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The introduction of renewable energy introduces operational challenges for the modern multi-energy system. To accommodate the uncertainty, this paper proposes an online probabilistic energy flow for the hydrogen-power-heat system. First, a hydrogen-power-heat system model is established to depict the interdependency of multiple energy, in which hydrogen fuel cells interconnect hydrogen, power, and heat systems by converting the hydrogen into power and heat. The probabilistic energy flow is further built considering the uncertain wind power. An efficient algorithm based on multi-parametric programming (MPP) is proposed to enhance the computational performance of probabilistic multi-energy flow for online applications. The parameter region of the probabilistic multi-energy flow in MPP model is divided into multiple critical regions (CR). Each CR reveals a unique mapping relationship from uncertain wind power to system optimal solutions. Probabilistic energy flow could be quickly calculated based on mapping relationship rather than solving optimization problem. Therefore, the proposed method could be applied in online energy flow calculation. Numerical results tested on a 6–6-8 system and an improved 40–118 − 13 system validate the accuracy and efficiency of the proposed method in probabilistic energy flow calculation. • Online rapid computational method for probabilistic energy flow is proposed for hydrogen-power-heat system. • Parameter hyperspace of uncertain wind power in multi-parametric programming is divided into a set of critical regions. • Mapping relationship is applied to quickly obtain optimal solution. • Two test systems are provided to validate effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, the CO 2 super/transcritical power cycle has gained significant attention as the most widely studied power cycle. The accurate thermodynamic properties data is very important for cycle design and performance analysis. In this study, the Kiselev's crossover method based on the renormalization group theory is used to improve the classic SRK equation of state in non-critical region and reproduce the critical fluctuation phenomenon in critical region. The nonlinear equations method and interior-point method are used in the parameter fitting of crossover SRK (CSRK) to get the optimal parameters. The replaced method avoids the problem that Newton iteration method is prone to divergence and falling into local optima. The thermodynamic properties of CO 2 including the VLE properties, heat capacity and speed of sound are calculated by CSRK, respectively. The results show the calculation of the non-critical region is improved, and the critical fluctuation phenomenon in the near-critical region is described accurately, especially the second-order thermodynamic properties calculation results is improved from 3.65 % to 2.80 % compared with our previous work. [ABSTRACT FROM AUTHOR]

We develop a passive control strategy for suppressing thermoacoustic instability in a bluff-body stabilized premixed turbulent combustor. When the equivalence ratio is varied, there is a transition from combustion noise to thermoacoustic instability via intermittency in the combustor. We perform simultaneous acoustic pressure, 2D-PIV, and CH * chemiluminescence measurements to capture the pressure fluctuations, the velocity field, and the heat release rate (HRR) field during the transition. We measure the spatial distribution of the amplitude of turbulent velocity at the acoustic frequency, time-averaged vorticity, time-averaged HRR, and Rayleigh index and identify various regions of significance. We implement a passive control strategy by targeting these regions with a steady injection of secondary micro-jet of air to optimize the injection location and determine the critical region. Targeting the critical region with secondary air leads to greater than 20 dB suppression of the dominant thermoacoustic mode. We observe that the coherent structure forming from the shear layer following the dump plane gets suppressed, leading to an incoherent spatial distribution of HRR fluctuations. We find that the turbulent velocity amplitude correctly identifies the critical region for optimized passive control during thermoacoustic instability. In contrast, the Rayleigh index identifies the region of the most significant acoustic driving; however, it does not identify the region most sensitive to control. Finally, we extend our analysis by determining the spatial distribution of the Hurst exponent measured from the turbulent velocity field. We show that the Hurst exponent identifies the critical region during thermoacoustic instability and intermittency, unlike the other physical measures. Thus, we develop a smart passive control method by combining the need for finding critical regions in the combustor with the predictive capabilities of the Hurst exponent. [ABSTRACT FROM AUTHOR]

