogen is selected to substitute LNG for the safety reason. A three-dimensional model is established to calculate the flow and heat transfer of supercritical nitrogen, and the maximum relative error between the simulation and experiment is 2.78%. Based on the simulation results, a non-uniform circumferential heat transfer coefficient distribution is found in the pseudo-critical region, and the mechanism of the non-uniformity is analyzed. The reason for the phenomenon that the top and bottom generatrices reach the peak value of the heat transfer coefficient at different positions is further revealed by analyzing the average thermo-physical properties in different regions of the boundary layer. The results showed that the secondary flow caused by buoyancy leads to a non-uniform distribution of the thermal boundary layer thickness on the radial section. Under the influence of buoyancy, the temperature of the buffer layer near the top and bottom generatrices reach the large specific heat region successively, leading the peak position of the heat transfer coefficient of them not appear synchronously. Overall, comparing to the no-buoyancy condition, the whole heat transfer coefficient increased, with the heat transfer enhancement at the bottom and side generatrices but deterioration at the top generatrix.

Experimental study of heat transfer characteristics in a coal-fired test facility under advanced ultra-supercritical conditions

The development of high parameter, large capacity, coal-fired utility boilers with improved performance, based on the operation and design experience of the current parameter level, is essential. In addition, the combination of theoretical algorithms and practical experimental data is of great significance for research into utility boilers. In this study, an experiment to observe the heat transfer characteristics of heating surfaces was conducted under advanced ultra-supercritical (A-USC) conditions on a coal-fired experiment platform with a coal feed capacity of 0.3 MWth. Four repeated experiments were performed to verify the reliability of the experimental data, the maximum relative error of all the experimental data was less than 7%, which indicates steady combustion performance and good repeatability. Significant heat transfer enhancement and deterioration was demonstrated and analyzed at the superheater near the pseudo-critical region at a pressure of 36 MPa. Outside of the pseudo-critical region, the heat transfer coefficients experienced continuous and smooth variation with changes in temperature. A distributed parameter model for temperature prediction was established based on the mass, momentum, and energy conservation law through the discretization of time and space. The results indicated that predicted temperatures were in good agreement with the experimental data. For the top and bottom furnace, the correlation by Mokry et al. was consistent with the experimental data. The correlations of Jackson et al., Swenson et al., and D.B et al. were used for accurate temperature predictions at the middle of the furnace, superheater, and reheater, respectively.

Experimental and simulation investigation on heat transfer characteristics of supercritical nitrogen in a new rib tube of open rack vaporizer

Open rack vaporizer (ORV), using seawater as heat source, is widely used in liquefied natural gas (LNG) receiving terminals. In this study, a new rib tube, with petal-shaped internal fins and rectangular straight external fins, is designed and tested. A series experiments are conducted to investigate the heat transfer and pressure drop characteristics of the supercritical nitrogen flow in the new rib tube and the smooth tube. The heat transfer coefficient of the rib tube is 66.3% larger than that of the smooth tube, and the frictional pressure drop in the rib tube is also smaller compared to that of the smooth tube. Different control variables affecting the heat transfer characteristics in the rib tube are studied, including the temperature of the water, the mass flow rate and the pressure of the nitrogen. Meanwhile, numerical simulation is conducted to further analyze the heat transfer coefficients near the pseudo-critical region. A new correlation is developed to accurately predict the heat transfer coefficients of the supercritical fluid in the new rib tube based on the experimental and simulation data. The new correlation shows a good agreement as 95% of the experimental data captured with an error within 20%. This study may provide reference for the research on the supercritical fluid flow and the heat transfer enhancement of the tube in ORV.

Prediction of the Binary Interaction Parameter of Carbon Dioxide/Alkanes Mixtures in the Pseudocritical Region.

The interaction parameters between two components need to be first determined to obtain the thermophysical properties of the binary mixtures. In this paper, the research progresses of the binary interaction parameter for CO2 and hydrocarbons (HCs) and their related mixtures are illustrated. Aiming at the physical property prediction of CO2/alkanes (C1–C10) binary mixtures in pseudocritical regions, the experimental data of CO2/alkanes (C1–C10) in the pseudocritical region available in the open literature are collected. Besides, the calculation of kij is carried out by five typically accepted correlations selected from the literature. The effects of temperature, pressure, carbon number, and acentric factor on kij are investigated. By researching the influence of the above five factors on kij, it reveals that temperature is the most important one. Considering the influence of the critical temperatures of mixtures, a simple correlation is proposed to evaluate kij for light HC mixtures in the pseudocritical region.

