Investigation on Liquid Density Data at the Bubble Point and

Aug 29, 2014 - Xiao-gang Qiao,* .... at the bubble point and the saturated vapor density data of ... the saturated liquid density data of HFC-404A at ...
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Investigation on Liquid Density Data at the Bubble Point and Equations for the Refrigerant HFC-404A over a Wide Temperature Range Xiao-gang Qiao,*,† Ying-jie Xu,‡ and Xiao-hong Han‡ †

Zhejiang College of Construction, Hangzhou 311321, China Institute of Refrigeration and Cryogenics, State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China

‡

ABSTRACT: Liquid density data at the bubble point of the refrigerant HFC-404A were measured at temperatures from (227 to 341) K. The experimental method used for this work was the single-cycle method. Liquid density experimental data of HFC-404A were correlated by the VDNS-type and the modified Rackett-type density equations, and the corresponding parameters for the density equations were given. The correlated results show that they agreed well with the experimental data. The absolute values of the average relative deviations of liquid density from the VDNS-type density equation and the modified Rackett-type density equation were 0.10 % and 0.09 %, respectively. Meanwhile, the experimental results were compared with the calculated results from the equation by Lemmon, the results showed that the experimental data agreed well with the calculated results from Lemmon, the absolute value of the average relative density deviations was 0.69 %. In addition, the Peng−Robinson (PR), Patel−Teja (PT), and Soave−Redlich−Kwong (SRK) equations of state were also used to calculate the liquid density of HFC-404A. The absolute values of the average relative liquid density deviations for PR, PT, and SRK equations were 0.87 %, 3.62 %, 7.92 %, respectively, and the absolute values of the maximum relative deviations for PR, PT, and SRK equations were 4.90 %, 6.79 % and 10.20 %, respectively. In actual applications, VDNS-type and modified Rackett-type density equations can be used to calculate the liquid density for HFC-404A with the given coefficients. Also, the equations for PR and PT can easily be used to calculate the liquid and vapor densities of HFC-404A.

1. INTRODUCTION To protect the ozone layer from atmospheric ozone depleting substances in the Montreal Protocol, many countries have developed alternative refrigerants to R502 in the commercial refrigeration sector, especially at medium and low temperatures. R502 is a mixture of HCFC-22 and CFC-115 with mass fractions of 0.488 and 0.512. Its normal boiling point is −45 °C and was an important refrigerant in low temperature applications due to its good thermodynamic performance. The provisions of Montreal Protocol have prohibited the use of CFC-115 and it was proposed to be phased out by the year 1996 in developed countries and before 2010 in developing countries. The deadline for the use of HCFC-22 is year 2020 in developed countries and year 2030 in developing countries.1,2 Considering the ozone depletion potential (ODP) of HCFC-22 and CFC-115, the research on refrigerant replacement for R502 has been one of hot topics in the refrigeration and airconditioning industry. Much research has been done to search for the new alternative refrigerants for R502 in recent years.3−10 For example, In the literature,7 the replacement of R502 by shortterm alternative mixtures such as HCFC-402A, HCFC-402B, HCFC-403B, and HCFC-408A had been suggested. However, the short-term alternatives will be forbidden in Europe in 2015 for HCFCs.4 Arora gave a brief summary of the alternative refrigerants for R502 before 2008 again.2 Literature9 presented © 2014 American Chemical Society

the detailed review about the refrigerant choices for commercial refrigeration, the reviewed results showed that when HC-290 or HFO (hydrofluoroolefin) is used for the chiller, the direct emission almost can be eliminated, but a cost penalty associated with extra safety precautions needs to be especially considered; based on the similar efficiency, HFO refrigerant is a possible successor to HFC-134a in the secondary medium temperature system application; CO2-transcritical refrigeration systems has a far higher operation pressures than conventional HFC-404A systems, which are not common in the supermarket refrigeration sector today; HFC-404A still is one of the main refrigerants in direct expansion in the low temperature range of (−35 °C to −40 °C). Llopis et al. pointed out that HFC-404A and HFC-507A still were among the main used refrigerants in commercial refrigeration, food processing, cold storage, and transport refrigeration, and they gave the detailed evaluation of HFC-404A and HFC-507A in an experimental double-stage vapor compression plant, they thought that it was difficult to recommend any of both refrigerants, probably the HFC-404A is advisible for high evaporating temperatures and the HFC-507A for low evaporating levels; however, their energy performance is comparable.10 Han et al. proposed the ternary nonazeotropic Received: June 4, 2014 Accepted: August 19, 2014 Published: August 29, 2014 2872

