Extended Corresponding States Research Articles

Measurements of the Viscosity of Hydrogen and a (Hydrogen + Methane) Mixture with a Two-Capillary Viscometer

AbstractMeasurements of the viscosity of pure hydrogen and a binary (hydrogen + methane) mixture with a nominal composition 90 mol % hydrogen are presented. The measurements were conducted with a two-capillary viscometer relative to helium along three isotherms of (298.15, 323.15, and 348.15) K and at pressures of up to 18 MPa. Expanded relative combined uncertainties in viscosity range from (0.65 to 2.7) % (k = 2) for the hydrogen data, and from (0.91 to 3.2) % (k = 2) for the (hydrogen + methane) data. The viscosity data are compared to experimental literature data and viscosity correlations implemented in the NIST REFPROP v10.0 database. Good agreement between this work’s data, literature data, and the viscosity correlation was achieved for pure hydrogen. The (hydrogen + methane) mixture was compared to the Extended Corresponding States (ECS) model implemented in REFPROP v10.0. Relative deviations between the experimental data and the ECS model exceed the experimental uncertainty and were found to exhibit a positive trend with increasing density and a weakly pronounced negative trend with increasing temperature. No experimental literature data are available at overlapping state regions. Nonetheless, deviations to the ECS model imply reasonable consistency of this work’s data and literature data. In addition to experimental viscosities, experimental zero-density viscosity ratios of the fluids under investigation and helium are reported. Fairly good agreement within the experimental uncertainty of this work with a highly accurate literature value and a value obtained from accurate ab initio calculated data was achieved for hydrogen.

Thermal Conductivity of Liquid trans-1,2-Dichloroethene (R-1130(E)): Measurement and Modeling

The thermal conductivity of liquid trans-1,2-dichloroethene (R-1130(E)) was measured at temperatures ranging from 240 K to 340 K and pressures up to 25 MPa using a transient hot-wire instrument. A total of 447 thermal conductivity data points were measured along six isotherms. Each isotherm includes data at nine pressures, which were chosen to be at equal density increments starting at a pressure of 0.1 MPa (or slightly above the saturation pressure of R-1130(E) at temperatures above its normal boiling point) to a maximum pressure of 25 MPa. The combined expanded uncertainty of the presented experimental data is 1.4% at a 95% confidence level. The experimental data were used to evaluate the performance of an extended corresponding states (ECS) model and a residual entropy scaling (RES) model. Both models were applied in a totally predictive mode, and in a mode where the experimental data were used to tune the model parameters. A volume-translated Peng–Robinson equation of state was used to provide thermodynamic properties needed to apply both models. In a totally predictive mode, the ECS model had an average absolute relative deviation (ΔAARD) of 6.89% relative to the experimental data with the largest deviation being − 8.33%. The RES model in a totally predictive mode showed an ΔAARD of 2.55% with the largest deviation being − 5.81%. When model parameters were fitted to the experimental data, both the ECS and the RES model represented the experimental data to within its uncertainty of 1.4%.

Empirical models of thermal conductivity of cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) with measurements using transient hot-wire method

This article represents the empirical modeling for thermal conductivity of cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) with new experimental measurements conducted in liquid and vapor phases using the well-established transient hot-wire method. These new experimental data, covering a temperature range of 313 to 414 K for liquid and 354 to 452 K for vapor phase at a pressure range of 0.20 to 4.0 MPa, have an expanded uncertainty of less than 2.17% for liquid and 2.41 % for vapor measurements at a 95 % confidence level (k = 2). The thermal conductivity model of this fluid is presented using the extended corresponding states (ECS) and modified fluid specific residual entropy scaling (RES) techniques with the help of recently published respective viscosity models. Using the adjustable parameters found during the modeling process, the extended corresponding states and the residual entropy scaling technique model equations can represent the experimental data within reported uncertainties. Furthermore, the average absolute deviations for thermal conductivity were found to be 0.96 % and 0.72 % using the ECS and the RES methods, respectively.

