The correlation dependence of thermal conductivity
of liquid refrigerants on the saturation line is developed as a simple function of temperature
:
(where
is the criterion unit,
, and
is the critical ...temperature). This dependence satisfies the requirements of dynamic scale theory (ST), and in particular, the passage to the limit
. The proposed correlation dependence is tested using the example of describing the thermal conductivity of 17 liquid substances in the range of state parameters from the saturation line to the critical pressure
and in the temperature range from the triple point temperature
T
tr
to
. The substances reviewed include nine fourth-generation refrigerants of hydrofluorochloro derivatives of olefins, seven hydrochlorofluorocarbons and hydrofluorocarbons, and C
3
H
8
. Using the description of
of C
3
H
8
as an example, it is shown that the proposed correlation dependence not only qualitatively but also quantitatively accurately conveys the behavior of
in the vicinity of the critical point. Based on the statistical analysis, it is shown that the proposed correlation with significantly less uncertainty describes the data on the thermal conductivity of liquid hydrofluorochloro derivatives of olefins both on the saturation line and in the single-phase region. Based on the proposed methodology, the thermal conductivity of the cis-isomer R1225ye(Z) is calculated for the first time in the temperature range
.
A heterogeneous double redundant hot-standby renewable system with Marshal–Olkin failure model is considered. Steady-state characteristics for such system are calculated. The problem of sensitivity ...of these characteristics to the shape of repair time distributions for this model is studied.
A method is proposed for predicting the thermal conductivity of liquid hydrofluoroolefins (HFOs) and hydrochlorofluoroolefins (HCFOs), which belong to the fourth generation of refrigerants, in the ...range of state parameters from the saturation line to the critical pressure (
p
cr
) and from the triple point of temperature (
T
tr
) to the critical temperature (
T
cr
). Within the framework of the methodology, two correlation dependences are proposed approved using the example of describing the thermal conductivity of eight liquid HFO and HCFO refrigerants in the temperature range from
T
tr
to
T
cr
. One of the correlations is based on the correlations of S. Yang et al., within the framework of which we took into account the requirements of the dynamic scale theory of the critical point, with the other being developed on the basis of the criterion unit of L. P. Filippov. It is shown that both correlations with low uncertainty describe data on the thermal conductivity of liquid HFO and HCFO refrigerants both on the saturation line and in the single-phase region. It is also shown that within the limits of experimental uncertainty, the modernized correlation of S. Yang et al. describes experimental data on the thermal conductivity of propane in the vicinity of the critical point. Based on the proposed method, tabulated data on the thermal conductivity of liquid refrigerant R1234ye(E) in the temperature range from 203.15 to 375.15 K were obtained for the first time.
A technique has been developed for constructing a unified fundamental equation of state of an individual substance for a wide range of state parameters. The technique is based on the Benedek ...hypothesis and the method of pseudocritical points, which are based on the assertion that the isochoric and isobaric heat capacities, the isothermal compressibility coefficient, and the speed of sound in the vicinity of the critical point on the critical and noncritical isochores are described by power-law dependences with the same critical indices. A unified fundamental equation of state of argon has been created that satisfies the requirements of the theory of scaling of critical phenomena, transforms into a virial equation of state in the gas region, satisfactorily conveys experimental data on density, isochoric and isobaric heat capacities, and sound speed within the uncertainty of the initial experimental data in the single-phase region in a wide range temperatures and pressures, on the phase equilibrium line in the range from the triple point to the critical point and in the near-critical region. On the basis of a unified fundamental equation of state, tables of standard reference data for argon were developed and certified in the temperature range of 83.806– 1200 K and pressures of 0.1–1000 MPa, and a statistical estimate of the accuracy of the tables was made.
Abstract
On the basis of the Clapeyron equation and the scale theory, expressions are developed for the “apparent” heat of vaporization
r
*
=
r
*
(
T
), vapor ρ
-
= ρ
-
(
T
) and liquid ρ
+
= ρ
+
(
T
...) branches of the saturation line of individual substances for the range of state parameters from the triple point (
p
t
,T
t
,ρ
t
) to the critical (
p
c
,T
c
,ρ
c
). The peculiarity of the proposed approach to the description of the saturation line is that all exponents of the components of the equations ρ
-
= ρ
-
(
T
) and ρ
+
= ρ
+
(
T
) are universal up to the universality of the critical indices α, β and Δ. In this case, the order parameter
d
s
= (ρ
+
− ρ
-
)/(2ρ
c
) and the average diameter
d
f
= (ρ
+
+ ρ
-
)/(2ρ
c
) − 1 of the saturation line satisfy the saturation line model 2β,1−α, which follows from the modern theory of critical phenomena. The method is tested on the example of describing the phase equilibrium line of refrigerant R1233zd(E) in the range from
T
t
= 195.15 K to
T
c
= 439.57 K. It is found that in the temperature range
T
t
,T
c
, the developed system of the mutually consistent equations
p
s
=
p
s
(
T
),
r
*
=
r
*
(
T
), ρ
-
= ρ
-
(
T
) and ρ
+
= ρ
+
(
T
) allows describing the data on the saturated vapor pressure
p
s
and densities ρ
-
and ρ
+
on the saturation line within the experimental uncertainty of these data.
