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Derived thermodynamic design data for Rankine power cycle systems operating on R216
Heat Recorery Systems Vol. 3. No. 4. pp. 321 to 325, 1983 Printed in Great Britain
Pergamon Press Ltd
DERIVED THERMODYNAMIC DESIGN DATA FOR RANKINE POWER CYCLE SYSTEMS OPERATING ON R216 P. KUMAR, S. DEVOTTA and F. A. HOLLAND Department of Chemical Engineering, University of Salford, Salford M5 4WT, England Abstract--The theoretical Rankine power cycle efficiencies r/R and the pressure ratios (PR) have been presented for Rankine power cycles operating on R216. These values are listed in tabular form for temperature drops of 10-75°C and for boiler temperatures 35--160°C in 5°C increments. A composite graph showing the relationship between r/R, TBo, (PR) and temperature drop (Tso - T c o ) illustrates the feasible operating range for R216 power cycle systems. The derived thermodynamic data can be used for the rapid preliminary design of Rankine power cycle systems operating on R216.
NOMENCLATURE Hx PBO Pco (PR) Tao Tco Vx ~/R 4~x
enthalpy of working fluid at state condition X (kJ kg- 1) vapour pressure of boiling working fluid (bar) vapour pressure of condensing working fluid (bar) pressure ratio, Pao/Pco (dimensionless) temperature of boiling working fluid (°C or K) temperature of condensing working fluid (°C or K) specific volume of the liquid working fluid at state condition X (m 3 kg- 1) Rankine power cycle efficiency (per cent) entropy of working fluid at state condition X (kJ kg- 1 K- 1).
INTRODUCTION
R216 HAS THE chemical formula C3C12F6, hexafluorodichloropropane. Its critical temperature and pressure are 453.1K and 27.55 bar respectively. Table 1 presents some physical data for R216. DERIVED THERMODYNAMIC DATA
An ideal Rankine power cycle involves four sequential operations, namely, isobaric boiling, isentropic expansion, isobaric condensation and isentropic compression. The ideal Rankine cycle is illustrated in Fig. 1 which is a plot of pressure P against enthalpy per unit mass H for R216. With reference to Fig. 1, the theoretical Rankine power cycle efficiency can be defined as ?/R =
(HR2 -- HD2 ) -- (HRt -- HD3 ) (HR2 --
Hat )
(1)
Since the expansion from R2 to D3 is isentropic, ~bR2= (~D2 where ~b is the entropy per unit mass. The enthalpy per unit mass of superheated vapour at D2 can be approximately related to the enthalpy per unit mass of the saturated vapour at point D1 by the equation Ho2 = H m + (~bR2 -- ~bm)Tco.
(2)
The quantity (HRI -- HD3) in equation (l) is the work input to the feed pump and is equal to VDa (PBo -- Pco) 100.0. Therefore, HR1 = HD3 + VD3(PBo -- Pco)100.0. 321
(3)
322
P. Kt;~taR. S. DEVOTTAand F. A. HOLLAND Table 1. Physical data for R216 Density (kg m -s)
Too CC) 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0 85.0 90.0 95.0 100.0 105.0 110.0 115.0 120.0 125.0 130.0 135.0 140.0 145.0 150.0 155.0 160.0 165.0
PBo (bar) 0.2383 0.3003 0.3744 0.4624 0.5660 0.6871 0.8275 0.9892 1.1745 1.3854 1.6243 1.8936 2.1956 2.5330 2.9079 3.3237 3.7831 4.2884 4.8434 5.4501 6.1127 6.8343 7.6115 8.4622 9.3781 t0.3715 11.4386 12.5907 13.8214 15.1441 16.5686 18.0884
19.7177 21.4613
Latent heat
Liquid
Vapour