Reporting of experimental viscosity data and modeling of transport properties of 1,1,1,3,3,3-hexafluoro-2-methoxypropane (HFE-356mmz) using extended corresponding states (ECS) and residual entropy scaling (RES) technique

As a novel low GWP working fluid 1,1,3,3,3-hexafluoro-2-methoxypropane (HFE-356mmz) is regarded as a promising candidate for high-temperature heat pumps and organic Rankine cycle. Recently, the experimental kinematic viscosity and thermal conductivity data of HFE-356mmz were published in the literature. However, at the time of that publication it was not possible to develop any mathematical model of the transport properties due to unavailability of an equation of state. In this work, we report dynamic viscosity data of HFE-356mmz together with mathematical models for dynamic viscosity and thermal conductivity using the extended corresponding states (ECS) and the residual entropy scaling (RES) technique. With R134a used as the reference fluid for ECS method, the transport shape factors and the other adjustable parameters were calculated by utilizing latest multi-parameter Helmholtz-energy-explicit-type equations of state for HFE-356mmz. Furthermore, slight modification of the original RES method has been adopted that removes the implicit dependency on the tuned ECS method. By using the adjustable parameters, the tuned ECS and RES transport equations can represent the experimental data within reported uncertainties. The average absolute deviations (AAD) for viscosity and thermal conductivity were found to be 0.85% and 0.76% using the tuned ECS and 0.83% and 0.44% using the modified RES method respectively.

Thermal conductivity prediction of pure refrigerants and mixtures based on entropy-scaling concept

The residual entropy scaling (RES) concept builds up connection between the transport properties and thermodynamic equation of state directly. However, the low-density divergence issue of the reduced dimensionless thermal conductivity might not be fixed properly through current literature models. This study proposes a new RES model coupled with the original perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) for the thermal conductivities of 11 typical refrigerants (including hydrocarbons, hydrofluorocarbons, hydrofluoroolefins and carbon dioxide) and their multicomponent mixtures. Model parameters are adjusted to saturated vapor and liquid data obtained from REFPROP. The combination of a modified reference thermal conductivity term as an extension of the original work by Rosenfeld et al. and the new formulation of the reduced term could provide reasonable predictive results for the investigated pure and mixture systems with AAD% of 3.95% and 5.76%, respectively. As expected, quasi-linear behaviors in both dilute and dense fluid regions could be observed for the refrigerant systems under study. The extended corresponding states (ECS) and the other two RES approaches reported in the literatures are used as reliable tools for assessing the predictive capability of the proposed model. However, the critical enhancement of thermal conductivity and the correction of the reference EoS especially near the critical point will be the priority in the future.

Viscosity prediction of pure refrigerants applying the residual entropy scaling theory coupled with a “Generalized Chart” parametrization method for the Statistical Associating Fluid Theory

The residual entropy scaling (RES) theory integrated with different thermodynamic Equation of States (EoS) have obtained several accurate and simple viscosity models of working fluids, which is crucial for designing and optimizing of the energy utilization system. However, the influence of parameterization methods on RES’s viscosity calculations is rarely mentioned in a systematic way. Hence, a robust parameterization method based on generalized relation between the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) EoS’s input parameters of 11 pure refrigerants (including hydrocarbons (HCs), CO2, hydrofluorocarbons (HFCs), hydrofluoroolefins (HFOs)) and their critical properties is introduced and coupled with a robust formulation of the reduced viscosity term in RES theory recently proposed by Dehlouz et al. Accurate vapor pressure calculations and near-constant difference between calculated liquid densities and high-accuracy correlation model in saturated state could be obtained with this parameterization method. Viscosities in vapor and liquid phases are exactly reproduced with an overall error of 3.14% applying the model proposed in this work, which is comparable to those from three RES models in literature and the extended corresponding states (ECS) model with overall errors of 3.36%, 3.22%, 3.41% and 1.77%, respectively. In addition, the divergence behavior in dilute region and the component-specific curves of dimensionless reduced viscosity and entropy variables are improved than other RES models under study to a certain extent. Meanwhile, as a supplement, the limitation of the above RES models on predicting viscosities in the near critical region is also discussed in detail.

Thermal Conductivity of Binary Mixtures of 1,1,1,2-Tetrafluoroethane(R-134a), 2,3,3,3-Tetrafluoropropene (R-1234yf), and trans-1,3,3,3-Tetrafluoropropene (R-1234ze(E)) Refrigerants.