Dramatic changes of thermophysical properties in the vicinity of critical point brings significant accelerating effect on the thermodynamic transitions of fluid. This study performs a confined geometric design with CO 2 fluids passing through the critical zone in microchannel. Such a problem formulation combines the compressible Navier-Stokes equations with different property formulations to obtain critical anomaly effects at complex critical transport coefficients. Three equations of state (van der Waals (vdW), Redlich-Kwong (R-K) and Peng-Robinson (P-R) state equations) and their corresponding thermodynamic relations are derived in solving the governing equations of flow and heat transfer equations. Basic results are found to be consistent with theoretical asymptotic analysis, with linearly curves of pressure and a sudden shift of density (425 kg/m3–502 kg/m3) and velocity (0.82 m/s to 0.97 m/s) profiles when the microchannel flow across the critical region. The cascade effect between weakened radial thermal conductivity (λ ∼ (ρ – 1)-1/2, c p ∼ (ρ - 1)−2) and enhanced fluid expansion (β p ∼ (ρ - 1)−2) in the critical region is also shown to cause a sharp negative transition in temperature. In addition, the simulations demonstrate a qualitative comparison for three state equations, and the distinctions in quantitative terms (negative temperature value are −0.1 (vdW), −0.17 (R-K), and − 0.23(P-R)) are found to originate from stronger divergence characteristics (the specific heat c p and thermal expansion coefficients β p) in P-R gases than vdW and R-K gases. [ABSTRACT FROM AUTHOR]

With the emerging application of near-critical fluid, the subject of equation of state (EoS) covering the critical point is of great significance as the thermodynamic behavior of fluids near the critical point is different. Although many different EoSs are available for fluids at the moment, the ones which can give good quantitative results are still rare. Therefore, it is essential to have a suitable model for proper prediction of fluids behavior and their thermodynamic properties near the critical region. In this study, the crossover translation, which applies the asymptotic behavior of fluids and scaling laws near and far from the critical point, was used. Thermodynamic properties including density, vapor pressure and isochoric heat capacity of fifteen pure components in the saturated state and single-phase region on different isotherms were investigated near the critical point by Soave-Redlich-Kwong (SRK) equation of state and crossover SRK EoS and the results were compared with experimental data. According to the results, crossover SRK EoS predicted all of the mentioned properties with quantitative accuracy. The average absolute percent deviation (AAPD) of the saturated liquid density, saturated vapor density, density on isotherms, vapor pressure and isochoric heat capacity based on crossover SRK EoS were 0.0060,0.1287, 0.0171, 0.057 and 2.53, respectively. [ABSTRACT FROM AUTHOR]

Approaching the critical region of hydrocarbon + water mixtures will lead to an unusual increment in miscibility. In this research, CPA EoS is satisfactorily applied to predict the properties of three hydrocarbon + water mixtures at near/supercritical temperatures. First, CPA EoS is applied to evaluate the density of pure water and hydrocarbons in a range of pressure at various temperatures. To make a comparison on CPA models, both SRK and PR are accounted in the physical term of the model. In the case of pure hydrocarbons, the effect of volume shift correction (VS) on modeling results is also investigated. Afterwards, CPA EoS is used to predict the density of mixtures and relative volume change of mixing for hydrocarbon rich phase of mixtures at various temperatures. The results revealed that CPA EoS would be a reliable choice to predict complex behavior of hydrocarbon + water mixtures in a wide range of pressures and temperatures. • SRK/PR-CPA are applied to estimate excess volume of water + hydrocarbon mixtures at high temperatures near critical region. • Impacts of pressure and temperature change, and volume shift on density and excess volume of mixtures are investigated. • The CPA models can predict densities of these complex mixtures with/without tuning the adjusting parameters. [ABSTRACT FROM AUTHOR]

Highlights • The thermal-hydraulic performance of a PCHE was investigated numerically. • The effect of sCO 2 thermophysical properties on flow and heat transfer was discussed. • The values of friction coefficient and Nusselt number were compared to the analytical solutions. Abstract A numerical analysis of the developing laminar flow and conjugate heat transfer in a rectangular micro-channel was performed for supercritical CO 2 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 CO 2 at supercritical conditions and their influence on fluid flow and heat transfer are presented and discussed. Liquid sodium and supercritical CO 2 (sCO 2) 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 sCO 2 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 sCO 2 properties. [ABSTRACT FROM AUTHOR]