1626.8 1613.8 1600.7 1587.3 1573.9 1560.4 1546.6 1532.8 1518.7 1504.5 1489.8 1475.1 1460.1 1444.7 1429.0 1412.9 1396.5 1379.8 1362.5 1344.7 1326.4 1307.5 1287.9 1267.6 1246.4 1224.2 1200.9 1176.4 1150.1 1122.1 1091.6 1058.0 1020.2 976.0
2.366 2.937 3.612 4.407 5.328 6.394 7.618 9.018 10.613 12.415 14.448 16.732 19.291 22.150 25.328 28.862 32.781 37.117 41.927 47.230 53.187 58.687 66.696 74.610 83.358 93.098 103.862 115.898 129.458 144.835 162.296 182.623 206.422 235.729
PV (barm~kg -I) 0.10075 0.10223 0.10364 0.10493 0.10623 0.10747 0.10863 0.10970 0.11067 0.11159 0.11242 0.11317 0.11382 0.11435 0.11481 0.11516 0.11541 0.11554 0.11552 0.11539 0.11493 0.11645 0.11412 0.11342 0.11250 0.11140 0.11013 0.10864 0.10676 0.10456 0.10209 0.09905 0.09552 0.09104
(kJkg -1)
(MJm -3)
129.890 128.097 126.341 124.567 122.838 121.073 119.352 117.592 115.853 114.117 112.359 110.580 108.808 106.993 105.148 103.300 101.378 99.441 97.441 95.410 93.295 91.095 88.829 86.434 83.945 81.331 78.570 75.604 72.432 69.017 65.288 61.127 56.481 51.023
0.3073 0.3763 0.4564 0.5490 0.6545 0.7741 0.9092 1.0604 1.2295 1.4168 1.6234 1.8502 2.0990 2.3699 2.6631 2.9814 3.3232 3.6910 4.0854 4.5062 4.9621 5.3461 5.9246 6.4489 6.9975 7.5717 8.1604 8.7624 9.3769 9.9961 10.5960 11.1632 11.6588 12.0275
Enthalpy of saturated vapour (kJ kg- l)
Mass of working fluid (kg M J - l)
229.890 233.077 236.298 239.521 242.781 246.018 249.307 252.569 255.851 259A36 262.434 265.718 269,013 272.300 275.574 278.849 282.104 285.351 288;577 291.800 294.991 298.141 301.280 304.362 307.402 310.395 313.323 316.160 318.905 321.553 324.045 326.333 328.373 330.005
7.6988 7.8066 7.9151 8.0278 8.1408 8.2595 8.3785 8.5040 8.6316 8.7630 8.9001 9.0432 9, ! 905 9.3464 9.51134 9.6805 9.8641 10.0562 10.2626 10.4811 10.7187 10.9776 11.2575 I 1.5695 11.9126 12.2954 12.7276 13.2268 ! 3,8060 14.4891 15.3166 16.3594 17.7052 19.5991
50
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:
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50 °
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,-
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o5, Z - S - - C - , " ll~ 120
i40
160
I
t
i
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i80 200 220 240 260 280 EnthoLpy per uni~. moss H ( kJ kg -~)
I
300
Fig. 1. Pressure against enthalpy per unit mass for R216.
31o
3.06 4.53 5.93 7.31 8.64 9.95 11.22 12.49 13.72 14.94 16.16 17.34 18.53 19.71
40.0 1.175
3.01 4.43 5.84 7.17 8.50 9.77 11.03 12.26 13.48 14.68 15.85 17.04 18.19 19.34
45.0 1.385
2.97 4.38 5.72 7.07 8.34 9.61 10.84 12.05 13.24 14.42 15.58 16.73 17.88 19.00
50.0 1.624
2.94 4.31 5.65 6.94 8.22 9.44 10.67 11.85 13.02 14.17 15.32 16.44 17.56 18.68
55.0 1.894
2.88 4.25 5.56 6.83 8.06 9.30 10.47 11.65 12.79 13.93 15.05 16.16 17.26 18.34
60.0 2.196
2.83 4.17 5.47 6.72 7.94 9.12 10.31 1 !.44 12.58 13.69 14.79 15.88 16.96 18.03
65.0 2.533
2.79 4.10 5.38 6.62 7.81 8.98 10.12 1 !.26 12.36 13.47 14.54 15.61 16.66 17.72
70.0 2.908
2.74 4.04 5.28 6.50 7.69 8.83 9.96 11.05 12.16 13.22 14.30 15.34 16.38 17.41
75.0 3.324
2.70 3.97 5.20 6.39 7.56 8.69 9.79 10.88 11.94 13.01 14.04 15.08 16.10 17.12
80.0 3.783
35.0 0.989
1.440 1.748 2.139 2.642 3.294 4.150 5.288 6.815 8.901 I 1.777 15.810 21.586 29.962 42.324
( T B o - Tco)(°C) 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0
