Measurement and Prediction Evaluation of Viscosity of Low GWP Mixtures R454B and R454C
論文ID: 24-38
詳細
論文ID: 24-38
This article investigates the experimental viscosity data and modeling of two binary refrigerant mixtures, R454B and R454C, recognized as low global warming potential (GWP) alternatives to conventional high-GWP refrigerants. Viscosity was measured for both refrigerants in liquid and vapor phases using a tandem capillary tube method. For R454B, the viscosity measurements spanned temperatures from (233 to 313) K in the liquid phase and (323 to 373) K in the vapor phase, under pressures up to 4.07 MPa. For R454C, measurements were taken from (233 to 343) K in the liquid phase and from (343 to 393) K in the vapor phase, with pressures reaching 4.01 MPa. The research used two sets of experiments focusing on low (233 to 293) K and high (303 to 393) K temperature ranges, adhering to the same measurement principles. The expanded uncertainties for viscosity in liquid and vapor phases were kept below 2.2% and 2.4%, respectively. Furthermore, prediction of viscosity of the two mixtures has been carried out using Extended Corresponding States (ECS) that comes with REFPROP version 10.0. It was observed that for vapor phase viscosity predicted by REFPROP is higher than the experimental value, especially for R454C.
*Graduate School of Science and Engineering, Saga University
(1 Honjo-machi, Saga, 840-8502, Japan)
**Department of Energy Science and Engineering, Khulna University of Engineering & Technology (Teligati, Fulbarigate, Khulna 9203, Khulna, 9203, Bangladesh)
*** Department of Mechanical Engineering, Saga University
(1 Honjo-machi, Saga, 840-8502, Japan)
**** International Institute for Carbon-Neutral Energy Research, Kyushu University
(Fukuoka-shi, 819-095, Japan)
This article investigates the experimental viscosity data and modeling of two binary refrigerant mixtures, R454B and R454C, recognized as low global warming potential (GWP) alternatives to conventional high-GWP refrigerants. Viscosity was measured for both refrigerants in liquid and vapor phases using a tandem capillary tube method. For R454B, the viscosity measurements spanned temperatures from (233 to 313) K in the liquid phase and (323 to 373) K in the vapor phase, under pressures up to 4.07 MPa. For R454C, measurements were taken from (233 to 343) K in the liquid phase and from (343 to 393) K in the vapor phase, with pressures reaching 4.01 MPa. The research used two sets of experiments focusing on low (233 to 293) K and high (303 to 393) K temperature ranges, adhering to the same measurement principles. The expanded uncertainties for viscosity in liquid and vapor phases were kept below 2.2% and 2.4%, respectively. Furthermore, prediction of viscosity of the two mixtures has been carried out using Extended Corresponding States (ECS) that comes with REFPROP version 10.0. It was observed that for vapor phase viscosity predicted by REFPROP is higher than the experimental value, especially for R454C.
Keywords: Refrigerant, Viscosity, Zeotropic mixtures, Tandem capillary tube method, ECS model.
1. Introduction
Global warming threatens human survival by causing sudden changes in the Earth's climate and long-term weather patterns. The usage of classic refrigerants like CFCs and HCFCs has a substantial impact on global warming1-2). It is difficult to discover a more dependable refrigerant since it must be non-toxic, low-flammable, have zero or near-zero ozone depletion potential (ODP), and have a low global warming potential3).
Although no one refrigerant provides an ideal solution, many traditional refrigerants have inferior thermodynamic properties, toxicity, chemical instability, varied levels of flammability, or extremely high operational pressures4). To solve these difficulties, Hydrofluorocarbon /hydrofluoroolefin (HFC/HFO) blends, in particular, are viewed favorably due to their low GWP, reduced flammability, and good performance5). Notably, R-454B [R32/R1234yf (68.9/31.1) mass fraction] and R-454C [R32/R1234yf (21.5/78.5) mass fraction] have been discovered as leading alternatives. These blends are popular in refrigeration and air conditioning applications because of their low GWP and excellent thermodynamic characteristics.
While there is substantial study on the thermodynamic properties of mixture refrigerants, studies on their transport properties, notably viscosity, are rather few. Yang et al.,6) shown some progress in this area by measuring the viscosity of six binary mixes of R32+R1234yf and R32+R1243zf. These measurements were performed in both the homogeneous liquid and gas phases with a vibrating-wire viscometer throughout a temperature range of (254 to 383) K and pressures ranging from (1 to 8) MPa, with total expanded uncertainties ranging from 3.2% to 5.0%. Furthermore, Dang et al., 7) investigated the viscosities of R1234yf and its binary mixes just in the vapor phase at atmospheric pressure using a falling-ball-type viscometer, reaching a combined expanded uncertainty of less than 1.5%.
Despite these contributions, thorough research on the transport properties of next-generation refrigerants, such as R454B a planned successor for R410A8) and R454C which is meant to replace R404A and R22 are still needed9). These gaps underscore the continuous need for targeted study into the physical characteristics of developing refrigerant formulations to support their usage in air conditioning and heat pump applications.