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Table 1. Comparison of Physical Characteristics for Refrigerants12,13 refrigerants physical characteristics constituents boiling point at 1.013 bar molecular weight flammability in air ODP (R11 = 1) GWP (CO2 = 1, 100 yrs) evaporating pressure at −20 °C condensing pressure at 40 °C pressure ratio critical temperature specific heat ratio Cp/Cv vapor at 5 °C total latent heat at −20 °C temperature glide in evaporator

units °C %

bar bar °C kJ/kg K

HFC-404A

R502

R125, R134a, R143a (44 %, 4 %, 52 % by weight) −46.2 97.6 nonflammable 0.00 3900 3.0 18.3 6.1 72.1 1.26 181 0.61

R22,R115 (48.8 %, 51.2 % by weight) −45.2 111.6 nonflammable 0.25 4700 2.9 16.6 5.7 80.2 1.25 157 0.00

341) K were measured and the density equations were given in this paper, this will be very important for promoting its applications in the actual refrigeration systems.

mixture of HFC-161/125/143a (15% / 45% / 40% by weight) as a promising alternative refrigerant to HFC-404A, but its application was very limited.11 As the above description, with the requirement increase of commercial refrigeration sector in the world, HFC-404A and HFC-507A still are the important refrigerants in the commercial refrigeration sector, especially at medium and low temperatures. HFC-507A is a binary azeotropic refrigerant composed of HFC-125/HFC-143a (50 %/50 % by weight) and its normal boiling point is slightly lower than that of R502. So it is popularly selected for low temperature applications at a temperature range of −40 °C to −45 °C, such as low temperature freezers. HFC-404A is a ternary-mixture refrigerant composed of HFC-125/HFC-143a/HFC-134a (44 %/52 %/4 % by weight) and its normal dew point and normal bubble point temperatures are very close to those of R502. The detailed physical characteristics of the refrigerants HFC-404A and R502 are shown in Table 1.12,13 Thus, HFC-404A is popularly used in commercial refrigeration systems from supermarket stores, and refrigerated transports at a temperature range of −35 °C to −40 °C. Therefore, research on the thermophysical properties of HFC-404A was further developed for the energy saving and the global environment protection to some extent. Some research on HFC-404A was done.14−18 But it is hard to obtain available liquid density data for refrigerant HFC-404A in the existing literatures. To date, some literature19−22 gave the some relative results about the density of HFC-404A, for example, Lemmon19 gave the Pseudo PureFluid Equations of State for calculating the liquid densities of R404A; Kleemiss20 mainly gave the liquid densities of HFC404A in the subcooled area; Fujiwara et al. 21 gave the density data of HFC-404A from the superheat state to the subcooled area, and the density data referred to the whole density data of HFC-404A (they did not be specified for the saturated liquid densities of HFC-404A at the bubble point); Bouchot22 measured the lots of density data of HFC-404A, including the density data in the superheat area, the density data in the subcooled area, the saturated liquid density data of HFC-404A at the bubble point and the saturated vapor density data of HFC-404A at the dew point in two phase area. Among the data, the saturated liquid density data of HFC-404A at the bubble point were measured at the temperature range from 253 K to 333 K, the total number of data points were 9. In order to supplement the available data, the liquid density data at bubble point for HFC-404A in the temperature range from (227 to

2. EXPERIMENTS 2.1. Sample. The sample of HFC-404A (HFC-125/HFC143a/HFC-134a (44 %/52 %/4 % by weight)) was purchased from Honeywell Company with a minimum purity of 99.9 % (mass fraction), a maximum acidity of 1 ppm, a maximum moisture of 10 ppm and a maximum evaporated residue of 100 ppm. Before it was used, there was no further purification to be done. 2.2. Experimental Equipment and Procedures. Experimental investigation was developed in a experimental device with a recirculating still, seen in Figure 1, very similar to the