1.419 !.709 2.075 2.540 3.137 3.911 4.928 6.278 8.091 10.568 13.983 18.771 25.628 35.574
40.0 1.175
1.400 1.674 2.016 2.448 2.996 3.701 4.614 5.813 7.405 9.544 12.465 16.494 22.141 30.230
45.0 1.385
1.383 1.642 1.963 2.364 2.870 3.513 4.339 5.410 6.815 8.683 11.190 14.615 19.338 25.960
50.0 1.624
1.367 1.612 1.914 2.288 2.756 3.345 4.815 5.058 6.306 7.945 10.122 13.045 17.038 22.544
55.0 1.894
1.352 1.585 1.869 2.219 2.653 3.196 3.879 4.748 5.865 7.312 9.212 I 1.736 15.125 19.755
60.0 2.196
1.338 1.559 1.828 2.157 2.560 3.061 3.687 4.475 5.478 6.766 8.435 10.627 13.539 17.449
65.0 2.533
1.324 1.536 1.790 2.099 2.476 2.939 3.514 4.234 5.137 6.289 7.767 9.684 12.200 15.543
70.0 2.908
1.312 1.514 1.755 2.046 2.399 2.830 3.360 4.017 4.837 5.872 7.188 8.878 I 1.069 13.945
75.0 3.324
1.301 1.494 1.723 1.998 2.329 2.73t 3.221 3.824 4.572 5.506 6.684 8.182 10.105 12.599
80.0 3.783
2.67 3.91 5.12 6.29 7.43 8.55 9.64 10.70 11.75 12.78 13.82 14.82 15.83 16.82
85.0 4.288
1.290 1.475 1.693 1.953 2.265 2.640 3.095 3.651 4.335 5.183 6.241 7.576 9.274 1 [.455
85.0 4.288
Table 2b. Pressure ratios (PR) for a range of temperature drops and boiling temperatures for R216
3.13 4.60 6.05 7.43 8.80 10.12 11.43 12.71 13.96 15.22 16.44 17.66 18.87 20.07
35.0 0.989
TBo(°C) PBo(bar)
10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0
( T . o - Tco)(°C)
THo(°C) PBo(bar)
1.280 1.457 1.666 1.912 2.206 2.558 2.982 3.496 4.124 4.896 5.853 7.049 8.557 10.474
90.0 4.843
2.62 3.85 5.03 6.19 7.31 8.40 9.47 10.53 11.55 12.57 13.57 14.58 15.55 16.54
90.0 4.843
Table 2a. Theoretical Rankine power cycle efificiencies r/. for a range of temperature drops and boiling temperatures for R216
1.271 1.441 1.640 1.874 2.152 2.482 2.878 3.355 3.934 4.640 5.509 6.586 7.932 9.629
95.0 5.450
2.60 3.81 4.97 6.10 7.20 8.27 9.32 10.36 1 !.37 12.37 13.36 14.32 15.31 16.26
95.0 5.450
O
O
.-1
( T . o - Tco)f'C) 10.0 15.0 20.0 25,0 30.0 35;0 40.0 45.0 ~11 55.11 60.0 65.0 70.0 75.0
Tno(~'C) P~o(bar)
(TRo- Tco)(' C) 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0
TBo{"C) puo(bar)
2.50 3.69 4.81 5.90 6.96 8.00 9.01 10.00 10.98 11.95 12.91 13.85 14.78 15.70
105.0 6.834
2.49 3.64 4.76 5.83 6.87 7.88 8.87 9.85 10.81 I 1.76 12.70 13.63 14.54 15.45
I 10.0 7.612
2.45 3.57 4.66 5.73 6.75 7.75 8.72 9.68 10.62 I 1.55 12.47 13.38 14.29 15.18
I 15.0 8.464
2.39 3.53 4.59 5.62 6.64 7.62 8.58 9.52 10.44 11.35 12.25 13.15 14.04 14.92
120.0 9.378
2.38 3.46 4.53 5.54 6.52 7.50 8.43 .9.36 10.26 I 1.16 12.05 12.92 13.79 14.66
2.34 3.42 4.44 5.46 6.42 7.35 8.29 9.19 10.09 10.96 I 1:83 12.69 13.55 14.40
2.29 3.36 4.37 5.34 6.31 7.23 8.13 9.03 9.90 10.76 I 1.62 12.46 13.30 14.13
2.24 3.28 4.28 5.24 6.16 7.09 7.97 8.84 9.71 10,55 11.39 12.22 13.04 13.87
2.24 3.25 4.22 5.17 6.08 6.95 7.84 8.69 9.52 10.37 11.19 12.00 12.81 13.61
2.23 3.21 4.15 5.07 5.96 6.83 7.67 8.53 9.34 10.15 10.97 11.76 12.56 13.35
1.262 1.425 1.616 1;839 2.102 2.413 2.784 3.228 3,763 4.412 5,205 6.179 7.387 8.897
100.0 6.113
1.254 1.411 1.594 1.806 2.056 2.350 2.698 3. I 12 3.¢g~,~ 4.,)07 4.933 5.8 ! 8 6;908 8.258
105.0 6.834 1.245 1.397 1.572 1.775 2.012 2.290 2.618 3.005 3.467 4,020 4.686 5.494 6.481 7.694
110.0 7.612 1.239 1.385 1.553 1.747 1.974 2.237 2.547 Z911 3.341 31855 4.470 5.2 ! 1 6.109 7.206