The purpose of this study was to explore the viscosity of refrigerants R454B and R454C, measuring their properties across a broad range of temperatures in both liquid and vapor phases. Additionally, the findings were compared with data from REFPROP version 10.0 for both phases and the ECS method was explained for these refrigerants. The tandem capillary tube method, which enables evaluations across a wide range of temperatures and pressures, is used to measure the viscosity of R454B and R454C. A viscometer with two capillary tubes connected in series and oriented horizontally makes up the main experimental setup. By reducing the end effects that are commonly present in capillary tube measurements, this particular setup improves the data's accuracy.
The sample materials utilized, a thorough explanation of the experimental equipment, and an explanation of the working principles behind the measurements will all be covered in detail in next sections of this study.
2. Experimental Section
2.1. Sample materials
The test fluid samples were purchased from Chemours Mitsui Fluoroproducts Co., Ltd. These samples follow the standard mass fractions for refrigerant mixtures, specifically R454B, which is composed of R32 and R1234yf at 68.9% to 31.1%, and R454C, consisting of R32 and R1234yf at 21.5% to 78.5%. Prior to viscosity measurements, we verified the composition of the mixtures using a gas chromatography machine (Shimazu GC-2014 AT). The analysis confirmed that R454B consisted of 68.92% R32 and 31.08% R1234yf, while R454C was comprised of 21.55% R32 and 78.45% R1234yf.
2.2 Dynamic viscosity measurement apparatus
The dynamic viscosities of the zeotropic mixtures under investigation are determined using the tandem capillary tube method, which is based on Hagen-Poiseuille's Law. Using the established tandem capillary tube method, our laboratory designed and constructed two experimental setups with distinct measurement ranges to enhance the scope of our investigations. One setup operates within a low-temperature range (233 to 293) K, while the other covers a high-temperature range (303 to 393) K. The sample was introduced into the apparatus in its liquid phase.
Detailed methodologies and procedural steps for these experiments are extensively outlined in other publications by our research group. The high-temperature range setup has been utilized to measure the viscosity of various pure refrigerants and their mixtures, contributing valuable data to the field10-16).
This section details modifications made to the experimental setup, which are designed for applications in the low temperature range depicted in Figure 1. While adhering to basic principles, these adjustments optimize the setup for effective viscosity measurement under such conditions. The core of the modified apparatus includes two Pyrex capillary tubes, differentiated by length and diameter; the longer tube measures 50.21 mm with an inner diameter of 0.0567 mm, and the shorter tube is 24.78 mm long with an inner diameter of 0.0569 mm. The precise dimensions of these tubes were determined using a micro-head spectral-interference laser displacement meter (Model KEYENCE SI-FD 500).
Key components of the system include a syringe pump, which facilitates the circulation of the refrigerant at controlled, low flow rates, and a Coriolis flowmeter (mini CORIFLOW M12) for accurate mass flow rate measurement. A thermostatic water bath is utilized to maintain the required experimental conditions. Temperature is monitored using a platinum resistance thermometer (Pt100) and a K-type thermocouple. A sight glass attached to a pressure vessel allows for the observation of the refrigerant level, while the experimental pressure is maintained using helium gas and measured with a pressure transducer (Model PG-100 KU, KYOWA). Additionally, two high-precision differential pressure transducers (Model PDU-A-50KP, KYOWA) measure the pressure drop across each capillary tube.
Fig.1 Schematic flow diagram of the low temperature range tandem capillary tubes viscometer
Additionally, the validity of this experimental method has been affirmed by Miyara et al., 10) who have independently verified the accuracy and reliability of the tandem capillary tube method for viscosity measurements across these diverse temperature ranges. This dual-range capability allows for a more comprehensive understanding of refrigerant behavior under varying thermal conditions.
The relationship between the viscosity 𝜂 and the pressure drop Δ𝑃 of fluids flowing through a horizontal tube with radius a and length L can be quantified using the formula (1) specific to the tandem capillary tubes method:
where the subscripts 𝑙 and 𝑠 denote the long and short tubes, respectively. This methodological adaptation allows for a more comprehensive analysis by addressing the unique dynamics of each tube in the tandem arrangement.
2.3 Uncertainty calculation for the viscosity measurement
The uncertainty calculation for the viscosity of refrigerant mixtures R454B and R454C was conducted using the methodology outlined in the revised Guide to the Expression of Uncertainty in Measurement (GUM). Miyara et al., 10) noted that the effects of temperature on capillary tube dimensions are minimal due to the low thermal expansion coefficient of Pyrex glass, which is only 3.25×10-6 K-1 when using high-temperature range apparatus. To mitigate these effects, they implemented the following correction equation for the radius:
α represents the thermal expansion coefficient of the Pyrex glass tube, and Δ𝑇 is the temperature difference between the experimental conditions and the room temperature at which the diameter was measured. This formula is also applied for measurements in the low temperature range, where the influence of temperature is shown to be only 1.13×10-5 K-1.