Figure 1. Experimental apparatus of the refrigerant density:23 1, thermostated bath; 2,vessel; 3, cooling coil; 4, autocascade refrigeration system; 5, heating coil; 6, high accuracy PT thermometer; 7, thermometer; 8, stirrer; 9, mass flowmeter; 10, micropump; 11, Kelthley 2001 data collector; 12, high accuracy temperature controller; 13, PC; 14, vacuum pump; 15, high accuracy pressure transducer.

information from Han et al.23 In the experimental apparatus, an equilibrium cell made from a stainless steel was used. In the equilibrium cell, the glass window was fixed to observe the state of the working fluid. A motor blender with variable speeds is used to shorten the equilibrium process. The vapor phase cycle is driven by a circulating pump (Model: GAH-T23.PVS.B, Micropump). The system temperature is measured by a fourhead 25-platinum resistance thermometer (Model: WZPB-I, China) and a Keithley 2002 data acquisition/switch unit, the four-head 25-platinum resistance thermometer has an uncertainty of 1 mK (ITS), and the temperature fluctuation in the thermostated bath is less than 5 mK/30 min. The standard temperature uncertainty for the system is within 10 mK. The 2873

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Table 2. Experimental Data of the Pressures and Saturated Densities for HFC-404A at the Bubble Point and Their Responding Calculating Results for the Saturated Densities at Bubble Point by Equations 1 and 2 and the Equation of Lemmon within the Temperature Range of (227 to 341) Ka eq 1 T

pexp

K

kPa

227.25 229.00 231.13 233.65 236.65 238.93 241.17 243.67 246.15 248.80 251.46 253.53 256.20 258.87 261.54 264.32 267.17 269.53 272.30 274.85 277.35 279.96 282.79 285.27 287.82 290.35 292.99 295.62 298.31 300.94 303.74 306.35 309.09 311.74 314.35 316.99 319.60 322.18 324.88 327.98 330.72 333.30 335.45 337.95 340.20 341.31

104.8 113.9 125.2 140.0 160.8 176.4 194.2 214.0 233.4 262.5 290.9 314.5 345.5 382.2 418.1 458.2 506.9 546.0 597.5 645.4 692.4 749.7 820.3 887.6 955.3 1024.3 1093.0 1176.6 1264.8 1353.2 1442.8 1550.8 1660.6 1782.9 1892.8 2006.6 2135.4 2274.8 2417.6 2588.3 2730.5 2918.6 3058.0 3215.5 3344.0 3468.7

ρexpL kg m

−3

1311.81 1306.65 1299.96 1292.07 1282.70 1275.33 1268.12 1260.13 1251.99 1243.21 1234.49 1227.39 1218.32 1209.06 1199.78 1189.72 1179.44 1170.43 1159.85 1149.89 1139.93 1129.44 1118.41 1107.93 1097.24 1086.13 1074.43 1062.34 1049.79 1037.02 1022.97 1009.51 994.81 980.42 965.08 948.95 931.51 912.66 892.87 867.04 843.76 816.24 793.34 762.75 734.21 713.96

ρcalL kg m

−3

1313 1307 1300 1292 1282 1275 1268 1260 1251 1243 1234 1227 1218 1209 1200 1190 1180 1171 1161 1151 1141 1131 1119 1109 1098 1087 1075 1062 1050 1037 1022 1009 994 979 963 947 930 912 893 868 845 820 797 766 731 711

equation by Lemmon19

eq 2 δρb % −0.08 −0.03 −0.01 0.01 0.04 0.04 0.04 0.05 0.04 0.03 0.04 0.03 0.02 0.01 0.01 −0.01 −0.01 −0.04 −0.06 −0.08 −0.10 −0.10 −0.06 −0.07 −0.04 −0.04 −0.02 −0.01 0.02 0.04 0.06 0.09 0.12 0.18 0.20 0.21 0.16 0.02 0.01 −0.16 −0.13 −0.48 −0.46 −0.39 0.41 0.47

ρcalL kg m

−3

1311 1306 1299 1292 1282 1275 1268 1260 1252 1244 1235 1228 1219 1210 1200 1190 1180 1171 1160 1151 1141 1130 1119 1108 1097 1086 1074 1062 1049 1036 1022 1009 994 979 963 947 930 912 893 868 844 820 797 766 732 712