115.0 8.464 1.232 1.372 1.534 1.721 I;936 2.187 2.479 2.821 3.225 3.702 4.271 4.952 5.773 6.769
120.0 9.378
2. i I 3.07 4.00 4.86 5.70 6.53 7.34 8.14 8.92 9.72 1{).48 11.25 12.02 12.78
1.225 1.365 1.518 1.697 1.903 2.141 2.4:!8 2.741 3.120 3.567 4.095 4.724 5.477 6.385
1.220 1.351 1.503 1.674 1.871 2.098 2.361 Z667 3.023 3.441 3.933 4.515 5.209 6.040
1.214 1.343 1.487 1.654 ! .842 2.060 Z310 2.599 2.9.'i6 3,328 3;'I88 4.329 4.970 5.734
1.208 1.333 1.474 1,633 1.816 2.022 2.261 21536 2.853 3,223 3.653 4.158 4.753 5.456
1.203 1.324 1.460 1.6!5 1.789 1.990 2,216 2.478 2.779 3 127 3:531 4.003 4.557 5.208
1.199 1.316 1.449 1.598 1.767 1.958 2.177 2.425 2.711 3.040 3.421 3.864 4.380 4.985
1.194 1.309 1.437 1.581 1.744 1.929 2.137 2.376 2.647 2.959 3.319 3.734 4.218 4:781
1.190 1.302 1.427 1.566 1.724 1.901 2.103 2.330 2.591 2.885 3.226 3.618 4.071 4.598
125.0 130.0 135.0 140.0 145.0 150.0 155.0 160.0 10.371 1 1 . 4 3 7 1 2 . 5 9 0 13.821 1 5 . 1 4 5 1 6 . 5 6 9 1 8 . 0 8 7 19.719
2.15 3.15 4.06 4.95 5.83 6.68 7.51 8.32 9.14 9.93 10.72 11.51 12.29 13.07
125.0 130.0 135.0 140.0 145.0 150.0 155.0 160.0 1 0 . 3 7 1 1 1 . 4 3 7 1 2 . 5 9 0 13.821 1 5 . 1 4 5 1 6 . 5 6 9 1 8 . 0 8 7 19.719
Table 3b. Presst,re ratios (PR) for a range of temperature drops and boiling temperatures for R216
2.56 3.76 4.89 6.00 7.08 8.13 9.16 10.17 11.18 12.16 13.13 14.09 15.03 15.99
100.0 6.113
Table 3a. Theoretical Rankine power cycle etliciencies tlR for a range of temperature drops and boiling temperatures for R216
>-
e'~
>-
O
>
¢7
325
Derived thermodynamic design data for Rankine po~er cycle systems 16
'5"C 6:
'O*C u
~5"C
"6 -5
50oC
,% !
o3 i< t~
55"C
c.
50"C
r~ o
o
"O
~5"C I o.
40"C
k-
E
35"C
40
60
80
IO0
120
140
f 60
BoiLing temperature 78o (*C) Fig. 2. Theoretical Rankine power cycle efficiency against boiling temperature for R216 for various pressure ratios and gross temperature drops.
The compressibility of the liquid is so low that the work input to the feed pump is generally neglected. This approximation is good only when the boiler pressure is comparatively low and the latent heat of vaporisation of the working fluid is relatively high. Equations (1)-(3) can be used to calculate t/R values for any desired boiling temperatures TBo and temperature drop (TBo -- Tco) from the saturation properties of the working fluid. The theoretical Rankine power cycle efficiency r/R and the pressure ratio (PR), which is the ratio of the corresponding saturation pressures in the boiler and the condenser PBo/Pco, have been calculated for R216 for temperature drops of 10-75~C and for boiling temperatures 35--160°C in 5°C increments. The basic thermodynamic properties of R216 used in the calculation have been taken from the published tables [H. M. Meacock, Refrigeration Processes, p. 170, Pergamon Press, Oxford (1979)]. The calculated t/R and (PR) values for R216 are listed in Tables 2 and 3. Figure 2 shows the relationship between the theoretical Rankine power cycle efficiency t/R, the boiling temperature TBo, the temperature drop (TBo -- Tco) and the pressure ratio (PR). If any two of these four parameters are fixed then the other two are determined automatically. In practice the boiling temperature TBO and temperature drop (TBo -- Tco) are usually fixed thus determining the values of r/R and (PR).
