Equations of state for solids under strong compression

2001 ◽  
Vol 216 (9) ◽  
Author(s):  
Wolfgang Holzapfel
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Equations Of State ◽  
Theoretical Background ◽  
Anomalous Behaviour ◽  
State Data ◽  
Strong Compression ◽  
Pressure Scale ◽  
Insight Into

AbstractVarious approaches for the representation of equation of state data for solids under strong compression are discussed. The theoretical background for reasonable extrapolations to higher pressures and higher as well as lower temperatures is described. The distinction between ideal, regular, and anomalous behaviour allows to gain deeper insight into the electronic changes occurring in various solids under strong compression. The discussion of experimental data for various regular solids leads finally to an estimate of the accuracy obtained in the present realisation of a practical pressure scale based on equation of state measurements.

scholarly journals Drawing PT-phase envelopes and calculating critical points for multicomponent systems using flash calculations

2020 ◽  
Vol 15 (1) ◽  
pp. 46-54
Author(s):  
L. A. Toro
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Critical Points ◽  
Isopropyl Alcohol ◽  
Equations Of State ◽  
Mixing Rules ◽  
Mixing Rule ◽  
Multicomponent Systems ◽  
Activity Coefficient Model ◽  
Robinson Equation

Objectives. This study aims to draw PT-phase envelopes and calculate the critical points for multicomponent systems using flash calculations.Methods. Flash calculations with an equation of state and a mixing rule were used to construct phase envelopes for multicomponent systems. In general, the methodology uses the Soave–RedlichKwong equation of state and Van der Waals mixing rules; and the Peng–Robinson equation of state with Wong–Sandler mixing rules and the non-random two-liquid activity coefficient model.Results. The method was applied to the following mixtures: ethane (1)–butane (2) (four different compositions); ethane (1)–propane (2) (four different compositions); butane (1)–carbon dioxide (2) (three different compositions); C2C3C4C5C6 (one composition); isobutane–methanol–methyl tertbutyl ether–1-butene (one composition); and propylene–water–isopropyl alcohol–diisopropyl ether (one composition).Conclusions. Our results agreed to a large extent with the experimental data available in the literature. For mixtures that contained CO2 , the best results were obtained using the PengRobinson equation of state and the Wong–Sandler mixing rules. Our methodology, based on flash calculations, equations of state, and mixing rules, may be viewed as a shortcut procedure for drawing phase envelopes and estimating critical points of multicomponent systems.

scholarly journals Thermal evolution of Uranus and Neptune

2019 ◽  
Vol 632 ◽  
pp. A70 ◽  
Author(s):  
Ludwig Scheibe ◽  
Nadine Nettelmann ◽  
Ronald Redmer
Keyword(s):  
Equation Of State ◽  
Solar Energy ◽  
Equations Of State ◽  
Thermal Evolution ◽  
Cooling Time ◽  
State Data ◽  
Planetary Model ◽  
Input Parameters ◽  
Adiabatic Cooling

The brightness of Neptune is often found to be in accordance with an adiabatic interior, while the low luminosity of Uranus challenges this assumption. Here we apply revised equation of state data of hydrogen, helium, and water and compute the thermal evolution of Uranus and Neptune assuming an adiabatic interior. For this purpose, we have developed a new planetary model and evolution code. We investigate the influence of albedo, solar energy influx, and equations of state of H and He, and water on the cooling time. Our cooling times of about τU = 5.1 × 109 yr for Uranus and τN = 3.7 × 109 yr for Neptune bracket the known age of the planets of 4.56 × 109 yr implying that neither planet’s present-day luminosity can be explained by adiabatic cooling. We also find that uncertainties on input parameters such as the level of irradiation matter generally more for Uranus than for Neptune. Our results suggest that in contrast to common assumptions, neither planet is fully adiabatic in the deeper interior.