δρb % 0.08 0.08 0.05 0.03 0.02 0.00 −0.02 −0.02 −0.03 −0.04 −0.03 −0.04 −0.04 −0.04 −0.03 −0.04 −0.02 −0.04 −0.05 −0.06 −0.07 −0.07 −0.02 −0.03 −0.01 0.00 0.02 0.02 0.05 0.06 0.07 0.10 0.12 0.18 0.19 0.21 0.16 0.03 0.03 −0.13 −0.07 −0.42 −0.40 −0.37 0.33 0.30

ρcalL kg m

−3

1305 1300 1293 1285 1276 1269 1261 1253 1245 1236 1228 1221 1211 1202 1193 1183 1172 1164 1153 1144 1134 1123 1112 1102 1091 1080 1068 1056 1043 1031 1016 1003 988 973 957 941 924 906 886 861 837 811 788 756 721 700

δρb % 0.52 0.51 0.54 0.55 0.52 0.50 0.56 0.57 0.56 0.58 0.53 0.52 0.60 0.58 0.57 0.56 0.63 0.55 0.59 0.51 0.52 0.57 0.57 0.54 0.57 0.56 0.60 0.60 0.65 0.58 0.68 0.64 0.68 0.76 0.84 0.84 0.81 0.73 0.77 0.70 0.80 0.64 0.67 0.88 1.80 2.67

Standard uncertainties u are u(T) = 0.01 K, u(ρexpL) = 0.5 kg m−3, u(pexp) = 1.6 kPa. bδρ is relative density deviation, and it is defined as δρ = ((ρcalL −ρexpL)/(ρexpL)) × 100 %. a

literature.23 The standard uncertainty for the density measurement is within 0.5 kg m−3. Need to explain: before the experimental measurement, the actual temperature of the fluid in the resonance pipe was considered, that is, the different temperature measurement points were set to measure the temperature difference, and then the insulation thickness was added further. In addition, when

pressure is measured by a pressure transducer (Model: PMP4010, Drunk), and the data are also logged by the Keithley 2002 data acquisition/switch unit. The standard pressure uncertainty is within 1.6 kPa. The liquid density is measured by a high accuracy mass flowmeter (Model: CMF025, EMERSON), and its principle is shown in the 2874

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⎛ρ − ρ ⎞ calL expL ⎟ × 100% δρ = ⎜⎜ ⎟ ρ ⎝ ⎠ expL

the experiment was done, the insulation box was covered in the whole exposed parts to enhance the insulation effect. The experimental procedures are described as follows. First, the cell was evacuated to remove the inert gases and others. Then, the certain amount of HFC-404A was charged to > 98 % of the cell’s volume filled with liquid (the liquid phase composition of HFC-404A was measured by a gas chromatograph (GC), which was equipped with a Flame Ionization Detector (FID) (model: GC112A, China), and the standard uncertainty in the measurements of the composition is 0.003 in mole fraction); thus, vapor space corrections were negligible. Third, the system temperature was kept constant by controlling the temperature of the thermostated bath. The vapor in the cell was circulated continuously by the circulating pump to quicken the thermal equilibrium state. Usually, 2 h or more was sufficient to obtain a thermal equilibrium state between the cell and the thermostated bath. Finally, when the desired temperature was obtained, the temperatures, pressures and liquid densities in the equilibrium cell were recorded by the responding measurement equipment. 2.3. Experimental Data. Before the experiment for refrigerant HFC-404A was done, the experimental data (T − P − ρexpL) of the refrigerant HCFC-22 were first measured to verify the reliability of the experimental apparatus, and compared with the results in the literature.12 On the basis of these, the liquid densities of HFC-161 also had been conducted23 and the liquid densities at bubble point of the mixtures HFC-32/125/161 and HFC-407C had been developed by Wang et al.24 From the above research, it can be suggested that the experimental device has good reliability and stability. Based on those work, the experimental data (T − P − ρexpL) at bubble point of the refrigerant HFC-404A were developed, seen in Table 2.

Figure 2. T−density diagrams of the refrigerant HFC-404A by using VDNS-type equation (eq 1), the modified Rackett-type equation (eq 2), equation by Lemmon, and PR, PT, and SRK equations.