Pergamon Press Ltd
DERIVED THERMODYNAMIC DESIGN DATA FOR RANKINE POWER CYCLE SYSTEMS OPERATING ON R216 P. KUMAR, S. DEVOTTA and F. A. HOLLAND Department of Chemical Engineering, University of Salford, Salford M5 4WT, England Abstract--The theoretical Rankine power cycle efficiencies r/R and the pressure ratios (PR) have been presented for Rankine power cycles operating on R216. These values are listed in tabular form for temperature drops of 10-75°C and for boiler temperatures 35--160°C in 5°C increments. A composite graph showing the relationship between r/R, TBo, (PR) and temperature drop (Tso - T c o ) illustrates the feasible operating range for R216 power cycle systems. The derived thermodynamic data can be used for the rapid preliminary design of Rankine power cycle systems operating on R216.
NOMENCLATURE Hx PBO Pco (PR) Tao Tco Vx ~/R 4~x
enthalpy of working fluid at state condition X (kJ kg- 1) vapour pressure of boiling working fluid (bar) vapour pressure of condensing working fluid (bar) pressure ratio, Pao/Pco (dimensionless) temperature of boiling working fluid (°C or K) temperature of condensing working fluid (°C or K) specific volume of the liquid working fluid at state condition X (m 3 kg- 1) Rankine power cycle efficiency (per cent) entropy of working fluid at state condition X (kJ kg- 1 K- 1).
INTRODUCTION
R216 HAS THE chemical formula C3C12F6, hexafluorodichloropropane. Its critical temperature and pressure are 453.1K and 27.55 bar respectively. Table 1 presents some physical data for R216. DERIVED THERMODYNAMIC DATA
An ideal Rankine power cycle involves four sequential operations, namely, isobaric boiling, isentropic expansion, isobaric condensation and isentropic compression. The ideal Rankine cycle is illustrated in Fig. 1 which is a plot of pressure P against enthalpy per unit mass H for R216. With reference to Fig. 1, the theoretical Rankine power cycle efficiency can be defined as ?/R =
(HR2 -- HD2 ) -- (HRt -- HD3 ) (HR2 --
Hat )
(1)
Since the expansion from R2 to D3 is isentropic, ~bR2= (~D2 where ~b is the entropy per unit mass. The enthalpy per unit mass of superheated vapour at D2 can be approximately related to the enthalpy per unit mass of the saturated vapour at point D1 by the equation Ho2 = H m + (~bR2 -- ~bm)Tco.
(2)
The quantity (HRI -- HD3) in equation (l) is the work input to the feed pump and is equal to VDa (PBo -- Pco) 100.0. Therefore, HR1 = HD3 + VD3(PBo -- Pco)100.0. 321
(3)
322
P. Kt;~taR. S. DEVOTTAand F. A. HOLLAND Table 1. Physical data for R216 Density (kg m -s)
Too CC) 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0 85.0 90.0 95.0 100.0 105.0 110.0 115.0 120.0 125.0 130.0 135.0 140.0 145.0 150.0 155.0 160.0 165.0
PBo (bar) 0.2383 0.3003 0.3744 0.4624 0.5660 0.6871 0.8275 0.9892 1.1745 1.3854 1.6243 1.8936 2.1956 2.5330 2.9079 3.3237 3.7831 4.2884 4.8434 5.4501 6.1127 6.8343 7.6115 8.4622 9.3781 t0.3715 11.4386 12.5907 13.8214 15.1441 16.5686 18.0884
19.7177 21.4613
Latent heat
Liquid
Vapour
1626.8 1613.8 1600.7 1587.3 1573.9 1560.4 1546.6 1532.8 1518.7 1504.5 1489.8 1475.1 1460.1 1444.7 1429.0 1412.9 1396.5 1379.8 1362.5 1344.7 1326.4 1307.5 1287.9 1267.6 1246.4 1224.2 1200.9 1176.4 1150.1 1122.1 1091.6 1058.0 1020.2 976.0