This approach incorporated the law of propagation of uncertainty, aligning with recommendations from Bell17) and the JCGM 100 publication18) by the Joint Committee for Guides in Metrology. The precision of viscosity measurements can be affected by various factors related to the experimental apparatus, including potential errors in the dimensions of the Pyrex capillary tubes, the pressure drops across these tubes, the flow rate, and the conditions under which temperature and pressure measurements are taken. Additionally, the uncertainty associated with estimating the percentage composition of the compounds in the refrigerant mixture using gas chromatography (Shimazu GC-2014 AT) is taken into consideration. The calibration uncertainty of the gas chromatography method was maintained within ±0.2%, ensuring that the mass fraction values calculated from the calibration curve were accurate and consistent.
In this study, the uncertainties arising from the pressure drop and flow rate were identified as particularly significant, due to their higher levels of unpredictability and substantial impact on the overall uncertainty of the viscosity measurements. The combined standard uncertainty was calculated by taking the positive square root of the sum of the variances of these input parameters, as detailed in Equation (3). This calculation is crucial for ensuring the reliability and accuracy of the viscosity data obtained for these refrigerant mixtures.
These standard uncertainties are categorized as Type A (random) or Type B (systematic). The analysis was performed at 95% confidence level, accounting for all relevant variables, and indicated that the expanded uncertainties for the liquid phase of the refrigerants were below 2.2%. Using the tandem capillary tubes method, the total standard uncertainty of the viscosity measurements for R454B and R454C was determined, was found to be 2.3%, disregarding any variations due to experimental conditions.
3. Results and discussion
3.1. Apparatus Reliability Test
Miyara et al., 10) employed R134a to verify the accuracy of the apparatus designed for high-temperature measurements. Additionally, R32 was used as a reference fluid to confirm the reliability and stability of the measurements of low temperature apparatus before the test mixture fluid viscosity measurements19-20). The viscosity of R32 was measured at temperatures ranging from 233 K to 293 K and pressures from 2.02 to 4.08 MPa in the liquid phase. The expanded standard uncertainty of these measurements of liquid R32 was found to be better than 2.15%. The experimental data were compared with calculated data using REFPROP version 10.0, which includes experimental data from Huber et al.,21). The deviations between the experimental and calculated data ranged from a maximum of -1.82% to a minimum of -0.14%, with most of the measured data falling within ±1.5% deviations. This shows a good agreement between the measured viscosity of R32 and the calculated values from REFPROP, confirming the reliability of the measurement apparatus and technique.
3.2. Viscosity of R454B
The viscosity of R454B was determined using the tandem capillary tube method at a variety of temperatures and pressures for liquid and vapor phases, respectively. The experimental conditions for various measurements are detailed in figure 2, where the vapor-liquid saturation line is described by the equation of state provided by Bell et al.,22). To ensure reproducibility, each viscosity measurement for R454B was conducted three times under the same temperature and pressure conditions, as noted in reference. A minimum half-hour interval was allowed between measurements to accommodate slight variations in pressure and temperature. The viscosity for both refrigerants was measured across a temperature range of 233 K to 313 K for the liquid phase and 323 K to 373 K for the vapor phase. The pressure settings ranged from 2 MPa to 4 MPa in both liquid phase and vapor phase. The results for liquid and vapor phase viscosities are recorded in Tables 1 and 2, respectively.
Fig. 2 Temperature and pressure experimental ranges for R-454B
Fig. 3 Viscosity of liquid R454B as a function of density.
Figure 3 presents a plot of liquid viscosity data of R454B on an η−ρ diagram, where 𝜂 represents viscosity and 𝜌 denotes density. The viscosities vary from 94.5 to 246.1 μPa.s, exhibiting an exponential increase with rising density. At a constant temperature, the viscosities increase as pressure increases, whereas they decrease with an increase in temperature at a fixed pressure. The trends in the data are similar to those in REFPROP version 10.0, although the REFPROP data shows slightly higher deviations from the experimental data.
Fig.4 Viscosity of vapor R454B as a function of density.
Figure 4 displays the viscosities of the vapor phase as a function of density, plotted at various pressures and temperatures. Unlike the liquid viscosities, the vapor viscosities increase with rising pressure at a constant temperature and also with increasing temperature at a constant pressure. The measured viscosities of R454B vapor ranged from 13.7 to 16.9 μPa.s. The data for the vapor phase are more scattered compared to those of the liquid phase, likely due to variations in flow rate and differential pressures in the Pyrex capillary tubes used for measurement. It is observed that the experimental data are lower than those predicted by REFPROP.