From the results in Table 2 and Figure 2, it can be seen that the results correlated by eqs 1 and 2 revealed a good agreement with existing experimental data within a wide range of temperatures and pressures, the absolute value of the average relative deviation of the liquid density from eq 1 was 0.10 %, and the absolute value of the average derivation of the liquid density from eq 2 was 0.09 %. The results correlated by eq 2 were slightly superior to those from eq 1. The parameters of eq 1 and eq 2 are given in Table 4. Also, the saturated density results at the bubble point were obtained by the equation from Lemmon,19 the calculated results were shown in Table 2. From Table 2, it can be seen that the experimental data agreed well with the calculated results from Lemmon,19 the absolute value of the average relative density deviations was 0.69 %. In addition, the cubic equation of state is simple, which is widely used to correlate the density of refrigerants. In this work, Peng−Robinson (PR) equation-of-state (EOS),27 Patel−Teja (PT) EOS,28 and Soave−Redlich−Kwong (SRK) EOS29 combined with the common VDW mixing rule were selected to correlate the density of HFC-404A. The temperature and the liquid mole fraction (HFC-404A (HFC-125(1)/HFC-134a(2)/ HFC-143a(3), 44 %/4 %/52 % by weight, (0.35782/0.03826/ 0.60392) by mole fraction))) were known, and the pressure and the liquid density were calculated according to the phase equilibrium theory (the bubble point calculation was conducted). To make the result more reasonable, the pressure effect was considered in the objective function, shown in eq 3. Saturated liquid densities at bubble point and pressures obtained by PR, PT, and SRK equations are shown in Table 3 and Figure 2, and the interactive parameters of the PR, PT, and SRK equations were given in Table 4. It can be seen that the deviations from the SRK equation were largest among the three equations. The absolute value of the average relative density deviation from the SRK equation was 7.92 % and its absolute value of the maximum relative density deviation was up to 10.20 %; the absolute values of the average relative density deviations for PR and PT equations were 0.87 % and 3.62 %, respectively, and the absolute values of the maximum relative density deviations for PR and PT equations were 4.90 % and 6.79 % respectively. For PR equations, about 95 % deviations were within 1.6 %. The relative liquid density deviations of experimental data from the calculated values with VDNS-type equation, the modified Rackett-type equation and PR, PT, and SRK equations were given in Figure 3. Meanwhile,

3. RESULTS AND DISCUSSION In this work, the VDNS-type equation [eq 1]26 and the modified Rackett-type equation [eq 2]23 are used to correlate the saturated liquid density. The expressions are shown in the following ρr = 1 + B1τ 0.35 + B2 τ 2 + B3τ 3 + B4 τ 4

ρr ′ = (C1 + C2τ )−(C 3 + τ

2/7

)

(1)

(2)

where ρr = ρ/ρc, B1, B2, B3, and B4 are parameters of eq 1, τ = 1 − (T/Tc), ρ′r = ρ/(Pc/(RTc)), and C1, C2, C3 are the parameters of eq 2. For the correlation of the experimental data, a computer program was developed by applying the least-squares method for fitting an objective function. The objective function using eqs 1 and 2 is 1 OF = Np

2⎞ ⎛⎛ ⎞2 ⎛ p − pcalL ⎞ ⎟ exp L ⎜⎜ ρexpL − ρcalL ⎟ ⎟ ⎜ ∑ ⎜⎜⎜ ⎟ +⎜ ⎟ ⎟⎟ ρexpL pexpL ⎠ ⎠⎠ ⎝ j ⎝⎝ j

(4)

Np

(3)

where ρexpL is the experimental liquid density, and ρcalL is the calculated liquid density. The correlated results were given in Table 2 and Figure 2. The deviation, δρ (%) referred to the following expression. 2875

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Table 3. Correlated Results of the Refrigerant HFC-404A by Using PR, PT, and SRK Equations within the Temperature Range of (227 to 341) Ka PR T/K

ρcalL

δρb

K

kg m−3

%

227.25 229.00 231.13 233.65 236.65 238.93 241.17 243.67 246.15 248.80 251.46 253.53 256.20 258.87 261.54 264.32 267.17 269.53 272.30 274.85 277.35 279.96 282.79 285.27 287.82 290.35 292.99 295.62 298.31 300.94 303.74 306.35 309.09 311.74 314.35 316.99 319.60 322.18 324.88 327.98 330.72 333.30 335.45 337.95 340.20 341.31