Numerical analysis on heat transfer of supercritical pressure LNG in serpentine tube

In this paper, a numerical model is built considering the structure and operation characteristics of typical submerged combustion vaporizer. Based on this model, the flow and thermal performance of LNG in serpentine tube under supercritical pressure are predicted numerically, the impacts of operation parameters on thermal performance are analyzed, and 8 heat transfer correlations are introduced to evaluate the heat transfer of LNG in serpentine tube, which are compared with that of the simulation results. The simulation results reveal that there is a significant non-uniformity of heat transfer along the serpentine tube, especially in the bend sections, where the turbulent structure is rebuilt on account of the secondary flow and reverse flow resulting from the interaction of thermophysical properties and geometry configuration, leading to the remarkable variation on temperature and heat transfer coefficient. The pressure and heat flux play important roles on thermal performance of LNG under supercritical pressure in serpentine tube especially close to the pseudo-critical region. The simulation data is compared with that of 8 empirical heat transfer correlations, and the contrast results indicate that most of the correlations have just the similar trend with the calculation one, only Yamagata’s correlation proximately conforms with the calculation results in large specific heat region, the reason for the non-conformance is that the correlations are suitable for straight tube without considering the effects caused by geometric configuration of bend region and reverse flow on heat transfer, so an adaptive correlation of serpentine tube is expected for the future studies.

Experimental study on the grid-enhanced heat transfer at supercritical pressures in rod bundle

Experimental results of spacer grid effect on the heat transfer under supercritical pressure conditions are investigated. The experiments are carried out in an electrically heated 19-rod bundle cooled with supercritical Freon R134a. Standard spacer grids with blockage ratio of 0.29 are equipped into the bundle. The local wall temperatures and heat transfer coefficients along the flow direction of the bundle are measured. An interpolation method to determine the fully developed Nusselt number at supercritical conditions is reported. The results indicate that the enhanced heat transfer is limited within 30 bundle diameters downstream of the spacer grids. A peak heat transfer enhancement is observed near the pseudo critical region, which cannot be captured by the subcritical correlations. Considering the maximum heat transfer enhancement as a function of dimensionless temperature ratio, an original approach for deriving the grid-enhanced heat transfer correlation for supercritical applications is presented and the corresponding correlation has been established.

Lee-Yang zeros in lattice QCD for searching phase transition points

We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, 〈n〉, are calculated at the pure imaginary chemical potential iμqI, where no sign problem occurs. Then, the canonical partition functions, ZC(n,T,V), up to some maximal values of n are estimated through fitting theoretically motivated functions to 〈n〉, which are used to compute the Lee-Yang zeros. We study the temperature dependence of the distributions of the Lee-Yang zeros around the pseudo-critical temperature region T/Tc=0.84-1.35.In the distributions of the Lee-Yang zeros, we observe the Roberge-Weiss phase transition at T/Tc≥1.20. We discuss the dependence of the behaviors of Lee-Yang zeros on the maximal value of n, so that we can estimate a reliable infinite volume limit.

The heat transfer of supercritical CO2 in helically coiled tube: Trade-off between curvature and buoyancy effect

Supercritical CO2 Rankine cycle has great development potential as a power cycle for converting low-grade thermal energy into electricity. Better understanding of supercritical CO2 heat transfer in helically coiled tubes (HCTs) is required for design and operation of supercritical CO2 Rankine cycle power systems. In this work, the SST k∼ω model is employed. A new dimensionless buoyancy parameter Ψ is proposed which denotes the ratio of gravitational buoyancy force to overall curvature effect. Furthermore, a flow regimes map is proposed based on the inclination angle of the dividing streamline between the two vortexes and buoyancy parameter Ψ. The mixed convection region in HCT is decomposed into a gravitational buoyancy force dominated heat transfer region (B Region α>45°) and a curvature effect dominated heat transfer region (C Region α<45°). Subsequently, the effects of HCT geometry on heat transfer mechanisms are respectively investigated in B and C Region, which help us better understanding the relationship of the buoyancy criterion and flow characteristics. The results indicate that the effects of coiled pitch and coiled diameter on heat transfer can be neglected in B Region. In C Region, the heat transfer is suppressed as coiled pitch increases and it will appear oscillation when torsion effect is strong enough. In addition, the heat transfer is enhanced with curvature increases but except for near the pseudo-critical region.

