Pseudo-critical Temperature Research Articles

Numerical study on the density wave oscillation of supercritical water in parallel multichannel system

Abstract A time-domain model is proposed to study the density wave instability of supercritical water in parallel multichannel system. The present model splits the flow domain along each channel based on the collocated mesh method, and adopts an iterative solution to solve the coupling among multiple channels. The model is verified firstly by the experimental data obtained in open literature. After that, the model is used to study the effect of the key parameters on the density wave instability of supercritical water in parallel multichannel system (such as, adding different perturbations, inlet fluid temperature, and so on). Moreover, the influence mechanisms of these key parameters on the density wave oscillation of supercritical water are also explained. It is found that out-of-phase oscillation occurs between the perturbation channels (which are added with the perturbation) and the rest other channels, and the amount of perturbation channels has little effect on oscillation period and system stability. The system stability first decreases and then increases with the inlet fluid temperature, and the system has the worst stability when the inlet fluid temperature is equal to a critical value, denoted by Tin-cr. This is because that the variation of the fluid density along the system will reach the maximum when the inlet fluid temperature is near Tin-cr, which makes the system most unstable. Tin-cr is always lower than the pseudo-critical temperature of supercritical water at the corresponding pressure. Tin-cr has no obvious change with system pressure.

Finite volume effects on the chiral phase transition from Dyson–Schwinger equations of QCD

Within the framework of Dyson–Schwinger equations of QCD, we study the finite volume effects on the chiral phase transition, especially the influence on the position of the possible pseudo-critical end point (pCEP). The results show that in the chiral limit case (the current quark mass m=0), the absolute value of quark condensate decreases for smaller volumes, and more interestingly, so does the pseudo-critical temperature Tc(μ=0), which is in agreement with the Polyakov Nambu–Jona-Lasinio model result and opposite to the Polyakov linear sigma model prediction. These conclusions hold for m>0 case in our calculations. Moreover, the results of pCEP as a function of different volumes show that T of pCEP also decreases for smaller volumes, but μ of pCEP will increase, which are qualitatively more close to Polyakov linear sigma model results. For our model setup, results for systems with a size larger than (5 fm)3 closely approximate those from infinite volume, but if the volume is smaller, the corrections are non-negligible, even significantly affect signatures of the results from an infinite system. There also exists some possibility that, if the system size is too small, the whole phase transition would be crossover, which means no pCEP exists at all. It is no doubt that, finite volume effects deserve further researches.

Chiral observables and topology in hot QCD with two families of quarks

We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected susceptibility, on lattices with spacings as fine as 0.065 fm. For most observables spacing effects are below statistical errors, which enables us to identify lattice results with continuum estimates. Our estimate of the pseudocritical temperature compares favorably with continuum results from staggered and domain wall fermions, confirming that a dynamical charm does not contribute in the transition region. From the high temperature behaviour of the disconnected chiral susceptibility we infer the topological susceptibility, which encodes relevant properties of the QCD axion, a plausible Dark Matter candidate. The topological susceptibility thus measured exhibits a power-law decay for $T/T_c \gtrsim 2$, with an exponent close to the one predicted by the Dilute Instanton Gas Approximation (DIGA). Close to $T_c$ the temperature dependent effective exponent seems to approach the DIGA result from above, a behaviour which would support recent analytic calculations based on an Instantons-dyons model. These results constrain the mass of a hypothetic QCD post-inflationary axion, once an assumption concerning the relative contribution of axions to Dark Matter is made.