1308 1303 1297 1289 1281 1274 1267 1259 1251 1243 1234 1227 1218 1208 1199 1189 1178 1169 1158 1147 1137 1126 1114 1103 1091 1079 1066 1053 1039 1025 1010 996 980 964 948 931 914 896 877 854 832 818 802 782 764 754

−0.33 −0.31 −0.25 −0.21 −0.16 −0.12 −0.09 −0.07 −0.05 −0.03 −0.04 −0.03 −0.04 −0.05 −0.08 −0.09 −0.13 −0.15 −0.18 −0.21 −0.25 −0.31 −0.43 −0.49 −0.59 −0.67 −0.78 −0.88 −1.01 −1.12 −1.25 −1.39 −1.53 −1.70 −1.81 −1.91 −1.93 −1.85 −1.82 −1.54 −1.36 0.28 1.06 2.51 4.00 4.90

ρcalV 5.7 6.2 6.7 7.5 8.5 9.3 10.1 11.1 12.2 13.5 14.9 16.0 17.6 19.2 21.0 23.1 25.3 27.3 29.8 32.3 34.9 37.7 41.1 44.3 47.7 51.4 55.5 59.9 64.7 69.8 75.7 81.6 88.2 95.3 105.1 116.5 127.5 139.2 153.2 171.0 189.1 209.4 229.2 256.9 289.5 310.1

SRK pcal

δpc

ρcalL

δρb

ρcalV

kPa

%

kg m−3

%

106.3 115.3 127.0 142.1 161.9 178.2 195.6 216.4 238.8 264.5 292.5 315.8 347.9 382.5 419.5 461.0 506.6 546.9 597.2 646.5 697.8 754.4 819.7 880.2 945.9 1014.3 1089.8 1169.0 1254.3 1342.0 1440.2 1536.4 1641.6 1748.8 1859.2 1975.8 2096.2 2219.0 2353.9 2515.7 2663.3 2968.2 3106.3 3272.6 3427.5 3505.9

1.37 1.24 1.43 1.49 0.67 1.03 0.71 1.15 2.31 0.77 0.57 0.42 0.72 0.06 0.34 0.60 −0.06 0.16 −0.06 0.17 0.78 0.63 −0.07 −0.82 −0.98 −0.97 −0.29 −0.65 −0.84 −0.83 −0.18 −0.93 −1.14 −1.91 −1.78 −1.53 −1.84 −2.45 −2.64 −2.80 −2.46 1.70 1.58 1.77 2.50 1.07

1178 1174 1169 1163 1156 1150 1144 1138 1131 1124 1117 1111 1104 1096 1088 1080 1071 1064 1055 1046 1038 1029 1020 1011 1002 992 983 973 962 952 940 929 917 906 894 882 870 857 844 832 818 805 794 782 770 764

−10.2 −10.1 −10.1 −10.0 −9.9 −9.8 −9.8 −9.7 −9.6 −9.6 −9.5 −9.5 −9.4 −9.4 −9.3 −9.3 −9.2 −9.1 −9.1 −9.0 −8.9 −8.9 −8.8 −8.8 −8.7 −8.6 −8.5 −8.5 −8.4 −8.2 −8.1 −8.0 −7.8 −7.6 −7.4 −7.0 −6.6 −6.1 −5.5 −4.1 −3.0 −1.3 0.1 2.5 4.9 6.2

5.7 6.2 6.8 7.5 8.5 9.3 10.1 11.1 12.2 13.4 14.7 15.8 17.4 19.0 20.8 22.8 25.0 26.9 29.3 31.7 34.2 37.0 40.3 43.2 46.5 50.1 54.0 58.1 62.7 67.5 73.0 78.3 84.5 91.0 97.8 105.3 113.1 121.7 131.5 767.2 754.2 742.2 729.0 711.8 697.7 690.6

PT pcal

δpc

ρcalL

δρb

kPa

%

kg m−3

%

106.9 115.9 127.5 142.5 162.1 178.3 195.5 216.1 238.2 263.7 291.4 314.4 346.1 380.2 416.7 457.6 502.6 542.3 591.8 640.4 690.8 746.6 810.8 870.2 934.7 1002.2 1076.4 1154.3 1238.2 1324.4 1421.1 1515.1 1619.3 1724.9 1833.7 1949.0 2067.0 2189.6 2323.7 2648.2 2810.9 2970.6 3108.6 3274.9 3429.9 3508.3