Figure 5 highlights the deviations between the viscosity experimental data of R454B for both the liquid and vapor phases and the data calculated using REFPROP. In the liquid phase, the maximum deviation from the reference data was -2.33%, with a mean deviation of -2.00%. This comparison suggests that the measurement uncertainty for viscosity should be improved to better than ± 2.19%. In the vapor phase, the maximum deviation from the reference data reached -3.15%, with -2.47% mean deviation. These findings indicate that to achieve more reliable results, the measurement uncertainty of viscosity should be enhanced to better than ± 2.33%.
Fig.5 Deviations between experimental data and REFPROP v10.0 data
at liquid and vapor phase of R454B
3.3. Viscosity of R454C
The distribution of viscosity measurements for temperature and pressure is presented in figure 6, where a saturated line was drawn using the methodology from Bell et al.,22). Figure 7 illustrates the measured liquid viscosity data for R454C across a temperature range from 233.0 to 334.3 K and pressures from 2.0 to 4.1 MPa. The data show that the viscosity varies as a function of density and temperature. Specifically, in the liquid phase, the viscosity of R454C increases with an increase in density and decreases as the temperature rises. The trends observed in the data are comparable to those in REFPROP version 10.0, although it is noted that the calculation data exhibit slightly greater deviations from the experimental findings.
Figure 8 displays the measured vapor viscosity data for R454C across temperatures ranging from 342.4 to 392.5 K and pressures from 2.0 to 4.0 MPa. The vapor phase data exhibits some differences from the liquid phase, primarily due to variations in pressure and the less stable flow rates in both short and long tubes. In the vapor phase, the viscosity of R454C increases with both rising density and temperature. When these measurements are compared with REFPROP, it is noted that the experimental vapor phase viscosity values for R454C are lower than those predicted by the software.
Fig. 6 Temperature and pressure experimental ranges for R-454C
Fig. 7 Viscosity of R454C liquid in relation to its density.
Fig.8 Viscosity of R454C vapor in relation to its density.
Fig.9 Deviations between experimental data and REFPROP v10.0 data
at liquid and vapor phase of R454C
Figure 9 presents the deviations between the experimental viscosity data for R454C in both liquid and vapor phases and the values calculated using REFPROP. In the liquid phase, the experimental data shows a maximum deviation from the reference data of -3.99% and a mean deviation of -2.56%. These comparisons suggest that improvements are needed to reduce the measurement uncertainty for viscosity to better than ± 2.19%. In the vapor phase, the deviations are more significant, with a maximum deviation reaching -12.84% and a mean deviation of -11.77%. Based on these results, it is indicated that to achieve more accurate and reliable outcomes, the measurement uncertainty of viscosity should be refined to better than ± 2.20%. The viscosity data for the liquid and vapor phases are presented in Tables 3 and 4, respectively.
4. Viscosity model using extended corresponding states
REFPROP uses Extended Corresponding States (ECS) technique for modeling viscosity of mixtures where the constituent fluids are of similar kind. The details of this method can be found elsewhere23-25). According to the technique viscosity of a binary mixture is given by
Where,
The conformal coordinates 
5. Conclusions
This research investigates the experimental data viscosity of refrigerants R454B and R454C over a wide range of temperatures and pressures to determine how these variables influence their viscosity. The viscosity of R454B was measured in the liquid phase from 233 K (-40°C) to 313 K (40°C) and in the vapor phase from 323 K (50°C) to 373 K (100°C), with pressures reaching up to 4.07 MPa. The viscosity of R454C was recorded from 233 K (-40°C) to 343 K (70°C) in the liquid phase and from 343 K (70°C) to 393 K (120°C) in the vapor phase, with pressures up to 4.0 MPa. The expanded uncertainty (k = 2) for these viscosity measurements is estimated at 2.3%. The results were also compared with data from REFPROP version 10.0 for both phases. For R454B, within the liquid phase, deviations from the reference data reached a maximum of -2.33%, with an average deviation of -2.00%. In the vapor phase, the maximum deviation observed was -3.15%, with an average deviation of -2.47%. Conversely, for R454C, the liquid phase showed a maximum deviation from the reference data of -3.99% and an average deviation of -2.56%. In the vapor phase, the discrepancies were more pronounced, exhibiting a maximum deviation of -12.84% and an average deviation of -11.77%.
Acknowledgments
The authors gratefully recognize the work's funding from the New Energy and Industrial Technology Development Organization (NEDO).