The Evaluation of the Equations of State Used for the Joule-Thomson Effect Analysis in the Dry Gas Seal

2015 ◽  
Vol 752-753 ◽  
pp. 391-395 ◽  
Author(s):  
Cheng Xiang Deng ◽  
Peng Yun Song
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Equation Of State ◽  
Equations Of State ◽  
Gas Flows ◽  
Thomson Effect ◽  
Effect Analysis ◽  
Real Gas ◽  
Dry Gas Seal ◽  
Thomson Coefficient

The Joule-Thomson (JT) effect will occur when the gas flows through the components of filters, valves, orifices and end faces in the system of the dry gas seal, which may cause the temperature of the seal gas to decrease, and even the emergence of liquid condensation. Generally, the Joule-Thomson effect is reflected by the Joule-Thomson coefficient. As to the hydrogen, nitrogen, carbon dioxide and air, which are often met in the dry gas seal, the corresponding Joule-Thomson (JT) coefficients were calculated by four classical equations of state (EOS) of VDW, RK, SRK and PR, which are compared with the experimental data in the literature. The results show that the JT coefficients calculated by RK equation are most close to the experimental data in the literature, whose relative error is lowest and less than 4%. When the JT effect of real gas in the dry gas seal is analyzed, the RK equation of state is recommend.

scholarly journals Modelling 3D Steam Turbine Flow Using Thermodynamic Properties of Steam Iapws-95

2016 ◽  
Vol 23 (1) ◽  
pp. 61-67 ◽  
Author(s):  
A.V. Rusanow ◽  
P. Lampart ◽  
N.V. Pashchenko ◽  
R.A. Rusanov
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Steam Turbine ◽  
Equations Of State ◽  
Three Dimensional ◽  
Steam Turbines ◽  
Perfect Gas ◽  
Van Der Waals Equation ◽  
Approximate Equations

Abstract An approach to approximate equations of state for water and steam (IAPWS-95) for the calculation of three-dimensional flows of steam in turbomachinery in a range of operation of the present and future steam turbines is described. Test calculations of three-dimensional viscous flow in an LP steam turbine using various equations of state (perfect gas, Van der Waals equation, equation of state for water and steam IAPWS-95) are made. The comparison of numerical results with experimental data is also presented.

scholarly journals Development and Experimental Validation of Real Fluid Models for CFD Calculation of ORC and Steam Turbine Flows

Materials ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 6879
Author(s):  
Andrii Rusanov ◽  
Roman Rusanov ◽  
Piotr Klonowicz ◽  
Piotr Lampart ◽  
Grzegorz Żywica ◽  
...  
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Steam Turbine ◽  
Thermodynamic Parameters ◽  
Equations Of State ◽  
Computational Cost ◽  
Organic Rankine Cycle ◽  
Rankine Cycle ◽  
Large Power ◽  
Wide Range

The article describes an interpolation–analytical method of reconstruction of the IAPWS-95 equations of state and the modified Benedict–Webb–Rubin equations of state with 32 terms (mBWR32). The method enables us to provide the thermodynamic closure in 3D computational fluid dynamics (CFD) calculations of turbomachinery flows with real working media, such as steam and Organic Rankine Cycle (ORC) fluids. The described approach allows for the sufficient accuracy of 3D flow calculations and does not require a significant increase in computational cost over perfect gas calculations. The method is validated against experimental data from measurements and compared with computational results from the model using the Tammann equation of state. Three turbine blading systems are considered—a multi-stage configuration from a low-pressure cylinder of a large-power steam turbine and two ORC microturbines working with organic media HFE7100 and R227ea. The calculation results obtained using the described method of approximation of the IAPWS-95 and mBWR32 equations exhibit satisfactory agreement with the experimental data, considering pressures, temperatures and enthalpies in key sections, as well as turbine power and efficiency in a wide range of changing thermodynamic parameters. In contrast, the Tammann equation of state provides acceptable results only for relatively small changes of thermodynamic parameters.

scholarly journals Prediction Of Solubility Of Solid N-Paraffins In Supercritical Fluids Using Modified Redlich-Kwong Equation Of State

REAKTOR ◽  
2017 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Ratnawati Ratnawati
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Supercritical Fluids ◽  
Equations Of State ◽  
Adjustable Parameter ◽  
The Other ◽  
Average Deviation ◽  
Data Points ◽  
Better Than