Numerical investigation on local heat transfer characteristics of S-CO2 in horizontal semicircular microtube

The nuclear reactor system with supercritical carbon dioxide (S-CO2) as working fluid has good prospects in generation IV reactors. The printed circuit heat exchanger (PCHE) is a promising candidate for recuperator in S-CO2 Brayton cycle. However, the dramatic variations of S-CO2 thermophysical properties and the geometrical factors of PCHE microchannels make S-CO2 heat transfer mechanisms complex. Grasping the S-CO2 heat transfer mechanisms provides references and theoretical supports for the design of PCHE. In this paper, localized heat transfer characteristics of S-CO2 heated in a horizontal semicircular microtube were investigated numerically. The mathematical and physical models in simulating the heat transfer characteristics of supercritical fluid were validated by experimental data. The effects of pressure, mass flux, heat flux and tube geometry on S-CO2 local heat transfer characteristics near the pseudocritical temperature were studied. The results demonstrate that the dramatic variations of thermophysical properties in pseudocritical region have significant effects on heat transfer mechanisms. The distributions of specific heat (Cp) dominate the heat transfer characteristics when the effects of buoyancy are neglectable. In low mass flux or high heat flux cases, the buoyancy effects strongly influence the heat transfer mechanisms by changing the sectional parameters distributions and intensifying the secondary flow, resulting in deterioration of localized heat transfer capacity.

Investigation on heat transfer of in-tube supercritical water cooling accompanying out-tube pool boiling

Heat transfer of in-tube supercritical fluid cooling accompanying out-tube pool boiling was investigated. A smooth horizontal circular tube with an inside-diameter of 20 mm was submerged in a water pool at atmospheric pressure. Test parameters of in-tube were as follows: Pressure: 23–28 MPa, mass flux: 600–1000 kg·m−2·s−1, fluid temperature: 400–725 K, and the temperature difference between bulk and wall: 300–374 K. A thermal amplification system based on out-tube pool boiling was used to improve the measurement accuracy of local heat duty near pseudocritical region. According to the experiment, the transition from nucleate boiling to film boiling in the pool occurred near the pseudo-critical fluid region. Sharp variation on thermo-physical properties led to the peak value of heat transfer coefficient in the pseudo-critical region. The pool boiling heat flux increased gradually to 1.19 MW·m−2 near the pseudocritical point. Based on the experimental data, a modified Gnielinski equation was adopted to predict the heat transfer coefficient of in-tube supercritical fluid cooling with out-tube pool boiling. The thermophysical property ratio of the wall to the bulk as well as the effect of buoyancy were taken into consideration in the new correlation. The predicted correlation has an error of less than 20% to the experimental data.

Anomalous Properties of Some Fluids − with High Relevance in Energy Engineering − in Their Pseudo-critical (Widom) Region

Recent results are shown about the peculiarities of the pseudo-critical region, with special emphasis on properties important for energy production and conversion. The property-map of some materials, which are relevant as model fluids or as working / cooling fluids in energy engineering (argon, methane, water and carbon dioxide) and their relative positions to various adiabats – influencing their stability through the anomalous properties – are presented. Some potential technological problems related to the existence of these anomalies are discussed.

Performance Test of the Air-Cooled Finned-Tube Supercritical CO2 Sink Heat Exchanger

This technical paper presents results of an air-cooled supercritical CO2 (sCO2) finned-tube sink heat exchanger (HX) performance test comprising wide range of variable parameters (26–166 °C, 7–10 MPa, 0.1–0.32 kg/s). The measurement covered both supercritical and subcritical pressures including transition of pseudocritical region in the last stages of the sink HX. The test was performed in a newly built sCO2 experimental loop which was constructed within Sustainable Energy (SUSEN) project at Research Centre Rez (CVR). The experimental setup along with the boundary conditions are described in detail; hence, the gained data set can be used for benchmarking of system thermal hydraulic codes. Such benchmarking was performed on the open source Modelica-based code ClaRa. Both steady-state and transient thermal hydraulic analyses were performed using the simulation environment DYMOLA 2018 on a state of the art PC. The results of calculated averaged overall heat transfer coefficients (using Gnielinski correlation for sCO2 and IPPE or VDI for the air) and experimentally determined values shows reasonably low error of + 25% and – 10%. Hence, using the correlations for the estimation of the heat transfer in the sink HX with a similar design and similar conditions gives a fair error and thus is recommended.

