A new equation of state for chlorodifluoromethane (R22) covering the entire fluid region from 116 K to 550 K at pressures up to 200 MPa

A new equation of state in the form of a fundamental equation explicit in the dimensionless Helmholtz free energy has been developed for chlorodifluoromethane (R 22). This equation, which contains 22 fitted coefficients, covers the entire fluid region from 116 K (triple point temperature) to 550 K at pressures up to 200 MPa. The mathematical form of the equation was determined with the help of a new method to optimize its structure. New pressure-density-temperature data in the liquid region and especially new vapour pressures and saturated liquid densities, as well as speed of sound data have been incorporated to extend the range of validity and to improve the accuracy of properties calculated with this equation beyond that of previous formulations. Independent equations are also included for the vapour pressure as well as for the saturated liquid and vapour densities. The uncertainty of the new wide-range equation of state can roughly be given as follows: ± 0.1% in density (with the exception of the critical region), ± 1% in heat capacity, ± 0.5% in speed of sound in the liquid and 0.1% in speed of sound in the gas phase. The new equation of state corresponds to the International Temperature Scale of 1990 (ITS-90).     

A simple set of equations of state for process calculations and its application to R134a and R152a

This paper reports a useful set of equations which enables the consistent and reliable calculation of thermodynamic properties. This set of equations consists of a vapour pressure equation, an equation for the gas phase p, v, T properties, an equation giving the saturated liquid densities and an equation for the specific heat capacity in the ideal gas domain. These equations are of a simple structure because the critical region is excluded. Therefore, for a preliminary investigation only few experimental data points are required for parameter regression, which makes this set of equations suitable for ‘new’ refrigerants. The relationships for enthalpy and entropy are derived from these equations and evaluation procedures are summarized. Examples are given for the refrigerants R134a and R152a.     

New vapour pressure measurements for argon and nitrogen and a new method for establishing rational vapour pressure equations

When collecting the thermodynamic properties of the pure fluids, nitrogen and argon, only a few reliable experimental values were found in some ranges of the areas of interest in spite of a relatively high quantity of measured data. Unfortunately the available experimental values are based on different temperature scales. New vapour pressure measurements for argon and nitrogen have been performed with specially developed low temperature equipment, to obtain some idea of the quality of the data available in this area.In parallel with the growing number of experimental vapour pressures, different formulae for representing the vapour pressure curves have been used by many authors. These equations are tested critically. Most of the relationships tested can only moderately fulfil the demands expected from such equations, especially in the critical range. Therefore, a new method of establishing a rational vapour pressure equation is presented here. The method has been used for nitrogen and argon without any restriction as to general validity. For these two substances the coefficients of a new vapour pressure equation are also given.     

近共沸制冷剂R290/R134a PVTx性质的实验研究

为了获得混合制冷剂R134a/R290的热物性数据,搭建了高精度PVTx实验系统。以Burnett法为基础,测定了R134a/R290质量分数为50%/50%、55%/45%和60%/40%在温度为252 K~320 K的PVT性质,并且拟合了三种不同配比的混合工质的气态维里方程。实验数据与方程的平均误差为1%左右,具有较好的重合度。     

Experimental densities for compressed R134a

This paper reports densities of compressed R134a (1,1,1,2-tetrafluoroethane) determined by using a contiuously weighed pycnometer at 20 K intervals between 180 and 380 K at pressures from slightly greater than the vapour pressure to 70 MPa. The results are accurate to within ±0.1%. Saturated liquid densities derived by extrapolation from the experimental values agree with other reported values to within ±0.3%.     