Three equation of state are used to predict solubilities of solid n-pafaffins in supercritical fluids. The equations are the Redlich-Kwong, the Soave-Redlich-Kwong, and equation proposed by Hartono et.al. (2003; 2004). Both the last two equations were formed by modificating the Redlich-Kwong equqtion of state. With the binary interactions parameter, kif , equals zero, the equations proposed by Hartono et.al. is better than both the Redlich-Kwong and the Soave-Redlich-Kwong equations of state are. Upon optimization with kif as the adjustable parameter, the equation of state proposed by Hartono et.al. is closer to the experimental data than the other equqtions are. For 142 data points of 12 systems the equation proposed by Hartono et. Al. gives the average deviation of 36.6%, while the Redlich-Kwong and the Soave-Redlich-Kwong give 66.7% and 65.8%, respectively.Keywords : equation of state, solubility, supercritical

Wilsak-Thodos Equation of State for Refrigerants

2013 ◽  
Author(s):  
E. D. Rogdakis ◽  
I. P. Koronaki ◽  
E. Gorgoraptis
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Simple Form ◽  
Thermophysical Properties ◽  
Equations Of State ◽  
Environmentally Friendly ◽  
Density Dependent ◽  
Environmental Friendly ◽  
Different Sources ◽  
Interesting Equation

In recent years different equations of state for environmentally friendly refrigerants have been developed from different sources of experimental data which, in many cases, use a very large number of auxiliary functions and coefficients. A rather interesting equation that has not been recollected lately, proposed by Wilsak and Thodos in 1985, appears to have a convenient form for effective and significantly accurate calculations of the thermophysical properties of substances. Wilsak-Thodos equation of state presents a relatively simple form as it correlates experimental data with the corresponding ones at saturation and contains only three density dependent functions. For this reason, this study attempts to identify the coefficients of the equation approximating accurately the experimental data and attributing in an integrated manner with auxiliary equations for some of the most common of the environmental friendly refrigerants.

SITE-SPECIFIC EQUATIONS OF STATE FOR COASTAL SEA AREAS AND INLAND WATER BODIES

2017 ◽  
Author(s):  
Natalia Andrulionis ◽  
Natalia Andrulionis ◽  
Ivan Zavialov ◽  
Ivan Zavialov ◽  
Elena Kovaleva ◽  
...  
Keyword(s):  
Equation Of State ◽  
Black Sea ◽  
Water Samples ◽  
Equations Of State ◽  
Sea Water ◽  
Ionic Composition ◽  
Water Bodies ◽  
Aral Sea ◽  
The Black Sea ◽  
Coastal Sea

This article presents a new method of laboratory density determination and construction equations of state for marine waters with various ionic compositions and salinities was developed. The validation of the method was performed using the Ocean Standard Seawater and the UNESCO thermodynamic equation of state (EOS-80). Density measurements of water samples from the Aral Sea, the Black Sea and the Issyk-Kul Lake were performed using a high-precision laboratory density meter. The obtained results were compared with the density values calculated for the considered water samples by the EOS-80 equation. It was shown that difference in ionic composition between Standard Seawater and the considered water bodies results in significant inaccuracies in determination of water density using the EOS-80 equation. Basing on the laboratory measurements of density under various salinity and temperature values we constructed a new equation of state for the Aral Sea and the Black Sea water samples and estimated errors for their coefficients.

Properties of Refrigerants from Cubic Equations of State

2008 ◽  
Vol 59 (5) ◽  
Author(s):  
Viorel Feroiu ◽  
Dan Geana ◽  
Catinca Secuianu
Keyword(s):  
Experimental Data ◽  
Vapor Pressure ◽  
Equations Of State ◽  
Ternary Mixtures ◽  
Volumetric Properties ◽  
Mixing Rules ◽  
Saturation Curve ◽  
Equilibrium Thermodynamic ◽  
Liquid Equilibrium ◽  
Binary And Ternary Mixtures

Vapour � liquid equilibrium, thermodynamic and volumetric properties were predicted for three pure hydrofluorocarbons: difluoromethane (R32), pentafluoroethane (R125) and 1,1,1,2 � tetrafluoroethane (R134a) as well as for binary and ternary mixtures of these refrigerants. Three cubic equations of state GEOS3C, SRK (Soave � Redlich � Kwong) and PR (Peng � Robinson) were used. A wide comparison with literature experimental data was made. For the refrigerant mixtures, classical van der Waals mixing rules without interaction parameters were used. The GEOS3C equation, with three parameters estimated by matching several points on the saturation curve (vapor pressure and corresponding liquid volumes), compares favorably to other equations in literature, being simple enough for applications.

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