A total of 2160 thermal conductivity data points, measured using a transient hot-wire instrument, are reported for binary mixtures of R-134a, R-1234yf, and R-1234ze(E) refrigerants from 200 to 340 K to pressures of 12 MPa for mixtures containing R-1234yf and to 50 MPa for R-134a/1234ze(E) mixtures. Data are reported at compositions of approximately (0.33/0.67) mole fraction and (0.67/0.33) mole fraction for each binary mixture investigated. The estimated relative expanded uncertainty of the thermal conductivity measurements is less than 2%. The data are used to refit binary interaction parameters for the Extended Corresponding States (ECS) model implemented in REFPROP (version 10.0). Additionally, the data in this study are used to assess the performance of a generalized entropy scaling model for refrigerants. Finally, the strengths and weaknesses of the ECS and entropy scaling models are compared.

Viscosity measurements of CO2-rich; CO2 + N2 and CO2 + H2 mixtures in gas or supercritical phase at temperatures between 273 and 473 K and pressures up to 8.7 MPa

New experimental viscosity data of three binary CO2-rich mixtures with approximate mole fractions of 0.93 CO2 + 0.07 H2, 0.80 CO2 + 0.20 H2, and 0.90 CO2 + 0.10 N2 are reported. The measurements were performed at four different isotherms between 273 K and 473 K. Two independent rotating body viscometers with different pressure range were utilized, suitable for measurement of pressures up to 2 MPa and 20 MPa, respectively. The maximum expanded combined relative uncertainty (k = 2) in viscosity was 0.25% for the data obtained from the low-pressure viscometer and 0.6% for the data measured by the high-pressure viscometer. The experimental data were compared to the data estimated by the extended corresponding states (ECS) model implemented in the NIST REFPROP 10.0 database. The maximum deviation between the model and the new data is 1.86%. The data measured with the two apparatuses agree within the estimated uncertainty.

Thermal conductivity measurements and correlations of pure R1243zf and binary mixtures of R32 + R1243zf and R32 + R1234yf

Thermal conductivity measurements of pure R1243zf and binary mixtures of R32 + R1243zf and R32 + R1234yf were conducted in the homogeneous liquid and vapour phases with a transient hot-wire technique. The mole fractions of R32 are 0.25, 0.50, and 0.75 in both binary systems. The temperature range of the measurements was from (264.1 to 405.6) K with pressures ranging between (0.9 and 6.1) MPa. The transient hot-wire apparatus was validated with measurements of pure CO2 in both the liquid and vapour regions. The relative combined expanded uncertainty (k = 2) in the experimental thermal conductivity was approximately 2.0 %. The relative deviations of the measured thermal conductivities from those calculated using the extended corresponding states (ECS) model as implemented in the software REFPROP 10 were between (−13 and 10) % in the vapour phase, and between (−14 and 1) % in the liquid phase. Additionally, the performance of a new approach to predicting fluid transport properties, the residual entropy scaling model incorporating the cubic-plus-association equation of state (RES-CPA model) was tested for these mixtures by first determining the scaling parameter of pure R1243zf. The RES-CPA model was then able to predict the mixture thermal conductivities generally within 10 %, which is similar to the ECS model; however no additional parameters were introduced to the RES-CPA model to describe binary interactions.

Universal parameters of the extended corresponding states (ECS) model for hydrofluoroolefin refrigerants

• New universal parameters of the ECS model are presented for HFO refrigerants. • They are based on the saturation properties of well-studied eight refrigerants. • Typical deviations are within 1% for vapor pressures and within 3% for saturated liquid densities. • They are sufficient accuracies for the preliminary evaluation of novel refrigerants. New universal parameters of the extended corresponding states (ECS) model are presented for hydrofluoroolefin (HFO) refrigerants. The ECS model employing the universal parameters successfully represents the saturation properties. For well-studied HFO refrigerants, which were used to determine the universal parameters, typical deviations between estimations with the ECS model and calculated values with accurate equations of state are within 1 % for vapor pressures and within 3% for saturated liquid densities at reduced temperatures from 0.6 to 0.9. Similar deviations are expected for other HFO refrigerants if reliable experimental values for the critical parameters and acentric factors are available. If these values are less reliable, larger deviations could be observed, up to 3 % and 8 % for vapor pressures and saturated liquid densities, respectively. The ECS model presented here is readily implemented and provides reasonable accuracies; therefore, it is suitable for the preliminary evaluation of novel refrigerants.