The determination of equations of state for nitrogen and oxygen

Methods of developing accurate thermodynamic equations of state for oxygen and nitrogen using least squares fitting to experimental data from the literature are presented and evaluated. A discussion of the critical evaluation and selection of experimental data is included. The selection of an appropriate functional form for the equation of state, weighting of the data points for least squares fitting, and the simultaneous fitting of various thermodynamic data including PVT data, isochoric heat capacity measurements, and saturation density values are presented. The resulting equation accurately represents all the data, and exhibits correct functional behaviour for the PVT surface and the derivatives used in the calculation of derived properties. Techniques of constraining the equation of state to be consistent with measured critical point parameters and with a vapour pressure equation determined from separate measurements of saturation properties are discussed. The equations developed in the work described here conform to the Maxwell criterion and may be used for the calculation of properties by continuous integration along isotherms through the two-phase region. Comparisons of the selected property values calculated from the equations of state with experimental PVT, C_p, and C_v data used in the development of equations are included. The calculations of the liquid properties by continuous integration along the isotherms and by use of the Clapeyron equation are compared.     

An equation of state for 1,1-difluroethane (HFC 152a)

An equation of state for 1,1-difluoroethane (HFC 152a, CH₃CHF₂) has been developed on the basis of reliable experimental data including PVT, liquid C_p, and saturated-liquid-density data measured by our group. It is a non-dimensionalized virial equation whose functional form is the same as that originally developed for 1,1,1,2-tetrafluoroethane (HFC 134a) in our group. The effective range is for pressures up to 15 MPa, temperatures from 230 to 450 K, and densities to 1000 kg m⁻³. The equation represents reliable PVT measurements within ± 1% in pressure for the superheated vapour and supercritical fluid, while within ±0.5% in density for the compressed liquid. In addition, it should be noted that the equation represents the other essential thermodynamic properties including vapour pressures, saturated-liquid/ vapour densities, isobaric/isochoric specific heats and sound velocity in both the liquid and gaseous phase of HFC 152a.     

Saturation properties of the refrigerant 143A

1,1,1-Trifluoroethane (CH₃---CF₃; R143a) is currently under consideration as a potential candidate as a component in refrigerant mixtures. Among other things, the accurate knowledge of saturation properties of the pure fluids is a pre-requisite for evaluation of mixture properties. There is a considerable amount of scatter in the available data for R143a. This article presents a conciliation of saturation property data for this refrigerant. Vapour pressures, saturated liquid and vapour densities have been correlated so that the ancilliary equations are related through a power β used for the temperature functions. The coefficients of the equations have been determined from a weighted least squares method using all the available data. The surface tension, viscosity and thermal conductivity in the saturated liquid phase have also been correlated.     

低温流体空化特性的数值计算研究

采用数值计算的方法研究了液氮和液氢的空化流动特性。为了考虑温度影响,控制方程采用了连续方程、动量方程及能量方程,并应用二次开发方法在商业软件中引入Merkle 空化模型及物质属性,物性参数随流场温度变化而不断更新。分别对液氮和液氢几个工况进行了计算,并与实验结果进行了对比。结果发现,在液氮和液氢中,当流体温度接近临界点时,热力学效应表现显著。热力学效应显著主要表现在空穴变短、水蒸汽含量减少和汽液界面变的模糊。由于密度比、饱和蒸汽压随温度变化梯度等物质属性的不同,相对液氮,液氢的热力学效应更加明显。     

Measurements of molar heat capacity at constant volume (Cv) for 1,1,1,2-tetrafluoroethane (R134a)

The molar heat capacity at constant volume was measured by applying an adiabatic method. Heat capacities at 310 state conditions were measured. Measurements were made on liquid in equilibrium with its vapour, and on compressed liquid samples of 1,1,1,2-tetrafluoroethane (R134a), at temperatures from 172 to 343 K with pressures as high as 35 MPa. In the course of these measurements, a determination of the triple point temperature (169.85 ± 0.01 K) was made. For the high purity (0.9999 +) sample, results were obtained for two-phase (C_v⁽²⁾), saturated liquid (C_σ) and single-phase (C_v) molar heat capacities as a function of measured temperature,pressure and density. The maximum probable uncertainty of the heat capacity values is estimated not exceed ±0.5%.     

