Giancarlo Scalabrin

A Reference Multiparameter Thermal Conductivity Equation for Carbon Dioxide with an Optimized Functional Form

A new thermal conductivity equation λ=λ(T,ρ) in a multiparameter format was developed for carbon dioxide through the application of an optimization technique of the functional form. The proposed equation is valid for temperatures from the triple point (Tt=216.592K; Pt=0.51795MPa) to 1000K and pressures up to 200MPa. The calculation of density, which is an independent variable of the equation, from the experimental (T,P) conditions is performed with a high accuracy equation of state for the fluid. The thermal conductivity equation shows an average absolute deviation of 1.19% on the selected 1407 primary data points. Its performances are slightly better than those of the corresponding conventional model by Vesovic et al. [J. Phys. Chem. Ref. Data 19, 763 (1990)] available from the literature; moreover the new equation is simpler to use in particular for the near-critical region. Tables of generated values of carbon dioxide thermal conductivity are provided for check of the code implementations and for quick...

Vapor-Phase Helmholtz Equation for HFC-227ea from Speed-of-Sound Measurements

This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea). The measurements were obtained in a stainless-steel spherical resonator with a volume of ∼900 cm3 at temperatures between 260 and 380 K and at pressures up to 500 kPa. Ideal-gas heat capacities and acoustic virial coefficients are directly produced from the data. A Helmholtz equation of state of high accuracy is proposed, whose parameters are directly obtained from speed-of-sound data fitting. The ideal-gas heat capacity data are fit by a functions and used when fitting the Helmholtz equation for the vapor phase. From this equation of state other thermodynamic state function are derived. Due to the high accuracy of the equation, only very precise experimental data are suitable for the model validation and only density measurements have these requirements. A very high accuracy is reached in density prediction, showing the obtained Helmholtz equation to be very reliable. The deduced vapor densities are furthermore compared with those obtained from acoustic virial coefficients with the temperature dependences calculated from hard-core square-well potentials.

A viscosity equation of state for R134a through a multi-layer feedforward neural network technique

A multi-layer feedforward neural network (MLFN) technique is adopted for developing a viscosity equation η = η(ρ, T) for R134a. The results obtained are very promising, with an average absolute deviation (AAD) of 0.63% for the currently available 571 primary data points, and are a significant improvement over those of a corresponding conventional equation in the literature. The method requires a high accuracy equation of state for the fluid in order to convert the experimental P, T into the independent variables p, T, but such an equation may not be available for the target fluid. Aiming at overcoming this difficulty, a viscosity implicit equation of state in the form T = T(η, P), avoiding the density variable, is developed for the liquid surface. The attained accuracy level is equivalent to that of the former equation. The proposed technique, being completely correlative and non theoretically founded, is also a powerful tool for experimental data screening.

A predictive density model in a corresponding states format. Application to pure and mixed refrigerants

A three parameters density model based on Corresponding States (CS) technique is proposed as a means of predicting the density of pure fluids and their mixtures on the entire PρT (PρTx) surface. The studied fluids belong to two conformal families of the new refrigerant fluids generation: the halogenated alkanes (HA) and the hydrofluoroethers (HFE). The new model is based on an original scaling factor parameter that is determined only on a saturated liquid density experimental value. Using two accurate dedicated equations of state (EoS) as references, the same structure of the Teja CS model is maintained, substituting the classical acentric factor with the new defined scaling parameter. Through this model, the density of the refrigerant fluids considered can be calculated on the whole surface with an accuracy level similar to that of the dedicated equations. The model is validated against experimental data for HFC refrigerants including fluoropropanes, fluorobutanes and fluoroethers. A comparison is also proposed with available density models regarded of high accuracy level.

Compressed Liquid and Supercritical Densities of 1,1,1,2,3,3,3-Heptafluoropropane (R227ea)

Densities of 1,1,1,2,3,3,3-heptafluoropropane (R227ea) have been measured with a computer-controlled high-temperature high-pressure vibrating-tube densimeter system (DMA-HDT) in the sub- and supercritical states. The densities were measured at temperatures from 278 to 473 K and pressures up to 30 MPa (overall 257 data points), whereby a density range between 285 and 1588 kg⋅m−3 was covered. The uncertainty in the density measurement was estimated to be better than ±0.2 kg⋅m−3. The experimental data of R227ea were correlated with a virial-type equation of state (EoS) and compared with published data. A comparison is also made with a recent wide-range dedicated equation of state for R227ea.