2.366 2.937 3.612 4.407 5.328 6.394 7.618 9.018 10.613 12.415 14.448 16.732 19.291 22.150 25.328 28.862 32.781 37.117 41.927 47.230 53.187 58.687 66.696 74.610 83.358 93.098 103.862 115.898 129.458 144.835 162.296 182.623 206.422 235.729
PV (barm~kg -I) 0.10075 0.10223 0.10364 0.10493 0.10623 0.10747 0.10863 0.10970 0.11067 0.11159 0.11242 0.11317 0.11382 0.11435 0.11481 0.11516 0.11541 0.11554 0.11552 0.11539 0.11493 0.11645 0.11412 0.11342 0.11250 0.11140 0.11013 0.10864 0.10676 0.10456 0.10209 0.09905 0.09552 0.09104
(kJkg -1)
(MJm -3)
129.890 128.097 126.341 124.567 122.838 121.073 119.352 117.592 115.853 114.117 112.359 110.580 108.808 106.993 105.148 103.300 101.378 99.441 97.441 95.410 93.295 91.095 88.829 86.434 83.945 81.331 78.570 75.604 72.432 69.017 65.288 61.127 56.481 51.023
0.3073 0.3763 0.4564 0.5490 0.6545 0.7741 0.9092 1.0604 1.2295 1.4168 1.6234 1.8502 2.0990 2.3699 2.6631 2.9814 3.3232 3.6910 4.0854 4.5062 4.9621 5.3461 5.9246 6.4489 6.9975 7.5717 8.1604 8.7624 9.3769 9.9961 10.5960 11.1632 11.6588 12.0275
Enthalpy of saturated vapour (kJ kg- l)
Mass of working fluid (kg M J - l)
229.890 233.077 236.298 239.521 242.781 246.018 249.307 252.569 255.851 259A36 262.434 265.718 269,013 272.300 275.574 278.849 282.104 285.351 288;577 291.800 294.991 298.141 301.280 304.362 307.402 310.395 313.323 316.160 318.905 321.553 324.045 326.333 328.373 330.005
7.6988 7.8066 7.9151 8.0278 8.1408 8.2595 8.3785 8.5040 8.6316 8.7630 8.9001 9.0432 9, ! 905 9.3464 9.51134 9.6805 9.8641 10.0562 10.2626 10.4811 10.7187 10.9776 11.2575 I 1.5695 11.9126 12.2954 12.7276 13.2268 ! 3,8060 14.4891 15.3166 16.3594 17.7052 19.5991
50
20-RI
:
Z e
j
.ioo_*c_
03 ~
rsoc o,/
J
2--
/
50 °
~dy. . . . . . . . . . .
,-
/DZ
oA 7 ~P"
// /
25"c_z.~"
o5, Z - S - - C - , " ll~ 120
i40
160
I
t
i
I
i80 200 220 240 260 280 EnthoLpy per uni~. moss H ( kJ kg -~)
I
300
Fig. 1. Pressure against enthalpy per unit mass for R216.
31o
3.06 4.53 5.93 7.31 8.64 9.95 11.22 12.49 13.72 14.94 16.16 17.34 18.53 19.71
40.0 1.175
3.01 4.43 5.84 7.17 8.50 9.77 11.03 12.26 13.48 14.68 15.85 17.04 18.19 19.34
45.0 1.385
2.97 4.38 5.72 7.07 8.34 9.61 10.84 12.05 13.24 14.42 15.58 16.73 17.88 19.00
50.0 1.624
2.94 4.31 5.65 6.94 8.22 9.44 10.67 11.85 13.02 14.17 15.32 16.44 17.56 18.68
55.0 1.894
2.88 4.25 5.56 6.83 8.06 9.30 10.47 11.65 12.79 13.93 15.05 16.16 17.26 18.34
60.0 2.196
2.83 4.17 5.47 6.72 7.94 9.12 10.31 1 !.44 12.58 13.69 14.79 15.88 16.96 18.03
65.0 2.533
2.79 4.10 5.38 6.62 7.81 8.98 10.12 1 !.26 12.36 13.47 14.54 15.61 16.66 17.72
70.0 2.908
2.74 4.04 5.28 6.50 7.69 8.83 9.96 11.05 12.16 13.22 14.30 15.34 16.38 17.41
75.0 3.324
2.70 3.97 5.20 6.39 7.56 8.69 9.79 10.88 11.94 13.01 14.04 15.08 16.10 17.12
80.0 3.783
35.0 0.989
1.440 1.748 2.139 2.642 3.294 4.150 5.288 6.815 8.901 I 1.777 15.810 21.586 29.962 42.324
( T B o - Tco)(°C) 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0
1.419 !.709 2.075 2.540 3.137 3.911 4.928 6.278 8.091 10.568 13.983 18.771 25.628 35.574
40.0 1.175
1.400 1.674 2.016 2.448 2.996 3.701 4.614 5.813 7.405 9.544 12.465 16.494 22.141 30.230
45.0 1.385