Accurate results for fluids at thermal equilibrium, valid both outside and inside the critical region, are difficult to obtain due to the singular nature of this region. However, for simple models like interacting hard spheres and the Ising model high accuracy has been obtained by use of SCOZA (self-consistent Ornstein-Zernike approximation). Here this approach is extended to one component fluids more generally. Outside the critical region good analytic approximations may be obtained by use of statistical mechanical results that are adjusted to experimental data and/or computer simulations. However, such approximations typically will be of mean field type in the sense that the usual singular behavior in the critical region and in the transition to it, is not present. Here the SCOZA is generalized such that approximations accurate outside the critical region are utilized as basic input in the SCOZA problem. The singular behavior is connected to correlations of increasing range that develop as the critical point is approached. These correlations contribute both to the internal energy and compressibility of the fluid, and they give another contribution to the SCOZA partial differential equation. Accurate results in the critical region are expected to be obtained by adjusting one or a few parameters. • The SCOZA is extended to fluids more generally. Earlier it was developed to improve upon the MSA. • By this extension also equations of state known well outside the critical region, can be input to the SCOZA problem. • The SCOZA gives a rather accurate description of the critical region with its singular behavior. • Solution of the SCOZA problem is expected to give accurate results also in the critical region for the fluid of interest. [ABSTRACT FROM AUTHOR]

The critical point is the end point of a phase equilibrium curve; liquid and its vapor can coexist under designated points. Close to the critical point, thermophysical properties present clear variations, especially in the region of 0.85 P cr ∼ P cr . Latent heat and liquid density in this region decrease more quickly than in lower-pressure areas, resulting in unique boiling heat transfer behavior. This region is also called the near-critical region. However, only a few scholars have discussed the heat transfer phenomenon; thus, it is difficult to ascertain the near-critical region’s properties and characteristics from extant literature. In the present study, we conduct experimental investigations to explore the specificities of the heat transfer characteristics of carbon dioxide in horizontal flow within the near-critical region in a circular channel with a diameter of 4 mm. The operating pressure ranges from 6.26 MPa to 7.3 MPa with a mass flow rate between 200 and 400 kg/m 2  s, heat flux between 5 and 140 kW/m 2 , and test section inlet temperature of −5 °C. Then, we examine the inner-wall temperature and heat transfer coefficient profiles at different pressures within the near-critical region. The results show that at high heat flux, departure from nucleate boiling (DNB) phenomenon presents with a sudden decrease in the heat transfer coefficient in the subcooled region. The higher the heat flux, the more seriously deteriorating the heat transfer is. Interestingly, the temperature reaches its peak in the post-DNB region rather than at the critical vapor quality point. With an increase in pressure, DNB occurs early with lower vapor quality, and the temperature peak decreases at the given heat flux and mass flux. On the contrary, DNB is delayed with an increase in mass flux. A series of boiling heat transfer correlations in a subcooled region, two-phase flow region, and superheated region are proposed in addition to a new predictive correlation for critical heat flux in the near-critical region at a given mass flux. [ABSTRACT FROM AUTHOR]

This experimental work is aimed at characterizing the effect of scraper board (SB) in reducing the rotating air layer around a grinding wheel and introducing the better method of application of scraper board and fluid delivery into the grinding zone. Zero pressure at the grinding zone is reported to achieve by placing the scraper board at an optimal location along the wheel periphery. The grinding ratio improved by 35.6% and 119%, surface roughness decreased by 36% and 54.2% while the requirement of specific energy is reduced by 50.8% and 57.3% when scraper board is positioned at the critical distance in comparison to the 57.5° position and no scraper board respectively. [ABSTRACT FROM AUTHOR]

Prestressed concrete bridges with corrugated steel webs have emerged as one of the promising bridge forms. However, the presence of prestressing tendons and shear-deformable corrugated steel webs with negligible axial stiffness complicates the formation of plastic hinges under applied loading to failure. The full-range structural behaviour of these bridges and plastic hinge formation are therefore studied experimentally and numerically. The more localised flange plastic hinge caused by both web shear deformation and local flange bending interacts with the full-depth plastic hinge of such a bridge. Tests show that the full-range structural behaviour of the bridge is mainly governed by the localised flange plastic hinges. A formula is proposed to predict the equivalent interactive plastic hinge length, which helps to predict the full-range structural behaviour taking into account the presence of external prestressing tendons. Some design recommendations are also provided. [ABSTRACT FROM AUTHOR]