References
Supplementary data
Table 1 Experimental data for the liquid viscosity of R454B
|
|
|
η | T | P | η | |
|---|---|---|---|---|---|---|
|
|
|
µPa s | K | MPa | µPa s | |
| 233.30 | 2.005 | 241.84 | 273.13 | 2.507 | 153.18 | |
| 233.33 | 2.011 | 241.29 | 273.13 | 3.003 | 154.33 | |
| 233.07 | 2.018 | 242.36 | 273.07 | 3.005 | 154.21 | |
| 233.05 | 2.501 | 243.26 | 273.12 | 3.009 | 154.23 | |
| 233.06 | 2.505 | 243.30 | 273.09 | 3.501 | 154.95 | |
| 233.03 | 2.506 | 243.09 | 273.08 | 3.501 | 155.07 | |
| 233.05 | 3.005 | 244.04 | 273.16 | 3.503 | 154.78 | |
| 233.07 | 3.006 | 244.24 | 273.07 | 4.000 | 156.16 | |
| 233.13 | 3.008 | 243.92 | 273.09 | 4.001 | 155.93 | |
| 233.13 | 3.506 | 245.13 | 273.18 | 4.004 | 155.90 | |
| 233.17 | 3.506 | 245.02 | 283.09 | 1.986 | 135.80 | |
| 233.16 | 3.507 | 245.53 | 283.17 | 2.003 | 135.96 | |
| 233.14 | 4.007 | 246.15 | 283.14 | 2.005 | 136.02 | |
| 233.26 | 4.012 | 245.41 | 283.10 | 2.500 | 136.86 | |
| 233.21 | 4.021 | 245.85 | 283.21 | 2.502 | 136.80 | |
| 243.11 | 2.003 | 215.27 | 283.15 | 2.503 | 136.52 | |
| 243.29 | 2.005 | 215.23 | 283.18 | 3.007 | 137.69 | |
| 243.14 | 2.005 | 215.33 | 283.22 | 3.009 | 137.73 | |
| 243.17 | 2.501 | 215.80 | 283.09 | 3.016 | 137.88 | |
| 243.22 | 2.503 | 216.02 | 283.14 | 3.501 | 138.74 | |
| 243.14 | 2.506 | 216.14 | 283.13 | 3.508 | 138.60 | |
| 243.19 | 3.006 | 217.17 | 283.10 | 3.509 | 138.56 | |
| 243.14 | 3.016 | 216.82 | 283.18 | 3.970 | 139.52 | |
| 243.13 | 3.019 | 216.74 | 283.13 | 4.001 | 139.56 | |
| 243.07 | 3.503 | 217.61 | 283.09 | 4.002 | 139.45 | |
| 243.05 | 3.504 | 217.94 | 293.21 | 2.001 | 120.49 | |
| 243.08 | 3.507 | 217.91 | 293.24 | 2.002 | 120.72 | |
| 243.11 | 4.005 | 218.66 | 293.19 | 2.009 | 120.73 | |
| 243.08 | 4.007 | 218.79 | 293.14 | 2.502 | 121.90 | |
| 243.09 | 4.010 | 218.84 | 293.08 | 2.507 | 121.85 | |
| 253.10 | 2.002 | 191.44 | 293.20 | 2.508 | 121.70 | |
| 253.07 | 2.005 | 191.54 | 293.08 | 3.007 | 122.53 | |
| 253.12 | 2.009 | 191.26 | 293.15 | 3.009 | 122.51 | |
| 253.12 | 2.498 | 192.43 | 293.23 | 3.011 | 122.66 | |
| 253.14 | 2.502 | 192.50 | 293.05 | 3.498 | 123.86 | |
| 253.17 | 2.502 | 192.36 | 293.18 | 3.502 | 123.47 | |
| 253.11 | 3.000 | 193.16 | 293.15 | 3.504 | 123.65 | |
| 253.13 | 3.001 | 193.00 | 293.25 | 4.000 | 124.51 | |
| 253.10 | 3.003 | 192.92 | 293.22 | 4.006 | 124.65 | |
| 253.11 | 3.502 | 193.79 | 293.28 | 4.009 | 124.57 | |
| 253.12 | 3.504 | 194.10 | 303.23 | 2.001 | 106.20 | |
| 253.13 | 3.508 | 193.87 | 303.19 | 2.002 | 106.34 | |
| 253.11 | 4.004 | 195.04 | 303.19 | 2.006 | 106.53 | |
| 253.14 | 4.007 | 195.23 | 303.00 | 2.507 | 107.89 | |
| 253.16 | 4.008 | 195.14 | 302.98 | 2.510 | 107.77 | |
| 263.20 | 2.000 | 170.45 | 303.03 | 2.514 | 107.73 | |
| 263.11 | 2.004 | 170.46 | 302.92 | 3.007 | 108.78 | |
| 263.12 | 2.004 | 170.68 | 302.97 | 3.010 | 108.95 | |
| 263.14 | 2.500 | 171.39 | 302.95 | 3.014 | 108.85 | |
| 263.15 | 2.505 | 171.33 | 302.87 | 3.504 | 109.92 | |