1.99 1.77 1.84 1.79 0.83 1.09 0.68 1.02 2.09 0.47 0.18 −0.04 0.18 −0.53 −0.33 −0.14 −0.86 −0.68 −0.96 −0.78 −0.22 −0.41 −1.15 −1.96 −2.15 −2.15 −1.52 −1.90 −2.11 −2.13 −1.51 −2.30 −2.49 −3.25 −3.12 −2.87 −3.20 −3.75 −3.89 2.32 2.95 1.78 1.66 1.85 2.57 1.14

1279 1274 1268 1260 1251 1243 1236 1228 1220 1210 1201 1193 1184 1174 1163 1152 1141 1131 1119 1108 1096 1084 1071 1058 1045 1032 1018 1003 988 972 955 941 929 918 917 915 912 907 899 886 872 853 834 806 740 726

−2.47 −2.48 −2.47 −2.47 −2.49 −2.50 −2.52 −2.56 −2.59 −2.64 −2.72 −2.76 −2.85 −2.94 −3.05 −3.16 −3.30 −3.40 −3.54 −3.69 −3.84 −4.02 −4.28 −4.48 −4.72 −4.96 −5.25 −5.54 −5.88 −6.23 −6.62 −6.79 −6.65 −6.36 −4.94 −3.53 −2.10 −0.65 0.68 2.24 3.30 4.52 5.14 5.72 0.80 0.90

ρcalV 5.7 6.1 6.7 7.4 8.4 9.2 10.1 11.1 12.2 13.5 14.8 16.0 17.5 19.2 21.1 23.1 25.4 27.4 29.9 32.4 35.0 38.0 41.4 44.6 48.1 51.9 56.1 60.6 65.4 70.6 76.6 82.6 89.3 96.1 103.2 111.2 119.8 129.6 141.3 156.7 173.2 191.1 209.5 235.0 262.9 282.6

pcal

δpc

kPa

%

105.4 114.4 126.2 141.3 161.0 177.5 194.8 215.7 238.2 264.1 292.2 315.6 347.9 382.7 420.1 461.9 507.9 548.6 599.5 649.4 701.2 758.7 824.9 886.3 953.1 1022.9 1099.8 1180.7 1267.4 1357.1 1457.7 1554.6 1659.3 1763.7 1864.8 1973.3 2086.1 2205.4 2338.3 2500.5 2655.8 2810.3 2948.7 3117.5 3427.6 3505.9

0.58 0.51 0.75 0.89 0.16 0.59 0.33 0.83 2.06 0.59 0.46 0.36 0.72 0.14 0.47 0.79 0.20 0.48 0.32 0.61 1.28 1.20 0.56 −0.14 −0.23 −0.13 0.63 0.35 0.20 0.29 1.03 0.25 −0.08 −1.08 −1.48 −1.66 −2.31 −3.05 −3.28 −3.39 −2.74 −3.71 −3.58 −3.05 2.50 1.07

Standard uncertainties u are u(T) = 0.01 K, u(ρexpL) = 0.5 kg m−3, u(pexp) = 1.6 kPa. bδρ is relative density deviation, and it is defined as δρ = ((ρcalL − ρexpL)/(ρexpL)) × 100 %. cδp is relative pressure deviation, and it is defined as δρ = ((ρcalL − ρexpL)/(ρexpL)) × 100 %. a

the relative pressure derivations were calculated, seen in Table 3. The absolute values of the average relative pressure deviations for PR, PT, and SRK equations were 1.09 %, 1.11 %, and 1.62 %, respectively, and the calculated results had a good agreement with the experimental data. In addition, the vapor density of HFC-404A by PR and PT equations with the obtained interactive parameters from liquid density data at bubble point can be easily calculated and are shown in Table 3.