Equations of state for ethylene and propylene

Equations of state for ethylene and propylene are given, representing the whole experimentally determined region up to 50 MPa. The twenty adjustable coefficients of the equation of state, a modified Benedict-Webb-Rubin equation of state, have been determined using recent experimental data and considering the thermodynamic equilibrium conditions for the co-existing liquid and vapour phases. The results of the equations of state are compared with experimental data.     

The use of an MHV-2 equation of state for modeling the thermodynamic properties of refrigerant mixtures

This paper reports on the development and application of a thermodynamic model based on the second-order Modified Huron Vidal equation of state (MHV-2) to predict the properties of ternary mixtures of the refrigerants R32, R125, and R134a. The mixing rules of this equation of state have been used to incorporate directly an activity-coefficient model for the excess Gibbs free energy. The parameters for the activity-coefficient model have been derived from experimental VLE data for binary mixtures. This methodology has enabled the production of a thermodynamically consistent model which can be used to predict the phase equilibria of R32/R125/R134a mixtures. The input data used in the model are presented in the paper and the predictions of the model are compared with available experimental data. The model has been used to predict the behavior of ternary refrigerant blends of R32/R125/R134a in fractionation scenarios, such as liquid charging and vapor leakage, which are of direct interest to the refrigeration industry. Details of these applications and comparisons with experimental data are discussed, along with other general uses of the thermodynamic model.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, USA.     

Transport properties of 1,1,1,2-tetrafluoroethane (R134a)

New equations for the thermal conductivity and the viscosity of R134a that are valid in a wide range of pressures and temperatures are presented. They were obtained through a theoretically based, critical evaluation of the available experimental data, which showed considerable inconsistencies between data sets, in particular in the vapor phase. In the critical region the observed enhancement in the thermal conductivity is well represented by a crossover model for the transport properties of fluids. Since thermodynamic properties enter into the calculation of the critical enhancement of the transport properties, a new fundamental equation for the critical region was developed also.Paper dedicated to Professor Joseph Kestin.     

Thermophysical properties of refrigerant R134a

Experimental results of measurements of the thermodynamic and transport properties of refrigerant R134a are presented for the temperature range 240–400 K and pressures up to 89 bar. The thermal properties of the saturated refrigerant were also determined. The results from this study showed that the dependence of viscosity on temperature near the critical region was nonlinear. This observation shows that errors resulting from using previous literature data for design purposes could vary from about 1.5% at 251 K to 30% at 343 K. A computer (IBM PC) was used to obtain empirical relationships for evaluating the thermophysical properties of R134a based on various sets of independent variables.     

A modified Benedict-Webb-Rubin equation of state for methane using recent experimental data

A 33 term modified Benedict-Webb-Rubin equation of state is presented for methane. The adjustable parameters in the equation of state have been estimated using recent experimental data and least squares techniques which include the thermodynamic equilibrium conditions for the co-existing liquid and vapour phases. Comparisons of the new equation of state and an older modified Benedict-Webb-Rubin equation of state to experimental data are given.     

A New Method for Liquid Viscosity Measurements: Inclined-Tube Viscometry

In this article, a method which can be used to measure the viscosity of liquids with an inclined tube at high pressures and for low-boiling substances is described. The measurement equation was established. The measuring methods for two unknown parameters which are in the measurement equation are presented, and a viscosity measurement system was designed and constructed, which consists of an experimental cell, an inclination-angle control subsystem, a constant temperature subsystem, and a data collection and process subsystem. At atmospheric pressure, the kinematic viscosity of pure water was measured at temperatures from 273.15 K to 333.15 K to demonstrate the performance of the apparatus. The results show that the absolute average relative deviation is 0.84% in comparison with reliable literature values. The kinematic viscosity of saturated liquid R134a and R600a were also measured at temperatures from 273.15 K to 295.15 K and 273.15 K to 300.15 K, respectively, and the corresponding absolute average relative deviations are 1.04% and 1.02% in comparison with reliable literature values. These experimental results demonstrate the performance of the apparatus, while providing estimates of the uncertainty and reliability of the experimental system.     