High pressure viscosity measurements of ternary (methane + propane + heptane) mixtures

Prediction of thermophysical properties for natural gas mixtures close to the mixture's critical point and cricondenbar (the maximum pressure at which two fluid phases can co-exist) is challenging but important as often natural gas processes operate close to these conditions. Here we present a comprehensive study of the viscosity of (CH4 + C3H8 + C7H16) mixtures with heptane fractions up to 15 mol%. Accurate measurements of saturated-phase and compressed-fluid (single phase) viscosities, at temperatures from 200 K to 423 K and pressures up to 35 MPa, are presented. The collected data were compared with the prediction of the extended corresponding states (ECS) model, with relative deviations spanning between (−20 to 11) % from the model. Additionally, pure component parameters needed for the residual entropy scaling (RES) model were fit to literature data and then applied predictively to mixtures viscosity without any additional fit parameters. The relative deviation of the measured viscosities from values calculated with the RES model is generally within 15%. This work demonstrates that no current model satisfactorily predict mixtures viscosity, and that high quality experimental data are needed to anchor the methods used to design and optimize natural gas processing.

Supercritical Jet Modeled by a Hybrid Extended Corresponding States Method

In the framework of large eddy simulation, a supercritical jet has been modeled by using the extended corresponding states (ECS) method, the cubic Peng–Robinson (PR) equation of state, as well as the ideal gas law. The accuracy of ECS and PR was first verified for a binary mixture against the standard data. A zone-adaptive hybrid ECS/ideal method was developed to efficiently model the supercritical jet while maintaining accuracy, because most of the flow region can be approximately described by the ideal gas law. Quick expansion and local speedup driven by the drastic heating were observed during the development of the supercritical jet. By using the hybrid ECS method, the predictions are consistent with those calculated by the original ECS method, with a speedup ratio of 5–10 achieved. The hybrid ECS method was generalized by defining the expression formulas that describe the isosurface in the pressure–temperature–composition space for typical fuel mixtures.

Thermal conductivity measurements of refrigerant mixtures containing hydrofluorocarbons (HFC-32, HFC-125, HFC-134a), hydrofluoroolefins (HFO-1234yf), and carbon dioxide (CO2)

Thermal conductivity measurements of eight binary refrigerant mixtures were conducted in the homogeneous liquid and vapour phases with the transient hot-wire technique. The temperature range of the measurements spanned from (224.3 to 386.6)K with pressures ranging between (1.0 and 6.5)MPa. The binary mixtures were equimolar (R125 + R32), (R32 + R134a), (R32 + CO2), (R125 + R134a), (R125 + CO2), (R134a + R1234yf), (R134a + CO2) and (R1234yf + CO2). Additionally, two multi-component mixtures, (R32 + R1234yf + CO2) and (R32 + R1234yf + R134a + R125 + CO2), were investigated. The transient hot-wire apparatus was validated with measurements of pure CO2 in the liquid and vapour regions. The relative combined expanded uncertainty (k = 2) in the experimental thermal conductivity was on the order of 2.0%. The relative deviations of the measured thermal conductivities in the vapour phase from those calculated using the extended corresponding states (ECS) model with default binary interaction parameters (BIPs), as implemented in the software REFPROP 10, were between (−12 and +8)%, while those in the liquid phase were between (−15 and +4)%. The new experimental data were used to tune the BIPs in the ECS model. Significant improvements were observed especially in the liquid phase of the five-component mixture, with the root-mean-square of the relative difference between the experimental data and the model estimation reduced by a factor of nearly three.