Experimental investigation on flow and heat transfer instabilities of RP-3 aviation kerosene in a vertical miniature tube under supercritical pressures

This paper presents experimental investigations on flow and heat transfer instabilities of RP-3 aviation kerosene under supercritical pressures in a vertical tube with inner diameter of 2 mm. The flow changes from laminar to the transition regime as the fuel is heated, which resulted from decrease of fluid density and increase of velocity. A 13-component surrogate model of RP-3 aviation kerosene is used to calculate the thermophysical properties of fuel. Under large wall heat flux conditions, instabilities in flow and heat transfer are observed when the inner wall temperature and outlet fluid temperature approach the pseudo-critical temperature, respectively. The former is accompanied with enhancement in heat transfer and could be explained by the pseudo-boiling mechanisms. Thermally-induced pressure oscillations due to drastic density variation is found to be the reason for the latter case. The effects of inlet pressure, wall heat flux and inlet Reynolds number on flow and heat transfer instabilities are also studied. It is found that higher inlet pressures and heat fluxes can weaken the flow instabilities. The influence of inlet Reynolds number is more complicated, different types of flow instabilities could be observed with the increase of inlet Reynolds number. In addition, stability boundaries are obtained based on the experiments data, which could be used to quantitatively predict the occurrence of flow and heat transfer instabilities.

Supercritical “boiling” number, a new parameter to distinguish two regimes of carbon dioxide heat transfer in tubes

The objective of this paper is to develop a criterion to predict the onset of heat transfer deterioration (HTD) for supercritical CO2 heat transfer. A new mechanism is proposed by assuming supercritical pseudo-boiling. Before bulk fluid reaches pseudo-critical temperature (Tpc), the tube cross-section contains a vapor layer and a liquid-like fluid. The saturation temperature interface is defined at T = Tpc, inside and outside which are a vapor layer (T > Tpc) and a subcooled liquid (T < Tpc). The subcritical boiling number is extended to supercritical “boiling” number, defined as SBO = qw/(Gipc), where qw, G and ipc are heat flux, mass flux, and CO2 enthalpy at Tpc, respectively. SBO, by coupling the density ratio between “liquid” and “vapor”, represents the competition between vapor expansion induced momentum force and inertia force. The experiment of supercritical CO2 heat transfer is performed in a 10.0 mm inner diameter tube, covering ranges of P = 7.5–21.1 MPa, G = 488–1600 kg/m2s and qw = 74–413 kW/m2. Surprisingly, the onset of HTD is found to occur at a critical SBO which is 5.126×10−4 and the critical heat flux is expressed as qCHF=5.126×10−4Gipc. It is shown that our new criterion is also suitable for other experiments reported in literature, providing a general guidance to design and operate SCO2 heaters to avoid HTD.

Improvement of heat-transfer correlations for supercritical methane coolant in rectangular channel

In this article, the conjugate heat transfer of the methane coolant inside a rectangular channel is studied and the related Nusselt correlations are improved. The compressible methane flow enters the cooling channel at supercritical pressure and subcritical temperature. The coolant flow absorbs heat from the heated walls and exits the channel with a supercritical temperature. An in-house solver is developed employing Semi-Implicit Method for Pressure-Linked Equations-Consistent (SIMPLEC) algorithm accompanied by the appropriate thermodynamic and transport property relations for the supercritical conditions of the methane coolant. The solver is validated with the experimental data found in the open literature. The behavior of pseudo-critical temperature and density versus pressure are studied and new relations are proposed. The accuracy of different Nusselt relations for estimating heat transfer coefficient of methane at supercritical pressures is evaluated. The variation of thermo-fluidic parameter correction factors (i.e. non-dimensional density, temperature, isobaric specific heat, viscosity, and thermal conductivity) through the cooling channel is investigated. Further, the current Nusselt relations are developed, and improved correlations are proposed for methane at the supercritical pressure inside a rectangular channel. The accuracy of the modified correlations is studied at different outlet pressures, heat transfer, and mass flow rates.