| 263.08 | 2.505 | 171.57 | 302.97 | 3.507 | 109.99 | |
| 263.17 | 3.001 | 172.29 | 302.92 | 3.513 | 109.87 | |
| 263.10 | 3.003 | 172.32 | 303.29 | 3.995 | 110.54 | |
| 263.06 | 3.003 | 172.60 | 303.01 | 4.005 | 110.96 | |
| 263.14 | 3.500 | 173.62 | 303.10 | 4.014 | 110.84 | |
| 263.17 | 3.502 | 173.31 | 313.78 | 3.001 | 94.50 | |
| 263.09 | 3.504 | 173.54 | 313.79 | 3.002 | 94.47 | |
| 263.14 | 4.004 | 174.50 | 313.56 | 3.011 | 94.76 | |
| 263.15 | 4.005 | 174.38 | 313.57 | 3.512 | 96.08 | |
| 263.15 | 4.009 | 174.46 | 313.90 | 3.515 | 95.66 | |
| 273.07 | 2.001 | 152.29 | 313.81 | 3.521 | 95.91 | |
| 273.17 | 2.002 | 152.23 | 313.68 | 4.006 | 97.08 | |
| 273.11 | 2.027 | 152.48 | 313.61 | 4.007 | 97.16 | |
| 273.07 | 2.504 | 153.35 | 313.63 | 4.008 | 97.21 | |
| 273.16 | 2.506 | 153.08 |
Standard uncertainties due to pressure and temperature are u(P) = 0.004 MPa and u(T) = 0.02 K
Combined standard uncertainty 
Table 2 Experimental data for the vapor viscosity of R454B
|
|
|
η | T | P | η | |
|---|---|---|---|---|---|---|
|
|
|
µPa s | K | MPa | µPa s | |
| 322.64 | 2.023 | 13.76 | 353.80 | 3.507 | 15.89 | |
| 322.66 | 2.025 | 13.69 | 353.90 | 4.017 | 16.49 | |
| 322.79 | 2.023 | 13.74 | 353.48 | 4.053 | 16.46 | |
| 333.70 | 2.006 | 14.22 | 353.60 | 4.066 | 16.51 | |
| 333.59 | 2.014 | 14.21 | 363.18 | 2.044 | 15.48 | |
| 333.72 | 2.018 | 14.22 | 363.12 | 2.049 | 15.50 | |
| 332.72 | 2.505 | 14.48 | 363.05 | 2.066 | 15.53 | |
| 332.70 | 2.513 | 14.47 | 363.39 | 2.502 | 15.74 | |
| 332.80 | 2.516 | 14.45 | 363.44 | 2.516 | 15.72 | |
| 333.96 | 3.001 | 14.85 | 363.53 | 2.520 | 15.71 | |
| 333.78 | 3.004 | 14.83 | 363.50 | 3.013 | 15.94 | |
| 333.53 | 3.018 | 14.90 | 363.43 | 3.016 | 15.93 | |
| 343.34 | 2.035 | 14.63 | 363.37 | 3.019 | 15.94 | |
| 343.08 | 2.052 | 14.61 | 363.67 | 3.501 | 16.24 | |
| 343.10 | 2.062 | 14.64 | 363.71 | 3.503 | 16.26 | |
| 342.60 | 2.502 | 14.87 | 363.76 | 3.504 | 16.25 | |
| 343.24 | 2.507 | 14.84 | 364.00 | 4.016 | 16.67 | |
| 343.02 | 2.509 | 14.85 | 363.44 | 4.026 | 16.66 | |
| 343.52 | 3.002 | 15.13 | 363.78 | 4.032 | 16.68 | |
| 343.83 | 3.002 | 15.17 | 373.17 | 2.006 | 15.86 | |
| 343.70 | 3.012 | 15.14 | 372.98 | 2.019 | 15.89 | |
| 343.69 | 3.504 | 15.64 | 372.72 | 2.032 | 15.90 | |
| 343.76 | 3.508 | 15.68 | 372.93 | 2.517 | 16.07 | |
| 343.58 | 3.525 | 15.66 | 373.43 | 2.526 | 16.09 | |
| 353.64 | 2.029 | 15.07 | 373.72 | 2.530 | 16.10 | |
| 353.42 | 2.038 | 15.06 | 373.40 | 3.005 | 16.34 | |
| 353.24 | 2.060 | 15.06 | 373.36 | 3.009 | 16.33 | |
| 353.43 | 2.512 | 15.23 | 373.44 | 3.018 | 16.31 | |
| 353.60 | 2.513 | 15.26 | 373.48 | 3.507 | 16.57 | |
| 353.12 | 2.520 | 15.26 | 373.54 | 3.514 | 16.56 | |
| 353.15 | 3.028 | 15.53 | 373.52 | 3.520 | 16.59 | |
| 353.19 | 3.050 | 15.56 | 373.92 | 4.011 | 16.92 | |
| 353.19 | 3.050 | 15.51 | 373.52 | 4.012 | 16.91 | |
| 353.19 | 3.489 | 15.87 | 373.83 | 4.015 | 16.94 | |
| 353.33 | 3.499 | 15.86 |
