Equation of state for He4, including a regular and a scalar part

Bezverkhy, P. P.; Martynets, V. G.; Matizen, É. V.

doi:10.1063/1.3253391

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…, are not satisfied). We see, then, that δ eff is a sensitive measure of the shape of the isotherm, and can uncover anomalies even when the description of P ( ρ ) is in sensible agreement with simulation or experiment . In the section Comparison with a Crossover Model, a different type of crossover model is explored, one that reaches the correct asymptotic limit as ρ → ρ c (shown in Figure a, –×–).…”

Section: Critical Isotherms From Approximantsmentioning

confidence: 96%

“…4, —, A J ) using ρ c , P c , T c , and virial coefficients as inputs (Table ). (a) Lennard–Jones fluid: additional equations of state taken from Kolafa and Nezbeda (○) and Johnson et al ( □ ), which were constructed using molecular simulation data; (b) He‐4: additional equations of state taken from the NIST WebBook (○) and Bezverkhy et al (●), constructed using data from experiments; and (c) GCPM water: WEOS J taken from Kim et al (curves with symbols, abbreviated as W J ). Error‐bars specify the 68% uncertainty, propagated from uncertainty in the virial coefficients.…”

Section: Critical Isotherms From Approximantsmentioning

confidence: 99%

“…The semiempirical equation of state for helium‐4, given in Bezverkhy et al, is used to represent data from experiments in Figures b and b (shown as –•–). In this model, a classical part and nonclassical part are combined through a Gaussian crossover function.…”

Section: Critical Isotherms From Approximantsmentioning

confidence: 99%

“…Literature values (‐ ‐ ‐) for ethane, pentane, and argon are taken from the “restricted linear model” given in Behnejad et al (see references therein). For helium‐4, we compare against the D 0 of the semiempirical model given in Bezverkhy et al For the van der Waals model, D 0 = 3/2. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.…”

Section: Critical Properties From Approximantsmentioning

confidence: 99%

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Critical isotherms from virial series using asymptotically consistent approximants

et al. 2014

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The low-density equation of state of a fluid along its critical isotherm is considered. An asymptotically consistent approximant is formed having the correct leading-order scaling behavior near the vapor-liquid critical point, while retaining the correct low-density behavior as expressed by the virial equation of state. The formulation is demonstrated for the Lennard-Jones fluid, and models for helium, water, and n-alkanes. The ability of the approximant to augment virial series predictions of critical properties is explored, both in conjunction with and in the absence of criticalproperty data obtained by other means. Given estimates of the critical point from molecular simulation or experiment, the approximant can refine the critical pressure or density by ensuring that the critical isotherm remains well-behaved from low density to the critical region. Alternatively, when applied in the absence of other data, the approximant remedies a consistent underestimation of the critical density when computed from the virial series alone. V C 2014 American Institute of Chemical Engineers AIChE J, 60: 3336-3349, 2014 Keywords: virial equation of state, critical phenomena, crossover, approximant, Lennard-Jones P c . When solved using a sufficiently high-order virial series, these predictions for T c and P c are often close to simulation data and/or experiments, but those for q c are consistently about 10% too low in such a comparison. 4,8 Underestimation of the critical density by the virial series is connected to the nonclassical behavior of real fluids at the critical point, for which critical scaling laws assert that q c is a branch-point singularity of the function P(q) along the critical isotherm. In the context of critical phenomena, the molar In this section, critical isotherms are constructed using given values of the critical density q c , critical pressure P c , Values are given in Lennard-Jones units. Virial coefficients are from Schultz et al. 5 q c,AJ is the corrected critical density given by the smallest positive root of (7), which takes the following as inputs: d 5 4.789; P c , q c , and T c as predicted by the virial series at each order J (given above); and the corresponding virial coefficients (taken from an interpolation). Numbers in parentheses specify the 68% uncertainty on the last digit, propagated from uncertainty in the virial coefficients (with the exception of the simulation values). a Predicted using (7) with P c,sim , T c,sim , and the first seven virial coefficients taken at T c,sim (from an interpolation) as inputs.

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Section: Critical Isotherms From Approximantsmentioning

confidence: 96%

Section: Critical Isotherms From Approximantsmentioning

confidence: 99%

Section: Critical Isotherms From Approximantsmentioning

confidence: 99%

Section: Critical Properties From Approximantsmentioning

confidence: 99%

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Critical isotherms from virial series using asymptotically consistent approximants

et al. 2014

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“…The most wellknown reference tables [5] are calculated for CO 2 by a multiconstant regular Span and Wagner EoS (SW EoS, 58 adjustable constants and 35 different powerlaw indices). Articles [6,7] represent the thermal combined equation of state, including a new 11constant EoS for the regular region and scaling 6constant EoS for the critical region of states, a unifed description of the thermal and caloric properties of carbon dioxide and for helium. In paper [8] proposes the crossover cubicplusassociation equation of state.…”

Section: Introductionmentioning

confidence: 99%

Modification of scaled equation of state to determine the pressure in the CO2 critical region

Vorobieva

2022

TAPR

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The object of the research is carbon dioxide and its pressure distribution depending on the range of temperature and density in the region of the critical point. One of the most problematic areas of methods for finding thermodynamic parameters of a real gas is insufficient accuracy in calculations in the places of occurrence and rapid development of fluctuation phenomena, which are inherent in phase transitions of the first and second terms. For a more detailed and accurate description of the nature of the thermodynamic parameters in the region of the critical point, scaling and crossover equations of state were developed. Such equations, due to the presence of regular and scaling parts, allow describing the thermodynamic parameters of a real gas not only directly near the critical point, but also at some distance from it, maintaining a small error relative to experimental data. The article proposes an equation of state, which contains a scaling part described according to the rules of statistical physics, and a regular part in the form of a classical cubic equation of state. The equation is used to calculate the pressure of carbon dioxide in the region around the critical point from 300 K to 305 K. The article proposes a correlation equation for the scaling correction of the regular part (Redlich-Kwong-Aungier model) of the crossover equation of state, which is related to the scaling part the equation of state is a crossover function. The obtained results for the pressure in the critical region showed good agreement with the baseline data. The error relative to the experimental data is halved compared to the original model of the Redlich-Kwong-Aungier equation. The obtained results ensure the applicability of the proposed method in the temperature range from 300 K to 305 K. Due to the simplicity of the form of the regular equation of state and the small number of empirical coefficients for the large-scale equation of state, the obtained method can be used for practical problems of computational hydrodynamics without spending a lot of computing time.

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