Measurement and modeling of the viscosity of (nitrogen + carbon dioxide) mixtures at temperatures from (253.15 to 473.15) K with pressures up to 2 MPa

Abstract The viscosity of pure nitrogen and of three (nitrogen + carbon dioxide) mixtures was measured over the temperature range from (253.15 to 473.15) K with pressures up to 2 MPa utilizing a rotating-body viscometer. The relative combined expanded uncertainty (k = 2) in viscosity was estimated to be between (0.14 and 0.19)% for nitrogen. For the binary gas mixtures, the uncertainty ranged between (0.19 and 0.39)%. The new data for nitrogen show very good agreement with experimental data from the literature and with recent ab initio calculations. The experimental data for the binary mixtures were compared with an Extended Corresponding States (ECS) model as implemented in the NIST REFPROP 9.1 database. The relative deviations of the data from the model were generally found to increase in magnitude with increasing density and ranged between (−2.1 and 0.4)% near the greatest density studied. The experimental data were correlated using the modified Enskog theory for hard sphere mixtures correct to the second viscosity virial coefficient. In this analysis, the effective hard-sphere diameters determining (a) the zero-density viscosity and (b) the leading term in the radial distribution function at contact were correlated as functions of temperature. The resulting model was found to represent all measured data with absolute relative deviations

Viscosity of CO2-rich mixtures from 243 K to 423 K at pressures up to 155 MPa: New experimental viscosity data and modelling

Abstract The viscosities of three multi-component CO2-rich mixtures were measured using the classical capillary tube technique. The tests were conducted at pressures from 1 to 155 MPa at various temperatures from 243 to 423 K in the gas, liquid and supercritical regions. Correlative and predictive models were evaluated using the measured experimental viscosity data. The correlative model, i.e., Lohrenz-Bray-Clark (LBC) model, was tuned to match the experimental data (CO2-LBC after tuning) and predictive models were modified by replacing the reference fluids. The predictive models in this work are based on the corresponding states (CS) theory models. The one reference fluid corresponding states model is the model originally developed by Pedersen which was modified by changing the reference fluid from methane to CO2 (called hereafter to CO2-Pedersen); two reference fluid corresponding states model is the Aasberg-Petersen (CS2) approach which was modified by selecting CO2 as reference fluid for CO2-rich fluids instead of n-decane which is suitable for hydrocarbons (CO2-CS2 model). The SUPERTRAPP predictive model, based on the extended corresponding states (ECS) theory, was also modified by changing the reference fluid propane to carbon dioxide (CO2-SUPERTRAPP). Comparisons for the investigated mixtures show that the overall Absolute Average Deviation (AAD) for the CO2-Pedersen, CO2-SUPERTRAPP, CO2-CS2 and CO2-LBC are 3.8%, 4.6%, 5.3% and 9.2%, respectively. Overall, the CO2-Pedesen viscosity model is the most accurate model when predicting the viscosity of the investigated CO2-rich mixtures. As the viscosity is a function of density, the effect of the mixture density on the mixture viscosity was investigated. Also, the viscosity reduction of pure CO2 due to the presence of impurities in each system was demonstrated.

Viscosity measurements of R32 and R410A to 350 MPa

Viscosity measurements were performed with a falling cylinder viscometer on difluoromethane (R32) and the refrigerant blend R410A (R32 + R125 with 50% by mass) at the temperatures 313.15 K, 348.15 K, and 393.15 K with pressures of 350 MPa. The measurement results are compared with literature data and with data calculated using an extended corresponding states (ECS) model. The agreement with literature data is closer for R410A than for R32 while the deviations from the ECS model are higher for R410A than for R32. Correlations that represent the new results as functions of temperature and pressure within their uncertainty are also reported.

Kerosene/GOx dynamic combustion characteristics in a mixing layer under supercritical conditions using the LES-FPV approach

A large eddy simulation (LES) for kerosene/GOx combustion in a mixing layer under supercritical conditions is conducted using the flamelet progress variable (FPV) method. To apply real gas effects, several real gas equations of states (EOSes) are validated with extended corresponding states (ECSes) by comparing thermodynamic properties. The Redlich-Kwong Peng-Robinson (RK-PR) EOS is applied in this study to achieve greater accuracy. The flamelet solution indicates that the flame structure is not affected by varying the oxidizer inlet temperature, but the flame surface location is influenced. A non-reacting calculation shows a finger-like structure rotating in counterclockwise with a certain periodic interval. For the reacting case, totally different flow characteristics are observed because of the dilatation and flame dissipation rate locally various. The shear layer in the reacting case has a wider angle in the downward direction than the shear layer in the non-reacting case. Because the FPV method treats all possible flame states, the dynamic flame structures are observed – detached, folded, quenched, stretched and reignited. In particular, the isolated flame is discussed in detail, and its creation process is introduced. After its creation, the isolated flame is divided into two areas – extinction and re-ignition. The premixed flame regime initiates the re-ignition process. The flame anchoring process behind a splitter tip is also investigated. Scattering species profiles in mixture fraction space are evaluated in this simulation. The averaged flame temperature is much lower (except near the splitter tip) than the instantaneous flame temperature due to the constant flame shedding downstream.