Standard uncertainties due to pressure and temperature are u(P) = 0.003 MPa and u(T) = 0.02 K
Combined standard uncertainty
Table 3 Experimental data for the liquid viscosity of R454C
|
|
|
η | T | P | η | |
|---|---|---|---|---|---|---|
|
|
|
µPa s | K | MPa | µPa s | |
| 233.11 | 2.003 | 276.77 | 283.27 | 2.999 | 155.98 | |
| 233.02 | 2.007 | 277.36 | 283.19 | 3.001 | 156.27 | |
| 233.14 | 2.010 | 277.15 | 283.22 | 3.001 | 156.37 | |
| 233.06 | 2.494 | 279.32 | 283.17 | 3.500 | 157.62 | |
| 233.07 | 2.498 | 278.71 | 283.20 | 3.503 | 157.63 | |
| 233.05 | 2.504 | 278.75 | 283.17 | 3.506 | 157.74 | |
| 233.12 | 2.998 | 279.43 | 283.19 | 3.999 | 159.38 | |
| 233.20 | 3.000 | 278.70 | 283.17 | 4.004 | 159.28 | |
| 233.06 | 3.003 | 279.55 | 283.10 | 4.005 | 159.16 | |
| 233.31 | 3.497 | 279.07 | 293.07 | 2.000 | 137.18 | |
| 233.04 | 3.503 | 280.34 | 293.14 | 2.002 | 137.05 | |
| 233.11 | 3.509 | 280.45 | 293.17 | 2.006 | 136.89 | |
| 233.03 | 3.991 | 282.79 | 293.21 | 2.496 | 138.15 | |
| 233.03 | 3.999 | 283.12 | 293.18 | 2.504 | 138.44 | |
| 233.08 | 4.005 | 282.12 | 293.17 | 2.507 | 138.42 | |
| 243.16 | 1.999 | 245.29 | 293.21 | 3.000 | 139.43 | |
| 243.26 | 2.005 | 245.39 | 293.24 | 3.002 | 139.27 | |
| 243.14 | 2.007 | 245.59 | 293.17 | 3.003 | 139.43 | |
| 243.30 | 2.498 | 245.24 | 293.13 | 3.499 | 140.70 | |
| 243.18 | 2.503 | 245.91 | 293.07 | 3.501 | 140.76 | |
| 243.14 | 2.505 | 245.32 | 293.20 | 3.506 | 140.65 | |
| 243.13 | 3.007 | 246.54 | 293.17 | 3.994 | 142.11 | |
| 243.15 | 3.007 | 246.83 | 293.19 | 4.001 | 142.03 | |
| 243.10 | 3.009 | 247.39 | 293.13 | 4.002 | 142.09 | |
| 243.28 | 3.489 | 247.90 | 303.83 | 2.016 | 120.42 | |
| 243.16 | 3.504 | 248.22 | 303.85 | 2.018 | 120.44 | |
| 243.18 | 3.509 | 248.70 | 303.91 | 2.019 | 120.34 | |
| 243.11 | 4.002 | 250.05 | 303.96 | 2.512 | 121.70 | |
| 243.14 | 4.003 | 248.51 | 303.94 | 2.513 | 121.72 | |
| 243.12 | 4.006 | 248.94 | 304.19 | 2.517 | 121.39 | |
| 253.22 | 2.000 | 217.71 | 304.06 | 3.005 | 123.12 | |
| 253.17 | 2.002 | 217.69 | 304.05 | 3.007 | 123.12 | |
| 253.21 | 2.003 | 218.09 | 304.03 | 3.012 | 123.04 | |
| 253.11 | 2.499 | 219.47 | 302.17 | 3.502 | 127.33 | |
| 253.00 | 2.502 | 219.63 | 303.98 | 3.506 | 124.67 | |
| 253.12 | 2.505 | 219.15 | 303.98 | 3.508 | 124.64 | |
| 253.10 | 3.004 | 220.59 | 303.74 | 4.007 | 126.42 | |
| 253.15 | 3.008 | 219.53 | 303.73 | 4.012 | 126.49 | |
| 253.12 | 3.011 | 219.31 | 303.85 | 4.015 | 126.34 | |
| 253.10 | 3.500 | 221.15 | 312.41 | 2.008 | 107.08 |
| 253.15 | 3.503 | 220.78 | 312.41 | 2.016 | 107.24 | |
|---|---|---|---|---|---|---|
| 253.17 | 3.513 | 221.35 | 312.36 | 2.021 | 107.18 | |
| 253.21 | 3.999 | 221.72 | 312.88 | 2.505 | 108.10 | |
| 253.09 | 4.008 | 222.21 | 312.97 | 2.506 | 107.97 | |
| 253.04 | 4.010 | 222.52 | 312.84 | 2.506 | 108.19 | |
| 263.15 | 1.998 | 194.53 | 312.62 | 3.007 | 110.03 | |
| 263.15 | 2.001 | 194.42 | 312.63 | 3.013 | 110.08 | |
| 263.14 | 2.002 | 194.83 | 312.38 | 3.015 | 110.34 | |