• The crossover PC-SAFT EoS based on white's renormalization group corrections were developed. • The three parameters in the crossover PC-SAFT EoS introduced by the crossover process were fitted to the experimental data. • The phase behavior as well as derivative properties in the critical region and outside the critical region for several fluids such as CO 2 , n-alkanes and n-alkanols were investigated using the PC-SAFT EoS and the crossover PC-SAFT EoS. In order to improve the prediction accuracy of the thermophysical properties of fluid in near critical region, in this work, White's renormalization group (RG) corrections were applied to construct the crossover PC-SAFT EoS (simplified as PC-SAFT-RG). We first fit the three parameters introduced by the crossover process to the experimental data, then the phase behavior as well as derivative properties in the critical region and outside the critical region for several fluids such as CO 2 , n-alkanes and n-alkanols were investigated using the PC-SAFT EoS and the PC-SAFT-RG. Our results show that the PC-SAFT-RG is able to modify the behavior of the PC-SAFT EoS in the critical region and revert to classic behavior outside the critical region. The PC-SAFT-RG improves the PC-SAFT EoS's performances on the second derivative thermodynamic properties, with the average absolute relative deviations (AADs) of 9.96%, 6.99% and 3.91% for isobaric heat capacity, isochoric heat capacity and speed of sound respectively. [ABSTRACT FROM AUTHOR]

An equation of state with near-critical corrections is developed for water (H 2 O) and carbon dioxide (CO 2 ). The equation is constrained by the critical conditions and optimized with highly accurate pressure–volume–temperature ( PVT ) and phase equilibrium data at temperatures from the triple point to 647.096 K and pressures from zero to 80 MPa. The resulting equation is systematically checked in the above P – T range. For H 2 O, the vapor pressures are reproduced within 0.032%, with an average deviation of only 0.005%; the average deviations of the saturated vapor and liquid volumes, and the volumes in the single-phase regions are 0.047%, 0.019% and 0.058%, respectively. The maximum deviations of the above-mentioned volumes are 1.26%, 0.91% and 1.06%, respectively, which are all in the immediate vicinity of the critical point. Below 520 K, the deviations of PVT and saturation properties are all within 0.06%. For subcritical CO 2 , the average and maximum deviations of vapor pressures are 0.011%, 0.077%, respectively; the average deviations of the saturated vapor and liquid volumes, and the volumes in the single-phase regions are 0.099%, 0.058% and 0.126%, respectively. The largest deviations of the above volumes are 0.230%, 0.173% and 0.358%, respectively. For supercritical CO 2 below 650 K, the average volume deviation is 0.080%. The equation also agrees very well with many high-quality density and phase equilibrium data not used to fit the equation. The equation gives excellent prediction of fugacity coefficients, residual enthalpies and entropies and heats of vaporization, and can be extrapolated to 200 MPa for H 2 O, or to 100 MPa for CO 2 . The equation can serve as a good starting point for the thermodynamic modeling of many industrial and geological processes, including carbon capture and sequestration. [ABSTRACT FROM AUTHOR]

Accurate predictions of the thermodynamic properties of binary mixtures, especially in the critical region, are essential for many chemical process designs. In this study, based on the predictive crossover volume translation SRK equation of state (VTSRK EoS) presented in previous work, the crossover VTSRK EoS for binary mixtures was developed. Composition-dependent mixing rules with one adjustable binary interaction parameter, k ij , were used for the crossover equation to simplify the crossover EoS. The applicability of the crossver EoS was verified against two kinds of binary mixtures, including alkane + alkane and CO 2 + alkane mixtures, because of their wide applications. For the alkane + alkane mixtures with similar intermolecular interactions, the k ij in the vdW-1 mixing rules was set to zero which makes the calculation predictive. For the CO 2 + alkane mixtures which have large difference between intermolecular interactions, the vapor liquid equilibrium (VLE) and single phase pρT properties were calculated using k ij obtained from VLE or pρT experimental data at one temperature. The crossover VTSRK EoS gives better VLE and pρT representations than the VTSRK EoS, especially in the critical region. [ABSTRACT FROM AUTHOR]

A flow calorimeter was developed to measure the isobaric heat capacities of pure water at high pressure and high temperature up to supercritical region. Experimental isobaric heat capacities of pure water from 395 K to 665 K and pressure up to 26 MPa are presented. The total measurement uncertainties of temperature and pressure were ±0.02 K and ±3.88 kPa, respectively. The relative uncertainty of the isobaric heat capacity was estimated to be ±0.98%. The aim of this study is to provide new experimental data to complete the non-experimental data region and to check the accuracy of the IAPWS-95 formulation. The IAPWS-95 formulation shows great accuracy at temperatures under 623 K and at pressures under 22 MPa region. However, in the near-critical and supercritical region, its accuracy needs more experimental data for verification and to extend theories. [ABSTRACT FROM AUTHOR]