Numerical study on a novel hyperbolic inlet header in straight-channel printed circuit heat exchanger

Printed circuit heat exchangers (PCHEs) can be used as the recuperator and condenser in the supercritical CO2 (sCO2) Brayton cycle of fast cooled reactor (FCR) systems. Most researchers focused on heat transfer improvement of the core structure in previous literatures. However, the flow non-uniformity may seriously decrease the comprehensive performance of PCHEs by increasing the pressure loss. The sCO2 temperature in partial channels may be lower than the pseudo-critical temperature due to non-uniform flow distribution. Thereby, it is possible that the condenser may deviate from the steady operating condition and work inefficiently. In this paper, the flow non-uniformity of a straight-channel PCHE condenser with four different inlet headers is analyzed. Based on the streamline profile, a novel modified hyperbolic inlet header is proposed, which can reduce the flow non-uniformity by 46% compared with the current practical manufactured model. Simultaneously, the improvement of flow uniformity by the novel inlet header may increase the overall performance by 39.5%. Furthermore, the effect of core length is also investigated, and it is found that the flow non-uniformity can be minimized by varying the core length. Additionally, the relationship between the standard deviation of flow non-uniformity and the shape factor is quantitatively investigated and analyzed. Result shows that the flow non-uniformity can be expressed as a function of the shape factor and dimensionless core length. Finally, the correlations of the thermo-hydraulic performance of the straight-channel PCHE with corrections for flow non-uniformity are proposed.

불순물을 포함한 초임계 이산화탄소의 관 내측 열전달계수에 대한 예측모델의 검증

We propose a reliable prediction model for the application of the heat transfer coefficient of CO₂ mixture for the design of the pipeline in CCS (Carbon Capture, Transportation & Storage) technology. Accordingly, three prediction models; the Gnielinski model, the Dittus-Boelter model, and the Churchill-Bernstein model were compared with the experimental data obtained in the previous study. The prediction models showed that the heat transfer characteristics of CO₂ mixtures were relatively well predicted with the various parameters like type of the impurities, the mole fraction of the impurity, operational pressure, and mass flux. However, all the prediction models underestimated heat transfer coefficient near the pseudo-critical temperature. The Gnielinski model showed the highest predictive ability compared to other prediction models with a mean deviation of 12.63%, but it slightly overestimated the data under pseudo-critical temperature. The Dittus-Boelter model and the Churchill-Bernstein model predicted experimental data by 16.94% and 17.82%, respectively.

Numerical investigation on heat transfer of the supercritical fluid upward in vertical tube with constant wall temperature

The supercritical fluid has been extensively applied in many industry applications and heat transfer characteristics of the supercritical fluid play an important role in system safety and economic design. In this paper, heat transfer characteristics and mechanism of the supercritical fluid upward in vertical tube with constant wall temperature are numerically investigated. Heat transfer fluctuation phenomenon is found at the trans-critical section where fluid experiences the pseudo-critical point. Heat transfer fluctuation takes place only when the wall temperature is higher than the pseudo-critical temperature and the bulk temperature is lower than the pseudo-critical temperature. The traditional prediction correlation can’t predict heat transfer fluctuation at the trans-critical section correctly. Heatflux fluctuation is caused by the buoyancy effect. The buoyancy effect induces the periodic flow variation and the periodic convective heat transfer variation on the radial direction, which determine heatflux fluctuation on the wall. The fluctuation amplitude of heatflux on the wall decreases along the axial direction due to the weakened buoyancy effect. Influence of operating conditions on heat transfer of the supercritical fluid is investigated. R134a is chosen as the working fluid. Operating condition includes mass flow ranging from 500 to 800 kg/(m2 s), inlet temperature ranging from 313.15 to 343.15 K, wall temperature ranging from 403.15 to 433.15 K and operating pressure ranging from 4.35 to 5.04 MPa. It is observed that heat transfer coefficient rises with mass flow, wall temperature and operating pressure increasing, but it doesn’t vary obviously with inlet temperature. Fluctuation amplitude of heat transfer coefficient decreases with mass flow, wall temperature, inlet temperature and operating pressure increasing.