Also, the comparison was developed between the experimental data and the results from literature,22 shown in Table 5. From the compared results, it can be found that in the specified temperature range, the absolute value of the average relative density deviation is about 0.55 %, the absolute value of the minimum relative density deviation is 0.21 %, and the absolute value of the maximum relative density deviation is 0.75 %. 2876

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Table 4. Constant Values, B1, B2, B3, B4, C1, C2, C3, k1,2, k2,1, k1,3, k3,1, k2,3, and k3,2, of Equations 1 and 2 and PR, SRK, and PT Equations Derived by Fitting the Experimental Dataa,b parametersa

eq 1

B1 B2 B3 B4 C1 C2 C3 k1,2 = k2,1 k1,3 = k3,1 k2,3 = k3,2

2.2097 5.4880 −20.7242 26.9228

eq 2

PR

PT

SRK

−0.7174 0.0074 −0.7187

−0.1784 0.0034 −0.1593

−2.8063 −0.0408 −0.4704

modified Rackett-type density equations, and the parameters of the density equations are given. The correlated results showed that they had good agreement with the experimental data. The absolute values of the average relative liquid density deviations from VDNS-type density equation and from the modified Rackett-type density equation were 0.10 % and 0.09 %, respectively. Also, the experimental results were compared with the calculated results from the equation by Lemmon, the results revealed that the experimental data had a good agreement with the calculated results from Lemmon, and the absolute value of the average relative density deviations was 0.69 %. In addition, PR, PT, and SRK were selected to correlate the densities of HFC-404A. For PR equation, about 95 % of the density deviations were within 1.6 %. Meanwhile, the PR and PT equations can easily calculate the saturation vapor density of the dew point. These will have a good basis for engineering applications of the alternative refrigerants.

0.2628 0.0575 −0.7288

a

Standard uncertainties u are u(B1) = 0.0032; u(B2) = 0.0021; u(B3) = 0.0068; u(B4) = 0.0010; u(C1) = 0.0004; u(C2) = 0.0001; u(C3) = 0.0005. For PR: u(k1,2) = 0.0002; u(k1,3) = 0.00001; u(k2,3) = 0.0007. For PT: u(k1,2) = 0.0001; u(k1,3) = 0.00001; u(k2,3) = 0.0003. For SRK: u(k1,2) = 0.0006; u(k1,3) = 0.00006; u(k2,3) = 0.0005. bExperimental measurement range: T = 227 K to 341 K.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +86 571 8283 7936. Fax: +86 571 8795 3944. Funding

This work has been supported by the Nation Natural Science Foundation of China (No. 51176166). Notes

The authors declare no competing financial interest.

■

NOMENCLATURE

Symbols

PR equation of state dependent parameter (J m3 mol−2) b PR equation of state dependent parameters (m3 mol−1) B1, B2, B3, B4 Parameters of eq 1 C1, C2, C3 Parameters of eq 2 Np Number of experimental points OF Objective function p Equilibrium pressure (MPa) T Equilibrium Temperature (K) a

Figure 3. Relative liquid density deviation of experimental data from the calculated values with VDNS-type equation (eq 1), the modified Rackett-type equation (eq 2), equation by Lemmon, and PR, PT, and SRK equations.

Table 5. Compared Results of the Saturated Density at Bubble Point for Refrigerant HFC-404A between the Data in This Work and the Data from Literature22 T

ρinterpolation

ρBouchot

δρb

K

kg m−3

kg m−3

%

253.21 263.16 273.19 283.17 293.18 303.19 313.20 323.14 333.10

1228.4 1193.9 1156.3 1116.8 1073.6 1025.7 971.8 905.6 818.3

1222.1 1187.9 1149.8 1110.5 1067.9 1019.4 964.5 899.8 816.6

0.52 0.50 0.56 0.57 0.53 0.62 0.75 0.65 0.21

Greek letters

Δρ Deviation of ρ τ One minus reduced temperature Subscripts

Bouchot c cal exp i interpolation

b δρ is relative density deviation, and it is defined as δρ = ((ρcalL − ρexpL)/(ρexpL)) × 100 %.

j

■

Thus, the experimental results have a good agreement with the literature22 within the measurement temperature ranges.

Experimental data from literature22 Critical property Calculated property Experimental property ith pure refrigerant Interpolation value obtained by experimental data jth experimental point

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4. CONCLUSIONS In this paper, the density of the refrigerant HFC-404A was investigated in the range of temperatures from (227 to 341) K. Saturated liquid density experimental data at bubble point of HFC-404A were correlated by the VDNS-type and the 2877

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