Capillary tube selection for HCFC22 alternativesSélection de capillaires pour les frigorigènes de remplacement du HCFC22

In this paper, pressure drop through a capillary tube is modeled in an attempt to predict the size of capillary tubes used in residential air conditioners and also to provide simple correlating equations for practicing engineers. Stoecker's basic model was modified with the consideration of various effects due to subcooling, area contraction, different equations for viscosity and friction factor, and finally mixture effect. McAdams' equation for the two-phase viscosity and Stoecker's equation for the friction factor yielded the best results among various equations. With these equations, the modified model yielded the performance data that are comparable to those in the ASHRAE handbook. After the model was validated with experimental data for CFC12, HFC134a, HCFC22, and R407C, performance data were generated for HCFC22 and its alternatives, HFC134a, R407C, and R410A under the following conditions: condensing temperature; 40, 45, 50, 55°C, subcooling; 0, 2.5, 5°C, capillary tube diameter; 1.2–2.4 mm, mass flow rate; 5–50 g/s. These data showed that the capillary tube length varies uniformly with the changes in condensing temperature and subcooling. Finally, a regression analysis was performed to determine the dependence of mass flow rate on the length and diameter of a capillary tube, condensing temperature, and subcooling. Thus determined simple practical equations yielded a mean deviation of 2.4% for 1488 data obtained for two pure and two mixed refrigerants examined in this study.     

混合制冷剂R1234yf/R134a PVTx性质的实验研究

为了获得混合制冷剂R1234yf/R134a的热物性数据,本文利用Burnett法为基础搭建的高精度PVTx实验台,在温度为268~323 K时,测定了质量分数为55%/45%,50%/50%和45%/55%混合制冷剂R1234yf/R134a的PVT性质,最终拟合了三种不同配比的混合工质的气态维里方程,方程和实验数据具有较高的重合度。     

Application of a new selection algorithm to the development of a wide-range equation of state for refrigerant R134a

Refrigerant R134a (1,1.1,2-tetrafuoroethane) is a leading substitute for refrigerant R12. As such, there has been worldwide activity to develop accurate wide-range equations of state for this fluid. In this study. we have developed a new selection algorithm for determining high-accuracy equations of state in the Helmholtz representation. This method combines least-squares regression analysis with simulated annealing optimization. Simulated annealing, unlike stepwise regression, allows for the controlled acceptance of random increases in the objective function. Thus, this procedure produces a computationally efficient selection algorithm which is not susceptible to the function-space local-minima problems present in a purely stepwise regression approach. Two equations are presented in this work and compared against experimental data and other high-accuracy equations of state for R134a. One equation was produced strictly by using stepwise a regression algorithm, while the other was produced using the simulated-annealing selection algorithm. In both cases the temperature dependence of the equations was restricted to have no terms whose exponents were greater than live.Paper presented at the Twelfth Symposium on Thermophysical Properties. June 19–24, 1994, Boulder, Colorado, U.S.A.     

A fundamental equation of state for 1,1-difluoroethane (HFC-152a)

A fundamental equation ofstale for HFC-152a ( 1,1-dilluorocthane) is presented covering temperatures between the triple-point temperature ( 154.56 K) and 435 K for pressures up to 311 M Pa. The equation is based on reliable (p, g, T) data in the range mentioned above. These are generally represented within ±0.1 % of density. Furthermore. experimental values of the vapor pressure, the saturated liquid density, and some isobaric heat capacities in the liquid were included during the correlation process. The new equation of state is compared with experimental data and also with the equation of state developed by Tamatsu et al. Differences between the two equations of state generally result from using different experimental input data. It is shown that the new equation of state allows an accurate calculation of various thermodynamic properties for most technical applications.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder. Colorado. U.S.A.