Curvature of the pseudocritical line in QCD: Taylor expansion matches analytic continuation

We determine the curvature of the pseudo-critical line of $N_f = 2 + 1$ QCD with physical quark masses via Taylor expansion in the quark chemical potentials. We adopt a discretization based on stout improved staggered fermions and the tree level Symanzik gauge action; the location of the pseudocritical temperature is based on chiral symmetry restoration. Simulations are performed on lattices with different temporal extent ($N_t = 6, 8, 10$), leading to a continuum extrapolated curvature $\kappa = 0.0145(25)$, which is in very good agreement with the continuum extrapolation obtained via analytic continuation and the same discretization, $\kappa = 0.0135(20)$. This result eliminates the possible tension emerging when comparing analytic continuation with earlier results obtained via Taylor expansion.

QCD phase diagram in a magnetic background for different values of the pion mass

We investigate the behavior of the pseudocritical temperature of ${N}_{f}=2+1$ QCD as a function of a static magnetic background field for different values of the pion mass, going up to ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}660\text{ }\text{ }\mathrm{MeV}$. The study is performed by lattice QCD simulations, adopting a stout staggered discretization of the theory on lattices with ${N}_{t}=6$ slices in the Euclidean temporal direction; for each value of the pion mass the temperature is changed moving along a line of constant physics. We find that the decrease of ${T}_{c}$ as a function of $B$, which is observed for physical quark masses, persists in the whole explored mass range, even if the relative variation of ${T}_{c}$ appears to be a decreasing function of ${m}_{\ensuremath{\pi}}$, approaching zero in the quenched limit. The location of ${T}_{c}$ is based on the renormalized quark condensate and its susceptibility; determinations based on the Polyakov loop lead to compatible results. On the contrary, inverse magnetic catalysis, i.e., the decrease of the quark condensate as a function of $B$ in some temperature range around ${T}_{c}$, is not observed when the pion mass is high enough. That supports the idea that inverse magnetic catalysis might be a secondary phenomenon, while the modifications induced by the magnetic background on the gauge field distribution and on the confining properties of the medium could play a primary role in the whole range of pion masses.

Discussion on the fluid-to-fluid scaling of heat transfer at supercritical pressures

Supercritical carbon dioxide (SCO2) has been extensively adopted in heat-transfer experiments due to its low critical point compared to supercritical water (SCW). While it helps to largely reduce the technical difficulty and cost, the experimental results need to be extrapolated to SCW using a set of reliable and well-validated fluid-to-fluid scaling criteria. In the present paper, a criterion for scaling the mass flux in normal and enhanced heat transfer regimes was achieved by using Computational Fluid Dynamic (CFD) approaches. This criterion as well as the available scaling laws were assessed based on a wide range of the experimental data. It was found that Prandtl number shows a significant and nonmonotone effect on the scaling of mass flux (and consequently Nusselt number). Similar exponents of the Prandtl number were obtained using different approaches, but a constant exponent failed to capture the nonmonotone effect, especially when the bulk temperature surpasses the pseudo-critical temperature where large variations in the thermophysical properties appear. A modified scaling criterion, which is applicable to the heat transfer deterioration occurred at low mass fluxes, was proposed for the Nusselt number. The deviation from the experimental data was significantly reduced after Grashof number was incorporated into the criterion.

Bayesian analysis of quark spectral properties from the Dyson-Schwinger equation

We report results on the quark spectral function in the Landau gauge at finite temperature determined from its Dyson-Schwinger equation. Compared to earlier quenched results this study encompasses unquenched $N_f=2+1$ fermion flavors in the medium. For the reconstruction of real-time spectra we deploy a recent Bayesian approach (BR method) and develop a new prior in order to better assess the inherent systematic uncertainties. We identify the quark quasi-particle spectrum and analyze the (non-)appearance of zero modes at or around the pseudo-critical temperature. In both, the fully unquenched system and a simpler truncation using a model for the gluon propagator we observe a characteristic three-peak structure at zero three-momentum. The temperature dependence of these structures in case of the gluon propagator model is different than observed in previous studies. For the back-coupled and unquenched case we find interesting modifications at and around the pseudo-critical transition temperature.