We present a microscopic theory of the second-order phase transition in an interacting Bose gas that allows one to describe formation of an ordered condensate phase from a disordered phase across an entire critical region continuously. We derive the exact fundamental equations for a condensate wave function and the Green's functions, which are valid both inside and outside the critical region. They are reduced to the usual Gross–Pitaevskii and Beliaev–Popov equations in a low-temperature limit outside the critical region. The theory is readily extendable to other phase transitions, in particular, in the physics of condensed matter and quantum fields. [ABSTRACT FROM AUTHOR]

In the present work, using the principle of isomorphism and complete scaling method, a new scaled crossover parametric equation of state and a new representation for the refractive index of binary systems has been introduced. We have introduced a stepwise algorithm for calculating the mixing parameters defining scaling fields in terms of physical fields. Comparing the experimental data for five thermophysical properties and for eight binary liquid systems, it has been observed that this new approach is able to predict all thermophysical properties quite well. [ABSTRACT FROM AUTHOR]

Abstract: It has been proved that there are many indicators (petrophysical quantities) for the estimation of petroleum reservoirs. The value of information contained in each indicator is yet to be addressed. In this work, the most famous and applicable petrophysical quantities for a reservoir, which are the gamma emission (GR), sonic transient time (DT), neutron porosity (NPHI), bulk density (RHOB), and deep induced resistivity (ILD), have been analyzed in order to characterize a reservoir. The implemented technique is the well-logging method. Based on the log-normal model defined in random multiplicative processes, the probability distribution function (PDF) for the data sets is described. The shape of the PDF depends on the parameter which determines the efficiency of non-Gaussianity. When non-Gaussianity appears, it is a sign of uncertainty and phase transition in the critical regime. The large value and scale-invariant behavior of the non-Gaussian parameter is an indication of a new phase which proves adequate for the existence of petroleum reservoirs. Our results show that one of the indicators (GR) is more non-Gaussian than the other indicators, scale wise. This means that GR is a continuously critical indicator. But by moving windows with various scales, the estimated shows that the most appropriate indicator for distinguishing the critical regime is ILD, which shows an increase at the end of the measured region of the well. [Copyright &y& Elsevier]

Abstract: In our previous work [S. Azzouz, A. Rizi, A. Acidi, A. Abbaci, St. Cerc. St. CICBIA 11 (2) (2010) 235–241], we developed an interim thermodynamic property formulation for the supercritical n-hexane which incorporates non-analytic scaling laws in the critical region and reproduces the thermodynamic properties of n-hexane far away from the critical region. However, it appears that this equation of state gives unphysical values for critical amplitudes such as that of the compressibility above the critical point. In this work, we present a modification of this equation of state based on the pressure data of Grigoriev et al. group and those of Abdulagatov, the isochoric specific heat data of Amirkhanov et al. as well as the isobaric specific heat of Gerasimov et al. Comparison with different sets of thermodynamic-property data available is given. [Copyright &y& Elsevier]

Abstract: A predictive correlation relating isobaric liquid specific heat capacity to absolute temperature and elemental composition was recently reported. The Dadgostar–Shaw correlation, valid where C V ≫ T(∂V/∂T) P (∂P/∂T) V , is modified in the present work to accommodate the critical region and the consequent variation of liquid phase isobaric heat capacity among isomers at the same absolute temperature. The results obtained for a training data set and a test data set are presented and compared with results obtained with the Dadgostar–Shaw correlation, and two variants of the Rowlinson–Bondi correlation. The C P ° contribution is calculated using either compound specific correlations or the predictive universal Laštovka–Shaw equation for ideal gases. For pure hydrocarbon liquids where compound specific C P ° correlations, T c and ω are available, the Rowlinson–Bondi based approach should be used to compute saturated liquid heat capacities. If only T c and ω are available, the Rowlinson–Bondi based approach+the predictive Laštovka–Shaw equation for C P ° values is preferred. If the liquid is a multicomponent or ill-defined hydrocarbon liquid, the modified Dadgostar–Shaw correlation is preferred over the Dadgostar correlation as long as T c is available or can be estimated. The accuracy penalty for use of the modified Dadgostar–Shaw correlation appears small relative to either Rowlinson–Bondi based calculation approaches. [Copyright &y& Elsevier]