The use of environmentally friendly refrigerants, such as R1233zd(E), in low-temperature technology as an alternative to the currently used refrigerants R245fa, R134a, R123 is considered. Substance ...R1233zd(E) - trans-1-chloro-3,3,3-trifluoro-1-propene - refers to fluorinated hydrocarbon compounds. To calculate the equilibrium characteristics (density, entropy, etc.) of this substance, a unified fundamental equation of state is proposed that satisfies a number of requirements: the asymmetric nature of the behavior of a real fluid relative to the critical isochore is taken into account in accordance with modern physics of critical phenomena; the transition of this equation to the virial equation of state in the rarefied gas region is realized; in a wide vicinity of the critical point is consistent with the Berestov scaling equation. Based on the proposed equation of state in the temperature range 195.15–450 K and pressure 0.1–100 MPa for R1233zd(E), thermodynamic tables of standard reference data were calculated in the single-phase region and on the saturation line, including density, entropy and enthalpy, sound speed , isochoric and isobaric heat capacities, as well as the heat of vaporization. In accordance with GOST 34100.3-2017/ISO/IEC Guide 98-3:2008 and the international methodology recommended for assessing the uncertainty of tabulated data, the uncertainties of the characteristic values in the specified standard tables were evaluated. A comparative analysis of the characteristics of R1233zd(E) calculated from the proposed equation of state with experimental and published data is performed.
A unified fundamental equation of state has been developed for 2,3,3,3-tetrafluoropropene (R1234yf), a fourth-generation ozone-safe refrigerant, and a method for constructing the equation has been ...proposed. In the gas region, this equation transforms into an equation of state of the virial form, and in the vicinity of the critical point it satisfies the requirements of the modern scale theory of critical phenomena and transforms into the Widom scale equation. Based on a single fundamental equation of state in accordance with GOST R 8.614-2018, “GSI. State Service of Standard Reference Data. Basic Provisions,” we developed standard reference data GSSSD 380-2020 on density, enthalpy, isobaric heat capacity, isochoric heat capacity, entropy and speed of sound in R1234yf in the temperature ranges 230–420 K and pressures 0.1–20 MPa. We compared the calculated values of equilibrium properties with the most reliable experimental data obtained in well-known global laboratories and tabular data obtained from the known fundamental equations of state R1234yf. Uncertainties of tabulated data for saturated vapor pressure, density, enthalpy, isobaric heat capacity, isochoric heat capacity, entropy and speed of sound of 2,3,3,3-tetrafluoropropene are estimated – standard relative uncertainties for types A, B, total standard relative and expanded uncertainties. The results obtained in this work show that the proposed unified fundamental equation of state adequately describes the equilibrium properties of R1234yf in the above stated range of state parameters.
Fundamental equation of state for R1234yf Rykov, V A; Rykov, S V; Sverdlov, A V
Journal of physics. Conference series,
11/2019, Letnik:
1385, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Unified fundamental equation of state for R1234yf has been developed that satisfies the scaling critical point theory. It has been demonstrated that the proposed equation of state truly represents ...the peculiarities of the thermodynamic surface from the qualitative and quantitative point of view: first, in the regular part of the thermodynamic surface, secondly, in the region of strongly developed density fluctuations. The operating range of the equation of state has been determined on the basis of the benchmarking analysis with experimental and estimated data: for temperature 230 ≤ T ≤ 420 K; for pressure 0.001 < p < 20 MPa.
A system of mutually consistent equations describing the pressure
, vapor density
, and liquid density
on the phase equilibrium line of technically important substances in the range from the triple ...to critical points has been proposed. At the stage of development of this system, the following have been considered: (a) the features of the behavior of a number of properties (
,
,
,
is the average diameter of the saturation line, and
is the order parameter) in the critical region; (b) some concepts of the scale theory of critical phenomena and renormalization group theory, which was adapted by Wang L. et al. (2013) for substances with a given molecular structure, including SF
6
; (c) the Clausius–Clapeyron equation, in which the “apparent” vaporization heat
is used instead of the vaporization heat
. At the stage of approbation of this system of equations, a method for calculating the adjustable coefficients included in this system using the example of SF
6
, for which precision data on the thermal properties including the experimental (
,
,
,
) data are available, has been proposed. Using the proposed technique, the coefficients of the system of equations have been determined using the precision data for SF
6
and the calculated values of the SF
6
properties in a given temperature range have been obtained. The uncertainty of the calculated data has been statistically analyzed; in particular, the average squared deviations of the experimental (
,
,
,
) data from the corresponding equations have been found. It has been shown that the proposed system describes the listed properties with less uncertainty than that of the properties corresponding to the original equations of Funke et al. (2001). The temperature dependence
of the proposed model satisfactorily agrees with the model
developed by Wang et al. (2013) for the SF
6
critical region.
Here, the authors discuss the problem of describing the equilibrium properties of a substance in the vicinity of the critical point on the basis of the fundamental equation of state (FEoS) of a ...liquid and a gas in the absence of experimental information about the calorific properties of a given substance in this field of state parameters. FEoS has the following characteristics: in the region of low densities, FEoS transforms to the virial equation of state; in the asymptotic vicinity of the critical point, FEoS meets the requirements of the scaling theory of critical phenomena. The method is based on a new representation of the scaling hypothesis based on the Scofield-Litster-Ho linear model (LM), the Benedek hypothesis and the Lysenkov-Rykov ratio (LR) which establishes the relationship between LM parameters and the real liquid using the Pokrovsky transformations. Testing of the proposed method for constructing FEoS has been carried out using the example of describing the equilibrium properties of argon. It has been ascertained that the use of the LR ratio has allowed, firstly, reducing the number of individual FEoS parameters and, secondly, excluding the data about isochoric heat capacity CV related to the critical point wide vicinity from the calculation scheme.
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