Numerical study on cooling heat transfer of turbulent supercritical CO2 in large horizontal tubes

This paper presents the results of computational investigations on cooling heat transfer of turbulent sCO2 in three horizontal tubes with diameter of 15.75mm, 20.00mm and 24.36mm using RANS turbulence models at a pressure of P=8.0MPa. Four models with good prediction performance demonstrated in literature (RNG k-ε model and three other low-Reynolds number k-ε models of LS, YS and AKN) have been validated against experimental measurements and to observe that results from the AKN model are closer to experimental data. Details of heat transfer behaviour of sCO2 cooled in horizontal tubes within this diameter range are revealed and the influence of heat flux, tube diameter and buoyancy on heat transfer performance have been discussed. Results demonstrate that at Tb>Tpc (pseudocritical temperature), sCO2 heat transfer performance is enhanced as the heat flux and tube diameter increase; whereas at Tb<Tpc, the heat flux and tube diameter almost do not affect the heat transfer performance. The buoyancy effect only generates slight enhancement for turbulent heat transfer from sCO2 flowing in horizontal tubes with large diameters. However, as the values of Richardson number Ri that quantifies the buoyancy effects continue increasing within Ri>0.1, the buoyant force is enhanced, which in turn impairs the heat transfer near Tpc. This is a result contrary to past reports confined to small diameter tubes, which is mainly attributed to the accumulation of denser cold fluids at the bottom of the pipe when buoyancy effects are strong.

Quantum entanglement in the neighborhood of pseudo-transition for a spin-1/2 Ising-XYZ diamond chain

Recently has been observed for some one-dimensional models that exhibit unexpected pseudo-transitions and quasi-phases. This pseudo-transition resembles a first- and second-order phase transition simultaneously. One of those models is the spin-1/2 Ising-XYZ diamond chain, composed of Ising spin particles at the nodal sites and the Heisenberg spin particles at the interstitial sites. Where we assume Ising-type interaction between the nodal and interstitial sites, the Heisenberg-type interaction between interstitial sites, and with an external magnetic field applied along the z-axis. This model presents an exact analytical solution applying the transfer matrix technique, which shows 3 phases at zero temperature in the vicinity of pseudo-transition. The pseudo-transition separates quasi-phases, these quasi-phases still hold at a finite temperature most of the pattern configurations of a true phase at zero temperature. Here we study the quantum entanglement of pair spin particles in the quasi-phase regions, which can be measured through the concurrence. Then we observe an unexpected behavior in the concurrence, that is below pseudo-critical temperature the concurrence remains almost constant up to pseudo-critical temperature, but above the pseudo-critical temperature, the concurrence behaves as for the standard one-dimensional spin models. Further, we consider the entropy behavior of the system, below pseudo-critical temperature the entropy becomes almost null, while above pseudo-critical temperature the system exhibits standard behavior as for ordinary one-dimensional spin models.

Capabilities of high y+ wall approaches in predicting heat transfer to supercritical fluids in rod bundle geometries

The present paper summarises the results of the simulation of heat transfer to supercritical water in rod-bundle geometries by a CFD code, using wall function models. Two different sets of experimental data were considered, concerning both relatively high and low mass flux conditions and inlet temperature spanning from low to near-critical values.In past analyses, the unsuitability of low-Reynolds number turbulence models was observed in predicting heat transfer in rod bundles, when both high mass and heat flux values were imposed; in fact, large overestimations of wall temperatures were reported in such conditions. This motivated to try simpler models, such as the wall function approach, in order to investigate if, though expectedly not very accurate, they could at least reproduce the experimental data at an acceptable level.As reported in the present paper, the selected models, which adopt a “high y+” wall treatment (indicating wall functions in the STAR-CCM+ code), seem reasonably able at reproducing the general observed experimental trends. The present understanding of the phenomena and the available modelling techniques unfortunately do not allow obtaining better results when the wall or fluid temperature approach the pseudocritical value. However, the comparison with results obtained by low-Reynolds models shows that, at least when facing operating conditions similar to the ones considered in the present work, a downgrading of the adopted modelling techniques may be beneficial and allows obtaining reasonable results. Analyses were also performed considering conditions far from the pseudo-critical temperature, in which low-Reynolds models had provided good performance, reporting that the wall function approach seems effective also in these cases for obtaining first guess results.