1.383 1.642 1.963 2.364 2.870 3.513 4.339 5.410 6.815 8.683 11.190 14.615 19.338 25.960
50.0 1.624
1.367 1.612 1.914 2.288 2.756 3.345 4.815 5.058 6.306 7.945 10.122 13.045 17.038 22.544
55.0 1.894
1.352 1.585 1.869 2.219 2.653 3.196 3.879 4.748 5.865 7.312 9.212 I 1.736 15.125 19.755
60.0 2.196
1.338 1.559 1.828 2.157 2.560 3.061 3.687 4.475 5.478 6.766 8.435 10.627 13.539 17.449
65.0 2.533
1.324 1.536 1.790 2.099 2.476 2.939 3.514 4.234 5.137 6.289 7.767 9.684 12.200 15.543
70.0 2.908
1.312 1.514 1.755 2.046 2.399 2.830 3.360 4.017 4.837 5.872 7.188 8.878 I 1.069 13.945
75.0 3.324
1.301 1.494 1.723 1.998 2.329 2.73t 3.221 3.824 4.572 5.506 6.684 8.182 10.105 12.599
80.0 3.783
2.67 3.91 5.12 6.29 7.43 8.55 9.64 10.70 11.75 12.78 13.82 14.82 15.83 16.82
85.0 4.288
1.290 1.475 1.693 1.953 2.265 2.640 3.095 3.651 4.335 5.183 6.241 7.576 9.274 1 [.455
85.0 4.288
Table 2b. Pressure ratios (PR) for a range of temperature drops and boiling temperatures for R216
3.13 4.60 6.05 7.43 8.80 10.12 11.43 12.71 13.96 15.22 16.44 17.66 18.87 20.07
35.0 0.989
TBo(°C) PBo(bar)
10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0
( T . o - Tco)(°C)
THo(°C) PBo(bar)
1.280 1.457 1.666 1.912 2.206 2.558 2.982 3.496 4.124 4.896 5.853 7.049 8.557 10.474
90.0 4.843
2.62 3.85 5.03 6.19 7.31 8.40 9.47 10.53 11.55 12.57 13.57 14.58 15.55 16.54
90.0 4.843
Table 2a. Theoretical Rankine power cycle efificiencies r/. for a range of temperature drops and boiling temperatures for R216
1.271 1.441 1.640 1.874 2.152 2.482 2.878 3.355 3.934 4.640 5.509 6.586 7.932 9.629
95.0 5.450
2.60 3.81 4.97 6.10 7.20 8.27 9.32 10.36 1 !.37 12.37 13.36 14.32 15.31 16.26
95.0 5.450
O
O
.-1
( T . o - Tco)f'C) 10.0 15.0 20.0 25,0 30.0 35;0 40.0 45.0 ~11 55.11 60.0 65.0 70.0 75.0
Tno(~'C) P~o(bar)
(TRo- Tco)(' C) 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0
TBo{"C) puo(bar)
2.50 3.69 4.81 5.90 6.96 8.00 9.01 10.00 10.98 11.95 12.91 13.85 14.78 15.70
105.0 6.834
2.49 3.64 4.76 5.83 6.87 7.88 8.87 9.85 10.81 I 1.76 12.70 13.63 14.54 15.45
I 10.0 7.612
2.45 3.57 4.66 5.73 6.75 7.75 8.72 9.68 10.62 I 1.55 12.47 13.38 14.29 15.18
I 15.0 8.464
2.39 3.53 4.59 5.62 6.64 7.62 8.58 9.52 10.44 11.35 12.25 13.15 14.04 14.92
120.0 9.378
2.38 3.46 4.53 5.54 6.52 7.50 8.43 .9.36 10.26 I 1.16 12.05 12.92 13.79 14.66
2.34 3.42 4.44 5.46 6.42 7.35 8.29 9.19 10.09 10.96 I 1:83 12.69 13.55 14.40
2.29 3.36 4.37 5.34 6.31 7.23 8.13 9.03 9.90 10.76 I 1.62 12.46 13.30 14.13
2.24 3.28 4.28 5.24 6.16 7.09 7.97 8.84 9.71 10,55 11.39 12.22 13.04 13.87
2.24 3.25 4.22 5.17 6.08 6.95 7.84 8.69 9.52 10.37 11.19 12.00 12.81 13.61
2.23 3.21 4.15 5.07 5.96 6.83 7.67 8.53 9.34 10.15 10.97 11.76 12.56 13.35
1.262 1.425 1.616 1;839 2.102 2.413 2.784 3.228 3,763 4.412 5,205 6.179 7.387 8.897
100.0 6.113
1.254 1.411 1.594 1.806 2.056 2.350 2.698 3. I 12 3.¢g~,~ 4.,)07 4.933 5.8 ! 8 6;908 8.258
105.0 6.834 1.245 1.397 1.572 1.775 2.012 2.290 2.618 3.005 3.467 4,020 4.686 5.494 6.481 7.694
110.0 7.612 1.239 1.385 1.553 1.747 1.974 2.237 2.547 Z911 3.341 31855 4.470 5.2 ! 1 6.109 7.206
115.0 8.464 1.232 1.372 1.534 1.721 I;936 2.187 2.479 2.821 3.225 3.702 4.271 4.952 5.773 6.769
120.0 9.378