Dynamic characteristics of a cryogenic nitrogen swirl injector under supercritical conditions

A three dimensional large eddy simulation (LES) is conducted to investigate the dynamic characteristics of a cryogenic nitrogen swirl injector operating in supercritical high pressure conditions. To predict the precise thermodynamic properties under supercritical conditions, various real gas equations are validated by comparing them with extended corresponding states (ECS) data. The numerical results are also validated with 50-bar experimental data in terms of the spray angle and instability frequency behind the injector post. Various flow structures and swirl injector dynamics are observed and examined. They include the liquid film, gaseous core, spray angle, toroidal recirculation and the dominant unstable frequencies related with acoustic modes and flow oscillations induced by the helical vortex, Kelvin–Helmholtz instability. The unstable motions of the acoustics and flow are investigated using power spectrum densities (PSDs), proper orthogonal decomposition (POD) and band-pass filter methods. The inlet mass flow rate fluctuation causes liquid film and gaseous core instability. The gaseous core oscillates along the centerline at a low frequency of about the 100-Hz order. The pressure increases from 50 bar to 90 bar cause the surface boundary of the liquid film and gaseous core to become fainter and the gaseous core depth to become shorter. This results in a decrease of spray angle.

Viscosity of {xCO2 + (1 − x)CH4} with x = 0.5174 for temperatures between (229 and 348) K and pressures between (1 and 32) MPa

A vibrating wire instrument, in which the wire was clamped at both ends, was used to measure the viscosity of {xCO2+(1−x)CH4} with x=0.5174 with a combined uncertainty of 0.24μPa·s (a relative uncertainty of about 0.8%) at temperatures T between (229 and 348)K and pressures p from (1 to 32)MPa. The corresponding mass density ρ, estimated with the GERG-2008 equation of state, varied from (20 to 600)kg·m−3. The measured viscosities were consistent within combined uncertainties with data obtained previously for this system using entirely different experimental techniques. The new data were compared with three corresponding states-type models frequently used for predicting mixture viscosities: the Extended Corresponding States (ECS) model implemented in REFPROP 9.1; the SUPERTRAPP model implemented in MultiFlash 4.4; and a corresponding states model derived from molecular dynamics simulations of Lennard Jones fluids. The measured viscosities deviated systematically from the predictions of both the ECS and SUPERTRAPP models with a maximum relative deviations of 11% at (229K, 600kg·m−3) and −16% at (258K, 470kg·m−3), respectively. In contrast, the molecular dynamics based corresponding states model, which is predictive for mixtures in that it does not contain any binary interaction parameters, reproduced the density and temperature dependence of the measured viscosities well, with relative deviations of less than 4.2%.

Characteristics of compressible flow of supercritical kerosene

In this paper, compressible flow of aviation kerosene at supercritical conditions has been studied both numerically and experimentally. The thermophysical properties of supercritical kerosene are calculated using a 10-species surrogate based on the principle of extended corresponding states (ECS). Isentropic acceleration of supercritical kerosene to subsonic and supersonic speeds has been analyzed numerically. It has been found that the isentropic relationships of supercritical kerosene are significantly different from those of ideal gases. A two-stage fuel heating and delivery system is used to heat the kerosene up to a temperature of 820 K and pressure of 5.5 MPa with a maximum mass flow rate of 100 g/s. The characteristics of supercritical kerosene flows in a converging-diverging nozzle (Laval nozzle) have been studied experimentally. The results show that stable supersonic flows of kerosene could be established in the temperature range of 730 K-820 K and the measurements in the wall pressure agree with the numerical calculation.