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.

Different metastable equilibrium states in metallic glasses occurring far below and near the glass transition

Precise measurements of the high-frequency shear modulus of two bulk Zr- and Pd-based glasses in the initial and strongly preannealed states in a wide temperature range are performed. Isothermal structural relaxation of preannealed samples leads to either decrease or increase of the shear modulus. At temperatures below particular temperature Tpc, one observes cross-over relaxation (decrease→increase) of the shear modulus. The minimal shear modulus attained upon relaxation corresponds to the quasi-metastable equilibrium, which depends both on temperature and thermal prehistory. At higher temperatures T >Tpc, the relaxation always leads to shear modulus decrease towards the “true” metastable equilibrium, which depends only on temperature. The temperature Tpc for both glasses is by ≈ 25 K smaller than the calorimetric glass transition temperature. It is shown that this temperature constitutes the low temperature limit of the linear extrapolation of the shear modulus from the supercooled liquid state. By definition, the temperature Tpc corresponds to the pseudocritical temperature introduced by Kauzmann in 1948 (W. Kauzmann, Chem. Rev. 43 (1948) 219).A detailed discussion of the microscopic relaxation mechanism below and above Tpc based on the Interstitialcy theory is presented.

Experimental study of jet impingement cooling with carbon dioxide at supercritical pressures on micro structured surfaces

Jet impingement cooling with carbon dioxide at supercritical pressures on micro pin fin structured surfaces was studied experimentally to enhance the impingement cooling heat transfer. The effects of the microstructure, mass flow rate and heat flux on the heat transfer were studied using the MEMS (Micro-Electro-Mechanical System) based silicon chips for heating and simultaneous surface temperature measurement. The pressure was 7.85 Mpa, which is higher than the critical pressure of carbon dioxide of 7.38 MPa. The jet inlet temperature was 19.0 °C, which is lower than the pseudocritical temperature of 33.78 °C at 7.85 MPa. The mass flow rates were 14.4 kg/h and 20.7 kg/h with the heat flux varying from 0.01 to 0.35 MW/m2. The results showed that the surface area increased by the micro structured surfaces was the major reason for heat transfer enhancement with the circular pin fins giving greater heat transfer enhancement than the square pin fins with the same total surface area. The high specific heat fluid layer near the cooled surface at supercritical pressures enhanced the heat transfer rate with the average heat transfer coefficient first increasing with increasing heat flux and then decreasing with further increases in the heat flux.

In-tube convective heat transfer characteristics of CO2 mixtures in a pipeline

In the Carbon Capture, Transportation & Storage (CCS) process, CO2 is captured with impurities such as N2, CH4 and Ar and is transported under a supercritical state. In this study, the characteristics of in-tube convective heat transfer of CO2 mixtures such as CO2 + N2, CO2 + CH4 and CO2 + Ar were experimentally investigated under the land transportation conditions of the CCS process. The test tube was made of a cooper tube buried in a PVC (Polyvinyl Chloride) pipe which was compactly filled with sand, which simulated the land CO2 transportation. Mass flux was changed by 200, 400 and 600 kg m−2 s−1, and operational pressures were 80, 90, and 100 bar. Operational temperatures ranged from 25 to 55 °C. The heat transfer coefficient of the CO2 mixtures dominantly followed the trends of pure CO2; however, they were decided by the type and quantity of the impurity. When the CO2 mole fraction was changed from 1.00 to 0.95, the maximum heat transfer coefficient at the pseudo-critical temperature of CO2 + N2 and CO2 + CH4 decreased by 4389 W·m−2 K−1 and 2770 W·m−2 K−1, respectively. As the mass flux increased, the heat transfer coefficient increased in all of the CO2 mixtures.