Abstract: In the present work, we have extended a crossover parametric equation of state proposed by Agayan et al. [V.A. Agayan, M.A. Anisimov, J.V. Sengers, Phys. Rev. E 64 (2001) 026125] in order to take account of the asymmetric nature of fluids. To this end, we have used the concept of complete scaling which implies that the scaling fields are a combination of all physical fields. To test this extended equation of state, it has been applied to carbon dioxide and nitrogen fluids. In addition, by using this equation of state we have studied the temperature behaviour of diameter of the coexistence curve in close to and far from the critical point and compared it with one of the recent approach to nitrogen fluid. [Copyright &y& Elsevier]

Abstract: In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region. [Copyright &y& Elsevier]

Abstract: Numerical analysis has been carried out to investigate forced convective heat transfer to water near the critical region in a horizontal square duct. Near the critical point convective heat transfer in the duct is strongly coupled with large variation of thermophysical properties such as density and specific heat. Buoyancy force parameter has also severe variation with fluid temperature and pressure in the duct. There is flow acceleration along the horizontal duct resulted from fluid density decrease due to the heat transfer from the wall. Local heat transfer coefficient has large variation along the inner surface of the duct section and it depends on pressure. Nusselt number on the center of the bottom surface also has a peak where bulk fluid temperature is higher than the pseudocritical temperature and the peak decreases with the increase of pressure. Flow characteristics of velocity, temperature, and local heat transfer coefficient with water properties are presented and analyzed. Nusselt number distributions are also compared with other correlations for various pressures in the duct. [Copyright &y& Elsevier]

Abstract: This work presents an extension of a generalized van der Waals-type equation of state by including a crossover treatment to consider the fluctuations in the critical region. The original cubic equation depends on simple parameters of pure fluids, and it is able to reproduce vapor pressures and densities over a wide range of conditions, once the appropriate parametrization techniques are used. The equation is forced to reproduce the critical point by explicitly including this point into the fitting procedure. However, as all mean field theories, the equation does not take into account the fluctuations appearing as the critical region is approached. Hence, the non-analytical asymptotic behavior in the vicinity of the critical point is not well reproduced, leading to some inaccuracies in liquid and/or gas phase equilibria density calculations. To overcome this limitation we have applied a specific crossover treatment, based on White''s work [J. White, Fluid Phase Equilib. 75 (1992) 53–64; L.W. Salvino, J.A. White, J. Chem. Phys. 96 (1992) 4559–4568] from the renormalization group (RG) theory [K. Wilson, Phys. Rev. B4 (1971) 3174–3205]. This treatment is done by incorporating the scaling laws valid asymptotically close to the critical point. In addition to accurate density estimations far from and close to the critical point, the extended equation is also able to reproduce the universal critical exponents describing the approach to the critical point. The extended equation has been applied to two chemical families: the n-alkanes and 1-alkanols, as well as to other compounds of industrial interest, including carbon dioxide, ethylene, toluene, xenon and water, providing excellent agreement with experimental data. [Copyright &y& Elsevier]

Abstract: We present here results from the crossover soft-SAFT equation of state as applied to selected n-alkane/n-alkane and n-alkane/1-alkanol mixtures. The molecular parameters needed to apply the equation to experimental systems were obtained as a function of the molecular weight of the compounds, from published correlations. The fact that the equation takes into account the long range density and composition fluctuations appearing near the critical point enables it to predict with equal accuracy the behavior of the systems far from and close to the critical region. We have found that, for most of the mixtures investigated here, one size binary interaction parameter, with a fixed value for all systems, is enough to quantitatively predict the rich phase behavior shown by these mixtures, while for the case of very asymmetric mixtures, a second binary parameter, also independent of the thermodynamic conditions, is needed to quantitatively describe experimental data. Crossover soft-SAFT accurately reproduces transitions from type I to type V for the critical behavior of the methane/n-alkane and ethane/n-alkane homologous series. The equation also predicts in a quantitative manner the subcritical and critical behavior of the 1-propanol/n-hexane and ethanol/n-butane binary mixtures. Finally, we report speed of sounds of the mixture methane/n-butane and the heat capacities of the mixture 1-propanol/n-decane, in close agreement with experimental data. Results presented here encourage the development of molecular-based equations of state with a term taking into account the singular behavior in the near critical region, especially if one is searching for quantitative predictions in this region for further applications. [Copyright &y& Elsevier]