Numerical analysis of flow and conjugate heat transfer for supercritical CO2 and liquid sodium in square microchannels

A numerical analysis of the developing laminar flow and conjugate heat transfer in a rectangular micro-channel was performed for supercritical CO2 and liquid sodium as working fluids for better understanding of the flow and heat transfer mechanisms. Three-dimensional Navier-Stokes, energy, and Laplace equations describing simultaneously developing flow and conjugate heat transfer in multiple micro-channels were solved numerically using Fluent code for the parallel- and counter-flow arrangements. The physical and transport properties of CO2 at supercritical conditions and their influence on fluid flow and heat transfer are presented and discussed. Liquid sodium and supercritical CO2 (sCO2) were used as the heat transfer and hot and cold working fluids, respectively. The values of friction coefficient and Nusselt number predicted by the numerical analysis were compared to the analytical solutions from the literature. Numerical results show that large variations in sCO2 properties in the critical and pseudo-critical regions affect the flow and heat transfer. This effect diminishes for operating conditions (pressure and temperature) further away from the Critical Point. Also, in the fully-developed region the local values of wall shear stress and heat transfer coefficient are not constant, but are strong functions of the local heat flux at the solid-fluid interface which varies due to large variation in sCO2 properties.

Modeling convective heat transfer of supercritical carbon dioxide using an artificial neural network

Supercritical carbon dioxide (sCO2) is an ideal working fluid for an energy conversion system, which can be used in a wide variety of power-generation applications with increased efficiency. However, abrupt variations in its thermo-physical properties in pseudo-critical region make it difficult to accurately predict the heat transfer characteristics of sCO2 using traditional analyzing methods, which to some extent hinders the development of sCO2 power conversion technology. Therefore, it is critical to explore feasible approaches to accurately predict the characteristics of sCO2 heat transfer. In this study, the performance of representative empirical correlations of sCO2 heat transfer has been assessed with a databank collected from previous publications. The results of the assessment indicate that the existing correlations are not effective enough to describe sCO2 heat transfer, especially when it is in the pseudo-critical region. An artificial neural network (ANN) is therefore proposed to model sCO2 heat transfer with experimental datasets. The ANN model shows a great learning ability and satisfactory generalization performance with a correlation coefficient of 0.99 and a mean absolute percent error of 0.97% in the test dataset. The results show that the proposed ANN model is a more effective and efficient method to predict the heat transfer characteristics of sCO2 than empirical correlations. The feasibility of the ANN model in the prediction of heat transfer with significant buoyancy force or flow acceleration are also tested and discussed.

Experimental and numerical investigation on the isobaric heat capacity for methylcyclohexane at high temperature and high pressure

The reliable isobaric heat capacity data of methylcyclohexane are observed on basis of the convective mixing technique in the temperature range from 298.1 K to 775.4 K and pressure range from 3.5 MPa to 5 MPa. In the low temperature region, the isobaric heat capacity of methylcyclohexane increases gently as temperature rises. At the pseudo-critical region, the isobaric heat capacity increases sharply to a peak value and then decreases dramatically in a nearly symmetrical way. A five-parameter model and a 3-dimensional drawing of heat capacity are presented. Most data points are within the ±3% error band and the maximum absolute deviation is 4.34%. Based on real-fluid heat capacity data, a linked-list is embedded into the CFD code to simulate the flow characteristics of methylcyclohexane at different pressures. The reliability of measured method is validated by comparing the experimental results with simulation values. Furthermore, an experimental and numerical investigation on flow process of methylcyclohexane is carried out. For the fluids under different pressures, as the temperature reaches the pseudo-critical region successively, the difference of temperature along the tube changes from large to small.