Viscosity equations of pure fluids in an innovative extended corresponding states framework. II. Application to four fluids

Abstract This paper represents the second part of a work devoted to an innovative version of the historical extended corresponding states (ECS) technique for the development of viscosity equations on the whole ηTρ surface for individual fluids. In the first part [1] , the theoretical aspects of modelling the ECS transport properties modelling have been discussed, and the fundamental characteristics of the proposed method have been tested, using viscosity values generated from conventional dedicated viscosity equations. The very promising results suggest a move from generated to experimental data correlation to determine dedicated viscosity equations for a number of fluids for which conventional equations are available in literature. This is done in this second part, where the fluids studied are the alkane ethane and the haloalkane refrigerants R123, R134a and R152a. The absolute average deviations (AADs) obtained with primary data are, respectively, 1.04, 1.13, 0.92 and 0.71% with a significant improvement with respect to the conventional equations. Considering that the expected experimental accuracy for good viscosity data is generally in the range 1–2%, the obtained results seem to be very promising.

A corresponding states predictive model for the saturated liquid density of halogenated alkanes and of fluorinated propanes and ethers

Abstract A three-parameter corresponding states (CS) model is proposed here for the prediction of the saturated liquid density of pure fluids pertaining to the two conformal families of halogenated alkanes and hydrofluoroethers (HFE), most of which are either already used or proposed for use as refrigerants. Two fluids from each family were chosen for their acentric factor value and the availability of dedicated saturated liquid density equations and at first, on the basis of the three-parameter CS model by Teja et al., the saturated liquid density of a given fluid was obtained in reduced variables. Assuming experimental saturated liquid density data for several components of each of the two families of fluids, an improvement was then introduced, substituting the acentric factor with a new constant scaling factor. As a final result, the proposed liquid model has a predictive nature. The prediction accuracy reached by this new method is similar to that of the dedicated equations, where available, for all the fluids in a family. The result is particularly satisfactory for application requirements in refrigeration.

A Fundamental Equation of State for Sulfur Hexafluoride (SF6) in Extended Equation of State Format

An innovative method for the regression of thermodynamic properties of pure fluids was recently proposed. The technique, indicated as an extended equation of state, adopts a framework similar to the extended corresponding states method, but a cubic equation is assumed instead of the equation of state of the reference fluid and the shape functions are expressed through a multilayer feedforward neural network. The use of a neural network assures a very high flexibility of the functional form to be regressed, so the resulting model reaches a representation accuracy which is comparable to that attained by the state-of-the-art multiparameter equations of state in the representation of the thermodynamic properties of a pure fluid. The technique was applied here to sulfur hexafluoride aiming at drawing its dedicated equation of state in a heuristic mode directly from the available experimental data. For sulfur hexafluoride (critical point is at Tc=318.7232K and Pc=3.754983MPa), experimental data of several prope...

The viscosity surfaces of propane in the form of multilayer feed forward neural networks

The present work focuses on the development of a viscosity equation η=η(ρ,T) for propane through a multilayer feedforward neural network (MLFN) technique. Having been successfully applied to a variety of fluids so far, the proposed technique can be regarded as a general approach to viscosity modeling. The MLFN viscosity equation has been based on the available experimental data for propane: validation on the 969 primary data shows an average absolute deviation (AAD) of 0.29% in the temperature, pressure, and density range of applicability, i.e., 90 to 630 K, 0 to 60 MPa, and 0 to 730 kg⋅m−3. This result is very promising, especially when compared with experimental data uncertainty. The minimum amount of required data for setting up the MLFN has been investigated, to explore the minimum cost of the model. Comparisons with other viscosity models are presented regarding amount of input data, claimed accuracy, and range of applicability, with the aim of providing a guideline when viscosity has to be calculated for engineering purposes. A high accuracy equation of state for the conversion of variables from experimental P,T to operative ρ,T has to be provided. To overcome this requirement, two viscosity explicit equations in the form η=η(P,T) are also developed, for the liquid and for the vapor phases. The respective AADs are 0.58 and 0.22%, comparable with those of the former η=η(ρ,T) equation. Finally, the trend of the experimental viscosity second virial coefficient is reproduced and compared with that obtained from the MLFN.

The viscosity surfaces of R152a in the form of multilayer feed forward neural networks

Abstract A multilayer feedforward neural network (MLFN) technique is adopted for developing a viscosity equation η=η ρ,T for R152a. The results obtained are very promising, with an average absolute deviation (AAD) of 0.36% for the currently available 300 primary data points, and they are a significant improvement over those of a corresponding conventional equation in the literature. The method requires a high accuracy equation of state for the fluid in order to convert the experimental P,T into the independent variables ρ,T, but such equation may not be available for the target fluid. Aiming at overcoming this difficulty, two viscosity explicit equations in the form η=η P,T , avoiding the density variable, are also developed, one for the liquid surface and the other for the vapor one. The reached accuracy levels are equivalent to that of the former η=η ρ,T equation. The trend of the reduced second viscosity virial coefficient is correctly reproduced in the data range. The proposed technique, being heuristic and non theoretically founded, is also a powerful tool for experimental data screening.