Abstract: In our previous work [S.B. Kiselev, J.F. Ely, Fluid Phase. Equilib. 222–223 (2004) 149], we developed a generalized cubic (GC) EoS for pure fluids, which incorporates non-analytic scaling laws in the critical region and reproduces the thermodynamic properties of pure fluids with high accuracy, including the asymptotic scaling behavior of the isochoric heat capacity in the one- and two-phase regions. However, it appears that in some cases the GC EoS can give unphysical behavior when extrapolated to high temperatures and densities. In this work, we present a modification of the generalized cubic EoS, which in the critical region is physically equivalent to the GC EoS developed earlier, but is more reliable in its extrapolation to high temperatures. [Copyright &y& Elsevier]

Abstract: Densities of water–methanol mixtures at 573 and 588K and at pressures in the 100–200bar range have been measured with a vibrating-tube densimeter. Temperature and pressure dependence of the excess molar volumes together with the previous results was discussed. A large negative-to-positive sigmoidal change of the excess molar volumes as a function of methanol mole fraction was interpreted on the basis of an estimated critical locus of the mixtures. The volumetric behavior of the mixtures was compared with that of the previously reported water–benzene mixtures by estimating the relative volume change on mixing. A large negative volume change at the lower methanol concentrations is in sharp contrast to the large positive change for the water–benzene mixtures. This contrast may be attributable to characteristic features of aqueous solutions of hydrophilic and hydrophobic substances in the vicinity of the critical region. The behavior of the water–methanol mixtures at the lower methanol mole fractions was discussed in terms of the local solute–solvent structure by estimating radial distribution functions and self-diffusion coefficients from molecular dynamics calculations. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Common classical expressions for the molar excess Gibbs energy of mixing g E do not contain a contribution from composition fluctuations that are significant in the vicinity of the plait point for a ternary system. We propose a correction to g E based on reasonable phenomenological assumptions. This correction requires three ternary constants, but two are obtained from stability relations provided that we know the composition of the plait point. While the method proposed here is not predictive, it provides a consistent thermodynamic procedure for calculating the liquid–liquid phase diagram of a ternary system with a plait point. The proposed method is illustrated for three ternaries. When calculations are based on the classical expressions for g E alone, calculated results are in serious disagreement with experiment near critical conditions. Inclusion of the proposed correction for g E provides dramatic improvement. [Copyright &y& Elsevier]

Abstract: The thermodynamic properties of fluids are predicted using global equations of state. Among these thermodynamic properties, we consider the densities of the liquid and vapor phases, pressure, the caloric properties such as specific heat at constant volume and specific heat at constant pressure and the speed of sound. In the present work, we apply the crossover theory to these thermodynamic properties and give a comparison of the crossover model equation of state with the experimental thermodynamic property data of ethane. [Copyright &y& Elsevier]

Abstract: Based on White’s renormalization group (RG) theory and the statistical associating fluid theory, a new equation of state (EOS) is derived, which can be used for a variety of fluids, including non-polar, polar and associating chain fluids both inside and outside the critical region. The new EOS, with the advantage of not introducing any additional adjustable parameter to the RG transform for real fluids, yields satisfactory critical exponent, vapor–liquid coexistence densities and vapor pressures, pVT isotherms, and isobaric specific heats for pure fluids. Especially, much better results are obtained than the original EOS in the nearest vicinity of the critical point. [Copyright &y& Elsevier]

We have developed a generalized cubic (GC) EOS for pure fluids, which incorporates non-analytic scaling laws in the critical region and in the limit ρ→0 is transformed into the ideal gas equation EOS. The GC EOS contains 10 adjustable parameters and reproduces the thermodynamic properties of pure fluids with high accuracy, including the asymptotic scaling behavior of the isochoric heat capacity in the one- and two-phase regions. Unlike the crossover cubic EOS developed earlier [Fluid Phase. Equilibr. 147 (1998) 7], the GC EOS is based on the crossover sine model and can be extended into the metastable region for representing analytically connected van der Waals loops. In addition, using the GC EOS and the decoupled-mode theory (DMT) we have developed a generalized GC + DMT model, which reproduces the singular behavior of the thermal conductivity of pure fluids in and beyond the critical region. Unlike the DMT model based on the asymptotic crossover equation of state CREOS-97, the GC + DMT model is valid in the entire fluid state region at T≥Tb (where Tb is the binodal temperature), and at ρ→0 reproduces the dilute gas contributions for the transport coefficients. [Copyright &y& Elsevier]