| 263.16 | 2.497 | 196.22 | 312.68 | 3.505 | 111.52 | |
| 263.18 | 2.501 | 196.16 | 312.81 | 3.506 | 111.32 | |
| 263.18 | 2.502 | 195.63 | 312.72 | 3.509 | 111.41 | |
| 263.14 | 2.975 | 197.09 | 313.41 | 4.003 | 111.96 | |
| 263.17 | 3.006 | 197.07 | 313.54 | 4.007 | 111.83 | |
| 263.17 | 3.008 | 196.84 | 313.64 | 4.009 | 111.67 | |
| 262.93 | 3.499 | 198.51 | 323.38 | 2.512 | 92.56 | |
| 263.13 | 3.501 | 197.99 | 323.16 | 2.512 | 92.91 | |
| 263.19 | 3.505 | 198.03 | 323.09 | 2.519 | 93.00 | |
| 263.16 | 4.008 | 199.31 | 323.19 | 3.005 | 94.61 | |
| 263.23 | 4.011 | 199.30 | 323.16 | 3.010 | 94.71 | |
| 263.18 | 4.018 | 199.30 | 323.47 | 3.013 | 94.35 | |
| 273.11 | 2.002 | 172.72 | 323.47 | 3.508 | 96.17 | |
| 273.18 | 2.002 | 172.59 | 323.49 | 3.509 | 96.18 | |
| 273.10 | 2.010 | 172.45 | 323.41 | 3.518 | 96.32 | |
| 273.12 | 2.502 | 173.98 | 323.62 | 4.008 | 97.87 | |
| 273.12 | 2.506 | 174.31 | 323.40 | 4.010 | 98.19 | |
| 273.12 | 2.507 | 174.17 | 323.43 | 4.010 | 98.07 | |
| 273.22 | 3.000 | 175.71 | 333.51 | 2.998 | 79.70 | |
| 273.17 | 3.001 | 175.69 | 333.34 | 3.001 | 79.85 | |
| 273.10 | 3.002 | 175.64 | 333.44 | 3.012 | 79.79 | |
| 273.11 | 3.500 | 176.72 | 333.81 | 3.510 | 81.66 | |
| 273.11 | 3.503 | 176.45 | 333.73 | 3.513 | 81.83 | |
| 273.11 | 3.509 | 176.57 | 333.67 | 3.514 | 81.85 | |
| 273.14 | 3.977 | 177.94 | 334.24 | 4.008 | 83.36 | |
| 273.17 | 4.005 | 177.84 | 334.28 | 4.009 | 83.33 | |
| 273.18 | 4.010 | 177.91 | 334.23 | 4.010 | 83.44 | |
| 283.18 | 2.001 | 154.48 | 342.91 | 3.504 | 67.77 | |
| 283.09 | 2.001 | 154.68 | 343.05 | 3.507 | 67.56 | |
| 283.14 | 2.002 | 154.49 | 343.31 | 3.512 | 67.11 | |
| 283.20 | 2.500 | 155.44 | 343.12 | 3.995 | 70.39 | |
| 283.15 | 2.500 | 155.58 | 342.97 | 4.000 | 70.65 | |
| 283.17 | 2.508 | 155.62 | 343.22 | 4.002 | 70.27 |
Standard uncertainties due to pressure and temperature are u(P) = 0.004 MPa and u(T) = 0.02 K
Combined standard uncertainty
Table 4 Experimental data for the vapor viscosity of R454C
|
|
|
η | T | P | η | |
|---|---|---|---|---|---|---|
|
|
|
µPa s | K | MPa | µPa s | |
| 342.44 | 2.021 | 12.84 | 373.04 | 3.021 | 14.73 | |
| 342.74 | 2.010 | 12.85 | 373.50 | 4.014 | 16.46 | |
| 342.86 | 2.023 | 12.92 | 372.96 | 4.017 | 16.43 | |
| 352.53 | 2.023 | 13.56 | 373.44 | 4.026 | 16.44 | |
| 352.62 | 2.024 | 13.46 | 392.52 | 2.016 | 14.55 | |
| 352.59 | 2.043 | 13.52 | 392.50 | 2.021 | 14.52 | |
| 351.63 | 3.009 | 14.25 | 392.47 | 2.023 | 14.56 | |
| 352.34 | 3.010 | 14.35 | 392.69 | 3.004 | 15.24 | |
| 352.21 | 3.014 | 14.34 | 392.69 | 3.005 | 15.27 | |
| 372.99 | 2.018 | 14.07 | 392.55 | 3.008 | 15.26 | |
| 372.77 | 2.019 | 14.10 | 393.34 | 4.006 | 16.49 | |
| 372.89 | 2.032 | 14.11 | 393.30 | 4.015 | 16.52 | |
| 372.59 | 3.002 | 14.76 | 393.22 | 4.017 | 16.44 | |
| 373.20 | 3.018 | 14.76 |
Standard uncertainties due to pressure and temperature are u(P) = 0.003 MPa and u(T) = 0.02 K
Combined standard uncertainty