2. i I 3.07 4.00 4.86 5.70 6.53 7.34 8.14 8.92 9.72 1{).48 11.25 12.02 12.78
1.225 1.365 1.518 1.697 1.903 2.141 2.4:!8 2.741 3.120 3.567 4.095 4.724 5.477 6.385
1.220 1.351 1.503 1.674 1.871 2.098 2.361 Z667 3.023 3.441 3.933 4.515 5.209 6.040
1.214 1.343 1.487 1.654 ! .842 2.060 Z310 2.599 2.9.'i6 3,328 3;'I88 4.329 4.970 5.734
1.208 1.333 1.474 1,633 1.816 2.022 2.261 21536 2.853 3,223 3.653 4.158 4.753 5.456
1.203 1.324 1.460 1.6!5 1.789 1.990 2,216 2.478 2.779 3 127 3:531 4.003 4.557 5.208
1.199 1.316 1.449 1.598 1.767 1.958 2.177 2.425 2.711 3.040 3.421 3.864 4.380 4.985
1.194 1.309 1.437 1.581 1.744 1.929 2.137 2.376 2.647 2.959 3.319 3.734 4.218 4:781
1.190 1.302 1.427 1.566 1.724 1.901 2.103 2.330 2.591 2.885 3.226 3.618 4.071 4.598
125.0 130.0 135.0 140.0 145.0 150.0 155.0 160.0 10.371 1 1 . 4 3 7 1 2 . 5 9 0 13.821 1 5 . 1 4 5 1 6 . 5 6 9 1 8 . 0 8 7 19.719
2.15 3.15 4.06 4.95 5.83 6.68 7.51 8.32 9.14 9.93 10.72 11.51 12.29 13.07
125.0 130.0 135.0 140.0 145.0 150.0 155.0 160.0 1 0 . 3 7 1 1 1 . 4 3 7 1 2 . 5 9 0 13.821 1 5 . 1 4 5 1 6 . 5 6 9 1 8 . 0 8 7 19.719
Table 3b. Presst,re ratios (PR) for a range of temperature drops and boiling temperatures for R216
2.56 3.76 4.89 6.00 7.08 8.13 9.16 10.17 11.18 12.16 13.13 14.09 15.03 15.99
100.0 6.113
Table 3a. Theoretical Rankine power cycle etliciencies tlR for a range of temperature drops and boiling temperatures for R216
>-
e'~
>-
O
>
¢7
325
Derived thermodynamic design data for Rankine po~er cycle systems 16
'5"C 6:
'O*C u
~5"C
"6 -5
50oC
,% !
o3 i< t~
55"C
c.
50"C
r~ o
o
"O
~5"C I o.
40"C
k-
E
35"C
40
60
80
IO0
120
140
f 60
BoiLing temperature 78o (*C) Fig. 2. Theoretical Rankine power cycle efficiency against boiling temperature for R216 for various pressure ratios and gross temperature drops.
The compressibility of the liquid is so low that the work input to the feed pump is generally neglected. This approximation is good only when the boiler pressure is comparatively low and the latent heat of vaporisation of the working fluid is relatively high. Equations (1)-(3) can be used to calculate t/R values for any desired boiling temperatures TBo and temperature drop (TBo -- Tco) from the saturation properties of the working fluid. The theoretical Rankine power cycle efficiency r/R and the pressure ratio (PR), which is the ratio of the corresponding saturation pressures in the boiler and the condenser PBo/Pco, have been calculated for R216 for temperature drops of 10-75~C and for boiling temperatures 35--160°C in 5°C increments. The basic thermodynamic properties of R216 used in the calculation have been taken from the published tables [H. M. Meacock, Refrigeration Processes, p. 170, Pergamon Press, Oxford (1979)]. The calculated t/R and (PR) values for R216 are listed in Tables 2 and 3. Figure 2 shows the relationship between the theoretical Rankine power cycle efficiency t/R, the boiling temperature TBo, the temperature drop (TBo -- Tco) and the pressure ratio (PR). If any two of these four parameters are fixed then the other two are determined automatically. In practice the boiling temperature TBO and temperature drop (TBo -- Tco) are usually fixed thus determining the values of r/R and (PR).