The phase behaviors, constant volume heat capacity (Cv), and isothermal compressibility (KT) of ethane+ethanol and ethane+acetone binary mixtures have been measured in supercritical (SC) region and subcritical region near the critical point (CP) of the mixtures at 309.45 K. The experiments have also been carried at the conditions far from the critical point of the mixtures. It is demonstrated that in supercritical region there exists a maximum in Cv versus pressure curve (Cvmax) at fixed composition, which occurs at the pressure where KT is the largest. In subcritical region, Cv and KT increase sharply as pressure approaches the critical point or bubble point (BP), and the Cv at CP or BP can be several times larger than that of the fluids far from the phase separation pressures. On the basis of the experimental results, the intermolecular interaction is discussed. [Copyright &y& Elsevier]

Measurements of the excess molar enthalpy HmE and the excess molar volume VmE of {xC4H10)+(1−x)SF6} made in the supercritical region at the pressure p=8.00 MPa and seven temperatures over the range 311.25–425.75 K are reported. The measurements extend the range of similar measurements made at the pressure 6.00 MPa reported recently. The measurements were made using a flow mixing calorimeter followed by a vibrating tube densimeter. The results are compared with the Patel–Teja (PT) equation-of-state with parameters determined by solving a cubic equation as they recommend, and also with parameters determined by the method suggested by Valderrama–Cisternas (VC) who proposed equations in which the parameters are a function of the critical compressibility factor Zc. The overall fit to the HmE and VmE measurements obtained using the Valderrama and Cisternas equation is found to be better than that obtained using the parameters obtained by the method suggested by Patel and Teja. [Copyright &y& Elsevier]

• Understand superconductivity with high- T c by analyzing vortex dynamics. • Vortex liquid phases with a nonlinear activation energy. • Presence of critical region with different thermally activated flux motions. • Dimensional crossover on vortex liquid-to-glass transition. The temperature dependence of the electric resistivity measured in various magnetic fields was analyzed by the vortex glass theory and the thermally activated flux motion (TAFM) theory. The vortex glass-to-vortex liquid (GTL) transition T g obtained from the analysis shows a temperature dependence of B g T = B 0 1 - T / T c m. The vortex liquid region is divided into the critical region existing in a finite temperature region just above T g and the TAFM region present in the finite temperature region above it. In the critical region, the activation energy is expressed as U e f f = k B T T c - T / (T c - T g) , whereas in the TAFM region, the activity energy is expressed as temperature-nonlinear U T , B = U 0 B 1 - t q. In the GTL transition, (Ca 0.85 La 0.15) 10 (Pt 3 As 8)(Fe 2 As 2) 5 maintains the 3D vortex structure without exhibiting dimension crossover of the vortex, but Ca 10 (Pt 3 As 8)((Fe 0.92 Pt 0.08) 2 As 2) 5 exhibits the dimension crossover from the 3D vortex glass to the 2D vortex liquid. [ABSTRACT FROM AUTHOR]

In a systematic search for the QCD critical point in nuclear collisions, at the CERN SPS, it was found that intermittency measurements in the freeze-out state of central Si + Si collisions, at the maximum SPS energy, provide us with an indication of sizeable critical fluctuations. Also, rather recently, a weaker effect was traced in preliminary data of the Ar + Sc reaction for 10–20% most central collisions at (approximately) the same energy. However, the uncertainties in the analysis and the limitations of the experimental event statistics make the interpretation of the above measurements (NA49, NA61/SHINE) rather inconclusive, inviting for a further, phenomenological investigation with complementary tools and theoretical ideas. To this end, in the present work, we employ intermittency techniques within a model-independent analysis scheme (AMIAS), a novel method from Data Science [1] , in order to produce unbiased results for the parameters of the power-laws and in particular for the associated power-law exponent (intermittency index) ϕ 2. Using data-sets at different peripheralities, we also study the dependence of the ϕ 2 -value on the number of wounded nucleons, in order to uncover the approach to the critical point. With these findings and the help of Ising-QCD partition function, the interpretation of SPS intermittency measurements and their links to the critical region, are discussed. [ABSTRACT FROM AUTHOR]